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Development and Evaluation of 2D and 3D Image Quality Metrics by Simon Nicholas Murphy Graduate Program in Medical Physics Duke University Date:_______________________ Approved: ___________________________ Ehsan Samei, Supervisor ___________________________ James T. Dobbins, III ___________________________ Jennifer C. O'Daniel Thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in the Graduate Program in Medical Physics in the Graduate School of Duke University 2011
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Page 1: Development and Evaluation of 2D and 3D Image Quality ...

i

v

Development and Evaluation of 2D and 3D Image Quality Metrics

by

Simon Nicholas Murphy

Graduate Program in Medical Physics

Duke University

Date_______________________

Approved

___________________________

Ehsan Samei Supervisor

___________________________

James T Dobbins III

___________________________

Jennifer C ODaniel

Thesis submitted in partial fulfillment of

the requirements for the degree of Master of Science in the Graduate Program in Medical

Physics in the Graduate School

of Duke University

2011

ABSTRACT

Development and Evaluation of 2D and 3D Image Quality Metrics

by

Simon Nicholas Murphy

Graduate Program in Medical Physics

Duke University

Date_______________________

Approved

___________________________

Ehsan Samei Supervisor

___________________________

James T Dobbins III

___________________________

Jennifer C ODaniel

An abstract of a thesis submitted in partial

fulfillment of the requirements for the degree

of Master of Science in the Graduate Program in Medical Physics in the Graduate School

of Duke University

2011

Copyright by

Simon Nicholas Murphy

2011

iv

Abstract

With continuing advances in medical imaging technologies there is an increased

demand to extract quantitative information from images This has been particularly vital

in the effort to increase the efficacy and accuracy of diagnoses Quantitative information

is readily available in images because the acquisition techniques intrinsically involve

physical processes Quantitative image quality metrics are critical in the evaluation of

medical images for diagnostic merit particularly when used for the characterization and

comparison of different systems When such metrics are based on measurable physical

parameters they can provide valuable information for system optimization Image

quality describes the ldquogoodnessrdquo of an image in displaying information for a task This

thesis explored methods of measuring image quality for two scenarios (1) to

characterize 2D flat-panel detector performance and (2) to measure directional spatial

resolution for 3D images from breast tomosynthesis

In the first chapter two new wireless digital receptors (DRX-1C and DRX-1

Carestream Health Inc Rochester NY) were evaluated and compared to a conventional

flat-panel detector (Pixium 4600 Trixell Moirans France) on the basis of detective

quantum efficiency (DQE) A secondary goal was also to evaluate the filtration to

achieve specified beam qualities for the DQE measurements closely following the

methodology of the International Electrotechnical Commission (IEC) for radiation

v

qualities RQA5 and RQA9 All three DR systems demonstrated similar modulation

transfer functions (MTFs) at most frequency ranges while the DRX-1 showed lower

values near the cutoff of approximately 35 cyclesmm At each exposure the Pixium

4600 and DRX-1C demonstrated similar noise power spectrum (NPS) curves that

indicated better noise performance than the DRX-1 Zero-frequency DQEs for Pixium

4600 DRX-1C and DRX-1 were approximately 63 74 and 38 for RQA5 and 42

50 and 28 for RQA9 respectively In terms of DQE performance the DRX-1C image

receptor was found to be superior to the Pixium 4600 and DRX-1

In the second chapter the directional spatial resolution of simulated breast

tomosynthesis images was determined using a cone-based technique and a sphere

phantom Projections were simulated for a voxelized breast phantom with 12 mm

diameter sphere inserts using a fluence modeled from a 28 kVp beam incident upon an

indirect flat-panel detector with 200 micro m pixel size Characteristic noise and blurring for

each projection were added using cascaded systems analysis The projections were

reconstructed using a standard filtered backprojection technique producing a 3D

volume with an isotropic voxel size of 200 micro m Regions of interest (ROIs) that

completely encompassed single spheres were extracted and conical regions were

prescribed along the three axes extending from the centroid Voxels within a cone were

used to form an edge spread function (ESF) from which the directional MTF was

calculated A bin size of 002 mm and a conical range of 30 degrees were found optimal

vi

for maximizing accuracy and minimizing noise of the MTF A method for removing out-

of-plane artifacts of the ESFs along in-plane axes was investigated and yielded a

modified MTF The idea of separating the effective resolution and artifacts from the

measured ESF are expected to facilitate the interpretation of MTF measurements in

breast tomosynthesis Similar methods may be applied to characterize the spatial

resolution of other 3D imaging modalities

vii

Contents

Abstract iv

List of Tables x

List of Figures xi

Acknowledgements xiii

I Evaluation of 2D Digital Image Receptors 1

I1 Introduction 1

I2 Materials and Methods 3

I2i Detectors 3

I2ii Beam Characterization 3

I2iia X-ray Techniques 3

I2iib Data Linearization 4

I2iic Spectral Simulation 5

I2iii DQE Measurements 6

I2iiia Modulation Transfer Function 6

I2iiib Noise Power Spectrum 7

I2iiic DQE Calculation 8

I3 Results 9

I3i Data Linearization 9

I3ii Spectral Simulation 9

I3iii Modulation Transfer Function 12

viii

I3iv Noise Power Spectrum 12

I3v Detective Quantum Efficiency 19

I4 Discussion 20

I4i Comparisons of Detectors 20

I4ii Comparisons of Filtrations 21

I4iii Implications of Wireless DR 26

I5 Conclusions 26

II Directional MTF for Breast Tomosynthesis 28

II1 Introduction 28

II2 Materials and Methods 29

II2i Image Simulation 29

II2ii Uncorrected MTF 30

II2iii Theoretical Directional MTF 32

II2iv Modified MTF 33

II2v Preliminary Experimental Validation 34

II3 Results 35

II3i Reconstruction 35

II3ii Theoretical MTF 37

II3iii Uncorrected MTF 38

II3iv Comparison of Theoretical and Simulated MTFs 41

II3v Modified MTF for x and y 42

II3v Preliminary Experimental Validation 44

ix

II4 Discussion 46

II4i Evaluation of Cone-based Method 46

II4ii Separation of Artifact and Resolution Information 48

II5 Conclusions 49

References 50

x

List of Tables

Table 1 Physical Characteristics of Digital Image Receptors 4

Table 2 Beam Qualities and Required Filtrations 5

Table 3 Spectral Simulation Results 11

Table 4 Experimental MTF frequency locations for 1 mR exposure 22

Table 5 Estimated DQE values for 1 mR exposure by frequency bins 22

xi

List of Figures

Figure 1 MTF images for DRX-1C detector with radio-opaque edge test device with

arrows indicating the horizontal (left) and vertical (right) directions 7

Figure 2 NNPS image for DRX-1C detector indicating the top left ROI that served as the

reference for normalizing other ROIs in the image The ROI array was formed along the

directions indicated by the arrows The heel effect visible along the vertical axis of the

detector is an example of small variation in signal across the image 8

Figure 3 Original (left) and linearized (right) system responses for Pixium 4600 The

linearized system responses were measured from actual images The offsets are small

with respect to the slope sufficient enough for zero-offset conditions 10

Figure 4 Spectral simulations for RQA5 (top) and RQA9 (bottom) conditions Note the

similarities of spectral shapes of the normalized spectra (right) Also note the significant

differences in fluence between filtrations in the simulated spectra (left) 11

Figure 5 MTF results by detector (columns) and beam quality (rows) 13

Figure 6 Plots of MTF for RQA5 (top) and RQA9 (bottom) showing the relationships

between detectors (blue red and green) and by filtration (solid and dashed) 14

Figure 7 NNPS results by detector (columns) and beam quality (rows) 15

Figure 8 Plots of NNPS for RQA5 (top) and RQA9 (bottom) at 1 mR exposure showing

the relationships between detectors (blue red and green) and by filtration (solid and

dashed) 16

Figure 9 DQE results by detector (columns) and beam quality (rows) 17

Figure 10 Plots of DQE for RQA5 (top) and RQA9 (bottom) at 1 mR exposure showing

the relationships between detectors (blue red and green) and by filtration (solid and

dashed) 18

Figure 11 DRX1-C NNPS images at 1 mR for RQA5 with IEC filtration (left) and

alternative filtration (right) Images are equally windowed at 45 and leveled at 980 24

Figure 12 Depiction of the virtual image system 30

xii

Figure 13 Example of 30-degree cone prescribed along z axis of the sphere 32

Figure 14 Photograph of the imaging system with the acrylic sphere phantom

embedded in oil 34

Figure 15 View of the central slice of the breast phantom reconstruction before (top) and

after (bottom) background subtraction The z axis is through the page 36

Figure 16 3D rendering of the ROI volume (left) and cross-sectional views of the most

centrally located sphere with centroid indicated with red circle (right) 37

Figure 17 Theoretical 3D MTF results along the three major planes (top) and along x y

and z directions (bottom) Also note that the angular spread seen in the fx-fz plane is

equal to the angular range of 44deg for the acquisition 38

Figure 18 Uncorrected ESF (top) LSF (middle) and MTF (bottom) for x y and z

directions 40

Figure 19 Comparisons of the directional MTFs as calculated by the sphere method

(dashed line) by theoretical line profiles (light-weight line) by theoretical cone regions

(heavy-weight line) 41

Figure 20 Modified ESF (top) LSF (middle) and MTF (bottom) for x and y directions 43

Figure 21 Cross sectional views of the experimental sphere image with centroid

indicated with red circle 44

Figure 22 ESF (top) LSF (middle) and MTF (bottom) of real image for x y and z

directions 45

xiii

Acknowledgements

I would like to thank Ian Yorkston Mark Purdum and Van Huston of

Carestream Health Inc (Rochester NY) for their help with digital detector

measurements I would also like to thank Olav Christianson Samuel Richard Brian

Harrawood and Max Amurao for their assistance with collecting data and analyzing

results Special thanks go to my committee members for their helpful insights and

suggestions for this thesis Last but not least I want to express deep appreciation for the

support and mentorship provided by my advisor Dr Ehsan Samei

1

I Evaluation of 2D Digital Image Receptors

I1 Introduction

In the past decade many areas of radiological practice have seen a conversion

from screen films to the storage phosphor cassettes of computed radiography (CR) to the

active-matrix flat-panel detectors of digital radiography (DR) Both CR and DR are

digital systems that offer many potential benefits including but not limited to better

image quality wider dynamic range quicker readout lower radiation dose and higher

throughput [1-3] Even with advances in DR technologies such as improved detective

quantum efficiency (DQE) the primary radiographic system of today continues to be CR

A major obstacle to completely accepting DR is the high capital cost of acquiring an

entire system per examination room while also providing capability for portable

applications Recently manufacturers like Carestream Health Fuji and Toshiba have

introduced wireless digital image receptors that can serve as replacements for CR

cassettes As these are new technologies a further investigation to characterize these

detectors is warranted

In the case of radiographic receptors DQE has historically been the metric of

choice [4] because it indicates the ability of the image receptor to convert incident x-ray

photons into useable signal ndash essentially a measure of signal-to-noise ratio (SNR)

efficiency and overall system performance [23] DQE is observed across a range of

spatial frequencies for evaluating how the detector depicts small and large objects [3]

2

DQE metrics have been used in numerous studies to characterize CR phosphor-screens

as well as indirect and direct digital detectors [4-11] The importance of this highly

quantitative metric may be implied by the introduction of a DQE measurement standard

by the International Electrotechnical Commission (IEC) [12]

The standard measurement methodology of the International Electrotechnical

Commission (IEC) pertains to the image quality of 2D digital radiographic detectors

While the IEC formalism is well-developed some of the components that it requires are

not necessarily the most optimal for characterizing DQE This has been explored in

previous studies in terms of filtration material purity beam limitations and region of

interest (ROI) configuration [1314] To reduce the variability in the radiographic output

across various x-ray tubes due to inherent filtration differences the IEC formalism

prescribes specific additional aluminum filtration to attain radiation beam qualities

based on target half value layers (HVL) Achieving and verifying the desired HVL

however requires applying a substantial amount of aluminum at the exit window of the

x-ray tube which is often directed toward the ground This can be a logistical

inconvenience and can increase the risk of damage to the image receptor and

measurement equipment Similar beam qualities on the other hand may be attained

more conveniently using a thinner lighter filtration combination utilizing a higher Z

number material Care is warranted however as a previous study [6] had indicated that

the choice of filtration material could impact the DQE

3

The purpose of this study was two-fold First we aimed to evaluate and compare

two wireless image receptors with a conventional flat-panel detector on the basis of DQE

performance Second we compared DQE results using the IEC-prescribed filtration with

an alternative filtration For the latter an optimum filtration composition was

determined and compared with the IEC filtration on the basis of DQE

I2 Materials and Methods

I2i Detectors

The physical characteristics of the three digital image receptors evaluated in this

study are listed in Table 1 The Pixium 4600 was a conventional digital flat-panel The

DRX-1C and DRX-1 were both wireless digital cassettes that were tethered for the

purposes of this study All detectors were FDA approved and available commercially

Each detector was calibrated according to its manufacturer specifications to correct for

gain offset and bad pixels They were all dedicated for non-clinical laboratory research

purposes and hence could be operated under service settings that permitted acquisition

of raw (ie for processing) images

I2ii Beam Characterization

I2iia X-ray Techniques

All measurements for this study were taken with a well-characterized standard

radiographic system (Super80CP Philips Healthcare Andover MA) The x-ray tube had

an inherent filtration of 27 mm Al Free in-air exposures were measured using

4

Table 1 Physical Characteristics of Digital Image Receptors

Manufacturer Detector

Detector

type

Detector

material

Pixel pitch

(size) Array size

Imaging

area

Trixell

(Moirans France)

Pixium

4600 Indirect

CsITl

(CsI) 0143 mm

3121times3121

4 subpanels 45times45 cm2

Carestream Health Inc

(Rochester NY)

DRX-1C

(wireless) Indirect

CsITl

(CsI) 0139 mm

2560times3072

single panel 35times43 cm2

Carestream Health Inc

(Rochester NY)

DRX-1

(wireless) Indirect

G2O2STb

(GOS) 0139 mm

2560times3072

single panel 35times43 cm2

calibrated radiation meters (Mult-O-Meter Type 407 Unfors Instruments AB Billdal

Sweden) at 183 cm source-to-chamber-distance (SCD) The SCD also corresponded to

same plane as the image receptor surface The x-ray output was made to conform to IEC

beam quality definitions [1215] on the basis of half value layer (HVL) and peak

kilovoltage setting using an aluminum filtration (type-1100 99 purity) and an

alternative filtration consisting of copper (UNS C11000 999 purity) and aluminum

(type-1100 99 purity) The IEC radiation quality numbers (RQA) used in this study are

summarized in Table 2 HVLs were determined by iteratively adding successive

thicknesses of aluminum until reaching reduced exposure levels within a tolerance of

0485-0515 [12] As for the alternative filtration the aluminum was placed downstream

of the copper filter to attenuate characteristic radiation peaks from copper at

approximately 9 keV

I2iib Data Linearization

The system response function was determined for each detector and filtration

combination by acquiring flat-field images at increasing photon fluence until just before

5

Table 2 Beam Qualities and Required Filtrations

IEC Radiation

Quality Number

Peak

kilovoltage

Required

HVL

Required IEC

Filtration

Actual IEC

Filtration

Alternative

Filtration

RQA5 70 kVp 71 mm Al 21 mm Al 21 mm Al 05 mm Cu +

10 mm Al

RQA9 120 kVp 115 mm Al 42 mm Al 40 mm Al 104 mm Cu +

10 mm Al

For reasons of convenience these will be referred to as RQA5A RQA5C RQA9A and RQA9C

saturation levels To avoid the influence of detector backscatter on exposure

measurements a relationship for each filtration was first determined for two radiation

meters A target meter was placed at the central axis and a reference meter was placed at

the edge of the light field (large enough to cover the detectors) The reference meter

served as a surrogate for the target meter to avoid direct exposure measurements in the

plane of the image receptor Exposure relationships were determined before each

measurement set (ie detector and filtration combination) to account for changes in

temperature pressure and humidity The system response function was calculated by

using a regression of ADU (pixel value) versus exposure Images acquired for each

series were then converted to achieve a linear response with zero offset and scaled to

achieve high quantization (adequate dynamic range) Linearization of the detector

responses ensured that zero exposure corresponded to zero pixel value

I2iic Spectral Simulation

The effects of additional filtration on x-ray output spectra were observed with

spectral simulation software (XSPECT V40 Henry Ford Hospital Detroit MI) To more

6

adequately describe the performance of a typical X-ray generator inherent filtration of 3

mm oil 148 mm Pyrex glass and 2 mm aluminum was input into the simulation in

addition to the filters of interest The ideal signal to noise ratio squared or incident

photon fluence per exposure (q) was estimated for each filtration by integrating the

energy-dependent photon counts per unit exposure over all energy bins

I2iii DQE Measurements

The assessment of the linearized images followed the formalism described by

IEC 62220-1 for measuring the DQE [12] For this study the normal exposure level XN

was set at 1 mR to the detector surface as measured at the central axis perpendicular to

the anode-cathode axis

I2iiia Modulation Transfer Function

Spatial resolution was characterized by evaluating the presampled modulation

transfer function (MTF) along directions parallel (vertical) and perpendicular

(horizontal) to the anode-cathode axis using the angled-edge method [6-1013] A radio-

opaque edge test device [7] was placed in the center of the field at a pitch of

approximately 301 (about 2deg) to the axis perpendicular to that being measured as

shown in Figure 1 External lead apertures were not used [6] instead the internal

collimation from the radiographic unit was used to collimate the beam to the detector

area Raw images were acquired of the edge with the normal exposure level XN of 1 mR

at the detector face The procedure of calculating the MTF followed previously described

7

methods [6-1013] The edge spread function (ESF) was determined along lines crossing

the edge of the angled test device The derivative of the ESF was calculated to form the

line spread function (LSF) to which a Hanning filter was applied The MTF was then

calculated as the fast Fourier transform (FFT) of the LSF and normalized at the zero-

frequency axis To conform to IEC guidelines the MTF was resampled into frequency

steps of 005 cyclesmm [12]

Figure 1 MTF images for DRX-1C detector with radio-opaque edge test device with

arrows indicating the horizontal (left) and vertical (right) directions

I2iiib Noise Power Spectrum

Noise amplitude and texture were characterized by determining the normalized

noise power spectrum (NNPS) which was evaluated with flat field exposures at

approximate exposure levels of XN2 XN and 2XN (05 10 and 20 mR) to the image

receptor surface Analysis of the flat-field images followed previously defined methods

[41415] using over 4 million independent pixels with regions of interest (ROIs) of size

8

128x128 The NNPS images were detrended using a quadratic (second order)

background subtraction Small variations in exposure across ROIs were corrected by

normalizing pixel values of each ROI to the mean value in the top left ROI as shown in

Figure 2 The NNPS was then calculated with the 2D FFT including the zero-frequency

axes corresponding to the horizontal and vertical directions The results were then

resampled using 005 frequency bins according to IEC guidelines [12]

Figure 2 NNPS image for DRX-1C detector indicating the top left ROI that served as

the reference for normalizing other ROIs in the image The ROI array was formed

along the directions indicated by the arrows The heel effect visible along the vertical

axis of the detector is an example of small variation in signal across the image

I2iiic DQE Calculation

The DQE was calculated using the following relationship [615]

9

where the frequency-dependent MTF and NNPS were determined as described in

previous sections X was the exposure value in mR corresponding to the NNPS image

and q was the ideal signal to noise ratio squared in units of photonsmiddotmm-2middotmR-1 as

estimated from the spectral simulations

I3 Results

I3i Data Linearization

The detectors in this study provided raw ADU (or pixel) values in a linear scale

The data were converted using the following system conversion function

where Q(ij) is the raw image data m and b are slope and intercept parameters obtained

from linear regression of the system response function and I(ij) is the linearized scaled

data The factor of 1000 was found to scale I(ij) such that the maximum value was a

large 16-bit number Figure 3 shows the original and linearized system responses for the

Pixium 4600 Note that the y-intercepts of the regressions for the linearized responses

are negligible (lt 01) with respect to the slopes a sufficient condition for zero offset

considerations

I3ii Spectral Simulation

The spectral simulations of the IEC filtrations and alternative filtrations indicate

many similarities in their effective energies HVLs and overall shapes of normalized

spectra Results are summarized in Table 3

10

Pixium 4600 Original System

Response

Pixium 4600 Linearized System

Response R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 3 Original (left) and linearized (right) system responses for Pixium 4600 The

linearized system responses were measured from actual images The offsets are small

with respect to the slope sufficient enough for zero-offset conditions

y = 13971x - 13236

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x - 00106Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 13576x + 28292

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

7000

0000 1000 2000 3000 4000 5000

AD

U

Exposure (mR)

y = 99997x - 00067Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0000 1000 2000 3000 4000 5000

AD

U

Exposure (mR)

y = 13644x + 16167Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x + 00044

Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 13845x + 13541

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x - 00177

Rsup2= 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

11

Table 3 Spectral Simulation Results

Beam Quality Filtration

Mean Energy

(kV)

Photon Fluence

(mRmm2)

RQA5A 21 mm Al 5243 259543

RQA5C 05 mm Cu + 10 mm Al 5214 259554

diff 055 0004

RQA9A 40 mm Al 7619 273281

RQA9C 104 mm Cu + 10 mm Al 7579 273964

diff 052 025

Figure 4 Spectral simulations for RQA5 (top) and RQA9 (bottom) conditions Note

the similarities of spectral shapes of the normalized spectra (right) Also note the

significant differences in fluence between filtrations in the simulated spectra (left)

00E+00

50E+04

10E+05

15E+05

20E+05

25E+05

30E+05

35E+05

40E+05

45E+05

0 20 40 60 80

ph

oto

ns

mA

s-1

cm

-2

keV

RQA5 Spectra Comparison

21 mm Al

05 mm Cu + 10 mm Al

00

02

04

06

08

10

12

0 20 40 60 80

keV

RQA5 Normalized Spectra Comparison

21 mm Al

05 mm Cu +

10 mm Al

00E+00

50E+05

10E+06

15E+06

20E+06

25E+06

30E+06

35E+06

40E+06

45E+06

50E+06

0 50 100 150

ph

oto

ns

mA

s-1

cm

-2

keV

RQA9 Spectra Comparison

40 mm Al

104 mm Cu +

10 mm Al

00

02

04

06

08

10

12

0 50 100 150

keV

RQA9 Normalized Spectra Comparison

40 mm Al104 mm Cu + 10 mm Al

12

I3iii Modulation Transfer Function

The limiting spatial resolutions of the systems were indicated by the cutoff

frequencies which were approximately 35 cyclesmm for all three detectors The spatial

resolutions also demonstrated a good degree of isotropy as confirmed by the close

alignment of MTF curves between vertical and horizontal directions differentiated in

Figure 5 by dashed and solid lines respectively The MTF curves for the Pixium 4600

and DRX-1C were nearly equal to each other whereas the DRX-1 MTF curve showed a

more rapid decrease at high frequencies as shown in Figure 6 This difference may be

due to the differences in the inherent optical properties of the scintillating materials

where finer image details are provided by structured CsI more than by granulated GOS

There were no significant differences in MTF curves across beam qualities and filtrations

as shown by the curve comparisons in Figure 6 although the alternative filtration

produced slightly higher MTF curves as seen in Figure 4 Table 4 lists the experimental

specific spatial frequencies for varying levels of MTF

I3iv Noise Power Spectrum

The noise characteristics are indicated by the NNPS curves shown in Figure 7

The noise was similar for both horizontal and vertical directions As exposure increased

the NNPS decreased consistent with the characteristics of Poisson noise describing the

relationship between signal and noise in the presence of increased photon fluence At

13

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 5 MTF results by detector (columns) and beam quality (rows)

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

horizontal

vertical

14

Figure 6 Plots of MTF for RQA5 (top) and RQA9 (bottom) showing the relationships

between detectors (blue red and green) and by filtration (solid and dashed)

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm-1)

MTF

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm-1)

MTF

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

15

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 7 NNPS results by detector (columns) and beam quality (rows)

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

05 mR - horizontal

05 mR - vertical

10 mR - horizontal

10 mR - vertical

20 mR - horizontal

20 mR - vertical

16

Figure 8 Plots of NNPS for RQA5 (top) and RQA9 (bottom) at 1 mR exposure

showing the relationships between detectors (blue red and green) and by filtration

(solid and dashed)

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm-1)

NNPS (1 mR)

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm-1)

NNPS (1 mR)

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

17

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 9 DQE results by detector (columns) and beam quality (rows)

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

05 mR - horizontal

05 mR - vertical

10 mR - horizontal

10 mR - vertical

20 mR - horizontal

20 mR - vertical

18

Figure 10 Plots of DQE for RQA5 (top) and RQA9 (bottom) at 1 mR exposure showing

the relationships between detectors (blue red and green) and by filtration (solid and

dashed)

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm-1)

DQE (1 mR)

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm-1)

DQE

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

19

higher frequencies the NNPS curves of the Pixium 4600 and DRX-1 diverge slightly for

the different directions illustrating increased noise in the readout direction (vertical)

Differences in the noise characteristics were more apparent among detectors as

shown for 1 mR in Figure 8 The NNPS curve for the DRX-1 was higher in magnitude

across the entire frequency range than either the Pixium 4600 or DRX-1C which both

seemed to demonstrate reasonably similar NNPS curves The higher magnitude noise of

the DRX-1 indicates higher relative noise content overall Closer inspection of the NNPS

curves of the Pixium 4600 and DRX-1C detectors in Figure 7 revealed differences in the

spacing between the three exposure levels The gaps between the Pixium 4600 NNPS

curves do not correspond to the factor of two differences between each exposure level

especially at low- to mid- spatial frequencies suggesting a higher level of fixed pattern

noise additional noise with increasing exposure levels due to ineffective gain map

corrections Between filtration schemes the differences in NNPS curves for a given beam

quality were not substantial as shown in Figure 7

I3v Detective Quantum Efficiency

The DQE results are shown in Figure 9 DQE curves across exposure levels were

almost collinear except for Pixium 4600 and in general could be inferred from the

NNPS results Additionally the DQE curves demonstrated a relatively linear response

with spatial frequencies as expected for flat-panel detectors [9] Differences in DQE

among detectors were consistent for the most part with the type of scintillating material

20

As depicted for 1 mR exposure in Figure 10 differences between Pixium 4600 and DRX-

1C DQE curves correspond to the differences in their NNPS curves DRX-1 DQE curves

were consistently lower than either the Pixium 4600 or DRX-1C curves The DQE curves

for the alternative filtration were consistently higher than those for the IEC filtration

and the most noticeable differences were near the zero-frequency axis These effects can

be both attributed to ineffective gain map correction DQE values for 1 mR exposure are

listed in Table 5

I4 Discussion

I4i Comparisons of Detectors

The limiting spatial resolutions of all three detectors were almost exactly the

same considering that their pixel areas were similar in size The decrease in high-

frequency MTF of the DRX-1 compared to the other detectors is probably a result of

increased optical blurring due to the differences in the powdered structure of GOS

versus the needle-like structure of CsI [2] The fact that the DRX-1C and Pixium 4600

have comparable MTFs suggests similar scintillator thicknesses assuming that the

materials were processed alike

The noise of the three detectors demonstrated similar trends with each other The

higher NNPS curves of the DRX-1 detector are probably due also to the scintillating

material and its operation in converting photons into signal The conversion process is

less efficient because of the less favorable stopping power of the GOS compared to CsI

21

especially with higher energy beams The noise of the Pixium 4600 and DRX-1C were

similar except for the spacing between exposures The DRX-1C NNPS curve spacing is

consistent with a factor of two difference in exposure levels but the Pixium 4600 has a

smaller spacing The 05 mR NNPS curve of the Pixium 4600 is closer to that of the 05

mR NNPS curve of the DRX-1C This demonstrates that at higher exposures the Pixium

4600 produces a larger amount of additional noise beyond that explained by simple

stochastic effects It suggests bad performance in the gain map corrections

The DQE results indicate SNR properties of each detector The Pixium 4600 and

DRX-1C are comparable for the most part with the DRX-1C performing slightly better

The DRX-1 as predicted from MTF and NNPS results has a DQE much lower than

either of the previous two This is a reflection of the detection properties as provided by

its scintillator material The DQE of the DRX-1 however is comparable to CR image

receptors [2] The mid-frequency dips in the DQE for Pixium 4600 may be due to the

optical properties of the CsI phosphor layer which can affect the MTF in this manner

Because the DQE is calculated by squaring the MTF this effect at the mid-range

frequencies becomes more apparent The dips may also be further evidence of bad gain

map corrections

I4ii Comparisons of Filtrations

The alternative filtration closely matches for the most part the IEC-based

filtration for MTF NNPS and DQEs at RQA5 but not at RQA9 The filters do not have

22

Table 4 Experimental MTF frequency locations for 1 mR exposure

Detector Filtration

50 MTF

(mm-1)

40 MTF

(mm-1)

30 MTF

(mm-1)

20 MTF

(mm-1)

10 MTF

(mm-1)

Pixium

4600

RQA5A 115 145 185 245 330

RQA5C 125 155 195 250 345

RQA9A 110 175 175 235 330

RQA9C 125 155 195 255 345

DRX-1C

RQA5A 120 150 185 245 350

RQA5C 125 155 195 255 355

RQA9A 120 150 190 250 355

RQA9C 130 160 210 265 360

DRX-1

RQA5A 110 135 160 205 280

RQA5C 110 135 170 210 285

RQA9A 105 125 155 195 270

RQA9C 110 135 165 210 285

Table 5 Estimated DQE values for 1 mR exposure by frequency bins

Detector Filtration DQE(00 mm-1) DQE(10 mm-1) DQE(20 mm-1) DQE(30 mm-1)

Pixium

4600

RQA5A 62 42 32 21

RQA5C 63 45 36 25

RQA9A 41 27 30 13

RQA9C 43 33 27 19

DRX-1C

RQA5A 72 52 35 21

RQA5C 76 55 41 24

RQA9A 49 33 23 15

RQA9C 51 40 31 20

DRX-1

RQA5A 38 24 12 4

RQA5C 38 25 14 5

RQA9A 28 18 9 4

RQA9C 28 19 12 5

DQE values at the zero-frequency axis were estimated by the intercept of a linear fit of low-frequency data

but excluding most proximal to the axis due to large fluctuations Other estimated values are grouped into

frequency bins due to the noisiness of the data

23

considerable differences in the spatial resolutions of the detectors as expected The noise

responses for each filtration were also similar except at the lower frequencies of the

NNPS especially near the zero-frequency axis There observing the NNPS responses at

RQA5 for Pixium 4600 and DRX-1C in Figure 8 the NNPS for the IEC-based filtration

(solid lines) tend to drop faster than the NNPS for the alternative filtration This

subsequently appears as a drop in DQE near the zero-frequency axis shown for those

detectors in Figure 10 Overall as indicated in Table 5 the DQEs of the two filtrations

while similar in trend indicate that the alternative filtration increases the DQE by a

small amount of 3-5 Part of this may be explained by the slightly higher beam

energy which may be more optimal for the energy response of the detectors or may

weigh the pixel responses slightly considering that they are energy-integrating types

The most probable explanation is the gain map correction for the alternative filtration

where fixed pattern noise is more sufficiently reduced

A previous study [6] had discussed the choice of filter material in the analysis of

DQE when achieving the beam conditions defined by IEC It found that visible

nonuniformities were present with the higher purity aluminum filter (type-11999 alloy)

The low frequency mottle in the flat-field images for NPS measurements were also

attributed to structured noise from the grain size in the IEC-based filter with an

attenuating thickness that would reveal nonuniformities The mottle in the current study

was only observable under very narrow windowing as shown in Figure 11 Such low

24

frequency artifacts which are not readily noticeable may also be caused by shading

artifacts inverse square law or even the heel effect A possible method to correct for this

is a subtraction method by taking the average of the flat-field images for an exposure

level and then subtracting that from each of them This would remove nonuniformities

that were not corrected using a suboptimal gain map calibration

Figure 11 DRX1-C NNPS images at 1 mR for RQA5 with IEC filtration (left) and

alternative filtration (right) Images are equally windowed at 45 and leveled at 980

One convenient aspect of the copper and aluminum filtration is that it requires

much less tube current to achieve the same amount of exposure at the detector than the

much thicker aluminum filtration As shown in the non-normalized spectra in Figure 2

the exiting photon fluence exiting the copper and aluminum filtration is substantially

higher than that of the IEC-specified filtration This is due to the smaller total filtration

25

attenuation For extensive DQE analysis multiple sets of exposures may be acquired

before tube overheating becomes a concern

One limitation to the comparison of the two filtrations is that calibration

procedures specified copper and aluminum filtration at 80 kVp (for all detectors 05 mm

Cu and 10 mm Al) This may have influenced the results in favor of the alternative

filtration A further investigation involving the calibration procedures and performing

DQE measurements is encouraged Another factor may be influenced by the fact that the

tests were performed at 70 kVp and 120 kVp different from the recommended

calibration tube potential Clearly there would be differences in the linear attenuation

coefficients of the filters and different energy responses of the detectors themselves This

must be considered when interpreting DQE results The current results support a

previous study decades ago that described filtration of different material types in terms

of an aluminum equivalent [16] The results show that the two filtration schemes are

essentially equivalent when considering beam qualities and spatial resolutions The

NNPS and DQE results can be seen as close enough where their small differences are

insignificant when performing quality assurance tests in a clinical setting Overall our

results indicate that the alternative filtration with copper and aluminum may be more

convenient to use than the current IEC standard filtration

26

I4iii Implications of Wireless DR

This study has shown that wireless image receptors can have the same DQE

performance if not better than conventional flat-panel detectors They operate on the

same basic physical principles the new features offered by the DRX-1C and DRX-1 are

wireless communication with the workstation and electronics packaging technology

The latter feature may pose limitations for these units in terms of possible degradation

in the detectors in routine clinical conditions A consideration for future work would be

to longitudinally track DQE performance of the wireless detectors over time while being

utilized in a clinical environment In the end one must consider risks versus benefits of

choosing portable DR technology over CR one of which includes the cost and fragility

of DR detectors

The DQE performance of one wireless system is just as good as or better than

conventional systems as seen by the DRX-1C performance compared to the Pixium

4600 Wireless systems can also reduce the need for CR readers especially in portable

applications in other regions of the world (eg military hospitals developing countries)

However while DQE performance indicates the physical performance of the detector

system it is still unknown how it relates to observer performance

I5 Conclusions

Two wireless image receptors DRX-1C and DRX-1 were evaluated and

compared with the conventional DR flat-panel Pixium 4600 in terms of DQE

27

performance along with MTF and NNPS performances The detectors have similar

resolution properties although the DRX-1 is inferior at higher spatial frequencies The

NNPS and DQE results both indicate that the DRX-1C is superior to the DRX-1 and

comparable if not better to the Pixium 4600

The results from the filtration comparison indicate no substantial differences

between the IEC-based filtration and the copper-based alternative filtration Only slight

differences were found in the low frequency components of the NNPS and the DQE due

to the inherent nonuniformities of the IEC specified filtration Given the similarity of the

results and low attenuation advantage of the copper and aluminum filter its use is

encouraged

28

II Directional MTF for Breast Tomosynthesis

II1 Introduction

Breast tomosynthesis is an emerging 3D imaging modality that has potential use

for screening and diagnosis of breast cancer Breast tomosynthesis along with other 3D

techniques is preferable to planar imaging methods (eg mammography) because they

reduce anatomical noise by removing overlying structures above and below the plane of

an image slice [17-20] Recent advances in detectors and computer technology have

made digital tomosynthesis feasible

An image quality metric of particular importance in breast tomosynthesis is

spatial resolution Resolution is important to know in order to assess small-detail

structures such as microcalcifications A descriptive metric for characterizing spatial

resolution in the Fourier (or frequency) domain is the modulation transfer function

(MTF) Affected by reconstruction filters [21] the limited angular projections involved in

breast tomosynthesis results in highly anisotropic (or nonuniform) resolution Many

studies have looked only at characterizing the in-plane spatial resolution (ie in an

individual slice) with an elevated angled edge phantom [2223] A few studies have

looked at characterizing a more comprehensive 3D spatial resolution by using a

phantom with angled wires or tubes [24-26] However such studies require precise

mechanical alignment of the phantoms Several studies have explored a method using a

29

sphere phantom for the directional 3D MTF evaluation for microtomography [27] and

multi-slice CT [2829] This method has not yet been extended to breast tomosynthesis

This chapter focuses on breast tomosynthesis because it is highly anisotropic in

spatial resolution and like its predecessor mammography requires high spatial

resolution Additionally breast tomosynthesis acquisitions and reconstructions produce

several types of artifacts The use of a cone-based method using a sphere phantom [28] is

explored to characterize the directional 3D spatial resolution of simulated images from

breast tomosynthesis A technique for removing out-of-plane artifacts of the ESFs for the

in-plane axes is investigated to yield a modified MTF in a method that separates artifact

information from resolution information

II2 Materials and Methods

II2i Image Simulation

Breast tomosynthesis images were simulated by using a virtual imaging system

depicted in Figure 12 A volumetric breast phantom was voxelized as a rectangular mass

of uniform breast equivalent tissue of 4 cm thickness embedded with fifteen evenly

spaced plastic sphere inserts of 12 mm diameter The spheres were placed in a grid

formation within the central plane of the phantom The x-ray fluence was modeled from

a 28 kVp beam incident upon an indirect flat-panel detector with 200 micro m pixel size

Twenty-three projections within an angular range of 44deg were simulated using cascaded

systems analysis to generate characteristic 2D noise and spatial blurring [29] Each

30

projection was simulated to have an exposure of 174 mR with a fluence of 79 times 105

photonsmm-2 A standard filtered backprojection technique based on the Feldkamp

reconstruction algorithm [29] was used to reconstruct the projections and produce a

volumetric dataset with an isotropic voxel size of 200 micro m

Figure 12 Depiction of the virtual image system

II2ii Uncorrected MTF

To enable comparison of multiple spheres the reconstructed volume was

initially homogenized by performing a background subtraction based on a portion of the

volume devoid of spheres The voxel values were rescaled between one and zero to

eliminate negative values

31

The volumetric data were segmented to extract individual regions of interest

(ROIs) each containing a single sphere The ROIs extended along the full range of the z-

axis A thresholded ROI was generated by determining the exterior and interior voxels

relative to the sphere in the ROI The threshold value was set at 45 of the maximum

voxel value prior to thresholding The exterior and interior voxel values were then set to

values of 0 and 1 respectively Using the thresholded volume the center of mass was

calculated to determine the centroid The voxel values from the original ROI were

subsequently tabulated with the associated distances azimuthal angles and polar

angles relative to the centroid

Conical regions were prescribed along the positive and negative directions along

the three major axes extending from the centroid of the sphere as depicted in Figure 13

The axes about which the extent of the cone angle was delineated were defined with

the azimuthal and polar angles

Voxels with centers within the angular range of the cone were considered for

generating the edge spread function (ESF) To improve regularity of the distance

sampling interval the ESF values were rebinned to discrete distances corresponding to a

fraction of the voxel size Only voxels with distances ranging from the voxel size (ie

200 micro m) to the maximum distance were considered The ESFs from multiple spheres

were averaged together for each of the three major axes to produce an averaged ESF

which was further smoothed utilizing a Gaussian filter

32

Figure 13 Example of 30-degree cone prescribed along z axis of the sphere

The resulting ESF was then differentiated using the central difference method to

produce the line spread function (LSF) A Hanning filter with the same length as the LSF

was applied to zero out the tails of the LSF The presampled MTF was subsequently

computed as the amplitude of the Fourier transform of the LSF The MTF was

normalized with respect to the maximum value occurring within the range of the cutoff

frequency Binning size and conical range for the ESF were considered for maximizing

accuracy and minimizing noise of the MTF verified by comparison against the

theoretical MTF as determined in the previous section

II2iii Theoretical Directional MTF

The theoretical 3D MTF was calculated using a priori knowledge of the transfer

function of the virtual imaging system described in the previous section A phantom

was created with a set of point objects in a uniform and noise-free background with the

objects spanning across the volume of the breast [29] Twenty-one realizations were

33

generated from the reconstructed images of the point objects to yield a set of 3D point

spread functions (PSFs) The 3D fast Fourier transform (FFT) was performed for each 3D

PSF and averaged to give an ldquoexpectationrdquo 3D MTF [29] The theoretical directional

MTFs in the three major spatial axes were determined by line profiles along each of the

corresponding spatial frequency axes in the 3D MTF An additional theoretical MTF for

each direction was determined by using the application of conical regions along the axes

in frequency-space to take into account the contributions of MTF information from other

planes

II2iv Modified MTF

The tomosynthesis reconstruction is known to have edge enhancements which

affect the overall MTF by shifting the peaks of the MTF toward the higher frequencies

[23] The presence of this artifact complicates the interpretation of the actual spatial

resolution of the images Several steps were performed to remove the artifact

contribution to the resolution information particularly for the in-plane x and y

directions with the assumption that resolution information was contained immediately

near the edge

For the x-direction averaged ESF only values that were detected to be inside the

edge of the sphere were considered Those values were previously determined via

thresholding for calculating the centroid The ESF information corresponding to these

values was inversed and flipped about the detected edge to produce a symmetric

34

modified ESF The modified MTF was subsequently calculated from this modified ESF

as described in the previous section

For the y-direction averaged ESF an upward trend was found in the initial part

of the ESF This section was detrended with a polynomial fit and subtracted to produce a

flatter curve in that region The resulting detrended ESF was used to calculate the y axis

modified MTF

Figure 14 Photograph of the imaging system with the acrylic sphere phantom

embedded in oil

II2v Preliminary Experimental Validation

A clinical breast tomosynthesis system (Mammomat Inspiration Siemens AG

Munich Germany) was used to perform a preliminary evaluation of the cone-based

MTF technique The phantom for the experiment consisted of a single acrylic ball of 075

in diameter (SmallParts Seattle WA) suspended by a 0029 in diameter plastic filament

35

(Omniflex Zebco Tulsa OK) in an acrylic frame filled up to 4 in with vegetable oil

(Target Brands Inc Minneapolis MN) The system and phantom are shown in Figure

14 Twenty-five projections with an angular range of 44deg were acquired and subsequently

reconstructed to produce a volume with a voxel size of 01times01times10 mm3 The voxels were

reformatted to have an isotropic size of 01 mm The uncorrected ESF LSF and MTF

were calculated as described in the previous section

II3 Results

II3i Reconstruction

The reconstructed volume is shown in Figure 15 Notice the edge enhancement

along the x-direction as indicated by the sharp shadowing artifacts on either side of the

spheres The background was effectively homogenized using the background

subtraction technique This also took account of the curved edges of the breast phantom

With the close spacing of the spheres in the phantom the shadows along the x direction

for the fifteen spheres overlap with each other As the nine centrally located spheres

experience this effect the same way they were used for determining the ESF

A 3D rendering of the ROI containing a sphere shown in Figure 16 indicates the

anisotropic resolution of the reconstruction Note that the sphere is not accurately

reconstructed and has an oblong shape especially along the z axis Cross sectional views

of the ROI also in Figure 16 clearly demonstrate the edge enhancement causing a

shadow artifact in the x direction caused by the incomplete angular sampling of

36

tomosynthesis The sampling also introduces the triangular reconstruction of the sphere

as seen in the x-z plane Note the gradual edge drop-off in the z direction much beyond

the sphere radius

Figure 15 View of the central slice of the breast phantom reconstruction before (top)

and after (bottom) background subtraction The z axis is through the page

37

Figure 16 3D rendering of the ROI volume (left) and cross-sectional views of the most

centrally located sphere with centroid indicated with red circle (right)

II3ii Theoretical MTF

The theoretical MTFs for x y and z directions as determined from the line

profiles of the 3D MTF are shown in Figure 17 The theoretical MTF in the x direction

has a maximum value that is toward higher frequencies Its 10 response occurs at

about 125 cyclesmm which is at 50 of the cutoff frequency The rapid increase from

the zero-frequency intercept to the peak corresponds to the ramp filter used in filtered

backprojection which decreases the weighting of low frequency contributions due to the

incomplete angular sampling of the frequency-space The MTF does not reach a value of

0 at the zero-frequency intercept as it is very difficult to assess the zero-frequency

intercept due to the finite size of the phantom The theoretical MTF in the y direction

peaks at the zero-frequency intercept and reaches 20 proximal to the cutoff frequency

38

The 10 MTF is well beyond the cutoff frequency The theoretical MTF in the z direction

has a rapid drop-off at very low spatial frequencies indicating the lack of resolution in

that dimension

Figure 17 Theoretical 3D MTF results along the three major planes (top) and along x

y and z directions (bottom) Also note that the angular spread seen in the fx-fz plane is

equal to the angular range of 44deg for the acquisition

II3iii Uncorrected MTF

The ESF LSF and MTF using the cone-based method are shown for the x y and

z directions in Figure 18 It was found that a bin size of one-tenth the voxel size (002

mm) and a cone angle of 30deg to establish the ESF were enough to minimize noise and

maximize accuracy in the uncorrected MTFs considering the reasonable comparison of

the shapes of the MTF curves with the theoretical results in Figure 17 The LSFs are

generally noisy because differentiation of the ESF increases the amplitude of the noise

39

The data shown reflect a convolution with a smoothing Gaussian filter which was later

further corrected for in the reported MTF Nevertheless the high frequency components

of the noise are well beyond the MTF cutoff frequency of 25 cyclesmm and do not

impact the MTF results greatly

For the ESF in the x direction the shadow effect evident at the edge of the sphere

is visible as a steep decline followed by an increase Due to the finite distance range

provided by the ROI the ESF beyond the edge did not asymptotically reach the

background value The corresponding LSF demonstrates a low frequency modulation

that is indicated by the shift of 03 cyclesmm in the x direction for the peak of the MTF

The MTF exhibits a zero-frequency intercept that is non-zero unlike the theoretical MTF

and a 10 value at approximately 1 cyclesmm These features may be a direct

consequence of MTF information ldquocontaminationrdquo from y and z directions Furthermore

the ESF in the y direction demonstrates a reasonably shaped curve except for the slight

upward trend within the radius of the sphere which can be attributed to the shadow

artifact overlapping with the sphere volume The associated MTF has a peak shifted by

approximately 01 cyclesmm away from the axis and a 10 MTF occurring at

approximately 15 cyclesmm Both features which are not present in the theoretical

results may also be attributed to contaminant MTF information from x and z directions

The ESF in the z direction has a drop-off that occurs at a small fraction of the cutoff

frequency similar to that demonstrated by the theoretical MTF

40

Uncorrected ESF LSF and MTF

Figure 18 Uncorrected ESF (top) LSF (middle) and MTF (bottom) for x y and z

directions

41

Figure 19 Comparisons of the directional MTFs as calculated by the sphere method

(dashed line) by theoretical line profiles (light-weight line) by theoretical cone

regions (heavy-weight line)

II3iv Comparison of Theoretical and Simulated MTFs

The theoretical MTF results obtained from line profiles through the 3D MTF and

the simulated MTFs using the cone-based technique did not match very well except for

the general shape of the curves It was assumed in the previous section that the cone-

based technique contains information from other planes Figure 19 compares MTFs in

each direction for the two methods described in the methods and an additional method

based on conical regions of the 3D MTF The latter computes the MTF by averaging

contributions of the 3D MTF using the same cone prescription method used to define the

ESFs Comparison of the curves indicate some interesting correlations aside from the

fact that using conical regions with the 3D MTF results produce more noisy MTF results

partly due to the low sampling provided by the theoretical calculations The same

conclusions regarding the z direction MTF can be confirmed regardless of either

theoretical MTF procedures The experimental x direction MTF seems to agree best with

42

the line profile method whereas the y direction MTF agrees better with the cone region

method The fact that the experimental x direction MTF has a drop-off frequency that is

lower than those of either of the theoretical MTFs in Figure 19 suggests that this might

be due to integration of the z-direction in the in-plane slices considering how slices are

essentially averages of z direction information contained within it [33]

II3v Modified MTF for x and y

Modified ESF LSF and MTF curves for x and y directions are shown in Figure

20 The modified ESF and the resulting LSF in the x direction appear symmetric as

expected from the inverse and flip operation of the interior ESF about the detected edge

The modified MTF appears with less variation than the uncorrected MTF and the MTF

peak occurs at the zero-frequency axis The correction yields a 10 MTF at about 15

cyclesmm an improvement from the uncorrected MTF but still distant from the cutoff

frequency The modified ESF in the y direction demonstrates the detrended curve within

the sphere radius after a quadratic polynomial fit The resulting modified MTF still

appears similar to the uncorrected MTF except that the peak now coincides with the

zero-frequency axis For both x and y directions the low response of the modified MTFs

at the higher frequencies suggests that the contamination from other directions is

substantial due to the angular range of the cone

43

Modified ESF LSF and MTF

Figure 20 Modified ESF (top) LSF (middle) and MTF (bottom) for x and y directions

44

II3v Preliminary Experimental Validation

Cross-sections of the reconstructed sphere volume are shown in Figure 21

Relative to the simulation reconstructions the reconstructions of the experimental

phantom images produce lower contrast and higher noise The preliminary results

shown in Figure 22 indicate that our technique can be applied to actual experimental

breast tomosynthesis reconstructions However due to the noise exhibited by the MTF

curves for the x and y directions we did not determine the modified MTFs to separate

resolution and artifact information

Figure 21 Cross sectional views of the experimental sphere image with centroid

indicated with red circle

45

Uncorrected ESF LSF and MTF for Real Image

Figure 22 ESF (top) LSF (middle) and MTF (bottom) of real image for x y

and z directions

46

II4 Discussion

II4i Evaluation of Cone-based Method

The cone-based MTF technique was introduced by Thornton and Flynn [28] for

evaluation of volumetric CT images To utilize this technique as a characterization of a

3D system spatial resolution one must first consider the validity of the assumption of

shift invariance such that the same MTF result may be obtained regardless of the

location of the sphere The study by Zhao et al [23] found that there was no shift

variance for the MTF measurements along the vertical axis but this was only considering

the in-plane resolution along one axis On the other hand this study evaluated the MTF

with images simulated with cascaded systems analysis which includes conditions of

linearity and shift invariance Additionally the MTF was calculated by averaging the

ESF from several spheres in the same volume only after performing a background

subtraction This step was essential to account for the sensitivity of centroid calculations

as well as ensuring symmetric ESFs for opposing axes of the sphere ROIs

The measurement of MTF with the cone-based technique inherently

supersamples the edge of the sphere to increase signal-to-noise-ratio (SNR) of edge

information by averaging the contributions of each voxel to the ESF [713] This method

also takes into account the discrete sampling of the voxels by accounting for various

shifts of the edge in the voxel (also known as the partial volume effect) However using

the curved surface of the sphere phantom to approximate an edge along a given

47

direction naturally leads to contamination of information from other directions aside

from the one of interest Preferably a directional ESF should be created by using a single

radial line but this would limit the available voxels to obtain edge information An ideal

situation theoretically would be to use a larger-sized sphere such that the surface is

nearly flat and perpendicular to the axes of interest This would also permit a reduction

in the angular range of the cone and thus the introduction of out-of-plane information in

the resulting MTF However sphere size is a limitation in breast tomosynthesis and the

use of a large phantom might void the assumption of shift invariance of the spatial

resolution

The choice of a sphere phantom nevertheless may be based on the clinical need

to quickly acquire a single image for MTF evaluation especially for multiple directions

without presenting extra logistical challenges The use of a wire or edge phantom

requires more precise mechanical alignment to achieve the correct set up The edge

phantom [23] would require at least two images to sample all three dimensions In the

case of the three wire phantom [2425] all three dimensions of the frame must be aligned

simultaneously with respect to the axis of rotation A similar situation would be

encountered when considering a cubic phantom with the planes normal to the axis of

interest In contrast to these phantoms the sphere eliminates the need for precise

alignment especially with respect to three spatial dimensions simultaneously A sphere

48

has ideal symmetry in all directions and can be used to evaluate MTF in any arbitrary

direction

This study unlike others [242532] did not explore the effects of physical

parameters such as scatter or contrast on the final MTF result but it demonstrated the

feasibility of using the cone-based method with an actual breast tomosynthesis image of

a sphere phantom as shown in Error Reference source not found and Error Reference

source not found These effects should be addressed in future works A further look

into deriving the principles of comparing the theoretical MTF with the experimental

MTF using the cone-based method is further warranted

II4ii Separation of Artifact and Resolution Information

The focus of this study was to develop a technique for measuring spatial

resolution of tomosynthesis images The intrinsic artifacts from tomosynthesis

reconstructions however lead to uncharacteristic MTFs and possible misinterpretation

of the effective resolution information When considering previous techniques for

calculating the presampled MTF [713152328] the analysis was performed using an

edge or a line to produce the corresponding ESF The resolution information is

essentially contained only along the edge indicated by the need to calculate the LSF In a

way the method of extracting artifact information is to focus the analysis only on the

edge part of the ESF to calculate the modified MTF This will lead to a better

understanding of the limiting size of objects that may be seen in the reconstructed 3D

49

image The presampled MTF without correction should still be analyzed to understand

the entire system response Note that the ESFs attempt to reflect information only at the

detected edge of the sphere

II5 Conclusions

The directional MTF of a simulated breast tomosynthesis reconstruction was

determined by using the cone-based MTF technique demonstrating the feasibility of a

single phantom for MTF evaluation This study further presented methods of analyzing

only the edge information in the ESF to create a modified MTF along in-slice (x and y)

axes It can provide insight into the actual spatial resolution information contained in the

image while separating the resolution information from the information introduced by

artifacts caused by the reconstruction and insufficient volumetric sampling The idea of

separating the resolution and artifacts from the measured ESF are expected to facilitate

the interpretation of MTF measurements in breast tomosynthesis Similar methods may

be applied to characterize the resolution of other 3D imaging modalities

50

References

1 Garmer M Hannigs SP Jaumlger HJ et al ldquoDigital Radiography Versus

Conventional Radiology in Chest Imaging Diagnostic Performance of a Large-

Area Silicon Flat-Panel Detector in a Clinical CT-Controlled Studyrdquo American

Journal of Roentgenology Volume 74 75-80 (2000)

2 Cowen AR Kengyelics SM and Davies AG ldquoSolid-state flat-panel digital

radiography detectors and their physical imaging characteristics rdquoClinical

Radiology Volume 63 487-498 (2008)

3 Chotas HG Dobbins III JT and Ravin CE ldquoPrinciples of Digital

Radiography with Large-Area Electronically Readable Detectors A Review of

the Basicsrdquo Radiology Volume 210 Number 3 595-599 (1999)

4 Flynn MJ and Samei E Experimental comparison of noise and resolution for

2k and 4k storage phosphor radiography systems Medical Physics Volume 26

Number 8 1612-1623 (1999)

5 Rong XJ Shaw CC Liu X Lemacks MR and Thompson SK

ldquoComparison of an amorphous siliconcesium iodide flat-panel digital chest

radiography system with screenfilm and computed radiography systems ndash A

contrast-detail phantom studyrdquo Medical Physics Volume 28 Number 11 2328-

2335 (2001)

6 Ranger NT Samei E Dobbins III JT and Ravin CE Measurement of the

detective quantum efficiency in digital detectors consistent with the IEC 62220-1

standard Practical considerations regarding the choice of filter material

Medical Physics Volume 30 Number 7 2305-2311 (2005)

7 Samei E Buhr E Granfors P Vandenbroucke D and Wang X Comparison

of edge analysis techniques for the determination of the MTF of digital

radiographic systems Physics in Medicine and Biology Volume 50 3613-3625

(2005)

8 Samei E and Flynn MJ An experimental comparison of detector performance

for computed radiography systems Medical Physics Volume 29 Number 4 447-

459 (2002)

51

9 Samei E and Flynn MJ An experimental comparison of detector performance

for direct and indirect digital radiography systems Medical Physics Volume 30

Number 4 608-622 (2003)

10 Samei E Ranger NT MacKenzie A Honey ID Dobbins III JT and Ravin

CE Effective DQE (eDQE) and speed of digital radiographic systems An

experimental methodology Medical Physics Volume 36 Number 8 3806-3817

(2009)

11 Samei E Ranger NT MacKenzie A Honey ID Dobbins III JT and Ravin

CE Detector or System Extending the Concept of Detective Quantum

Efficiency to Characterize the Performance of Digital Radiographic Imaging

Systems Radiology Volume 249 Number 3 926-937 (2008)

12 ldquoIEC 62220-1 Medical Electrical Equipment ndash Characteristics of Digital X-Ray

Imaging Devices ndash Part 1 Determination of the Detective Quantum Efficiencyrdquo

International Electrotechnical Commission Geneva Switzerland (2003)

13 Samei E Ranger NT Dobbins III JT and Chen Y Intercomparison of

methods for image quality characterization I Modulation transfer function

Medical Physics Volume 33 Number 5 1454-1465 (2006)

14 Dobbins III JT Samei E Ranger NT and Chen Y Intercomparison of

methods for image quality characterization II Noise power spectrum Medical

Physics Volume 33 Number 5 1466-1475 (2006)

15 Samei E Flynn MJ and Reimann DA A method for measuring the

presampled MTF of digital radiographic systems using an edge test device

Medical Physics Volume 25 Number 1 102-113 (1998)

16 Nagel HD ldquoAluminum equivalence of materials used in diagnostic radiology

and its dependence on beam qualityrdquo Physics in Medicine and Biology Volume

31 Number 12 1381-1399 (1986)

17 Niklason LT Christian BT Niklason LE et al ldquoDigital Tomosynthesis in

Breast Imagingrdquo Radiology Volume 205 399-406 (1997)

18 Gur D ldquoTomosynthesis Potential Clinical Role in Breast Imagingrdquo American

Journal of Roentgenology Volume 189 614-615 (2007)

52

19 Park JM Franken Jr EA Garg M Fajardo LL and Niklason LT ldquoBreast

Tomosynthesis Present Considerations and Future Applicationsrdquo

RadioGraphics Volume 27 S231-S240 (2007)

20 Good WF Abrams GS Catullo VJ Chough DM Ganott MA Hakim

CM and Gur D ldquoDigital Breast Tomosynthesis A Pilot Observer Studyrdquo

American Journal of Roentgenology Volume 190 865-869 (2008)

21 Hu Y-H Zhao W Mertelmeier T and Ludwig J ldquoImage Artifact in Digital

Breast Tomosynthesis and Its Dependence on System and Reconstruction

Parametersrdquo IWDM 2008 LNCS 5116 628-634 (2008)

22 Chen Y Lo JY Ranger NT Samei E Dobbins III JT ldquoMethodology of

NEQ(f) analysis for optimization and comparison of digital breast tomosynthesis

acquisition techniques and reconstruction algorithmsrdquo Proceedings of SPIE

Volume 6510 65101I (2007)

23 Zhao B Zhou J Hu Y-H Mertelmeier T Ludwig J and Zhao W

ldquoExperimental validation of a three-dimensional linear system model for breast

tomosynthesisrdquo Medical Physics Volume 36 Number 1 240-251 (2009)

24 Madhav P Brzymialkiewicz CN Cutler SJ Bowsher JE and Tornai MP

ldquoCharacterizing the MTF in 3D for a Quantized SPECT Camera Having Arbitrary

Trajectoriesrdquo 2005 IEEE Nuclear Science Symposium Conference Record 1722-

1726 (2005)

25 Madhav P McKinley RL Samei E Bowsher JE and Tornai MP ldquoA Novel

Method to Characterize the MTF in 3D for Computed Mammotomographyrdquo

Proceedings of SPIE Volume 6142 61421Y (2006)

26 Hu Y-H Zhao B and Zhao W ldquoImage artifacts in digital breast

tomosynthesis Investigation of the effects of system geometry and

reconstruction parameters using a linear system approachrdquo Medical Physics

Volume 35 Number 12 5242-5252 (2008)

27 Seifert A and Flynn MJ ldquoResolving power of 3D x-ray microtomography

systemsrdquo Proceedings of SPIE Volume 4682 407-413 (2002)

28 Thornton MM and Flynn MJ Measurement of the spatial resolution of a

clinical volumetric computed tomography scanner using a sphere phantom

Proceedings of SPIE Volume 6142 61421Z (2006)

53

29 Baek J Pelc NJ ldquoUse of sphere phantoms to measure the 3D MTF of FDK

reconstructionsrdquo Proceedings of SPIE Volume 7961 79610D (2011)

30 Richard S and Samei E ldquoQuantitative imaging in breast tomosynthesis and CT

Comparison of detection and estimation task performancerdquo Medical Physics

Volume 37 Number 6 2627-2637 (2010)

31 Chen Y Lo JY and Dobbins III JT ldquoImpulse response analysis for several

digital tomosynthesis mammography reconstruction algorithmsrdquo Proceedings of

SPIE Volume 5745 541-549 (2005)

32 Zhao B and Zhao W ldquoThree-dimensional linear system analysis for breast

tomosynthesisrdquo Medical Physics Volume 35 Number 12 5219-5232 (2008)

33 Wu G Mainprize JG Boone JM and Yaffe MJ ldquoEvaluation of scatter

effects on image quality for breast tomosynthesisrdquo Medical Physics Volume 36

Number 10 4425-4432 (2009)

Page 2: Development and Evaluation of 2D and 3D Image Quality ...

ABSTRACT

Development and Evaluation of 2D and 3D Image Quality Metrics

by

Simon Nicholas Murphy

Graduate Program in Medical Physics

Duke University

Date_______________________

Approved

___________________________

Ehsan Samei Supervisor

___________________________

James T Dobbins III

___________________________

Jennifer C ODaniel

An abstract of a thesis submitted in partial

fulfillment of the requirements for the degree

of Master of Science in the Graduate Program in Medical Physics in the Graduate School

of Duke University

2011

Copyright by

Simon Nicholas Murphy

2011

iv

Abstract

With continuing advances in medical imaging technologies there is an increased

demand to extract quantitative information from images This has been particularly vital

in the effort to increase the efficacy and accuracy of diagnoses Quantitative information

is readily available in images because the acquisition techniques intrinsically involve

physical processes Quantitative image quality metrics are critical in the evaluation of

medical images for diagnostic merit particularly when used for the characterization and

comparison of different systems When such metrics are based on measurable physical

parameters they can provide valuable information for system optimization Image

quality describes the ldquogoodnessrdquo of an image in displaying information for a task This

thesis explored methods of measuring image quality for two scenarios (1) to

characterize 2D flat-panel detector performance and (2) to measure directional spatial

resolution for 3D images from breast tomosynthesis

In the first chapter two new wireless digital receptors (DRX-1C and DRX-1

Carestream Health Inc Rochester NY) were evaluated and compared to a conventional

flat-panel detector (Pixium 4600 Trixell Moirans France) on the basis of detective

quantum efficiency (DQE) A secondary goal was also to evaluate the filtration to

achieve specified beam qualities for the DQE measurements closely following the

methodology of the International Electrotechnical Commission (IEC) for radiation

v

qualities RQA5 and RQA9 All three DR systems demonstrated similar modulation

transfer functions (MTFs) at most frequency ranges while the DRX-1 showed lower

values near the cutoff of approximately 35 cyclesmm At each exposure the Pixium

4600 and DRX-1C demonstrated similar noise power spectrum (NPS) curves that

indicated better noise performance than the DRX-1 Zero-frequency DQEs for Pixium

4600 DRX-1C and DRX-1 were approximately 63 74 and 38 for RQA5 and 42

50 and 28 for RQA9 respectively In terms of DQE performance the DRX-1C image

receptor was found to be superior to the Pixium 4600 and DRX-1

In the second chapter the directional spatial resolution of simulated breast

tomosynthesis images was determined using a cone-based technique and a sphere

phantom Projections were simulated for a voxelized breast phantom with 12 mm

diameter sphere inserts using a fluence modeled from a 28 kVp beam incident upon an

indirect flat-panel detector with 200 micro m pixel size Characteristic noise and blurring for

each projection were added using cascaded systems analysis The projections were

reconstructed using a standard filtered backprojection technique producing a 3D

volume with an isotropic voxel size of 200 micro m Regions of interest (ROIs) that

completely encompassed single spheres were extracted and conical regions were

prescribed along the three axes extending from the centroid Voxels within a cone were

used to form an edge spread function (ESF) from which the directional MTF was

calculated A bin size of 002 mm and a conical range of 30 degrees were found optimal

vi

for maximizing accuracy and minimizing noise of the MTF A method for removing out-

of-plane artifacts of the ESFs along in-plane axes was investigated and yielded a

modified MTF The idea of separating the effective resolution and artifacts from the

measured ESF are expected to facilitate the interpretation of MTF measurements in

breast tomosynthesis Similar methods may be applied to characterize the spatial

resolution of other 3D imaging modalities

vii

Contents

Abstract iv

List of Tables x

List of Figures xi

Acknowledgements xiii

I Evaluation of 2D Digital Image Receptors 1

I1 Introduction 1

I2 Materials and Methods 3

I2i Detectors 3

I2ii Beam Characterization 3

I2iia X-ray Techniques 3

I2iib Data Linearization 4

I2iic Spectral Simulation 5

I2iii DQE Measurements 6

I2iiia Modulation Transfer Function 6

I2iiib Noise Power Spectrum 7

I2iiic DQE Calculation 8

I3 Results 9

I3i Data Linearization 9

I3ii Spectral Simulation 9

I3iii Modulation Transfer Function 12

viii

I3iv Noise Power Spectrum 12

I3v Detective Quantum Efficiency 19

I4 Discussion 20

I4i Comparisons of Detectors 20

I4ii Comparisons of Filtrations 21

I4iii Implications of Wireless DR 26

I5 Conclusions 26

II Directional MTF for Breast Tomosynthesis 28

II1 Introduction 28

II2 Materials and Methods 29

II2i Image Simulation 29

II2ii Uncorrected MTF 30

II2iii Theoretical Directional MTF 32

II2iv Modified MTF 33

II2v Preliminary Experimental Validation 34

II3 Results 35

II3i Reconstruction 35

II3ii Theoretical MTF 37

II3iii Uncorrected MTF 38

II3iv Comparison of Theoretical and Simulated MTFs 41

II3v Modified MTF for x and y 42

II3v Preliminary Experimental Validation 44

ix

II4 Discussion 46

II4i Evaluation of Cone-based Method 46

II4ii Separation of Artifact and Resolution Information 48

II5 Conclusions 49

References 50

x

List of Tables

Table 1 Physical Characteristics of Digital Image Receptors 4

Table 2 Beam Qualities and Required Filtrations 5

Table 3 Spectral Simulation Results 11

Table 4 Experimental MTF frequency locations for 1 mR exposure 22

Table 5 Estimated DQE values for 1 mR exposure by frequency bins 22

xi

List of Figures

Figure 1 MTF images for DRX-1C detector with radio-opaque edge test device with

arrows indicating the horizontal (left) and vertical (right) directions 7

Figure 2 NNPS image for DRX-1C detector indicating the top left ROI that served as the

reference for normalizing other ROIs in the image The ROI array was formed along the

directions indicated by the arrows The heel effect visible along the vertical axis of the

detector is an example of small variation in signal across the image 8

Figure 3 Original (left) and linearized (right) system responses for Pixium 4600 The

linearized system responses were measured from actual images The offsets are small

with respect to the slope sufficient enough for zero-offset conditions 10

Figure 4 Spectral simulations for RQA5 (top) and RQA9 (bottom) conditions Note the

similarities of spectral shapes of the normalized spectra (right) Also note the significant

differences in fluence between filtrations in the simulated spectra (left) 11

Figure 5 MTF results by detector (columns) and beam quality (rows) 13

Figure 6 Plots of MTF for RQA5 (top) and RQA9 (bottom) showing the relationships

between detectors (blue red and green) and by filtration (solid and dashed) 14

Figure 7 NNPS results by detector (columns) and beam quality (rows) 15

Figure 8 Plots of NNPS for RQA5 (top) and RQA9 (bottom) at 1 mR exposure showing

the relationships between detectors (blue red and green) and by filtration (solid and

dashed) 16

Figure 9 DQE results by detector (columns) and beam quality (rows) 17

Figure 10 Plots of DQE for RQA5 (top) and RQA9 (bottom) at 1 mR exposure showing

the relationships between detectors (blue red and green) and by filtration (solid and

dashed) 18

Figure 11 DRX1-C NNPS images at 1 mR for RQA5 with IEC filtration (left) and

alternative filtration (right) Images are equally windowed at 45 and leveled at 980 24

Figure 12 Depiction of the virtual image system 30

xii

Figure 13 Example of 30-degree cone prescribed along z axis of the sphere 32

Figure 14 Photograph of the imaging system with the acrylic sphere phantom

embedded in oil 34

Figure 15 View of the central slice of the breast phantom reconstruction before (top) and

after (bottom) background subtraction The z axis is through the page 36

Figure 16 3D rendering of the ROI volume (left) and cross-sectional views of the most

centrally located sphere with centroid indicated with red circle (right) 37

Figure 17 Theoretical 3D MTF results along the three major planes (top) and along x y

and z directions (bottom) Also note that the angular spread seen in the fx-fz plane is

equal to the angular range of 44deg for the acquisition 38

Figure 18 Uncorrected ESF (top) LSF (middle) and MTF (bottom) for x y and z

directions 40

Figure 19 Comparisons of the directional MTFs as calculated by the sphere method

(dashed line) by theoretical line profiles (light-weight line) by theoretical cone regions

(heavy-weight line) 41

Figure 20 Modified ESF (top) LSF (middle) and MTF (bottom) for x and y directions 43

Figure 21 Cross sectional views of the experimental sphere image with centroid

indicated with red circle 44

Figure 22 ESF (top) LSF (middle) and MTF (bottom) of real image for x y and z

directions 45

xiii

Acknowledgements

I would like to thank Ian Yorkston Mark Purdum and Van Huston of

Carestream Health Inc (Rochester NY) for their help with digital detector

measurements I would also like to thank Olav Christianson Samuel Richard Brian

Harrawood and Max Amurao for their assistance with collecting data and analyzing

results Special thanks go to my committee members for their helpful insights and

suggestions for this thesis Last but not least I want to express deep appreciation for the

support and mentorship provided by my advisor Dr Ehsan Samei

1

I Evaluation of 2D Digital Image Receptors

I1 Introduction

In the past decade many areas of radiological practice have seen a conversion

from screen films to the storage phosphor cassettes of computed radiography (CR) to the

active-matrix flat-panel detectors of digital radiography (DR) Both CR and DR are

digital systems that offer many potential benefits including but not limited to better

image quality wider dynamic range quicker readout lower radiation dose and higher

throughput [1-3] Even with advances in DR technologies such as improved detective

quantum efficiency (DQE) the primary radiographic system of today continues to be CR

A major obstacle to completely accepting DR is the high capital cost of acquiring an

entire system per examination room while also providing capability for portable

applications Recently manufacturers like Carestream Health Fuji and Toshiba have

introduced wireless digital image receptors that can serve as replacements for CR

cassettes As these are new technologies a further investigation to characterize these

detectors is warranted

In the case of radiographic receptors DQE has historically been the metric of

choice [4] because it indicates the ability of the image receptor to convert incident x-ray

photons into useable signal ndash essentially a measure of signal-to-noise ratio (SNR)

efficiency and overall system performance [23] DQE is observed across a range of

spatial frequencies for evaluating how the detector depicts small and large objects [3]

2

DQE metrics have been used in numerous studies to characterize CR phosphor-screens

as well as indirect and direct digital detectors [4-11] The importance of this highly

quantitative metric may be implied by the introduction of a DQE measurement standard

by the International Electrotechnical Commission (IEC) [12]

The standard measurement methodology of the International Electrotechnical

Commission (IEC) pertains to the image quality of 2D digital radiographic detectors

While the IEC formalism is well-developed some of the components that it requires are

not necessarily the most optimal for characterizing DQE This has been explored in

previous studies in terms of filtration material purity beam limitations and region of

interest (ROI) configuration [1314] To reduce the variability in the radiographic output

across various x-ray tubes due to inherent filtration differences the IEC formalism

prescribes specific additional aluminum filtration to attain radiation beam qualities

based on target half value layers (HVL) Achieving and verifying the desired HVL

however requires applying a substantial amount of aluminum at the exit window of the

x-ray tube which is often directed toward the ground This can be a logistical

inconvenience and can increase the risk of damage to the image receptor and

measurement equipment Similar beam qualities on the other hand may be attained

more conveniently using a thinner lighter filtration combination utilizing a higher Z

number material Care is warranted however as a previous study [6] had indicated that

the choice of filtration material could impact the DQE

3

The purpose of this study was two-fold First we aimed to evaluate and compare

two wireless image receptors with a conventional flat-panel detector on the basis of DQE

performance Second we compared DQE results using the IEC-prescribed filtration with

an alternative filtration For the latter an optimum filtration composition was

determined and compared with the IEC filtration on the basis of DQE

I2 Materials and Methods

I2i Detectors

The physical characteristics of the three digital image receptors evaluated in this

study are listed in Table 1 The Pixium 4600 was a conventional digital flat-panel The

DRX-1C and DRX-1 were both wireless digital cassettes that were tethered for the

purposes of this study All detectors were FDA approved and available commercially

Each detector was calibrated according to its manufacturer specifications to correct for

gain offset and bad pixels They were all dedicated for non-clinical laboratory research

purposes and hence could be operated under service settings that permitted acquisition

of raw (ie for processing) images

I2ii Beam Characterization

I2iia X-ray Techniques

All measurements for this study were taken with a well-characterized standard

radiographic system (Super80CP Philips Healthcare Andover MA) The x-ray tube had

an inherent filtration of 27 mm Al Free in-air exposures were measured using

4

Table 1 Physical Characteristics of Digital Image Receptors

Manufacturer Detector

Detector

type

Detector

material

Pixel pitch

(size) Array size

Imaging

area

Trixell

(Moirans France)

Pixium

4600 Indirect

CsITl

(CsI) 0143 mm

3121times3121

4 subpanels 45times45 cm2

Carestream Health Inc

(Rochester NY)

DRX-1C

(wireless) Indirect

CsITl

(CsI) 0139 mm

2560times3072

single panel 35times43 cm2

Carestream Health Inc

(Rochester NY)

DRX-1

(wireless) Indirect

G2O2STb

(GOS) 0139 mm

2560times3072

single panel 35times43 cm2

calibrated radiation meters (Mult-O-Meter Type 407 Unfors Instruments AB Billdal

Sweden) at 183 cm source-to-chamber-distance (SCD) The SCD also corresponded to

same plane as the image receptor surface The x-ray output was made to conform to IEC

beam quality definitions [1215] on the basis of half value layer (HVL) and peak

kilovoltage setting using an aluminum filtration (type-1100 99 purity) and an

alternative filtration consisting of copper (UNS C11000 999 purity) and aluminum

(type-1100 99 purity) The IEC radiation quality numbers (RQA) used in this study are

summarized in Table 2 HVLs were determined by iteratively adding successive

thicknesses of aluminum until reaching reduced exposure levels within a tolerance of

0485-0515 [12] As for the alternative filtration the aluminum was placed downstream

of the copper filter to attenuate characteristic radiation peaks from copper at

approximately 9 keV

I2iib Data Linearization

The system response function was determined for each detector and filtration

combination by acquiring flat-field images at increasing photon fluence until just before

5

Table 2 Beam Qualities and Required Filtrations

IEC Radiation

Quality Number

Peak

kilovoltage

Required

HVL

Required IEC

Filtration

Actual IEC

Filtration

Alternative

Filtration

RQA5 70 kVp 71 mm Al 21 mm Al 21 mm Al 05 mm Cu +

10 mm Al

RQA9 120 kVp 115 mm Al 42 mm Al 40 mm Al 104 mm Cu +

10 mm Al

For reasons of convenience these will be referred to as RQA5A RQA5C RQA9A and RQA9C

saturation levels To avoid the influence of detector backscatter on exposure

measurements a relationship for each filtration was first determined for two radiation

meters A target meter was placed at the central axis and a reference meter was placed at

the edge of the light field (large enough to cover the detectors) The reference meter

served as a surrogate for the target meter to avoid direct exposure measurements in the

plane of the image receptor Exposure relationships were determined before each

measurement set (ie detector and filtration combination) to account for changes in

temperature pressure and humidity The system response function was calculated by

using a regression of ADU (pixel value) versus exposure Images acquired for each

series were then converted to achieve a linear response with zero offset and scaled to

achieve high quantization (adequate dynamic range) Linearization of the detector

responses ensured that zero exposure corresponded to zero pixel value

I2iic Spectral Simulation

The effects of additional filtration on x-ray output spectra were observed with

spectral simulation software (XSPECT V40 Henry Ford Hospital Detroit MI) To more

6

adequately describe the performance of a typical X-ray generator inherent filtration of 3

mm oil 148 mm Pyrex glass and 2 mm aluminum was input into the simulation in

addition to the filters of interest The ideal signal to noise ratio squared or incident

photon fluence per exposure (q) was estimated for each filtration by integrating the

energy-dependent photon counts per unit exposure over all energy bins

I2iii DQE Measurements

The assessment of the linearized images followed the formalism described by

IEC 62220-1 for measuring the DQE [12] For this study the normal exposure level XN

was set at 1 mR to the detector surface as measured at the central axis perpendicular to

the anode-cathode axis

I2iiia Modulation Transfer Function

Spatial resolution was characterized by evaluating the presampled modulation

transfer function (MTF) along directions parallel (vertical) and perpendicular

(horizontal) to the anode-cathode axis using the angled-edge method [6-1013] A radio-

opaque edge test device [7] was placed in the center of the field at a pitch of

approximately 301 (about 2deg) to the axis perpendicular to that being measured as

shown in Figure 1 External lead apertures were not used [6] instead the internal

collimation from the radiographic unit was used to collimate the beam to the detector

area Raw images were acquired of the edge with the normal exposure level XN of 1 mR

at the detector face The procedure of calculating the MTF followed previously described

7

methods [6-1013] The edge spread function (ESF) was determined along lines crossing

the edge of the angled test device The derivative of the ESF was calculated to form the

line spread function (LSF) to which a Hanning filter was applied The MTF was then

calculated as the fast Fourier transform (FFT) of the LSF and normalized at the zero-

frequency axis To conform to IEC guidelines the MTF was resampled into frequency

steps of 005 cyclesmm [12]

Figure 1 MTF images for DRX-1C detector with radio-opaque edge test device with

arrows indicating the horizontal (left) and vertical (right) directions

I2iiib Noise Power Spectrum

Noise amplitude and texture were characterized by determining the normalized

noise power spectrum (NNPS) which was evaluated with flat field exposures at

approximate exposure levels of XN2 XN and 2XN (05 10 and 20 mR) to the image

receptor surface Analysis of the flat-field images followed previously defined methods

[41415] using over 4 million independent pixels with regions of interest (ROIs) of size

8

128x128 The NNPS images were detrended using a quadratic (second order)

background subtraction Small variations in exposure across ROIs were corrected by

normalizing pixel values of each ROI to the mean value in the top left ROI as shown in

Figure 2 The NNPS was then calculated with the 2D FFT including the zero-frequency

axes corresponding to the horizontal and vertical directions The results were then

resampled using 005 frequency bins according to IEC guidelines [12]

Figure 2 NNPS image for DRX-1C detector indicating the top left ROI that served as

the reference for normalizing other ROIs in the image The ROI array was formed

along the directions indicated by the arrows The heel effect visible along the vertical

axis of the detector is an example of small variation in signal across the image

I2iiic DQE Calculation

The DQE was calculated using the following relationship [615]

9

where the frequency-dependent MTF and NNPS were determined as described in

previous sections X was the exposure value in mR corresponding to the NNPS image

and q was the ideal signal to noise ratio squared in units of photonsmiddotmm-2middotmR-1 as

estimated from the spectral simulations

I3 Results

I3i Data Linearization

The detectors in this study provided raw ADU (or pixel) values in a linear scale

The data were converted using the following system conversion function

where Q(ij) is the raw image data m and b are slope and intercept parameters obtained

from linear regression of the system response function and I(ij) is the linearized scaled

data The factor of 1000 was found to scale I(ij) such that the maximum value was a

large 16-bit number Figure 3 shows the original and linearized system responses for the

Pixium 4600 Note that the y-intercepts of the regressions for the linearized responses

are negligible (lt 01) with respect to the slopes a sufficient condition for zero offset

considerations

I3ii Spectral Simulation

The spectral simulations of the IEC filtrations and alternative filtrations indicate

many similarities in their effective energies HVLs and overall shapes of normalized

spectra Results are summarized in Table 3

10

Pixium 4600 Original System

Response

Pixium 4600 Linearized System

Response R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 3 Original (left) and linearized (right) system responses for Pixium 4600 The

linearized system responses were measured from actual images The offsets are small

with respect to the slope sufficient enough for zero-offset conditions

y = 13971x - 13236

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x - 00106Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 13576x + 28292

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

7000

0000 1000 2000 3000 4000 5000

AD

U

Exposure (mR)

y = 99997x - 00067Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0000 1000 2000 3000 4000 5000

AD

U

Exposure (mR)

y = 13644x + 16167Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x + 00044

Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 13845x + 13541

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x - 00177

Rsup2= 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

11

Table 3 Spectral Simulation Results

Beam Quality Filtration

Mean Energy

(kV)

Photon Fluence

(mRmm2)

RQA5A 21 mm Al 5243 259543

RQA5C 05 mm Cu + 10 mm Al 5214 259554

diff 055 0004

RQA9A 40 mm Al 7619 273281

RQA9C 104 mm Cu + 10 mm Al 7579 273964

diff 052 025

Figure 4 Spectral simulations for RQA5 (top) and RQA9 (bottom) conditions Note

the similarities of spectral shapes of the normalized spectra (right) Also note the

significant differences in fluence between filtrations in the simulated spectra (left)

00E+00

50E+04

10E+05

15E+05

20E+05

25E+05

30E+05

35E+05

40E+05

45E+05

0 20 40 60 80

ph

oto

ns

mA

s-1

cm

-2

keV

RQA5 Spectra Comparison

21 mm Al

05 mm Cu + 10 mm Al

00

02

04

06

08

10

12

0 20 40 60 80

keV

RQA5 Normalized Spectra Comparison

21 mm Al

05 mm Cu +

10 mm Al

00E+00

50E+05

10E+06

15E+06

20E+06

25E+06

30E+06

35E+06

40E+06

45E+06

50E+06

0 50 100 150

ph

oto

ns

mA

s-1

cm

-2

keV

RQA9 Spectra Comparison

40 mm Al

104 mm Cu +

10 mm Al

00

02

04

06

08

10

12

0 50 100 150

keV

RQA9 Normalized Spectra Comparison

40 mm Al104 mm Cu + 10 mm Al

12

I3iii Modulation Transfer Function

The limiting spatial resolutions of the systems were indicated by the cutoff

frequencies which were approximately 35 cyclesmm for all three detectors The spatial

resolutions also demonstrated a good degree of isotropy as confirmed by the close

alignment of MTF curves between vertical and horizontal directions differentiated in

Figure 5 by dashed and solid lines respectively The MTF curves for the Pixium 4600

and DRX-1C were nearly equal to each other whereas the DRX-1 MTF curve showed a

more rapid decrease at high frequencies as shown in Figure 6 This difference may be

due to the differences in the inherent optical properties of the scintillating materials

where finer image details are provided by structured CsI more than by granulated GOS

There were no significant differences in MTF curves across beam qualities and filtrations

as shown by the curve comparisons in Figure 6 although the alternative filtration

produced slightly higher MTF curves as seen in Figure 4 Table 4 lists the experimental

specific spatial frequencies for varying levels of MTF

I3iv Noise Power Spectrum

The noise characteristics are indicated by the NNPS curves shown in Figure 7

The noise was similar for both horizontal and vertical directions As exposure increased

the NNPS decreased consistent with the characteristics of Poisson noise describing the

relationship between signal and noise in the presence of increased photon fluence At

13

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 5 MTF results by detector (columns) and beam quality (rows)

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

horizontal

vertical

14

Figure 6 Plots of MTF for RQA5 (top) and RQA9 (bottom) showing the relationships

between detectors (blue red and green) and by filtration (solid and dashed)

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm-1)

MTF

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm-1)

MTF

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

15

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 7 NNPS results by detector (columns) and beam quality (rows)

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

05 mR - horizontal

05 mR - vertical

10 mR - horizontal

10 mR - vertical

20 mR - horizontal

20 mR - vertical

16

Figure 8 Plots of NNPS for RQA5 (top) and RQA9 (bottom) at 1 mR exposure

showing the relationships between detectors (blue red and green) and by filtration

(solid and dashed)

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm-1)

NNPS (1 mR)

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm-1)

NNPS (1 mR)

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

17

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 9 DQE results by detector (columns) and beam quality (rows)

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

05 mR - horizontal

05 mR - vertical

10 mR - horizontal

10 mR - vertical

20 mR - horizontal

20 mR - vertical

18

Figure 10 Plots of DQE for RQA5 (top) and RQA9 (bottom) at 1 mR exposure showing

the relationships between detectors (blue red and green) and by filtration (solid and

dashed)

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm-1)

DQE (1 mR)

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm-1)

DQE

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

19

higher frequencies the NNPS curves of the Pixium 4600 and DRX-1 diverge slightly for

the different directions illustrating increased noise in the readout direction (vertical)

Differences in the noise characteristics were more apparent among detectors as

shown for 1 mR in Figure 8 The NNPS curve for the DRX-1 was higher in magnitude

across the entire frequency range than either the Pixium 4600 or DRX-1C which both

seemed to demonstrate reasonably similar NNPS curves The higher magnitude noise of

the DRX-1 indicates higher relative noise content overall Closer inspection of the NNPS

curves of the Pixium 4600 and DRX-1C detectors in Figure 7 revealed differences in the

spacing between the three exposure levels The gaps between the Pixium 4600 NNPS

curves do not correspond to the factor of two differences between each exposure level

especially at low- to mid- spatial frequencies suggesting a higher level of fixed pattern

noise additional noise with increasing exposure levels due to ineffective gain map

corrections Between filtration schemes the differences in NNPS curves for a given beam

quality were not substantial as shown in Figure 7

I3v Detective Quantum Efficiency

The DQE results are shown in Figure 9 DQE curves across exposure levels were

almost collinear except for Pixium 4600 and in general could be inferred from the

NNPS results Additionally the DQE curves demonstrated a relatively linear response

with spatial frequencies as expected for flat-panel detectors [9] Differences in DQE

among detectors were consistent for the most part with the type of scintillating material

20

As depicted for 1 mR exposure in Figure 10 differences between Pixium 4600 and DRX-

1C DQE curves correspond to the differences in their NNPS curves DRX-1 DQE curves

were consistently lower than either the Pixium 4600 or DRX-1C curves The DQE curves

for the alternative filtration were consistently higher than those for the IEC filtration

and the most noticeable differences were near the zero-frequency axis These effects can

be both attributed to ineffective gain map correction DQE values for 1 mR exposure are

listed in Table 5

I4 Discussion

I4i Comparisons of Detectors

The limiting spatial resolutions of all three detectors were almost exactly the

same considering that their pixel areas were similar in size The decrease in high-

frequency MTF of the DRX-1 compared to the other detectors is probably a result of

increased optical blurring due to the differences in the powdered structure of GOS

versus the needle-like structure of CsI [2] The fact that the DRX-1C and Pixium 4600

have comparable MTFs suggests similar scintillator thicknesses assuming that the

materials were processed alike

The noise of the three detectors demonstrated similar trends with each other The

higher NNPS curves of the DRX-1 detector are probably due also to the scintillating

material and its operation in converting photons into signal The conversion process is

less efficient because of the less favorable stopping power of the GOS compared to CsI

21

especially with higher energy beams The noise of the Pixium 4600 and DRX-1C were

similar except for the spacing between exposures The DRX-1C NNPS curve spacing is

consistent with a factor of two difference in exposure levels but the Pixium 4600 has a

smaller spacing The 05 mR NNPS curve of the Pixium 4600 is closer to that of the 05

mR NNPS curve of the DRX-1C This demonstrates that at higher exposures the Pixium

4600 produces a larger amount of additional noise beyond that explained by simple

stochastic effects It suggests bad performance in the gain map corrections

The DQE results indicate SNR properties of each detector The Pixium 4600 and

DRX-1C are comparable for the most part with the DRX-1C performing slightly better

The DRX-1 as predicted from MTF and NNPS results has a DQE much lower than

either of the previous two This is a reflection of the detection properties as provided by

its scintillator material The DQE of the DRX-1 however is comparable to CR image

receptors [2] The mid-frequency dips in the DQE for Pixium 4600 may be due to the

optical properties of the CsI phosphor layer which can affect the MTF in this manner

Because the DQE is calculated by squaring the MTF this effect at the mid-range

frequencies becomes more apparent The dips may also be further evidence of bad gain

map corrections

I4ii Comparisons of Filtrations

The alternative filtration closely matches for the most part the IEC-based

filtration for MTF NNPS and DQEs at RQA5 but not at RQA9 The filters do not have

22

Table 4 Experimental MTF frequency locations for 1 mR exposure

Detector Filtration

50 MTF

(mm-1)

40 MTF

(mm-1)

30 MTF

(mm-1)

20 MTF

(mm-1)

10 MTF

(mm-1)

Pixium

4600

RQA5A 115 145 185 245 330

RQA5C 125 155 195 250 345

RQA9A 110 175 175 235 330

RQA9C 125 155 195 255 345

DRX-1C

RQA5A 120 150 185 245 350

RQA5C 125 155 195 255 355

RQA9A 120 150 190 250 355

RQA9C 130 160 210 265 360

DRX-1

RQA5A 110 135 160 205 280

RQA5C 110 135 170 210 285

RQA9A 105 125 155 195 270

RQA9C 110 135 165 210 285

Table 5 Estimated DQE values for 1 mR exposure by frequency bins

Detector Filtration DQE(00 mm-1) DQE(10 mm-1) DQE(20 mm-1) DQE(30 mm-1)

Pixium

4600

RQA5A 62 42 32 21

RQA5C 63 45 36 25

RQA9A 41 27 30 13

RQA9C 43 33 27 19

DRX-1C

RQA5A 72 52 35 21

RQA5C 76 55 41 24

RQA9A 49 33 23 15

RQA9C 51 40 31 20

DRX-1

RQA5A 38 24 12 4

RQA5C 38 25 14 5

RQA9A 28 18 9 4

RQA9C 28 19 12 5

DQE values at the zero-frequency axis were estimated by the intercept of a linear fit of low-frequency data

but excluding most proximal to the axis due to large fluctuations Other estimated values are grouped into

frequency bins due to the noisiness of the data

23

considerable differences in the spatial resolutions of the detectors as expected The noise

responses for each filtration were also similar except at the lower frequencies of the

NNPS especially near the zero-frequency axis There observing the NNPS responses at

RQA5 for Pixium 4600 and DRX-1C in Figure 8 the NNPS for the IEC-based filtration

(solid lines) tend to drop faster than the NNPS for the alternative filtration This

subsequently appears as a drop in DQE near the zero-frequency axis shown for those

detectors in Figure 10 Overall as indicated in Table 5 the DQEs of the two filtrations

while similar in trend indicate that the alternative filtration increases the DQE by a

small amount of 3-5 Part of this may be explained by the slightly higher beam

energy which may be more optimal for the energy response of the detectors or may

weigh the pixel responses slightly considering that they are energy-integrating types

The most probable explanation is the gain map correction for the alternative filtration

where fixed pattern noise is more sufficiently reduced

A previous study [6] had discussed the choice of filter material in the analysis of

DQE when achieving the beam conditions defined by IEC It found that visible

nonuniformities were present with the higher purity aluminum filter (type-11999 alloy)

The low frequency mottle in the flat-field images for NPS measurements were also

attributed to structured noise from the grain size in the IEC-based filter with an

attenuating thickness that would reveal nonuniformities The mottle in the current study

was only observable under very narrow windowing as shown in Figure 11 Such low

24

frequency artifacts which are not readily noticeable may also be caused by shading

artifacts inverse square law or even the heel effect A possible method to correct for this

is a subtraction method by taking the average of the flat-field images for an exposure

level and then subtracting that from each of them This would remove nonuniformities

that were not corrected using a suboptimal gain map calibration

Figure 11 DRX1-C NNPS images at 1 mR for RQA5 with IEC filtration (left) and

alternative filtration (right) Images are equally windowed at 45 and leveled at 980

One convenient aspect of the copper and aluminum filtration is that it requires

much less tube current to achieve the same amount of exposure at the detector than the

much thicker aluminum filtration As shown in the non-normalized spectra in Figure 2

the exiting photon fluence exiting the copper and aluminum filtration is substantially

higher than that of the IEC-specified filtration This is due to the smaller total filtration

25

attenuation For extensive DQE analysis multiple sets of exposures may be acquired

before tube overheating becomes a concern

One limitation to the comparison of the two filtrations is that calibration

procedures specified copper and aluminum filtration at 80 kVp (for all detectors 05 mm

Cu and 10 mm Al) This may have influenced the results in favor of the alternative

filtration A further investigation involving the calibration procedures and performing

DQE measurements is encouraged Another factor may be influenced by the fact that the

tests were performed at 70 kVp and 120 kVp different from the recommended

calibration tube potential Clearly there would be differences in the linear attenuation

coefficients of the filters and different energy responses of the detectors themselves This

must be considered when interpreting DQE results The current results support a

previous study decades ago that described filtration of different material types in terms

of an aluminum equivalent [16] The results show that the two filtration schemes are

essentially equivalent when considering beam qualities and spatial resolutions The

NNPS and DQE results can be seen as close enough where their small differences are

insignificant when performing quality assurance tests in a clinical setting Overall our

results indicate that the alternative filtration with copper and aluminum may be more

convenient to use than the current IEC standard filtration

26

I4iii Implications of Wireless DR

This study has shown that wireless image receptors can have the same DQE

performance if not better than conventional flat-panel detectors They operate on the

same basic physical principles the new features offered by the DRX-1C and DRX-1 are

wireless communication with the workstation and electronics packaging technology

The latter feature may pose limitations for these units in terms of possible degradation

in the detectors in routine clinical conditions A consideration for future work would be

to longitudinally track DQE performance of the wireless detectors over time while being

utilized in a clinical environment In the end one must consider risks versus benefits of

choosing portable DR technology over CR one of which includes the cost and fragility

of DR detectors

The DQE performance of one wireless system is just as good as or better than

conventional systems as seen by the DRX-1C performance compared to the Pixium

4600 Wireless systems can also reduce the need for CR readers especially in portable

applications in other regions of the world (eg military hospitals developing countries)

However while DQE performance indicates the physical performance of the detector

system it is still unknown how it relates to observer performance

I5 Conclusions

Two wireless image receptors DRX-1C and DRX-1 were evaluated and

compared with the conventional DR flat-panel Pixium 4600 in terms of DQE

27

performance along with MTF and NNPS performances The detectors have similar

resolution properties although the DRX-1 is inferior at higher spatial frequencies The

NNPS and DQE results both indicate that the DRX-1C is superior to the DRX-1 and

comparable if not better to the Pixium 4600

The results from the filtration comparison indicate no substantial differences

between the IEC-based filtration and the copper-based alternative filtration Only slight

differences were found in the low frequency components of the NNPS and the DQE due

to the inherent nonuniformities of the IEC specified filtration Given the similarity of the

results and low attenuation advantage of the copper and aluminum filter its use is

encouraged

28

II Directional MTF for Breast Tomosynthesis

II1 Introduction

Breast tomosynthesis is an emerging 3D imaging modality that has potential use

for screening and diagnosis of breast cancer Breast tomosynthesis along with other 3D

techniques is preferable to planar imaging methods (eg mammography) because they

reduce anatomical noise by removing overlying structures above and below the plane of

an image slice [17-20] Recent advances in detectors and computer technology have

made digital tomosynthesis feasible

An image quality metric of particular importance in breast tomosynthesis is

spatial resolution Resolution is important to know in order to assess small-detail

structures such as microcalcifications A descriptive metric for characterizing spatial

resolution in the Fourier (or frequency) domain is the modulation transfer function

(MTF) Affected by reconstruction filters [21] the limited angular projections involved in

breast tomosynthesis results in highly anisotropic (or nonuniform) resolution Many

studies have looked only at characterizing the in-plane spatial resolution (ie in an

individual slice) with an elevated angled edge phantom [2223] A few studies have

looked at characterizing a more comprehensive 3D spatial resolution by using a

phantom with angled wires or tubes [24-26] However such studies require precise

mechanical alignment of the phantoms Several studies have explored a method using a

29

sphere phantom for the directional 3D MTF evaluation for microtomography [27] and

multi-slice CT [2829] This method has not yet been extended to breast tomosynthesis

This chapter focuses on breast tomosynthesis because it is highly anisotropic in

spatial resolution and like its predecessor mammography requires high spatial

resolution Additionally breast tomosynthesis acquisitions and reconstructions produce

several types of artifacts The use of a cone-based method using a sphere phantom [28] is

explored to characterize the directional 3D spatial resolution of simulated images from

breast tomosynthesis A technique for removing out-of-plane artifacts of the ESFs for the

in-plane axes is investigated to yield a modified MTF in a method that separates artifact

information from resolution information

II2 Materials and Methods

II2i Image Simulation

Breast tomosynthesis images were simulated by using a virtual imaging system

depicted in Figure 12 A volumetric breast phantom was voxelized as a rectangular mass

of uniform breast equivalent tissue of 4 cm thickness embedded with fifteen evenly

spaced plastic sphere inserts of 12 mm diameter The spheres were placed in a grid

formation within the central plane of the phantom The x-ray fluence was modeled from

a 28 kVp beam incident upon an indirect flat-panel detector with 200 micro m pixel size

Twenty-three projections within an angular range of 44deg were simulated using cascaded

systems analysis to generate characteristic 2D noise and spatial blurring [29] Each

30

projection was simulated to have an exposure of 174 mR with a fluence of 79 times 105

photonsmm-2 A standard filtered backprojection technique based on the Feldkamp

reconstruction algorithm [29] was used to reconstruct the projections and produce a

volumetric dataset with an isotropic voxel size of 200 micro m

Figure 12 Depiction of the virtual image system

II2ii Uncorrected MTF

To enable comparison of multiple spheres the reconstructed volume was

initially homogenized by performing a background subtraction based on a portion of the

volume devoid of spheres The voxel values were rescaled between one and zero to

eliminate negative values

31

The volumetric data were segmented to extract individual regions of interest

(ROIs) each containing a single sphere The ROIs extended along the full range of the z-

axis A thresholded ROI was generated by determining the exterior and interior voxels

relative to the sphere in the ROI The threshold value was set at 45 of the maximum

voxel value prior to thresholding The exterior and interior voxel values were then set to

values of 0 and 1 respectively Using the thresholded volume the center of mass was

calculated to determine the centroid The voxel values from the original ROI were

subsequently tabulated with the associated distances azimuthal angles and polar

angles relative to the centroid

Conical regions were prescribed along the positive and negative directions along

the three major axes extending from the centroid of the sphere as depicted in Figure 13

The axes about which the extent of the cone angle was delineated were defined with

the azimuthal and polar angles

Voxels with centers within the angular range of the cone were considered for

generating the edge spread function (ESF) To improve regularity of the distance

sampling interval the ESF values were rebinned to discrete distances corresponding to a

fraction of the voxel size Only voxels with distances ranging from the voxel size (ie

200 micro m) to the maximum distance were considered The ESFs from multiple spheres

were averaged together for each of the three major axes to produce an averaged ESF

which was further smoothed utilizing a Gaussian filter

32

Figure 13 Example of 30-degree cone prescribed along z axis of the sphere

The resulting ESF was then differentiated using the central difference method to

produce the line spread function (LSF) A Hanning filter with the same length as the LSF

was applied to zero out the tails of the LSF The presampled MTF was subsequently

computed as the amplitude of the Fourier transform of the LSF The MTF was

normalized with respect to the maximum value occurring within the range of the cutoff

frequency Binning size and conical range for the ESF were considered for maximizing

accuracy and minimizing noise of the MTF verified by comparison against the

theoretical MTF as determined in the previous section

II2iii Theoretical Directional MTF

The theoretical 3D MTF was calculated using a priori knowledge of the transfer

function of the virtual imaging system described in the previous section A phantom

was created with a set of point objects in a uniform and noise-free background with the

objects spanning across the volume of the breast [29] Twenty-one realizations were

33

generated from the reconstructed images of the point objects to yield a set of 3D point

spread functions (PSFs) The 3D fast Fourier transform (FFT) was performed for each 3D

PSF and averaged to give an ldquoexpectationrdquo 3D MTF [29] The theoretical directional

MTFs in the three major spatial axes were determined by line profiles along each of the

corresponding spatial frequency axes in the 3D MTF An additional theoretical MTF for

each direction was determined by using the application of conical regions along the axes

in frequency-space to take into account the contributions of MTF information from other

planes

II2iv Modified MTF

The tomosynthesis reconstruction is known to have edge enhancements which

affect the overall MTF by shifting the peaks of the MTF toward the higher frequencies

[23] The presence of this artifact complicates the interpretation of the actual spatial

resolution of the images Several steps were performed to remove the artifact

contribution to the resolution information particularly for the in-plane x and y

directions with the assumption that resolution information was contained immediately

near the edge

For the x-direction averaged ESF only values that were detected to be inside the

edge of the sphere were considered Those values were previously determined via

thresholding for calculating the centroid The ESF information corresponding to these

values was inversed and flipped about the detected edge to produce a symmetric

34

modified ESF The modified MTF was subsequently calculated from this modified ESF

as described in the previous section

For the y-direction averaged ESF an upward trend was found in the initial part

of the ESF This section was detrended with a polynomial fit and subtracted to produce a

flatter curve in that region The resulting detrended ESF was used to calculate the y axis

modified MTF

Figure 14 Photograph of the imaging system with the acrylic sphere phantom

embedded in oil

II2v Preliminary Experimental Validation

A clinical breast tomosynthesis system (Mammomat Inspiration Siemens AG

Munich Germany) was used to perform a preliminary evaluation of the cone-based

MTF technique The phantom for the experiment consisted of a single acrylic ball of 075

in diameter (SmallParts Seattle WA) suspended by a 0029 in diameter plastic filament

35

(Omniflex Zebco Tulsa OK) in an acrylic frame filled up to 4 in with vegetable oil

(Target Brands Inc Minneapolis MN) The system and phantom are shown in Figure

14 Twenty-five projections with an angular range of 44deg were acquired and subsequently

reconstructed to produce a volume with a voxel size of 01times01times10 mm3 The voxels were

reformatted to have an isotropic size of 01 mm The uncorrected ESF LSF and MTF

were calculated as described in the previous section

II3 Results

II3i Reconstruction

The reconstructed volume is shown in Figure 15 Notice the edge enhancement

along the x-direction as indicated by the sharp shadowing artifacts on either side of the

spheres The background was effectively homogenized using the background

subtraction technique This also took account of the curved edges of the breast phantom

With the close spacing of the spheres in the phantom the shadows along the x direction

for the fifteen spheres overlap with each other As the nine centrally located spheres

experience this effect the same way they were used for determining the ESF

A 3D rendering of the ROI containing a sphere shown in Figure 16 indicates the

anisotropic resolution of the reconstruction Note that the sphere is not accurately

reconstructed and has an oblong shape especially along the z axis Cross sectional views

of the ROI also in Figure 16 clearly demonstrate the edge enhancement causing a

shadow artifact in the x direction caused by the incomplete angular sampling of

36

tomosynthesis The sampling also introduces the triangular reconstruction of the sphere

as seen in the x-z plane Note the gradual edge drop-off in the z direction much beyond

the sphere radius

Figure 15 View of the central slice of the breast phantom reconstruction before (top)

and after (bottom) background subtraction The z axis is through the page

37

Figure 16 3D rendering of the ROI volume (left) and cross-sectional views of the most

centrally located sphere with centroid indicated with red circle (right)

II3ii Theoretical MTF

The theoretical MTFs for x y and z directions as determined from the line

profiles of the 3D MTF are shown in Figure 17 The theoretical MTF in the x direction

has a maximum value that is toward higher frequencies Its 10 response occurs at

about 125 cyclesmm which is at 50 of the cutoff frequency The rapid increase from

the zero-frequency intercept to the peak corresponds to the ramp filter used in filtered

backprojection which decreases the weighting of low frequency contributions due to the

incomplete angular sampling of the frequency-space The MTF does not reach a value of

0 at the zero-frequency intercept as it is very difficult to assess the zero-frequency

intercept due to the finite size of the phantom The theoretical MTF in the y direction

peaks at the zero-frequency intercept and reaches 20 proximal to the cutoff frequency

38

The 10 MTF is well beyond the cutoff frequency The theoretical MTF in the z direction

has a rapid drop-off at very low spatial frequencies indicating the lack of resolution in

that dimension

Figure 17 Theoretical 3D MTF results along the three major planes (top) and along x

y and z directions (bottom) Also note that the angular spread seen in the fx-fz plane is

equal to the angular range of 44deg for the acquisition

II3iii Uncorrected MTF

The ESF LSF and MTF using the cone-based method are shown for the x y and

z directions in Figure 18 It was found that a bin size of one-tenth the voxel size (002

mm) and a cone angle of 30deg to establish the ESF were enough to minimize noise and

maximize accuracy in the uncorrected MTFs considering the reasonable comparison of

the shapes of the MTF curves with the theoretical results in Figure 17 The LSFs are

generally noisy because differentiation of the ESF increases the amplitude of the noise

39

The data shown reflect a convolution with a smoothing Gaussian filter which was later

further corrected for in the reported MTF Nevertheless the high frequency components

of the noise are well beyond the MTF cutoff frequency of 25 cyclesmm and do not

impact the MTF results greatly

For the ESF in the x direction the shadow effect evident at the edge of the sphere

is visible as a steep decline followed by an increase Due to the finite distance range

provided by the ROI the ESF beyond the edge did not asymptotically reach the

background value The corresponding LSF demonstrates a low frequency modulation

that is indicated by the shift of 03 cyclesmm in the x direction for the peak of the MTF

The MTF exhibits a zero-frequency intercept that is non-zero unlike the theoretical MTF

and a 10 value at approximately 1 cyclesmm These features may be a direct

consequence of MTF information ldquocontaminationrdquo from y and z directions Furthermore

the ESF in the y direction demonstrates a reasonably shaped curve except for the slight

upward trend within the radius of the sphere which can be attributed to the shadow

artifact overlapping with the sphere volume The associated MTF has a peak shifted by

approximately 01 cyclesmm away from the axis and a 10 MTF occurring at

approximately 15 cyclesmm Both features which are not present in the theoretical

results may also be attributed to contaminant MTF information from x and z directions

The ESF in the z direction has a drop-off that occurs at a small fraction of the cutoff

frequency similar to that demonstrated by the theoretical MTF

40

Uncorrected ESF LSF and MTF

Figure 18 Uncorrected ESF (top) LSF (middle) and MTF (bottom) for x y and z

directions

41

Figure 19 Comparisons of the directional MTFs as calculated by the sphere method

(dashed line) by theoretical line profiles (light-weight line) by theoretical cone

regions (heavy-weight line)

II3iv Comparison of Theoretical and Simulated MTFs

The theoretical MTF results obtained from line profiles through the 3D MTF and

the simulated MTFs using the cone-based technique did not match very well except for

the general shape of the curves It was assumed in the previous section that the cone-

based technique contains information from other planes Figure 19 compares MTFs in

each direction for the two methods described in the methods and an additional method

based on conical regions of the 3D MTF The latter computes the MTF by averaging

contributions of the 3D MTF using the same cone prescription method used to define the

ESFs Comparison of the curves indicate some interesting correlations aside from the

fact that using conical regions with the 3D MTF results produce more noisy MTF results

partly due to the low sampling provided by the theoretical calculations The same

conclusions regarding the z direction MTF can be confirmed regardless of either

theoretical MTF procedures The experimental x direction MTF seems to agree best with

42

the line profile method whereas the y direction MTF agrees better with the cone region

method The fact that the experimental x direction MTF has a drop-off frequency that is

lower than those of either of the theoretical MTFs in Figure 19 suggests that this might

be due to integration of the z-direction in the in-plane slices considering how slices are

essentially averages of z direction information contained within it [33]

II3v Modified MTF for x and y

Modified ESF LSF and MTF curves for x and y directions are shown in Figure

20 The modified ESF and the resulting LSF in the x direction appear symmetric as

expected from the inverse and flip operation of the interior ESF about the detected edge

The modified MTF appears with less variation than the uncorrected MTF and the MTF

peak occurs at the zero-frequency axis The correction yields a 10 MTF at about 15

cyclesmm an improvement from the uncorrected MTF but still distant from the cutoff

frequency The modified ESF in the y direction demonstrates the detrended curve within

the sphere radius after a quadratic polynomial fit The resulting modified MTF still

appears similar to the uncorrected MTF except that the peak now coincides with the

zero-frequency axis For both x and y directions the low response of the modified MTFs

at the higher frequencies suggests that the contamination from other directions is

substantial due to the angular range of the cone

43

Modified ESF LSF and MTF

Figure 20 Modified ESF (top) LSF (middle) and MTF (bottom) for x and y directions

44

II3v Preliminary Experimental Validation

Cross-sections of the reconstructed sphere volume are shown in Figure 21

Relative to the simulation reconstructions the reconstructions of the experimental

phantom images produce lower contrast and higher noise The preliminary results

shown in Figure 22 indicate that our technique can be applied to actual experimental

breast tomosynthesis reconstructions However due to the noise exhibited by the MTF

curves for the x and y directions we did not determine the modified MTFs to separate

resolution and artifact information

Figure 21 Cross sectional views of the experimental sphere image with centroid

indicated with red circle

45

Uncorrected ESF LSF and MTF for Real Image

Figure 22 ESF (top) LSF (middle) and MTF (bottom) of real image for x y

and z directions

46

II4 Discussion

II4i Evaluation of Cone-based Method

The cone-based MTF technique was introduced by Thornton and Flynn [28] for

evaluation of volumetric CT images To utilize this technique as a characterization of a

3D system spatial resolution one must first consider the validity of the assumption of

shift invariance such that the same MTF result may be obtained regardless of the

location of the sphere The study by Zhao et al [23] found that there was no shift

variance for the MTF measurements along the vertical axis but this was only considering

the in-plane resolution along one axis On the other hand this study evaluated the MTF

with images simulated with cascaded systems analysis which includes conditions of

linearity and shift invariance Additionally the MTF was calculated by averaging the

ESF from several spheres in the same volume only after performing a background

subtraction This step was essential to account for the sensitivity of centroid calculations

as well as ensuring symmetric ESFs for opposing axes of the sphere ROIs

The measurement of MTF with the cone-based technique inherently

supersamples the edge of the sphere to increase signal-to-noise-ratio (SNR) of edge

information by averaging the contributions of each voxel to the ESF [713] This method

also takes into account the discrete sampling of the voxels by accounting for various

shifts of the edge in the voxel (also known as the partial volume effect) However using

the curved surface of the sphere phantom to approximate an edge along a given

47

direction naturally leads to contamination of information from other directions aside

from the one of interest Preferably a directional ESF should be created by using a single

radial line but this would limit the available voxels to obtain edge information An ideal

situation theoretically would be to use a larger-sized sphere such that the surface is

nearly flat and perpendicular to the axes of interest This would also permit a reduction

in the angular range of the cone and thus the introduction of out-of-plane information in

the resulting MTF However sphere size is a limitation in breast tomosynthesis and the

use of a large phantom might void the assumption of shift invariance of the spatial

resolution

The choice of a sphere phantom nevertheless may be based on the clinical need

to quickly acquire a single image for MTF evaluation especially for multiple directions

without presenting extra logistical challenges The use of a wire or edge phantom

requires more precise mechanical alignment to achieve the correct set up The edge

phantom [23] would require at least two images to sample all three dimensions In the

case of the three wire phantom [2425] all three dimensions of the frame must be aligned

simultaneously with respect to the axis of rotation A similar situation would be

encountered when considering a cubic phantom with the planes normal to the axis of

interest In contrast to these phantoms the sphere eliminates the need for precise

alignment especially with respect to three spatial dimensions simultaneously A sphere

48

has ideal symmetry in all directions and can be used to evaluate MTF in any arbitrary

direction

This study unlike others [242532] did not explore the effects of physical

parameters such as scatter or contrast on the final MTF result but it demonstrated the

feasibility of using the cone-based method with an actual breast tomosynthesis image of

a sphere phantom as shown in Error Reference source not found and Error Reference

source not found These effects should be addressed in future works A further look

into deriving the principles of comparing the theoretical MTF with the experimental

MTF using the cone-based method is further warranted

II4ii Separation of Artifact and Resolution Information

The focus of this study was to develop a technique for measuring spatial

resolution of tomosynthesis images The intrinsic artifacts from tomosynthesis

reconstructions however lead to uncharacteristic MTFs and possible misinterpretation

of the effective resolution information When considering previous techniques for

calculating the presampled MTF [713152328] the analysis was performed using an

edge or a line to produce the corresponding ESF The resolution information is

essentially contained only along the edge indicated by the need to calculate the LSF In a

way the method of extracting artifact information is to focus the analysis only on the

edge part of the ESF to calculate the modified MTF This will lead to a better

understanding of the limiting size of objects that may be seen in the reconstructed 3D

49

image The presampled MTF without correction should still be analyzed to understand

the entire system response Note that the ESFs attempt to reflect information only at the

detected edge of the sphere

II5 Conclusions

The directional MTF of a simulated breast tomosynthesis reconstruction was

determined by using the cone-based MTF technique demonstrating the feasibility of a

single phantom for MTF evaluation This study further presented methods of analyzing

only the edge information in the ESF to create a modified MTF along in-slice (x and y)

axes It can provide insight into the actual spatial resolution information contained in the

image while separating the resolution information from the information introduced by

artifacts caused by the reconstruction and insufficient volumetric sampling The idea of

separating the resolution and artifacts from the measured ESF are expected to facilitate

the interpretation of MTF measurements in breast tomosynthesis Similar methods may

be applied to characterize the resolution of other 3D imaging modalities

50

References

1 Garmer M Hannigs SP Jaumlger HJ et al ldquoDigital Radiography Versus

Conventional Radiology in Chest Imaging Diagnostic Performance of a Large-

Area Silicon Flat-Panel Detector in a Clinical CT-Controlled Studyrdquo American

Journal of Roentgenology Volume 74 75-80 (2000)

2 Cowen AR Kengyelics SM and Davies AG ldquoSolid-state flat-panel digital

radiography detectors and their physical imaging characteristics rdquoClinical

Radiology Volume 63 487-498 (2008)

3 Chotas HG Dobbins III JT and Ravin CE ldquoPrinciples of Digital

Radiography with Large-Area Electronically Readable Detectors A Review of

the Basicsrdquo Radiology Volume 210 Number 3 595-599 (1999)

4 Flynn MJ and Samei E Experimental comparison of noise and resolution for

2k and 4k storage phosphor radiography systems Medical Physics Volume 26

Number 8 1612-1623 (1999)

5 Rong XJ Shaw CC Liu X Lemacks MR and Thompson SK

ldquoComparison of an amorphous siliconcesium iodide flat-panel digital chest

radiography system with screenfilm and computed radiography systems ndash A

contrast-detail phantom studyrdquo Medical Physics Volume 28 Number 11 2328-

2335 (2001)

6 Ranger NT Samei E Dobbins III JT and Ravin CE Measurement of the

detective quantum efficiency in digital detectors consistent with the IEC 62220-1

standard Practical considerations regarding the choice of filter material

Medical Physics Volume 30 Number 7 2305-2311 (2005)

7 Samei E Buhr E Granfors P Vandenbroucke D and Wang X Comparison

of edge analysis techniques for the determination of the MTF of digital

radiographic systems Physics in Medicine and Biology Volume 50 3613-3625

(2005)

8 Samei E and Flynn MJ An experimental comparison of detector performance

for computed radiography systems Medical Physics Volume 29 Number 4 447-

459 (2002)

51

9 Samei E and Flynn MJ An experimental comparison of detector performance

for direct and indirect digital radiography systems Medical Physics Volume 30

Number 4 608-622 (2003)

10 Samei E Ranger NT MacKenzie A Honey ID Dobbins III JT and Ravin

CE Effective DQE (eDQE) and speed of digital radiographic systems An

experimental methodology Medical Physics Volume 36 Number 8 3806-3817

(2009)

11 Samei E Ranger NT MacKenzie A Honey ID Dobbins III JT and Ravin

CE Detector or System Extending the Concept of Detective Quantum

Efficiency to Characterize the Performance of Digital Radiographic Imaging

Systems Radiology Volume 249 Number 3 926-937 (2008)

12 ldquoIEC 62220-1 Medical Electrical Equipment ndash Characteristics of Digital X-Ray

Imaging Devices ndash Part 1 Determination of the Detective Quantum Efficiencyrdquo

International Electrotechnical Commission Geneva Switzerland (2003)

13 Samei E Ranger NT Dobbins III JT and Chen Y Intercomparison of

methods for image quality characterization I Modulation transfer function

Medical Physics Volume 33 Number 5 1454-1465 (2006)

14 Dobbins III JT Samei E Ranger NT and Chen Y Intercomparison of

methods for image quality characterization II Noise power spectrum Medical

Physics Volume 33 Number 5 1466-1475 (2006)

15 Samei E Flynn MJ and Reimann DA A method for measuring the

presampled MTF of digital radiographic systems using an edge test device

Medical Physics Volume 25 Number 1 102-113 (1998)

16 Nagel HD ldquoAluminum equivalence of materials used in diagnostic radiology

and its dependence on beam qualityrdquo Physics in Medicine and Biology Volume

31 Number 12 1381-1399 (1986)

17 Niklason LT Christian BT Niklason LE et al ldquoDigital Tomosynthesis in

Breast Imagingrdquo Radiology Volume 205 399-406 (1997)

18 Gur D ldquoTomosynthesis Potential Clinical Role in Breast Imagingrdquo American

Journal of Roentgenology Volume 189 614-615 (2007)

52

19 Park JM Franken Jr EA Garg M Fajardo LL and Niklason LT ldquoBreast

Tomosynthesis Present Considerations and Future Applicationsrdquo

RadioGraphics Volume 27 S231-S240 (2007)

20 Good WF Abrams GS Catullo VJ Chough DM Ganott MA Hakim

CM and Gur D ldquoDigital Breast Tomosynthesis A Pilot Observer Studyrdquo

American Journal of Roentgenology Volume 190 865-869 (2008)

21 Hu Y-H Zhao W Mertelmeier T and Ludwig J ldquoImage Artifact in Digital

Breast Tomosynthesis and Its Dependence on System and Reconstruction

Parametersrdquo IWDM 2008 LNCS 5116 628-634 (2008)

22 Chen Y Lo JY Ranger NT Samei E Dobbins III JT ldquoMethodology of

NEQ(f) analysis for optimization and comparison of digital breast tomosynthesis

acquisition techniques and reconstruction algorithmsrdquo Proceedings of SPIE

Volume 6510 65101I (2007)

23 Zhao B Zhou J Hu Y-H Mertelmeier T Ludwig J and Zhao W

ldquoExperimental validation of a three-dimensional linear system model for breast

tomosynthesisrdquo Medical Physics Volume 36 Number 1 240-251 (2009)

24 Madhav P Brzymialkiewicz CN Cutler SJ Bowsher JE and Tornai MP

ldquoCharacterizing the MTF in 3D for a Quantized SPECT Camera Having Arbitrary

Trajectoriesrdquo 2005 IEEE Nuclear Science Symposium Conference Record 1722-

1726 (2005)

25 Madhav P McKinley RL Samei E Bowsher JE and Tornai MP ldquoA Novel

Method to Characterize the MTF in 3D for Computed Mammotomographyrdquo

Proceedings of SPIE Volume 6142 61421Y (2006)

26 Hu Y-H Zhao B and Zhao W ldquoImage artifacts in digital breast

tomosynthesis Investigation of the effects of system geometry and

reconstruction parameters using a linear system approachrdquo Medical Physics

Volume 35 Number 12 5242-5252 (2008)

27 Seifert A and Flynn MJ ldquoResolving power of 3D x-ray microtomography

systemsrdquo Proceedings of SPIE Volume 4682 407-413 (2002)

28 Thornton MM and Flynn MJ Measurement of the spatial resolution of a

clinical volumetric computed tomography scanner using a sphere phantom

Proceedings of SPIE Volume 6142 61421Z (2006)

53

29 Baek J Pelc NJ ldquoUse of sphere phantoms to measure the 3D MTF of FDK

reconstructionsrdquo Proceedings of SPIE Volume 7961 79610D (2011)

30 Richard S and Samei E ldquoQuantitative imaging in breast tomosynthesis and CT

Comparison of detection and estimation task performancerdquo Medical Physics

Volume 37 Number 6 2627-2637 (2010)

31 Chen Y Lo JY and Dobbins III JT ldquoImpulse response analysis for several

digital tomosynthesis mammography reconstruction algorithmsrdquo Proceedings of

SPIE Volume 5745 541-549 (2005)

32 Zhao B and Zhao W ldquoThree-dimensional linear system analysis for breast

tomosynthesisrdquo Medical Physics Volume 35 Number 12 5219-5232 (2008)

33 Wu G Mainprize JG Boone JM and Yaffe MJ ldquoEvaluation of scatter

effects on image quality for breast tomosynthesisrdquo Medical Physics Volume 36

Number 10 4425-4432 (2009)

Page 3: Development and Evaluation of 2D and 3D Image Quality ...

Copyright by

Simon Nicholas Murphy

2011

iv

Abstract

With continuing advances in medical imaging technologies there is an increased

demand to extract quantitative information from images This has been particularly vital

in the effort to increase the efficacy and accuracy of diagnoses Quantitative information

is readily available in images because the acquisition techniques intrinsically involve

physical processes Quantitative image quality metrics are critical in the evaluation of

medical images for diagnostic merit particularly when used for the characterization and

comparison of different systems When such metrics are based on measurable physical

parameters they can provide valuable information for system optimization Image

quality describes the ldquogoodnessrdquo of an image in displaying information for a task This

thesis explored methods of measuring image quality for two scenarios (1) to

characterize 2D flat-panel detector performance and (2) to measure directional spatial

resolution for 3D images from breast tomosynthesis

In the first chapter two new wireless digital receptors (DRX-1C and DRX-1

Carestream Health Inc Rochester NY) were evaluated and compared to a conventional

flat-panel detector (Pixium 4600 Trixell Moirans France) on the basis of detective

quantum efficiency (DQE) A secondary goal was also to evaluate the filtration to

achieve specified beam qualities for the DQE measurements closely following the

methodology of the International Electrotechnical Commission (IEC) for radiation

v

qualities RQA5 and RQA9 All three DR systems demonstrated similar modulation

transfer functions (MTFs) at most frequency ranges while the DRX-1 showed lower

values near the cutoff of approximately 35 cyclesmm At each exposure the Pixium

4600 and DRX-1C demonstrated similar noise power spectrum (NPS) curves that

indicated better noise performance than the DRX-1 Zero-frequency DQEs for Pixium

4600 DRX-1C and DRX-1 were approximately 63 74 and 38 for RQA5 and 42

50 and 28 for RQA9 respectively In terms of DQE performance the DRX-1C image

receptor was found to be superior to the Pixium 4600 and DRX-1

In the second chapter the directional spatial resolution of simulated breast

tomosynthesis images was determined using a cone-based technique and a sphere

phantom Projections were simulated for a voxelized breast phantom with 12 mm

diameter sphere inserts using a fluence modeled from a 28 kVp beam incident upon an

indirect flat-panel detector with 200 micro m pixel size Characteristic noise and blurring for

each projection were added using cascaded systems analysis The projections were

reconstructed using a standard filtered backprojection technique producing a 3D

volume with an isotropic voxel size of 200 micro m Regions of interest (ROIs) that

completely encompassed single spheres were extracted and conical regions were

prescribed along the three axes extending from the centroid Voxels within a cone were

used to form an edge spread function (ESF) from which the directional MTF was

calculated A bin size of 002 mm and a conical range of 30 degrees were found optimal

vi

for maximizing accuracy and minimizing noise of the MTF A method for removing out-

of-plane artifacts of the ESFs along in-plane axes was investigated and yielded a

modified MTF The idea of separating the effective resolution and artifacts from the

measured ESF are expected to facilitate the interpretation of MTF measurements in

breast tomosynthesis Similar methods may be applied to characterize the spatial

resolution of other 3D imaging modalities

vii

Contents

Abstract iv

List of Tables x

List of Figures xi

Acknowledgements xiii

I Evaluation of 2D Digital Image Receptors 1

I1 Introduction 1

I2 Materials and Methods 3

I2i Detectors 3

I2ii Beam Characterization 3

I2iia X-ray Techniques 3

I2iib Data Linearization 4

I2iic Spectral Simulation 5

I2iii DQE Measurements 6

I2iiia Modulation Transfer Function 6

I2iiib Noise Power Spectrum 7

I2iiic DQE Calculation 8

I3 Results 9

I3i Data Linearization 9

I3ii Spectral Simulation 9

I3iii Modulation Transfer Function 12

viii

I3iv Noise Power Spectrum 12

I3v Detective Quantum Efficiency 19

I4 Discussion 20

I4i Comparisons of Detectors 20

I4ii Comparisons of Filtrations 21

I4iii Implications of Wireless DR 26

I5 Conclusions 26

II Directional MTF for Breast Tomosynthesis 28

II1 Introduction 28

II2 Materials and Methods 29

II2i Image Simulation 29

II2ii Uncorrected MTF 30

II2iii Theoretical Directional MTF 32

II2iv Modified MTF 33

II2v Preliminary Experimental Validation 34

II3 Results 35

II3i Reconstruction 35

II3ii Theoretical MTF 37

II3iii Uncorrected MTF 38

II3iv Comparison of Theoretical and Simulated MTFs 41

II3v Modified MTF for x and y 42

II3v Preliminary Experimental Validation 44

ix

II4 Discussion 46

II4i Evaluation of Cone-based Method 46

II4ii Separation of Artifact and Resolution Information 48

II5 Conclusions 49

References 50

x

List of Tables

Table 1 Physical Characteristics of Digital Image Receptors 4

Table 2 Beam Qualities and Required Filtrations 5

Table 3 Spectral Simulation Results 11

Table 4 Experimental MTF frequency locations for 1 mR exposure 22

Table 5 Estimated DQE values for 1 mR exposure by frequency bins 22

xi

List of Figures

Figure 1 MTF images for DRX-1C detector with radio-opaque edge test device with

arrows indicating the horizontal (left) and vertical (right) directions 7

Figure 2 NNPS image for DRX-1C detector indicating the top left ROI that served as the

reference for normalizing other ROIs in the image The ROI array was formed along the

directions indicated by the arrows The heel effect visible along the vertical axis of the

detector is an example of small variation in signal across the image 8

Figure 3 Original (left) and linearized (right) system responses for Pixium 4600 The

linearized system responses were measured from actual images The offsets are small

with respect to the slope sufficient enough for zero-offset conditions 10

Figure 4 Spectral simulations for RQA5 (top) and RQA9 (bottom) conditions Note the

similarities of spectral shapes of the normalized spectra (right) Also note the significant

differences in fluence between filtrations in the simulated spectra (left) 11

Figure 5 MTF results by detector (columns) and beam quality (rows) 13

Figure 6 Plots of MTF for RQA5 (top) and RQA9 (bottom) showing the relationships

between detectors (blue red and green) and by filtration (solid and dashed) 14

Figure 7 NNPS results by detector (columns) and beam quality (rows) 15

Figure 8 Plots of NNPS for RQA5 (top) and RQA9 (bottom) at 1 mR exposure showing

the relationships between detectors (blue red and green) and by filtration (solid and

dashed) 16

Figure 9 DQE results by detector (columns) and beam quality (rows) 17

Figure 10 Plots of DQE for RQA5 (top) and RQA9 (bottom) at 1 mR exposure showing

the relationships between detectors (blue red and green) and by filtration (solid and

dashed) 18

Figure 11 DRX1-C NNPS images at 1 mR for RQA5 with IEC filtration (left) and

alternative filtration (right) Images are equally windowed at 45 and leveled at 980 24

Figure 12 Depiction of the virtual image system 30

xii

Figure 13 Example of 30-degree cone prescribed along z axis of the sphere 32

Figure 14 Photograph of the imaging system with the acrylic sphere phantom

embedded in oil 34

Figure 15 View of the central slice of the breast phantom reconstruction before (top) and

after (bottom) background subtraction The z axis is through the page 36

Figure 16 3D rendering of the ROI volume (left) and cross-sectional views of the most

centrally located sphere with centroid indicated with red circle (right) 37

Figure 17 Theoretical 3D MTF results along the three major planes (top) and along x y

and z directions (bottom) Also note that the angular spread seen in the fx-fz plane is

equal to the angular range of 44deg for the acquisition 38

Figure 18 Uncorrected ESF (top) LSF (middle) and MTF (bottom) for x y and z

directions 40

Figure 19 Comparisons of the directional MTFs as calculated by the sphere method

(dashed line) by theoretical line profiles (light-weight line) by theoretical cone regions

(heavy-weight line) 41

Figure 20 Modified ESF (top) LSF (middle) and MTF (bottom) for x and y directions 43

Figure 21 Cross sectional views of the experimental sphere image with centroid

indicated with red circle 44

Figure 22 ESF (top) LSF (middle) and MTF (bottom) of real image for x y and z

directions 45

xiii

Acknowledgements

I would like to thank Ian Yorkston Mark Purdum and Van Huston of

Carestream Health Inc (Rochester NY) for their help with digital detector

measurements I would also like to thank Olav Christianson Samuel Richard Brian

Harrawood and Max Amurao for their assistance with collecting data and analyzing

results Special thanks go to my committee members for their helpful insights and

suggestions for this thesis Last but not least I want to express deep appreciation for the

support and mentorship provided by my advisor Dr Ehsan Samei

1

I Evaluation of 2D Digital Image Receptors

I1 Introduction

In the past decade many areas of radiological practice have seen a conversion

from screen films to the storage phosphor cassettes of computed radiography (CR) to the

active-matrix flat-panel detectors of digital radiography (DR) Both CR and DR are

digital systems that offer many potential benefits including but not limited to better

image quality wider dynamic range quicker readout lower radiation dose and higher

throughput [1-3] Even with advances in DR technologies such as improved detective

quantum efficiency (DQE) the primary radiographic system of today continues to be CR

A major obstacle to completely accepting DR is the high capital cost of acquiring an

entire system per examination room while also providing capability for portable

applications Recently manufacturers like Carestream Health Fuji and Toshiba have

introduced wireless digital image receptors that can serve as replacements for CR

cassettes As these are new technologies a further investigation to characterize these

detectors is warranted

In the case of radiographic receptors DQE has historically been the metric of

choice [4] because it indicates the ability of the image receptor to convert incident x-ray

photons into useable signal ndash essentially a measure of signal-to-noise ratio (SNR)

efficiency and overall system performance [23] DQE is observed across a range of

spatial frequencies for evaluating how the detector depicts small and large objects [3]

2

DQE metrics have been used in numerous studies to characterize CR phosphor-screens

as well as indirect and direct digital detectors [4-11] The importance of this highly

quantitative metric may be implied by the introduction of a DQE measurement standard

by the International Electrotechnical Commission (IEC) [12]

The standard measurement methodology of the International Electrotechnical

Commission (IEC) pertains to the image quality of 2D digital radiographic detectors

While the IEC formalism is well-developed some of the components that it requires are

not necessarily the most optimal for characterizing DQE This has been explored in

previous studies in terms of filtration material purity beam limitations and region of

interest (ROI) configuration [1314] To reduce the variability in the radiographic output

across various x-ray tubes due to inherent filtration differences the IEC formalism

prescribes specific additional aluminum filtration to attain radiation beam qualities

based on target half value layers (HVL) Achieving and verifying the desired HVL

however requires applying a substantial amount of aluminum at the exit window of the

x-ray tube which is often directed toward the ground This can be a logistical

inconvenience and can increase the risk of damage to the image receptor and

measurement equipment Similar beam qualities on the other hand may be attained

more conveniently using a thinner lighter filtration combination utilizing a higher Z

number material Care is warranted however as a previous study [6] had indicated that

the choice of filtration material could impact the DQE

3

The purpose of this study was two-fold First we aimed to evaluate and compare

two wireless image receptors with a conventional flat-panel detector on the basis of DQE

performance Second we compared DQE results using the IEC-prescribed filtration with

an alternative filtration For the latter an optimum filtration composition was

determined and compared with the IEC filtration on the basis of DQE

I2 Materials and Methods

I2i Detectors

The physical characteristics of the three digital image receptors evaluated in this

study are listed in Table 1 The Pixium 4600 was a conventional digital flat-panel The

DRX-1C and DRX-1 were both wireless digital cassettes that were tethered for the

purposes of this study All detectors were FDA approved and available commercially

Each detector was calibrated according to its manufacturer specifications to correct for

gain offset and bad pixels They were all dedicated for non-clinical laboratory research

purposes and hence could be operated under service settings that permitted acquisition

of raw (ie for processing) images

I2ii Beam Characterization

I2iia X-ray Techniques

All measurements for this study were taken with a well-characterized standard

radiographic system (Super80CP Philips Healthcare Andover MA) The x-ray tube had

an inherent filtration of 27 mm Al Free in-air exposures were measured using

4

Table 1 Physical Characteristics of Digital Image Receptors

Manufacturer Detector

Detector

type

Detector

material

Pixel pitch

(size) Array size

Imaging

area

Trixell

(Moirans France)

Pixium

4600 Indirect

CsITl

(CsI) 0143 mm

3121times3121

4 subpanels 45times45 cm2

Carestream Health Inc

(Rochester NY)

DRX-1C

(wireless) Indirect

CsITl

(CsI) 0139 mm

2560times3072

single panel 35times43 cm2

Carestream Health Inc

(Rochester NY)

DRX-1

(wireless) Indirect

G2O2STb

(GOS) 0139 mm

2560times3072

single panel 35times43 cm2

calibrated radiation meters (Mult-O-Meter Type 407 Unfors Instruments AB Billdal

Sweden) at 183 cm source-to-chamber-distance (SCD) The SCD also corresponded to

same plane as the image receptor surface The x-ray output was made to conform to IEC

beam quality definitions [1215] on the basis of half value layer (HVL) and peak

kilovoltage setting using an aluminum filtration (type-1100 99 purity) and an

alternative filtration consisting of copper (UNS C11000 999 purity) and aluminum

(type-1100 99 purity) The IEC radiation quality numbers (RQA) used in this study are

summarized in Table 2 HVLs were determined by iteratively adding successive

thicknesses of aluminum until reaching reduced exposure levels within a tolerance of

0485-0515 [12] As for the alternative filtration the aluminum was placed downstream

of the copper filter to attenuate characteristic radiation peaks from copper at

approximately 9 keV

I2iib Data Linearization

The system response function was determined for each detector and filtration

combination by acquiring flat-field images at increasing photon fluence until just before

5

Table 2 Beam Qualities and Required Filtrations

IEC Radiation

Quality Number

Peak

kilovoltage

Required

HVL

Required IEC

Filtration

Actual IEC

Filtration

Alternative

Filtration

RQA5 70 kVp 71 mm Al 21 mm Al 21 mm Al 05 mm Cu +

10 mm Al

RQA9 120 kVp 115 mm Al 42 mm Al 40 mm Al 104 mm Cu +

10 mm Al

For reasons of convenience these will be referred to as RQA5A RQA5C RQA9A and RQA9C

saturation levels To avoid the influence of detector backscatter on exposure

measurements a relationship for each filtration was first determined for two radiation

meters A target meter was placed at the central axis and a reference meter was placed at

the edge of the light field (large enough to cover the detectors) The reference meter

served as a surrogate for the target meter to avoid direct exposure measurements in the

plane of the image receptor Exposure relationships were determined before each

measurement set (ie detector and filtration combination) to account for changes in

temperature pressure and humidity The system response function was calculated by

using a regression of ADU (pixel value) versus exposure Images acquired for each

series were then converted to achieve a linear response with zero offset and scaled to

achieve high quantization (adequate dynamic range) Linearization of the detector

responses ensured that zero exposure corresponded to zero pixel value

I2iic Spectral Simulation

The effects of additional filtration on x-ray output spectra were observed with

spectral simulation software (XSPECT V40 Henry Ford Hospital Detroit MI) To more

6

adequately describe the performance of a typical X-ray generator inherent filtration of 3

mm oil 148 mm Pyrex glass and 2 mm aluminum was input into the simulation in

addition to the filters of interest The ideal signal to noise ratio squared or incident

photon fluence per exposure (q) was estimated for each filtration by integrating the

energy-dependent photon counts per unit exposure over all energy bins

I2iii DQE Measurements

The assessment of the linearized images followed the formalism described by

IEC 62220-1 for measuring the DQE [12] For this study the normal exposure level XN

was set at 1 mR to the detector surface as measured at the central axis perpendicular to

the anode-cathode axis

I2iiia Modulation Transfer Function

Spatial resolution was characterized by evaluating the presampled modulation

transfer function (MTF) along directions parallel (vertical) and perpendicular

(horizontal) to the anode-cathode axis using the angled-edge method [6-1013] A radio-

opaque edge test device [7] was placed in the center of the field at a pitch of

approximately 301 (about 2deg) to the axis perpendicular to that being measured as

shown in Figure 1 External lead apertures were not used [6] instead the internal

collimation from the radiographic unit was used to collimate the beam to the detector

area Raw images were acquired of the edge with the normal exposure level XN of 1 mR

at the detector face The procedure of calculating the MTF followed previously described

7

methods [6-1013] The edge spread function (ESF) was determined along lines crossing

the edge of the angled test device The derivative of the ESF was calculated to form the

line spread function (LSF) to which a Hanning filter was applied The MTF was then

calculated as the fast Fourier transform (FFT) of the LSF and normalized at the zero-

frequency axis To conform to IEC guidelines the MTF was resampled into frequency

steps of 005 cyclesmm [12]

Figure 1 MTF images for DRX-1C detector with radio-opaque edge test device with

arrows indicating the horizontal (left) and vertical (right) directions

I2iiib Noise Power Spectrum

Noise amplitude and texture were characterized by determining the normalized

noise power spectrum (NNPS) which was evaluated with flat field exposures at

approximate exposure levels of XN2 XN and 2XN (05 10 and 20 mR) to the image

receptor surface Analysis of the flat-field images followed previously defined methods

[41415] using over 4 million independent pixels with regions of interest (ROIs) of size

8

128x128 The NNPS images were detrended using a quadratic (second order)

background subtraction Small variations in exposure across ROIs were corrected by

normalizing pixel values of each ROI to the mean value in the top left ROI as shown in

Figure 2 The NNPS was then calculated with the 2D FFT including the zero-frequency

axes corresponding to the horizontal and vertical directions The results were then

resampled using 005 frequency bins according to IEC guidelines [12]

Figure 2 NNPS image for DRX-1C detector indicating the top left ROI that served as

the reference for normalizing other ROIs in the image The ROI array was formed

along the directions indicated by the arrows The heel effect visible along the vertical

axis of the detector is an example of small variation in signal across the image

I2iiic DQE Calculation

The DQE was calculated using the following relationship [615]

9

where the frequency-dependent MTF and NNPS were determined as described in

previous sections X was the exposure value in mR corresponding to the NNPS image

and q was the ideal signal to noise ratio squared in units of photonsmiddotmm-2middotmR-1 as

estimated from the spectral simulations

I3 Results

I3i Data Linearization

The detectors in this study provided raw ADU (or pixel) values in a linear scale

The data were converted using the following system conversion function

where Q(ij) is the raw image data m and b are slope and intercept parameters obtained

from linear regression of the system response function and I(ij) is the linearized scaled

data The factor of 1000 was found to scale I(ij) such that the maximum value was a

large 16-bit number Figure 3 shows the original and linearized system responses for the

Pixium 4600 Note that the y-intercepts of the regressions for the linearized responses

are negligible (lt 01) with respect to the slopes a sufficient condition for zero offset

considerations

I3ii Spectral Simulation

The spectral simulations of the IEC filtrations and alternative filtrations indicate

many similarities in their effective energies HVLs and overall shapes of normalized

spectra Results are summarized in Table 3

10

Pixium 4600 Original System

Response

Pixium 4600 Linearized System

Response R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 3 Original (left) and linearized (right) system responses for Pixium 4600 The

linearized system responses were measured from actual images The offsets are small

with respect to the slope sufficient enough for zero-offset conditions

y = 13971x - 13236

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x - 00106Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 13576x + 28292

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

7000

0000 1000 2000 3000 4000 5000

AD

U

Exposure (mR)

y = 99997x - 00067Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0000 1000 2000 3000 4000 5000

AD

U

Exposure (mR)

y = 13644x + 16167Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x + 00044

Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 13845x + 13541

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x - 00177

Rsup2= 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

11

Table 3 Spectral Simulation Results

Beam Quality Filtration

Mean Energy

(kV)

Photon Fluence

(mRmm2)

RQA5A 21 mm Al 5243 259543

RQA5C 05 mm Cu + 10 mm Al 5214 259554

diff 055 0004

RQA9A 40 mm Al 7619 273281

RQA9C 104 mm Cu + 10 mm Al 7579 273964

diff 052 025

Figure 4 Spectral simulations for RQA5 (top) and RQA9 (bottom) conditions Note

the similarities of spectral shapes of the normalized spectra (right) Also note the

significant differences in fluence between filtrations in the simulated spectra (left)

00E+00

50E+04

10E+05

15E+05

20E+05

25E+05

30E+05

35E+05

40E+05

45E+05

0 20 40 60 80

ph

oto

ns

mA

s-1

cm

-2

keV

RQA5 Spectra Comparison

21 mm Al

05 mm Cu + 10 mm Al

00

02

04

06

08

10

12

0 20 40 60 80

keV

RQA5 Normalized Spectra Comparison

21 mm Al

05 mm Cu +

10 mm Al

00E+00

50E+05

10E+06

15E+06

20E+06

25E+06

30E+06

35E+06

40E+06

45E+06

50E+06

0 50 100 150

ph

oto

ns

mA

s-1

cm

-2

keV

RQA9 Spectra Comparison

40 mm Al

104 mm Cu +

10 mm Al

00

02

04

06

08

10

12

0 50 100 150

keV

RQA9 Normalized Spectra Comparison

40 mm Al104 mm Cu + 10 mm Al

12

I3iii Modulation Transfer Function

The limiting spatial resolutions of the systems were indicated by the cutoff

frequencies which were approximately 35 cyclesmm for all three detectors The spatial

resolutions also demonstrated a good degree of isotropy as confirmed by the close

alignment of MTF curves between vertical and horizontal directions differentiated in

Figure 5 by dashed and solid lines respectively The MTF curves for the Pixium 4600

and DRX-1C were nearly equal to each other whereas the DRX-1 MTF curve showed a

more rapid decrease at high frequencies as shown in Figure 6 This difference may be

due to the differences in the inherent optical properties of the scintillating materials

where finer image details are provided by structured CsI more than by granulated GOS

There were no significant differences in MTF curves across beam qualities and filtrations

as shown by the curve comparisons in Figure 6 although the alternative filtration

produced slightly higher MTF curves as seen in Figure 4 Table 4 lists the experimental

specific spatial frequencies for varying levels of MTF

I3iv Noise Power Spectrum

The noise characteristics are indicated by the NNPS curves shown in Figure 7

The noise was similar for both horizontal and vertical directions As exposure increased

the NNPS decreased consistent with the characteristics of Poisson noise describing the

relationship between signal and noise in the presence of increased photon fluence At

13

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 5 MTF results by detector (columns) and beam quality (rows)

00

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00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

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Spatial Freq (mm)

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MTF

Spatial Freq (mm)

MTF

horiz

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horizontal

vertical

14

Figure 6 Plots of MTF for RQA5 (top) and RQA9 (bottom) showing the relationships

between detectors (blue red and green) and by filtration (solid and dashed)

00

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MTF

Spatial Freq (mm-1)

MTF

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

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MTF

Spatial Freq (mm-1)

MTF

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

15

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 7 NNPS results by detector (columns) and beam quality (rows)

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

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NNPS

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05 mR - horizontal

05 mR - vertical

10 mR - horizontal

10 mR - vertical

20 mR - horizontal

20 mR - vertical

16

Figure 8 Plots of NNPS for RQA5 (top) and RQA9 (bottom) at 1 mR exposure

showing the relationships between detectors (blue red and green) and by filtration

(solid and dashed)

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm-1)

NNPS (1 mR)

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

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Spatial Freq (mm-1)

NNPS (1 mR)

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RQA9C-DRX-1C

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RQA9C-DRX-1

17

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 9 DQE results by detector (columns) and beam quality (rows)

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05 mR - vertical

10 mR - horizontal

10 mR - vertical

20 mR - horizontal

20 mR - vertical

18

Figure 10 Plots of DQE for RQA5 (top) and RQA9 (bottom) at 1 mR exposure showing

the relationships between detectors (blue red and green) and by filtration (solid and

dashed)

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DQE

Spatial Freq (mm-1)

DQE (1 mR)

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

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Spatial Freq (mm-1)

DQE

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RQA9C-DRX-1

19

higher frequencies the NNPS curves of the Pixium 4600 and DRX-1 diverge slightly for

the different directions illustrating increased noise in the readout direction (vertical)

Differences in the noise characteristics were more apparent among detectors as

shown for 1 mR in Figure 8 The NNPS curve for the DRX-1 was higher in magnitude

across the entire frequency range than either the Pixium 4600 or DRX-1C which both

seemed to demonstrate reasonably similar NNPS curves The higher magnitude noise of

the DRX-1 indicates higher relative noise content overall Closer inspection of the NNPS

curves of the Pixium 4600 and DRX-1C detectors in Figure 7 revealed differences in the

spacing between the three exposure levels The gaps between the Pixium 4600 NNPS

curves do not correspond to the factor of two differences between each exposure level

especially at low- to mid- spatial frequencies suggesting a higher level of fixed pattern

noise additional noise with increasing exposure levels due to ineffective gain map

corrections Between filtration schemes the differences in NNPS curves for a given beam

quality were not substantial as shown in Figure 7

I3v Detective Quantum Efficiency

The DQE results are shown in Figure 9 DQE curves across exposure levels were

almost collinear except for Pixium 4600 and in general could be inferred from the

NNPS results Additionally the DQE curves demonstrated a relatively linear response

with spatial frequencies as expected for flat-panel detectors [9] Differences in DQE

among detectors were consistent for the most part with the type of scintillating material

20

As depicted for 1 mR exposure in Figure 10 differences between Pixium 4600 and DRX-

1C DQE curves correspond to the differences in their NNPS curves DRX-1 DQE curves

were consistently lower than either the Pixium 4600 or DRX-1C curves The DQE curves

for the alternative filtration were consistently higher than those for the IEC filtration

and the most noticeable differences were near the zero-frequency axis These effects can

be both attributed to ineffective gain map correction DQE values for 1 mR exposure are

listed in Table 5

I4 Discussion

I4i Comparisons of Detectors

The limiting spatial resolutions of all three detectors were almost exactly the

same considering that their pixel areas were similar in size The decrease in high-

frequency MTF of the DRX-1 compared to the other detectors is probably a result of

increased optical blurring due to the differences in the powdered structure of GOS

versus the needle-like structure of CsI [2] The fact that the DRX-1C and Pixium 4600

have comparable MTFs suggests similar scintillator thicknesses assuming that the

materials were processed alike

The noise of the three detectors demonstrated similar trends with each other The

higher NNPS curves of the DRX-1 detector are probably due also to the scintillating

material and its operation in converting photons into signal The conversion process is

less efficient because of the less favorable stopping power of the GOS compared to CsI

21

especially with higher energy beams The noise of the Pixium 4600 and DRX-1C were

similar except for the spacing between exposures The DRX-1C NNPS curve spacing is

consistent with a factor of two difference in exposure levels but the Pixium 4600 has a

smaller spacing The 05 mR NNPS curve of the Pixium 4600 is closer to that of the 05

mR NNPS curve of the DRX-1C This demonstrates that at higher exposures the Pixium

4600 produces a larger amount of additional noise beyond that explained by simple

stochastic effects It suggests bad performance in the gain map corrections

The DQE results indicate SNR properties of each detector The Pixium 4600 and

DRX-1C are comparable for the most part with the DRX-1C performing slightly better

The DRX-1 as predicted from MTF and NNPS results has a DQE much lower than

either of the previous two This is a reflection of the detection properties as provided by

its scintillator material The DQE of the DRX-1 however is comparable to CR image

receptors [2] The mid-frequency dips in the DQE for Pixium 4600 may be due to the

optical properties of the CsI phosphor layer which can affect the MTF in this manner

Because the DQE is calculated by squaring the MTF this effect at the mid-range

frequencies becomes more apparent The dips may also be further evidence of bad gain

map corrections

I4ii Comparisons of Filtrations

The alternative filtration closely matches for the most part the IEC-based

filtration for MTF NNPS and DQEs at RQA5 but not at RQA9 The filters do not have

22

Table 4 Experimental MTF frequency locations for 1 mR exposure

Detector Filtration

50 MTF

(mm-1)

40 MTF

(mm-1)

30 MTF

(mm-1)

20 MTF

(mm-1)

10 MTF

(mm-1)

Pixium

4600

RQA5A 115 145 185 245 330

RQA5C 125 155 195 250 345

RQA9A 110 175 175 235 330

RQA9C 125 155 195 255 345

DRX-1C

RQA5A 120 150 185 245 350

RQA5C 125 155 195 255 355

RQA9A 120 150 190 250 355

RQA9C 130 160 210 265 360

DRX-1

RQA5A 110 135 160 205 280

RQA5C 110 135 170 210 285

RQA9A 105 125 155 195 270

RQA9C 110 135 165 210 285

Table 5 Estimated DQE values for 1 mR exposure by frequency bins

Detector Filtration DQE(00 mm-1) DQE(10 mm-1) DQE(20 mm-1) DQE(30 mm-1)

Pixium

4600

RQA5A 62 42 32 21

RQA5C 63 45 36 25

RQA9A 41 27 30 13

RQA9C 43 33 27 19

DRX-1C

RQA5A 72 52 35 21

RQA5C 76 55 41 24

RQA9A 49 33 23 15

RQA9C 51 40 31 20

DRX-1

RQA5A 38 24 12 4

RQA5C 38 25 14 5

RQA9A 28 18 9 4

RQA9C 28 19 12 5

DQE values at the zero-frequency axis were estimated by the intercept of a linear fit of low-frequency data

but excluding most proximal to the axis due to large fluctuations Other estimated values are grouped into

frequency bins due to the noisiness of the data

23

considerable differences in the spatial resolutions of the detectors as expected The noise

responses for each filtration were also similar except at the lower frequencies of the

NNPS especially near the zero-frequency axis There observing the NNPS responses at

RQA5 for Pixium 4600 and DRX-1C in Figure 8 the NNPS for the IEC-based filtration

(solid lines) tend to drop faster than the NNPS for the alternative filtration This

subsequently appears as a drop in DQE near the zero-frequency axis shown for those

detectors in Figure 10 Overall as indicated in Table 5 the DQEs of the two filtrations

while similar in trend indicate that the alternative filtration increases the DQE by a

small amount of 3-5 Part of this may be explained by the slightly higher beam

energy which may be more optimal for the energy response of the detectors or may

weigh the pixel responses slightly considering that they are energy-integrating types

The most probable explanation is the gain map correction for the alternative filtration

where fixed pattern noise is more sufficiently reduced

A previous study [6] had discussed the choice of filter material in the analysis of

DQE when achieving the beam conditions defined by IEC It found that visible

nonuniformities were present with the higher purity aluminum filter (type-11999 alloy)

The low frequency mottle in the flat-field images for NPS measurements were also

attributed to structured noise from the grain size in the IEC-based filter with an

attenuating thickness that would reveal nonuniformities The mottle in the current study

was only observable under very narrow windowing as shown in Figure 11 Such low

24

frequency artifacts which are not readily noticeable may also be caused by shading

artifacts inverse square law or even the heel effect A possible method to correct for this

is a subtraction method by taking the average of the flat-field images for an exposure

level and then subtracting that from each of them This would remove nonuniformities

that were not corrected using a suboptimal gain map calibration

Figure 11 DRX1-C NNPS images at 1 mR for RQA5 with IEC filtration (left) and

alternative filtration (right) Images are equally windowed at 45 and leveled at 980

One convenient aspect of the copper and aluminum filtration is that it requires

much less tube current to achieve the same amount of exposure at the detector than the

much thicker aluminum filtration As shown in the non-normalized spectra in Figure 2

the exiting photon fluence exiting the copper and aluminum filtration is substantially

higher than that of the IEC-specified filtration This is due to the smaller total filtration

25

attenuation For extensive DQE analysis multiple sets of exposures may be acquired

before tube overheating becomes a concern

One limitation to the comparison of the two filtrations is that calibration

procedures specified copper and aluminum filtration at 80 kVp (for all detectors 05 mm

Cu and 10 mm Al) This may have influenced the results in favor of the alternative

filtration A further investigation involving the calibration procedures and performing

DQE measurements is encouraged Another factor may be influenced by the fact that the

tests were performed at 70 kVp and 120 kVp different from the recommended

calibration tube potential Clearly there would be differences in the linear attenuation

coefficients of the filters and different energy responses of the detectors themselves This

must be considered when interpreting DQE results The current results support a

previous study decades ago that described filtration of different material types in terms

of an aluminum equivalent [16] The results show that the two filtration schemes are

essentially equivalent when considering beam qualities and spatial resolutions The

NNPS and DQE results can be seen as close enough where their small differences are

insignificant when performing quality assurance tests in a clinical setting Overall our

results indicate that the alternative filtration with copper and aluminum may be more

convenient to use than the current IEC standard filtration

26

I4iii Implications of Wireless DR

This study has shown that wireless image receptors can have the same DQE

performance if not better than conventional flat-panel detectors They operate on the

same basic physical principles the new features offered by the DRX-1C and DRX-1 are

wireless communication with the workstation and electronics packaging technology

The latter feature may pose limitations for these units in terms of possible degradation

in the detectors in routine clinical conditions A consideration for future work would be

to longitudinally track DQE performance of the wireless detectors over time while being

utilized in a clinical environment In the end one must consider risks versus benefits of

choosing portable DR technology over CR one of which includes the cost and fragility

of DR detectors

The DQE performance of one wireless system is just as good as or better than

conventional systems as seen by the DRX-1C performance compared to the Pixium

4600 Wireless systems can also reduce the need for CR readers especially in portable

applications in other regions of the world (eg military hospitals developing countries)

However while DQE performance indicates the physical performance of the detector

system it is still unknown how it relates to observer performance

I5 Conclusions

Two wireless image receptors DRX-1C and DRX-1 were evaluated and

compared with the conventional DR flat-panel Pixium 4600 in terms of DQE

27

performance along with MTF and NNPS performances The detectors have similar

resolution properties although the DRX-1 is inferior at higher spatial frequencies The

NNPS and DQE results both indicate that the DRX-1C is superior to the DRX-1 and

comparable if not better to the Pixium 4600

The results from the filtration comparison indicate no substantial differences

between the IEC-based filtration and the copper-based alternative filtration Only slight

differences were found in the low frequency components of the NNPS and the DQE due

to the inherent nonuniformities of the IEC specified filtration Given the similarity of the

results and low attenuation advantage of the copper and aluminum filter its use is

encouraged

28

II Directional MTF for Breast Tomosynthesis

II1 Introduction

Breast tomosynthesis is an emerging 3D imaging modality that has potential use

for screening and diagnosis of breast cancer Breast tomosynthesis along with other 3D

techniques is preferable to planar imaging methods (eg mammography) because they

reduce anatomical noise by removing overlying structures above and below the plane of

an image slice [17-20] Recent advances in detectors and computer technology have

made digital tomosynthesis feasible

An image quality metric of particular importance in breast tomosynthesis is

spatial resolution Resolution is important to know in order to assess small-detail

structures such as microcalcifications A descriptive metric for characterizing spatial

resolution in the Fourier (or frequency) domain is the modulation transfer function

(MTF) Affected by reconstruction filters [21] the limited angular projections involved in

breast tomosynthesis results in highly anisotropic (or nonuniform) resolution Many

studies have looked only at characterizing the in-plane spatial resolution (ie in an

individual slice) with an elevated angled edge phantom [2223] A few studies have

looked at characterizing a more comprehensive 3D spatial resolution by using a

phantom with angled wires or tubes [24-26] However such studies require precise

mechanical alignment of the phantoms Several studies have explored a method using a

29

sphere phantom for the directional 3D MTF evaluation for microtomography [27] and

multi-slice CT [2829] This method has not yet been extended to breast tomosynthesis

This chapter focuses on breast tomosynthesis because it is highly anisotropic in

spatial resolution and like its predecessor mammography requires high spatial

resolution Additionally breast tomosynthesis acquisitions and reconstructions produce

several types of artifacts The use of a cone-based method using a sphere phantom [28] is

explored to characterize the directional 3D spatial resolution of simulated images from

breast tomosynthesis A technique for removing out-of-plane artifacts of the ESFs for the

in-plane axes is investigated to yield a modified MTF in a method that separates artifact

information from resolution information

II2 Materials and Methods

II2i Image Simulation

Breast tomosynthesis images were simulated by using a virtual imaging system

depicted in Figure 12 A volumetric breast phantom was voxelized as a rectangular mass

of uniform breast equivalent tissue of 4 cm thickness embedded with fifteen evenly

spaced plastic sphere inserts of 12 mm diameter The spheres were placed in a grid

formation within the central plane of the phantom The x-ray fluence was modeled from

a 28 kVp beam incident upon an indirect flat-panel detector with 200 micro m pixel size

Twenty-three projections within an angular range of 44deg were simulated using cascaded

systems analysis to generate characteristic 2D noise and spatial blurring [29] Each

30

projection was simulated to have an exposure of 174 mR with a fluence of 79 times 105

photonsmm-2 A standard filtered backprojection technique based on the Feldkamp

reconstruction algorithm [29] was used to reconstruct the projections and produce a

volumetric dataset with an isotropic voxel size of 200 micro m

Figure 12 Depiction of the virtual image system

II2ii Uncorrected MTF

To enable comparison of multiple spheres the reconstructed volume was

initially homogenized by performing a background subtraction based on a portion of the

volume devoid of spheres The voxel values were rescaled between one and zero to

eliminate negative values

31

The volumetric data were segmented to extract individual regions of interest

(ROIs) each containing a single sphere The ROIs extended along the full range of the z-

axis A thresholded ROI was generated by determining the exterior and interior voxels

relative to the sphere in the ROI The threshold value was set at 45 of the maximum

voxel value prior to thresholding The exterior and interior voxel values were then set to

values of 0 and 1 respectively Using the thresholded volume the center of mass was

calculated to determine the centroid The voxel values from the original ROI were

subsequently tabulated with the associated distances azimuthal angles and polar

angles relative to the centroid

Conical regions were prescribed along the positive and negative directions along

the three major axes extending from the centroid of the sphere as depicted in Figure 13

The axes about which the extent of the cone angle was delineated were defined with

the azimuthal and polar angles

Voxels with centers within the angular range of the cone were considered for

generating the edge spread function (ESF) To improve regularity of the distance

sampling interval the ESF values were rebinned to discrete distances corresponding to a

fraction of the voxel size Only voxels with distances ranging from the voxel size (ie

200 micro m) to the maximum distance were considered The ESFs from multiple spheres

were averaged together for each of the three major axes to produce an averaged ESF

which was further smoothed utilizing a Gaussian filter

32

Figure 13 Example of 30-degree cone prescribed along z axis of the sphere

The resulting ESF was then differentiated using the central difference method to

produce the line spread function (LSF) A Hanning filter with the same length as the LSF

was applied to zero out the tails of the LSF The presampled MTF was subsequently

computed as the amplitude of the Fourier transform of the LSF The MTF was

normalized with respect to the maximum value occurring within the range of the cutoff

frequency Binning size and conical range for the ESF were considered for maximizing

accuracy and minimizing noise of the MTF verified by comparison against the

theoretical MTF as determined in the previous section

II2iii Theoretical Directional MTF

The theoretical 3D MTF was calculated using a priori knowledge of the transfer

function of the virtual imaging system described in the previous section A phantom

was created with a set of point objects in a uniform and noise-free background with the

objects spanning across the volume of the breast [29] Twenty-one realizations were

33

generated from the reconstructed images of the point objects to yield a set of 3D point

spread functions (PSFs) The 3D fast Fourier transform (FFT) was performed for each 3D

PSF and averaged to give an ldquoexpectationrdquo 3D MTF [29] The theoretical directional

MTFs in the three major spatial axes were determined by line profiles along each of the

corresponding spatial frequency axes in the 3D MTF An additional theoretical MTF for

each direction was determined by using the application of conical regions along the axes

in frequency-space to take into account the contributions of MTF information from other

planes

II2iv Modified MTF

The tomosynthesis reconstruction is known to have edge enhancements which

affect the overall MTF by shifting the peaks of the MTF toward the higher frequencies

[23] The presence of this artifact complicates the interpretation of the actual spatial

resolution of the images Several steps were performed to remove the artifact

contribution to the resolution information particularly for the in-plane x and y

directions with the assumption that resolution information was contained immediately

near the edge

For the x-direction averaged ESF only values that were detected to be inside the

edge of the sphere were considered Those values were previously determined via

thresholding for calculating the centroid The ESF information corresponding to these

values was inversed and flipped about the detected edge to produce a symmetric

34

modified ESF The modified MTF was subsequently calculated from this modified ESF

as described in the previous section

For the y-direction averaged ESF an upward trend was found in the initial part

of the ESF This section was detrended with a polynomial fit and subtracted to produce a

flatter curve in that region The resulting detrended ESF was used to calculate the y axis

modified MTF

Figure 14 Photograph of the imaging system with the acrylic sphere phantom

embedded in oil

II2v Preliminary Experimental Validation

A clinical breast tomosynthesis system (Mammomat Inspiration Siemens AG

Munich Germany) was used to perform a preliminary evaluation of the cone-based

MTF technique The phantom for the experiment consisted of a single acrylic ball of 075

in diameter (SmallParts Seattle WA) suspended by a 0029 in diameter plastic filament

35

(Omniflex Zebco Tulsa OK) in an acrylic frame filled up to 4 in with vegetable oil

(Target Brands Inc Minneapolis MN) The system and phantom are shown in Figure

14 Twenty-five projections with an angular range of 44deg were acquired and subsequently

reconstructed to produce a volume with a voxel size of 01times01times10 mm3 The voxels were

reformatted to have an isotropic size of 01 mm The uncorrected ESF LSF and MTF

were calculated as described in the previous section

II3 Results

II3i Reconstruction

The reconstructed volume is shown in Figure 15 Notice the edge enhancement

along the x-direction as indicated by the sharp shadowing artifacts on either side of the

spheres The background was effectively homogenized using the background

subtraction technique This also took account of the curved edges of the breast phantom

With the close spacing of the spheres in the phantom the shadows along the x direction

for the fifteen spheres overlap with each other As the nine centrally located spheres

experience this effect the same way they were used for determining the ESF

A 3D rendering of the ROI containing a sphere shown in Figure 16 indicates the

anisotropic resolution of the reconstruction Note that the sphere is not accurately

reconstructed and has an oblong shape especially along the z axis Cross sectional views

of the ROI also in Figure 16 clearly demonstrate the edge enhancement causing a

shadow artifact in the x direction caused by the incomplete angular sampling of

36

tomosynthesis The sampling also introduces the triangular reconstruction of the sphere

as seen in the x-z plane Note the gradual edge drop-off in the z direction much beyond

the sphere radius

Figure 15 View of the central slice of the breast phantom reconstruction before (top)

and after (bottom) background subtraction The z axis is through the page

37

Figure 16 3D rendering of the ROI volume (left) and cross-sectional views of the most

centrally located sphere with centroid indicated with red circle (right)

II3ii Theoretical MTF

The theoretical MTFs for x y and z directions as determined from the line

profiles of the 3D MTF are shown in Figure 17 The theoretical MTF in the x direction

has a maximum value that is toward higher frequencies Its 10 response occurs at

about 125 cyclesmm which is at 50 of the cutoff frequency The rapid increase from

the zero-frequency intercept to the peak corresponds to the ramp filter used in filtered

backprojection which decreases the weighting of low frequency contributions due to the

incomplete angular sampling of the frequency-space The MTF does not reach a value of

0 at the zero-frequency intercept as it is very difficult to assess the zero-frequency

intercept due to the finite size of the phantom The theoretical MTF in the y direction

peaks at the zero-frequency intercept and reaches 20 proximal to the cutoff frequency

38

The 10 MTF is well beyond the cutoff frequency The theoretical MTF in the z direction

has a rapid drop-off at very low spatial frequencies indicating the lack of resolution in

that dimension

Figure 17 Theoretical 3D MTF results along the three major planes (top) and along x

y and z directions (bottom) Also note that the angular spread seen in the fx-fz plane is

equal to the angular range of 44deg for the acquisition

II3iii Uncorrected MTF

The ESF LSF and MTF using the cone-based method are shown for the x y and

z directions in Figure 18 It was found that a bin size of one-tenth the voxel size (002

mm) and a cone angle of 30deg to establish the ESF were enough to minimize noise and

maximize accuracy in the uncorrected MTFs considering the reasonable comparison of

the shapes of the MTF curves with the theoretical results in Figure 17 The LSFs are

generally noisy because differentiation of the ESF increases the amplitude of the noise

39

The data shown reflect a convolution with a smoothing Gaussian filter which was later

further corrected for in the reported MTF Nevertheless the high frequency components

of the noise are well beyond the MTF cutoff frequency of 25 cyclesmm and do not

impact the MTF results greatly

For the ESF in the x direction the shadow effect evident at the edge of the sphere

is visible as a steep decline followed by an increase Due to the finite distance range

provided by the ROI the ESF beyond the edge did not asymptotically reach the

background value The corresponding LSF demonstrates a low frequency modulation

that is indicated by the shift of 03 cyclesmm in the x direction for the peak of the MTF

The MTF exhibits a zero-frequency intercept that is non-zero unlike the theoretical MTF

and a 10 value at approximately 1 cyclesmm These features may be a direct

consequence of MTF information ldquocontaminationrdquo from y and z directions Furthermore

the ESF in the y direction demonstrates a reasonably shaped curve except for the slight

upward trend within the radius of the sphere which can be attributed to the shadow

artifact overlapping with the sphere volume The associated MTF has a peak shifted by

approximately 01 cyclesmm away from the axis and a 10 MTF occurring at

approximately 15 cyclesmm Both features which are not present in the theoretical

results may also be attributed to contaminant MTF information from x and z directions

The ESF in the z direction has a drop-off that occurs at a small fraction of the cutoff

frequency similar to that demonstrated by the theoretical MTF

40

Uncorrected ESF LSF and MTF

Figure 18 Uncorrected ESF (top) LSF (middle) and MTF (bottom) for x y and z

directions

41

Figure 19 Comparisons of the directional MTFs as calculated by the sphere method

(dashed line) by theoretical line profiles (light-weight line) by theoretical cone

regions (heavy-weight line)

II3iv Comparison of Theoretical and Simulated MTFs

The theoretical MTF results obtained from line profiles through the 3D MTF and

the simulated MTFs using the cone-based technique did not match very well except for

the general shape of the curves It was assumed in the previous section that the cone-

based technique contains information from other planes Figure 19 compares MTFs in

each direction for the two methods described in the methods and an additional method

based on conical regions of the 3D MTF The latter computes the MTF by averaging

contributions of the 3D MTF using the same cone prescription method used to define the

ESFs Comparison of the curves indicate some interesting correlations aside from the

fact that using conical regions with the 3D MTF results produce more noisy MTF results

partly due to the low sampling provided by the theoretical calculations The same

conclusions regarding the z direction MTF can be confirmed regardless of either

theoretical MTF procedures The experimental x direction MTF seems to agree best with

42

the line profile method whereas the y direction MTF agrees better with the cone region

method The fact that the experimental x direction MTF has a drop-off frequency that is

lower than those of either of the theoretical MTFs in Figure 19 suggests that this might

be due to integration of the z-direction in the in-plane slices considering how slices are

essentially averages of z direction information contained within it [33]

II3v Modified MTF for x and y

Modified ESF LSF and MTF curves for x and y directions are shown in Figure

20 The modified ESF and the resulting LSF in the x direction appear symmetric as

expected from the inverse and flip operation of the interior ESF about the detected edge

The modified MTF appears with less variation than the uncorrected MTF and the MTF

peak occurs at the zero-frequency axis The correction yields a 10 MTF at about 15

cyclesmm an improvement from the uncorrected MTF but still distant from the cutoff

frequency The modified ESF in the y direction demonstrates the detrended curve within

the sphere radius after a quadratic polynomial fit The resulting modified MTF still

appears similar to the uncorrected MTF except that the peak now coincides with the

zero-frequency axis For both x and y directions the low response of the modified MTFs

at the higher frequencies suggests that the contamination from other directions is

substantial due to the angular range of the cone

43

Modified ESF LSF and MTF

Figure 20 Modified ESF (top) LSF (middle) and MTF (bottom) for x and y directions

44

II3v Preliminary Experimental Validation

Cross-sections of the reconstructed sphere volume are shown in Figure 21

Relative to the simulation reconstructions the reconstructions of the experimental

phantom images produce lower contrast and higher noise The preliminary results

shown in Figure 22 indicate that our technique can be applied to actual experimental

breast tomosynthesis reconstructions However due to the noise exhibited by the MTF

curves for the x and y directions we did not determine the modified MTFs to separate

resolution and artifact information

Figure 21 Cross sectional views of the experimental sphere image with centroid

indicated with red circle

45

Uncorrected ESF LSF and MTF for Real Image

Figure 22 ESF (top) LSF (middle) and MTF (bottom) of real image for x y

and z directions

46

II4 Discussion

II4i Evaluation of Cone-based Method

The cone-based MTF technique was introduced by Thornton and Flynn [28] for

evaluation of volumetric CT images To utilize this technique as a characterization of a

3D system spatial resolution one must first consider the validity of the assumption of

shift invariance such that the same MTF result may be obtained regardless of the

location of the sphere The study by Zhao et al [23] found that there was no shift

variance for the MTF measurements along the vertical axis but this was only considering

the in-plane resolution along one axis On the other hand this study evaluated the MTF

with images simulated with cascaded systems analysis which includes conditions of

linearity and shift invariance Additionally the MTF was calculated by averaging the

ESF from several spheres in the same volume only after performing a background

subtraction This step was essential to account for the sensitivity of centroid calculations

as well as ensuring symmetric ESFs for opposing axes of the sphere ROIs

The measurement of MTF with the cone-based technique inherently

supersamples the edge of the sphere to increase signal-to-noise-ratio (SNR) of edge

information by averaging the contributions of each voxel to the ESF [713] This method

also takes into account the discrete sampling of the voxels by accounting for various

shifts of the edge in the voxel (also known as the partial volume effect) However using

the curved surface of the sphere phantom to approximate an edge along a given

47

direction naturally leads to contamination of information from other directions aside

from the one of interest Preferably a directional ESF should be created by using a single

radial line but this would limit the available voxels to obtain edge information An ideal

situation theoretically would be to use a larger-sized sphere such that the surface is

nearly flat and perpendicular to the axes of interest This would also permit a reduction

in the angular range of the cone and thus the introduction of out-of-plane information in

the resulting MTF However sphere size is a limitation in breast tomosynthesis and the

use of a large phantom might void the assumption of shift invariance of the spatial

resolution

The choice of a sphere phantom nevertheless may be based on the clinical need

to quickly acquire a single image for MTF evaluation especially for multiple directions

without presenting extra logistical challenges The use of a wire or edge phantom

requires more precise mechanical alignment to achieve the correct set up The edge

phantom [23] would require at least two images to sample all three dimensions In the

case of the three wire phantom [2425] all three dimensions of the frame must be aligned

simultaneously with respect to the axis of rotation A similar situation would be

encountered when considering a cubic phantom with the planes normal to the axis of

interest In contrast to these phantoms the sphere eliminates the need for precise

alignment especially with respect to three spatial dimensions simultaneously A sphere

48

has ideal symmetry in all directions and can be used to evaluate MTF in any arbitrary

direction

This study unlike others [242532] did not explore the effects of physical

parameters such as scatter or contrast on the final MTF result but it demonstrated the

feasibility of using the cone-based method with an actual breast tomosynthesis image of

a sphere phantom as shown in Error Reference source not found and Error Reference

source not found These effects should be addressed in future works A further look

into deriving the principles of comparing the theoretical MTF with the experimental

MTF using the cone-based method is further warranted

II4ii Separation of Artifact and Resolution Information

The focus of this study was to develop a technique for measuring spatial

resolution of tomosynthesis images The intrinsic artifacts from tomosynthesis

reconstructions however lead to uncharacteristic MTFs and possible misinterpretation

of the effective resolution information When considering previous techniques for

calculating the presampled MTF [713152328] the analysis was performed using an

edge or a line to produce the corresponding ESF The resolution information is

essentially contained only along the edge indicated by the need to calculate the LSF In a

way the method of extracting artifact information is to focus the analysis only on the

edge part of the ESF to calculate the modified MTF This will lead to a better

understanding of the limiting size of objects that may be seen in the reconstructed 3D

49

image The presampled MTF without correction should still be analyzed to understand

the entire system response Note that the ESFs attempt to reflect information only at the

detected edge of the sphere

II5 Conclusions

The directional MTF of a simulated breast tomosynthesis reconstruction was

determined by using the cone-based MTF technique demonstrating the feasibility of a

single phantom for MTF evaluation This study further presented methods of analyzing

only the edge information in the ESF to create a modified MTF along in-slice (x and y)

axes It can provide insight into the actual spatial resolution information contained in the

image while separating the resolution information from the information introduced by

artifacts caused by the reconstruction and insufficient volumetric sampling The idea of

separating the resolution and artifacts from the measured ESF are expected to facilitate

the interpretation of MTF measurements in breast tomosynthesis Similar methods may

be applied to characterize the resolution of other 3D imaging modalities

50

References

1 Garmer M Hannigs SP Jaumlger HJ et al ldquoDigital Radiography Versus

Conventional Radiology in Chest Imaging Diagnostic Performance of a Large-

Area Silicon Flat-Panel Detector in a Clinical CT-Controlled Studyrdquo American

Journal of Roentgenology Volume 74 75-80 (2000)

2 Cowen AR Kengyelics SM and Davies AG ldquoSolid-state flat-panel digital

radiography detectors and their physical imaging characteristics rdquoClinical

Radiology Volume 63 487-498 (2008)

3 Chotas HG Dobbins III JT and Ravin CE ldquoPrinciples of Digital

Radiography with Large-Area Electronically Readable Detectors A Review of

the Basicsrdquo Radiology Volume 210 Number 3 595-599 (1999)

4 Flynn MJ and Samei E Experimental comparison of noise and resolution for

2k and 4k storage phosphor radiography systems Medical Physics Volume 26

Number 8 1612-1623 (1999)

5 Rong XJ Shaw CC Liu X Lemacks MR and Thompson SK

ldquoComparison of an amorphous siliconcesium iodide flat-panel digital chest

radiography system with screenfilm and computed radiography systems ndash A

contrast-detail phantom studyrdquo Medical Physics Volume 28 Number 11 2328-

2335 (2001)

6 Ranger NT Samei E Dobbins III JT and Ravin CE Measurement of the

detective quantum efficiency in digital detectors consistent with the IEC 62220-1

standard Practical considerations regarding the choice of filter material

Medical Physics Volume 30 Number 7 2305-2311 (2005)

7 Samei E Buhr E Granfors P Vandenbroucke D and Wang X Comparison

of edge analysis techniques for the determination of the MTF of digital

radiographic systems Physics in Medicine and Biology Volume 50 3613-3625

(2005)

8 Samei E and Flynn MJ An experimental comparison of detector performance

for computed radiography systems Medical Physics Volume 29 Number 4 447-

459 (2002)

51

9 Samei E and Flynn MJ An experimental comparison of detector performance

for direct and indirect digital radiography systems Medical Physics Volume 30

Number 4 608-622 (2003)

10 Samei E Ranger NT MacKenzie A Honey ID Dobbins III JT and Ravin

CE Effective DQE (eDQE) and speed of digital radiographic systems An

experimental methodology Medical Physics Volume 36 Number 8 3806-3817

(2009)

11 Samei E Ranger NT MacKenzie A Honey ID Dobbins III JT and Ravin

CE Detector or System Extending the Concept of Detective Quantum

Efficiency to Characterize the Performance of Digital Radiographic Imaging

Systems Radiology Volume 249 Number 3 926-937 (2008)

12 ldquoIEC 62220-1 Medical Electrical Equipment ndash Characteristics of Digital X-Ray

Imaging Devices ndash Part 1 Determination of the Detective Quantum Efficiencyrdquo

International Electrotechnical Commission Geneva Switzerland (2003)

13 Samei E Ranger NT Dobbins III JT and Chen Y Intercomparison of

methods for image quality characterization I Modulation transfer function

Medical Physics Volume 33 Number 5 1454-1465 (2006)

14 Dobbins III JT Samei E Ranger NT and Chen Y Intercomparison of

methods for image quality characterization II Noise power spectrum Medical

Physics Volume 33 Number 5 1466-1475 (2006)

15 Samei E Flynn MJ and Reimann DA A method for measuring the

presampled MTF of digital radiographic systems using an edge test device

Medical Physics Volume 25 Number 1 102-113 (1998)

16 Nagel HD ldquoAluminum equivalence of materials used in diagnostic radiology

and its dependence on beam qualityrdquo Physics in Medicine and Biology Volume

31 Number 12 1381-1399 (1986)

17 Niklason LT Christian BT Niklason LE et al ldquoDigital Tomosynthesis in

Breast Imagingrdquo Radiology Volume 205 399-406 (1997)

18 Gur D ldquoTomosynthesis Potential Clinical Role in Breast Imagingrdquo American

Journal of Roentgenology Volume 189 614-615 (2007)

52

19 Park JM Franken Jr EA Garg M Fajardo LL and Niklason LT ldquoBreast

Tomosynthesis Present Considerations and Future Applicationsrdquo

RadioGraphics Volume 27 S231-S240 (2007)

20 Good WF Abrams GS Catullo VJ Chough DM Ganott MA Hakim

CM and Gur D ldquoDigital Breast Tomosynthesis A Pilot Observer Studyrdquo

American Journal of Roentgenology Volume 190 865-869 (2008)

21 Hu Y-H Zhao W Mertelmeier T and Ludwig J ldquoImage Artifact in Digital

Breast Tomosynthesis and Its Dependence on System and Reconstruction

Parametersrdquo IWDM 2008 LNCS 5116 628-634 (2008)

22 Chen Y Lo JY Ranger NT Samei E Dobbins III JT ldquoMethodology of

NEQ(f) analysis for optimization and comparison of digital breast tomosynthesis

acquisition techniques and reconstruction algorithmsrdquo Proceedings of SPIE

Volume 6510 65101I (2007)

23 Zhao B Zhou J Hu Y-H Mertelmeier T Ludwig J and Zhao W

ldquoExperimental validation of a three-dimensional linear system model for breast

tomosynthesisrdquo Medical Physics Volume 36 Number 1 240-251 (2009)

24 Madhav P Brzymialkiewicz CN Cutler SJ Bowsher JE and Tornai MP

ldquoCharacterizing the MTF in 3D for a Quantized SPECT Camera Having Arbitrary

Trajectoriesrdquo 2005 IEEE Nuclear Science Symposium Conference Record 1722-

1726 (2005)

25 Madhav P McKinley RL Samei E Bowsher JE and Tornai MP ldquoA Novel

Method to Characterize the MTF in 3D for Computed Mammotomographyrdquo

Proceedings of SPIE Volume 6142 61421Y (2006)

26 Hu Y-H Zhao B and Zhao W ldquoImage artifacts in digital breast

tomosynthesis Investigation of the effects of system geometry and

reconstruction parameters using a linear system approachrdquo Medical Physics

Volume 35 Number 12 5242-5252 (2008)

27 Seifert A and Flynn MJ ldquoResolving power of 3D x-ray microtomography

systemsrdquo Proceedings of SPIE Volume 4682 407-413 (2002)

28 Thornton MM and Flynn MJ Measurement of the spatial resolution of a

clinical volumetric computed tomography scanner using a sphere phantom

Proceedings of SPIE Volume 6142 61421Z (2006)

53

29 Baek J Pelc NJ ldquoUse of sphere phantoms to measure the 3D MTF of FDK

reconstructionsrdquo Proceedings of SPIE Volume 7961 79610D (2011)

30 Richard S and Samei E ldquoQuantitative imaging in breast tomosynthesis and CT

Comparison of detection and estimation task performancerdquo Medical Physics

Volume 37 Number 6 2627-2637 (2010)

31 Chen Y Lo JY and Dobbins III JT ldquoImpulse response analysis for several

digital tomosynthesis mammography reconstruction algorithmsrdquo Proceedings of

SPIE Volume 5745 541-549 (2005)

32 Zhao B and Zhao W ldquoThree-dimensional linear system analysis for breast

tomosynthesisrdquo Medical Physics Volume 35 Number 12 5219-5232 (2008)

33 Wu G Mainprize JG Boone JM and Yaffe MJ ldquoEvaluation of scatter

effects on image quality for breast tomosynthesisrdquo Medical Physics Volume 36

Number 10 4425-4432 (2009)

Page 4: Development and Evaluation of 2D and 3D Image Quality ...

iv

Abstract

With continuing advances in medical imaging technologies there is an increased

demand to extract quantitative information from images This has been particularly vital

in the effort to increase the efficacy and accuracy of diagnoses Quantitative information

is readily available in images because the acquisition techniques intrinsically involve

physical processes Quantitative image quality metrics are critical in the evaluation of

medical images for diagnostic merit particularly when used for the characterization and

comparison of different systems When such metrics are based on measurable physical

parameters they can provide valuable information for system optimization Image

quality describes the ldquogoodnessrdquo of an image in displaying information for a task This

thesis explored methods of measuring image quality for two scenarios (1) to

characterize 2D flat-panel detector performance and (2) to measure directional spatial

resolution for 3D images from breast tomosynthesis

In the first chapter two new wireless digital receptors (DRX-1C and DRX-1

Carestream Health Inc Rochester NY) were evaluated and compared to a conventional

flat-panel detector (Pixium 4600 Trixell Moirans France) on the basis of detective

quantum efficiency (DQE) A secondary goal was also to evaluate the filtration to

achieve specified beam qualities for the DQE measurements closely following the

methodology of the International Electrotechnical Commission (IEC) for radiation

v

qualities RQA5 and RQA9 All three DR systems demonstrated similar modulation

transfer functions (MTFs) at most frequency ranges while the DRX-1 showed lower

values near the cutoff of approximately 35 cyclesmm At each exposure the Pixium

4600 and DRX-1C demonstrated similar noise power spectrum (NPS) curves that

indicated better noise performance than the DRX-1 Zero-frequency DQEs for Pixium

4600 DRX-1C and DRX-1 were approximately 63 74 and 38 for RQA5 and 42

50 and 28 for RQA9 respectively In terms of DQE performance the DRX-1C image

receptor was found to be superior to the Pixium 4600 and DRX-1

In the second chapter the directional spatial resolution of simulated breast

tomosynthesis images was determined using a cone-based technique and a sphere

phantom Projections were simulated for a voxelized breast phantom with 12 mm

diameter sphere inserts using a fluence modeled from a 28 kVp beam incident upon an

indirect flat-panel detector with 200 micro m pixel size Characteristic noise and blurring for

each projection were added using cascaded systems analysis The projections were

reconstructed using a standard filtered backprojection technique producing a 3D

volume with an isotropic voxel size of 200 micro m Regions of interest (ROIs) that

completely encompassed single spheres were extracted and conical regions were

prescribed along the three axes extending from the centroid Voxels within a cone were

used to form an edge spread function (ESF) from which the directional MTF was

calculated A bin size of 002 mm and a conical range of 30 degrees were found optimal

vi

for maximizing accuracy and minimizing noise of the MTF A method for removing out-

of-plane artifacts of the ESFs along in-plane axes was investigated and yielded a

modified MTF The idea of separating the effective resolution and artifacts from the

measured ESF are expected to facilitate the interpretation of MTF measurements in

breast tomosynthesis Similar methods may be applied to characterize the spatial

resolution of other 3D imaging modalities

vii

Contents

Abstract iv

List of Tables x

List of Figures xi

Acknowledgements xiii

I Evaluation of 2D Digital Image Receptors 1

I1 Introduction 1

I2 Materials and Methods 3

I2i Detectors 3

I2ii Beam Characterization 3

I2iia X-ray Techniques 3

I2iib Data Linearization 4

I2iic Spectral Simulation 5

I2iii DQE Measurements 6

I2iiia Modulation Transfer Function 6

I2iiib Noise Power Spectrum 7

I2iiic DQE Calculation 8

I3 Results 9

I3i Data Linearization 9

I3ii Spectral Simulation 9

I3iii Modulation Transfer Function 12

viii

I3iv Noise Power Spectrum 12

I3v Detective Quantum Efficiency 19

I4 Discussion 20

I4i Comparisons of Detectors 20

I4ii Comparisons of Filtrations 21

I4iii Implications of Wireless DR 26

I5 Conclusions 26

II Directional MTF for Breast Tomosynthesis 28

II1 Introduction 28

II2 Materials and Methods 29

II2i Image Simulation 29

II2ii Uncorrected MTF 30

II2iii Theoretical Directional MTF 32

II2iv Modified MTF 33

II2v Preliminary Experimental Validation 34

II3 Results 35

II3i Reconstruction 35

II3ii Theoretical MTF 37

II3iii Uncorrected MTF 38

II3iv Comparison of Theoretical and Simulated MTFs 41

II3v Modified MTF for x and y 42

II3v Preliminary Experimental Validation 44

ix

II4 Discussion 46

II4i Evaluation of Cone-based Method 46

II4ii Separation of Artifact and Resolution Information 48

II5 Conclusions 49

References 50

x

List of Tables

Table 1 Physical Characteristics of Digital Image Receptors 4

Table 2 Beam Qualities and Required Filtrations 5

Table 3 Spectral Simulation Results 11

Table 4 Experimental MTF frequency locations for 1 mR exposure 22

Table 5 Estimated DQE values for 1 mR exposure by frequency bins 22

xi

List of Figures

Figure 1 MTF images for DRX-1C detector with radio-opaque edge test device with

arrows indicating the horizontal (left) and vertical (right) directions 7

Figure 2 NNPS image for DRX-1C detector indicating the top left ROI that served as the

reference for normalizing other ROIs in the image The ROI array was formed along the

directions indicated by the arrows The heel effect visible along the vertical axis of the

detector is an example of small variation in signal across the image 8

Figure 3 Original (left) and linearized (right) system responses for Pixium 4600 The

linearized system responses were measured from actual images The offsets are small

with respect to the slope sufficient enough for zero-offset conditions 10

Figure 4 Spectral simulations for RQA5 (top) and RQA9 (bottom) conditions Note the

similarities of spectral shapes of the normalized spectra (right) Also note the significant

differences in fluence between filtrations in the simulated spectra (left) 11

Figure 5 MTF results by detector (columns) and beam quality (rows) 13

Figure 6 Plots of MTF for RQA5 (top) and RQA9 (bottom) showing the relationships

between detectors (blue red and green) and by filtration (solid and dashed) 14

Figure 7 NNPS results by detector (columns) and beam quality (rows) 15

Figure 8 Plots of NNPS for RQA5 (top) and RQA9 (bottom) at 1 mR exposure showing

the relationships between detectors (blue red and green) and by filtration (solid and

dashed) 16

Figure 9 DQE results by detector (columns) and beam quality (rows) 17

Figure 10 Plots of DQE for RQA5 (top) and RQA9 (bottom) at 1 mR exposure showing

the relationships between detectors (blue red and green) and by filtration (solid and

dashed) 18

Figure 11 DRX1-C NNPS images at 1 mR for RQA5 with IEC filtration (left) and

alternative filtration (right) Images are equally windowed at 45 and leveled at 980 24

Figure 12 Depiction of the virtual image system 30

xii

Figure 13 Example of 30-degree cone prescribed along z axis of the sphere 32

Figure 14 Photograph of the imaging system with the acrylic sphere phantom

embedded in oil 34

Figure 15 View of the central slice of the breast phantom reconstruction before (top) and

after (bottom) background subtraction The z axis is through the page 36

Figure 16 3D rendering of the ROI volume (left) and cross-sectional views of the most

centrally located sphere with centroid indicated with red circle (right) 37

Figure 17 Theoretical 3D MTF results along the three major planes (top) and along x y

and z directions (bottom) Also note that the angular spread seen in the fx-fz plane is

equal to the angular range of 44deg for the acquisition 38

Figure 18 Uncorrected ESF (top) LSF (middle) and MTF (bottom) for x y and z

directions 40

Figure 19 Comparisons of the directional MTFs as calculated by the sphere method

(dashed line) by theoretical line profiles (light-weight line) by theoretical cone regions

(heavy-weight line) 41

Figure 20 Modified ESF (top) LSF (middle) and MTF (bottom) for x and y directions 43

Figure 21 Cross sectional views of the experimental sphere image with centroid

indicated with red circle 44

Figure 22 ESF (top) LSF (middle) and MTF (bottom) of real image for x y and z

directions 45

xiii

Acknowledgements

I would like to thank Ian Yorkston Mark Purdum and Van Huston of

Carestream Health Inc (Rochester NY) for their help with digital detector

measurements I would also like to thank Olav Christianson Samuel Richard Brian

Harrawood and Max Amurao for their assistance with collecting data and analyzing

results Special thanks go to my committee members for their helpful insights and

suggestions for this thesis Last but not least I want to express deep appreciation for the

support and mentorship provided by my advisor Dr Ehsan Samei

1

I Evaluation of 2D Digital Image Receptors

I1 Introduction

In the past decade many areas of radiological practice have seen a conversion

from screen films to the storage phosphor cassettes of computed radiography (CR) to the

active-matrix flat-panel detectors of digital radiography (DR) Both CR and DR are

digital systems that offer many potential benefits including but not limited to better

image quality wider dynamic range quicker readout lower radiation dose and higher

throughput [1-3] Even with advances in DR technologies such as improved detective

quantum efficiency (DQE) the primary radiographic system of today continues to be CR

A major obstacle to completely accepting DR is the high capital cost of acquiring an

entire system per examination room while also providing capability for portable

applications Recently manufacturers like Carestream Health Fuji and Toshiba have

introduced wireless digital image receptors that can serve as replacements for CR

cassettes As these are new technologies a further investigation to characterize these

detectors is warranted

In the case of radiographic receptors DQE has historically been the metric of

choice [4] because it indicates the ability of the image receptor to convert incident x-ray

photons into useable signal ndash essentially a measure of signal-to-noise ratio (SNR)

efficiency and overall system performance [23] DQE is observed across a range of

spatial frequencies for evaluating how the detector depicts small and large objects [3]

2

DQE metrics have been used in numerous studies to characterize CR phosphor-screens

as well as indirect and direct digital detectors [4-11] The importance of this highly

quantitative metric may be implied by the introduction of a DQE measurement standard

by the International Electrotechnical Commission (IEC) [12]

The standard measurement methodology of the International Electrotechnical

Commission (IEC) pertains to the image quality of 2D digital radiographic detectors

While the IEC formalism is well-developed some of the components that it requires are

not necessarily the most optimal for characterizing DQE This has been explored in

previous studies in terms of filtration material purity beam limitations and region of

interest (ROI) configuration [1314] To reduce the variability in the radiographic output

across various x-ray tubes due to inherent filtration differences the IEC formalism

prescribes specific additional aluminum filtration to attain radiation beam qualities

based on target half value layers (HVL) Achieving and verifying the desired HVL

however requires applying a substantial amount of aluminum at the exit window of the

x-ray tube which is often directed toward the ground This can be a logistical

inconvenience and can increase the risk of damage to the image receptor and

measurement equipment Similar beam qualities on the other hand may be attained

more conveniently using a thinner lighter filtration combination utilizing a higher Z

number material Care is warranted however as a previous study [6] had indicated that

the choice of filtration material could impact the DQE

3

The purpose of this study was two-fold First we aimed to evaluate and compare

two wireless image receptors with a conventional flat-panel detector on the basis of DQE

performance Second we compared DQE results using the IEC-prescribed filtration with

an alternative filtration For the latter an optimum filtration composition was

determined and compared with the IEC filtration on the basis of DQE

I2 Materials and Methods

I2i Detectors

The physical characteristics of the three digital image receptors evaluated in this

study are listed in Table 1 The Pixium 4600 was a conventional digital flat-panel The

DRX-1C and DRX-1 were both wireless digital cassettes that were tethered for the

purposes of this study All detectors were FDA approved and available commercially

Each detector was calibrated according to its manufacturer specifications to correct for

gain offset and bad pixels They were all dedicated for non-clinical laboratory research

purposes and hence could be operated under service settings that permitted acquisition

of raw (ie for processing) images

I2ii Beam Characterization

I2iia X-ray Techniques

All measurements for this study were taken with a well-characterized standard

radiographic system (Super80CP Philips Healthcare Andover MA) The x-ray tube had

an inherent filtration of 27 mm Al Free in-air exposures were measured using

4

Table 1 Physical Characteristics of Digital Image Receptors

Manufacturer Detector

Detector

type

Detector

material

Pixel pitch

(size) Array size

Imaging

area

Trixell

(Moirans France)

Pixium

4600 Indirect

CsITl

(CsI) 0143 mm

3121times3121

4 subpanels 45times45 cm2

Carestream Health Inc

(Rochester NY)

DRX-1C

(wireless) Indirect

CsITl

(CsI) 0139 mm

2560times3072

single panel 35times43 cm2

Carestream Health Inc

(Rochester NY)

DRX-1

(wireless) Indirect

G2O2STb

(GOS) 0139 mm

2560times3072

single panel 35times43 cm2

calibrated radiation meters (Mult-O-Meter Type 407 Unfors Instruments AB Billdal

Sweden) at 183 cm source-to-chamber-distance (SCD) The SCD also corresponded to

same plane as the image receptor surface The x-ray output was made to conform to IEC

beam quality definitions [1215] on the basis of half value layer (HVL) and peak

kilovoltage setting using an aluminum filtration (type-1100 99 purity) and an

alternative filtration consisting of copper (UNS C11000 999 purity) and aluminum

(type-1100 99 purity) The IEC radiation quality numbers (RQA) used in this study are

summarized in Table 2 HVLs were determined by iteratively adding successive

thicknesses of aluminum until reaching reduced exposure levels within a tolerance of

0485-0515 [12] As for the alternative filtration the aluminum was placed downstream

of the copper filter to attenuate characteristic radiation peaks from copper at

approximately 9 keV

I2iib Data Linearization

The system response function was determined for each detector and filtration

combination by acquiring flat-field images at increasing photon fluence until just before

5

Table 2 Beam Qualities and Required Filtrations

IEC Radiation

Quality Number

Peak

kilovoltage

Required

HVL

Required IEC

Filtration

Actual IEC

Filtration

Alternative

Filtration

RQA5 70 kVp 71 mm Al 21 mm Al 21 mm Al 05 mm Cu +

10 mm Al

RQA9 120 kVp 115 mm Al 42 mm Al 40 mm Al 104 mm Cu +

10 mm Al

For reasons of convenience these will be referred to as RQA5A RQA5C RQA9A and RQA9C

saturation levels To avoid the influence of detector backscatter on exposure

measurements a relationship for each filtration was first determined for two radiation

meters A target meter was placed at the central axis and a reference meter was placed at

the edge of the light field (large enough to cover the detectors) The reference meter

served as a surrogate for the target meter to avoid direct exposure measurements in the

plane of the image receptor Exposure relationships were determined before each

measurement set (ie detector and filtration combination) to account for changes in

temperature pressure and humidity The system response function was calculated by

using a regression of ADU (pixel value) versus exposure Images acquired for each

series were then converted to achieve a linear response with zero offset and scaled to

achieve high quantization (adequate dynamic range) Linearization of the detector

responses ensured that zero exposure corresponded to zero pixel value

I2iic Spectral Simulation

The effects of additional filtration on x-ray output spectra were observed with

spectral simulation software (XSPECT V40 Henry Ford Hospital Detroit MI) To more

6

adequately describe the performance of a typical X-ray generator inherent filtration of 3

mm oil 148 mm Pyrex glass and 2 mm aluminum was input into the simulation in

addition to the filters of interest The ideal signal to noise ratio squared or incident

photon fluence per exposure (q) was estimated for each filtration by integrating the

energy-dependent photon counts per unit exposure over all energy bins

I2iii DQE Measurements

The assessment of the linearized images followed the formalism described by

IEC 62220-1 for measuring the DQE [12] For this study the normal exposure level XN

was set at 1 mR to the detector surface as measured at the central axis perpendicular to

the anode-cathode axis

I2iiia Modulation Transfer Function

Spatial resolution was characterized by evaluating the presampled modulation

transfer function (MTF) along directions parallel (vertical) and perpendicular

(horizontal) to the anode-cathode axis using the angled-edge method [6-1013] A radio-

opaque edge test device [7] was placed in the center of the field at a pitch of

approximately 301 (about 2deg) to the axis perpendicular to that being measured as

shown in Figure 1 External lead apertures were not used [6] instead the internal

collimation from the radiographic unit was used to collimate the beam to the detector

area Raw images were acquired of the edge with the normal exposure level XN of 1 mR

at the detector face The procedure of calculating the MTF followed previously described

7

methods [6-1013] The edge spread function (ESF) was determined along lines crossing

the edge of the angled test device The derivative of the ESF was calculated to form the

line spread function (LSF) to which a Hanning filter was applied The MTF was then

calculated as the fast Fourier transform (FFT) of the LSF and normalized at the zero-

frequency axis To conform to IEC guidelines the MTF was resampled into frequency

steps of 005 cyclesmm [12]

Figure 1 MTF images for DRX-1C detector with radio-opaque edge test device with

arrows indicating the horizontal (left) and vertical (right) directions

I2iiib Noise Power Spectrum

Noise amplitude and texture were characterized by determining the normalized

noise power spectrum (NNPS) which was evaluated with flat field exposures at

approximate exposure levels of XN2 XN and 2XN (05 10 and 20 mR) to the image

receptor surface Analysis of the flat-field images followed previously defined methods

[41415] using over 4 million independent pixels with regions of interest (ROIs) of size

8

128x128 The NNPS images were detrended using a quadratic (second order)

background subtraction Small variations in exposure across ROIs were corrected by

normalizing pixel values of each ROI to the mean value in the top left ROI as shown in

Figure 2 The NNPS was then calculated with the 2D FFT including the zero-frequency

axes corresponding to the horizontal and vertical directions The results were then

resampled using 005 frequency bins according to IEC guidelines [12]

Figure 2 NNPS image for DRX-1C detector indicating the top left ROI that served as

the reference for normalizing other ROIs in the image The ROI array was formed

along the directions indicated by the arrows The heel effect visible along the vertical

axis of the detector is an example of small variation in signal across the image

I2iiic DQE Calculation

The DQE was calculated using the following relationship [615]

9

where the frequency-dependent MTF and NNPS were determined as described in

previous sections X was the exposure value in mR corresponding to the NNPS image

and q was the ideal signal to noise ratio squared in units of photonsmiddotmm-2middotmR-1 as

estimated from the spectral simulations

I3 Results

I3i Data Linearization

The detectors in this study provided raw ADU (or pixel) values in a linear scale

The data were converted using the following system conversion function

where Q(ij) is the raw image data m and b are slope and intercept parameters obtained

from linear regression of the system response function and I(ij) is the linearized scaled

data The factor of 1000 was found to scale I(ij) such that the maximum value was a

large 16-bit number Figure 3 shows the original and linearized system responses for the

Pixium 4600 Note that the y-intercepts of the regressions for the linearized responses

are negligible (lt 01) with respect to the slopes a sufficient condition for zero offset

considerations

I3ii Spectral Simulation

The spectral simulations of the IEC filtrations and alternative filtrations indicate

many similarities in their effective energies HVLs and overall shapes of normalized

spectra Results are summarized in Table 3

10

Pixium 4600 Original System

Response

Pixium 4600 Linearized System

Response R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 3 Original (left) and linearized (right) system responses for Pixium 4600 The

linearized system responses were measured from actual images The offsets are small

with respect to the slope sufficient enough for zero-offset conditions

y = 13971x - 13236

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x - 00106Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 13576x + 28292

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

7000

0000 1000 2000 3000 4000 5000

AD

U

Exposure (mR)

y = 99997x - 00067Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0000 1000 2000 3000 4000 5000

AD

U

Exposure (mR)

y = 13644x + 16167Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x + 00044

Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 13845x + 13541

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x - 00177

Rsup2= 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

11

Table 3 Spectral Simulation Results

Beam Quality Filtration

Mean Energy

(kV)

Photon Fluence

(mRmm2)

RQA5A 21 mm Al 5243 259543

RQA5C 05 mm Cu + 10 mm Al 5214 259554

diff 055 0004

RQA9A 40 mm Al 7619 273281

RQA9C 104 mm Cu + 10 mm Al 7579 273964

diff 052 025

Figure 4 Spectral simulations for RQA5 (top) and RQA9 (bottom) conditions Note

the similarities of spectral shapes of the normalized spectra (right) Also note the

significant differences in fluence between filtrations in the simulated spectra (left)

00E+00

50E+04

10E+05

15E+05

20E+05

25E+05

30E+05

35E+05

40E+05

45E+05

0 20 40 60 80

ph

oto

ns

mA

s-1

cm

-2

keV

RQA5 Spectra Comparison

21 mm Al

05 mm Cu + 10 mm Al

00

02

04

06

08

10

12

0 20 40 60 80

keV

RQA5 Normalized Spectra Comparison

21 mm Al

05 mm Cu +

10 mm Al

00E+00

50E+05

10E+06

15E+06

20E+06

25E+06

30E+06

35E+06

40E+06

45E+06

50E+06

0 50 100 150

ph

oto

ns

mA

s-1

cm

-2

keV

RQA9 Spectra Comparison

40 mm Al

104 mm Cu +

10 mm Al

00

02

04

06

08

10

12

0 50 100 150

keV

RQA9 Normalized Spectra Comparison

40 mm Al104 mm Cu + 10 mm Al

12

I3iii Modulation Transfer Function

The limiting spatial resolutions of the systems were indicated by the cutoff

frequencies which were approximately 35 cyclesmm for all three detectors The spatial

resolutions also demonstrated a good degree of isotropy as confirmed by the close

alignment of MTF curves between vertical and horizontal directions differentiated in

Figure 5 by dashed and solid lines respectively The MTF curves for the Pixium 4600

and DRX-1C were nearly equal to each other whereas the DRX-1 MTF curve showed a

more rapid decrease at high frequencies as shown in Figure 6 This difference may be

due to the differences in the inherent optical properties of the scintillating materials

where finer image details are provided by structured CsI more than by granulated GOS

There were no significant differences in MTF curves across beam qualities and filtrations

as shown by the curve comparisons in Figure 6 although the alternative filtration

produced slightly higher MTF curves as seen in Figure 4 Table 4 lists the experimental

specific spatial frequencies for varying levels of MTF

I3iv Noise Power Spectrum

The noise characteristics are indicated by the NNPS curves shown in Figure 7

The noise was similar for both horizontal and vertical directions As exposure increased

the NNPS decreased consistent with the characteristics of Poisson noise describing the

relationship between signal and noise in the presence of increased photon fluence At

13

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 5 MTF results by detector (columns) and beam quality (rows)

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

horizontal

vertical

14

Figure 6 Plots of MTF for RQA5 (top) and RQA9 (bottom) showing the relationships

between detectors (blue red and green) and by filtration (solid and dashed)

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm-1)

MTF

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm-1)

MTF

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

15

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 7 NNPS results by detector (columns) and beam quality (rows)

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

05 mR - horizontal

05 mR - vertical

10 mR - horizontal

10 mR - vertical

20 mR - horizontal

20 mR - vertical

16

Figure 8 Plots of NNPS for RQA5 (top) and RQA9 (bottom) at 1 mR exposure

showing the relationships between detectors (blue red and green) and by filtration

(solid and dashed)

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm-1)

NNPS (1 mR)

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm-1)

NNPS (1 mR)

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

17

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 9 DQE results by detector (columns) and beam quality (rows)

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

05 mR - horizontal

05 mR - vertical

10 mR - horizontal

10 mR - vertical

20 mR - horizontal

20 mR - vertical

18

Figure 10 Plots of DQE for RQA5 (top) and RQA9 (bottom) at 1 mR exposure showing

the relationships between detectors (blue red and green) and by filtration (solid and

dashed)

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm-1)

DQE (1 mR)

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm-1)

DQE

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

19

higher frequencies the NNPS curves of the Pixium 4600 and DRX-1 diverge slightly for

the different directions illustrating increased noise in the readout direction (vertical)

Differences in the noise characteristics were more apparent among detectors as

shown for 1 mR in Figure 8 The NNPS curve for the DRX-1 was higher in magnitude

across the entire frequency range than either the Pixium 4600 or DRX-1C which both

seemed to demonstrate reasonably similar NNPS curves The higher magnitude noise of

the DRX-1 indicates higher relative noise content overall Closer inspection of the NNPS

curves of the Pixium 4600 and DRX-1C detectors in Figure 7 revealed differences in the

spacing between the three exposure levels The gaps between the Pixium 4600 NNPS

curves do not correspond to the factor of two differences between each exposure level

especially at low- to mid- spatial frequencies suggesting a higher level of fixed pattern

noise additional noise with increasing exposure levels due to ineffective gain map

corrections Between filtration schemes the differences in NNPS curves for a given beam

quality were not substantial as shown in Figure 7

I3v Detective Quantum Efficiency

The DQE results are shown in Figure 9 DQE curves across exposure levels were

almost collinear except for Pixium 4600 and in general could be inferred from the

NNPS results Additionally the DQE curves demonstrated a relatively linear response

with spatial frequencies as expected for flat-panel detectors [9] Differences in DQE

among detectors were consistent for the most part with the type of scintillating material

20

As depicted for 1 mR exposure in Figure 10 differences between Pixium 4600 and DRX-

1C DQE curves correspond to the differences in their NNPS curves DRX-1 DQE curves

were consistently lower than either the Pixium 4600 or DRX-1C curves The DQE curves

for the alternative filtration were consistently higher than those for the IEC filtration

and the most noticeable differences were near the zero-frequency axis These effects can

be both attributed to ineffective gain map correction DQE values for 1 mR exposure are

listed in Table 5

I4 Discussion

I4i Comparisons of Detectors

The limiting spatial resolutions of all three detectors were almost exactly the

same considering that their pixel areas were similar in size The decrease in high-

frequency MTF of the DRX-1 compared to the other detectors is probably a result of

increased optical blurring due to the differences in the powdered structure of GOS

versus the needle-like structure of CsI [2] The fact that the DRX-1C and Pixium 4600

have comparable MTFs suggests similar scintillator thicknesses assuming that the

materials were processed alike

The noise of the three detectors demonstrated similar trends with each other The

higher NNPS curves of the DRX-1 detector are probably due also to the scintillating

material and its operation in converting photons into signal The conversion process is

less efficient because of the less favorable stopping power of the GOS compared to CsI

21

especially with higher energy beams The noise of the Pixium 4600 and DRX-1C were

similar except for the spacing between exposures The DRX-1C NNPS curve spacing is

consistent with a factor of two difference in exposure levels but the Pixium 4600 has a

smaller spacing The 05 mR NNPS curve of the Pixium 4600 is closer to that of the 05

mR NNPS curve of the DRX-1C This demonstrates that at higher exposures the Pixium

4600 produces a larger amount of additional noise beyond that explained by simple

stochastic effects It suggests bad performance in the gain map corrections

The DQE results indicate SNR properties of each detector The Pixium 4600 and

DRX-1C are comparable for the most part with the DRX-1C performing slightly better

The DRX-1 as predicted from MTF and NNPS results has a DQE much lower than

either of the previous two This is a reflection of the detection properties as provided by

its scintillator material The DQE of the DRX-1 however is comparable to CR image

receptors [2] The mid-frequency dips in the DQE for Pixium 4600 may be due to the

optical properties of the CsI phosphor layer which can affect the MTF in this manner

Because the DQE is calculated by squaring the MTF this effect at the mid-range

frequencies becomes more apparent The dips may also be further evidence of bad gain

map corrections

I4ii Comparisons of Filtrations

The alternative filtration closely matches for the most part the IEC-based

filtration for MTF NNPS and DQEs at RQA5 but not at RQA9 The filters do not have

22

Table 4 Experimental MTF frequency locations for 1 mR exposure

Detector Filtration

50 MTF

(mm-1)

40 MTF

(mm-1)

30 MTF

(mm-1)

20 MTF

(mm-1)

10 MTF

(mm-1)

Pixium

4600

RQA5A 115 145 185 245 330

RQA5C 125 155 195 250 345

RQA9A 110 175 175 235 330

RQA9C 125 155 195 255 345

DRX-1C

RQA5A 120 150 185 245 350

RQA5C 125 155 195 255 355

RQA9A 120 150 190 250 355

RQA9C 130 160 210 265 360

DRX-1

RQA5A 110 135 160 205 280

RQA5C 110 135 170 210 285

RQA9A 105 125 155 195 270

RQA9C 110 135 165 210 285

Table 5 Estimated DQE values for 1 mR exposure by frequency bins

Detector Filtration DQE(00 mm-1) DQE(10 mm-1) DQE(20 mm-1) DQE(30 mm-1)

Pixium

4600

RQA5A 62 42 32 21

RQA5C 63 45 36 25

RQA9A 41 27 30 13

RQA9C 43 33 27 19

DRX-1C

RQA5A 72 52 35 21

RQA5C 76 55 41 24

RQA9A 49 33 23 15

RQA9C 51 40 31 20

DRX-1

RQA5A 38 24 12 4

RQA5C 38 25 14 5

RQA9A 28 18 9 4

RQA9C 28 19 12 5

DQE values at the zero-frequency axis were estimated by the intercept of a linear fit of low-frequency data

but excluding most proximal to the axis due to large fluctuations Other estimated values are grouped into

frequency bins due to the noisiness of the data

23

considerable differences in the spatial resolutions of the detectors as expected The noise

responses for each filtration were also similar except at the lower frequencies of the

NNPS especially near the zero-frequency axis There observing the NNPS responses at

RQA5 for Pixium 4600 and DRX-1C in Figure 8 the NNPS for the IEC-based filtration

(solid lines) tend to drop faster than the NNPS for the alternative filtration This

subsequently appears as a drop in DQE near the zero-frequency axis shown for those

detectors in Figure 10 Overall as indicated in Table 5 the DQEs of the two filtrations

while similar in trend indicate that the alternative filtration increases the DQE by a

small amount of 3-5 Part of this may be explained by the slightly higher beam

energy which may be more optimal for the energy response of the detectors or may

weigh the pixel responses slightly considering that they are energy-integrating types

The most probable explanation is the gain map correction for the alternative filtration

where fixed pattern noise is more sufficiently reduced

A previous study [6] had discussed the choice of filter material in the analysis of

DQE when achieving the beam conditions defined by IEC It found that visible

nonuniformities were present with the higher purity aluminum filter (type-11999 alloy)

The low frequency mottle in the flat-field images for NPS measurements were also

attributed to structured noise from the grain size in the IEC-based filter with an

attenuating thickness that would reveal nonuniformities The mottle in the current study

was only observable under very narrow windowing as shown in Figure 11 Such low

24

frequency artifacts which are not readily noticeable may also be caused by shading

artifacts inverse square law or even the heel effect A possible method to correct for this

is a subtraction method by taking the average of the flat-field images for an exposure

level and then subtracting that from each of them This would remove nonuniformities

that were not corrected using a suboptimal gain map calibration

Figure 11 DRX1-C NNPS images at 1 mR for RQA5 with IEC filtration (left) and

alternative filtration (right) Images are equally windowed at 45 and leveled at 980

One convenient aspect of the copper and aluminum filtration is that it requires

much less tube current to achieve the same amount of exposure at the detector than the

much thicker aluminum filtration As shown in the non-normalized spectra in Figure 2

the exiting photon fluence exiting the copper and aluminum filtration is substantially

higher than that of the IEC-specified filtration This is due to the smaller total filtration

25

attenuation For extensive DQE analysis multiple sets of exposures may be acquired

before tube overheating becomes a concern

One limitation to the comparison of the two filtrations is that calibration

procedures specified copper and aluminum filtration at 80 kVp (for all detectors 05 mm

Cu and 10 mm Al) This may have influenced the results in favor of the alternative

filtration A further investigation involving the calibration procedures and performing

DQE measurements is encouraged Another factor may be influenced by the fact that the

tests were performed at 70 kVp and 120 kVp different from the recommended

calibration tube potential Clearly there would be differences in the linear attenuation

coefficients of the filters and different energy responses of the detectors themselves This

must be considered when interpreting DQE results The current results support a

previous study decades ago that described filtration of different material types in terms

of an aluminum equivalent [16] The results show that the two filtration schemes are

essentially equivalent when considering beam qualities and spatial resolutions The

NNPS and DQE results can be seen as close enough where their small differences are

insignificant when performing quality assurance tests in a clinical setting Overall our

results indicate that the alternative filtration with copper and aluminum may be more

convenient to use than the current IEC standard filtration

26

I4iii Implications of Wireless DR

This study has shown that wireless image receptors can have the same DQE

performance if not better than conventional flat-panel detectors They operate on the

same basic physical principles the new features offered by the DRX-1C and DRX-1 are

wireless communication with the workstation and electronics packaging technology

The latter feature may pose limitations for these units in terms of possible degradation

in the detectors in routine clinical conditions A consideration for future work would be

to longitudinally track DQE performance of the wireless detectors over time while being

utilized in a clinical environment In the end one must consider risks versus benefits of

choosing portable DR technology over CR one of which includes the cost and fragility

of DR detectors

The DQE performance of one wireless system is just as good as or better than

conventional systems as seen by the DRX-1C performance compared to the Pixium

4600 Wireless systems can also reduce the need for CR readers especially in portable

applications in other regions of the world (eg military hospitals developing countries)

However while DQE performance indicates the physical performance of the detector

system it is still unknown how it relates to observer performance

I5 Conclusions

Two wireless image receptors DRX-1C and DRX-1 were evaluated and

compared with the conventional DR flat-panel Pixium 4600 in terms of DQE

27

performance along with MTF and NNPS performances The detectors have similar

resolution properties although the DRX-1 is inferior at higher spatial frequencies The

NNPS and DQE results both indicate that the DRX-1C is superior to the DRX-1 and

comparable if not better to the Pixium 4600

The results from the filtration comparison indicate no substantial differences

between the IEC-based filtration and the copper-based alternative filtration Only slight

differences were found in the low frequency components of the NNPS and the DQE due

to the inherent nonuniformities of the IEC specified filtration Given the similarity of the

results and low attenuation advantage of the copper and aluminum filter its use is

encouraged

28

II Directional MTF for Breast Tomosynthesis

II1 Introduction

Breast tomosynthesis is an emerging 3D imaging modality that has potential use

for screening and diagnosis of breast cancer Breast tomosynthesis along with other 3D

techniques is preferable to planar imaging methods (eg mammography) because they

reduce anatomical noise by removing overlying structures above and below the plane of

an image slice [17-20] Recent advances in detectors and computer technology have

made digital tomosynthesis feasible

An image quality metric of particular importance in breast tomosynthesis is

spatial resolution Resolution is important to know in order to assess small-detail

structures such as microcalcifications A descriptive metric for characterizing spatial

resolution in the Fourier (or frequency) domain is the modulation transfer function

(MTF) Affected by reconstruction filters [21] the limited angular projections involved in

breast tomosynthesis results in highly anisotropic (or nonuniform) resolution Many

studies have looked only at characterizing the in-plane spatial resolution (ie in an

individual slice) with an elevated angled edge phantom [2223] A few studies have

looked at characterizing a more comprehensive 3D spatial resolution by using a

phantom with angled wires or tubes [24-26] However such studies require precise

mechanical alignment of the phantoms Several studies have explored a method using a

29

sphere phantom for the directional 3D MTF evaluation for microtomography [27] and

multi-slice CT [2829] This method has not yet been extended to breast tomosynthesis

This chapter focuses on breast tomosynthesis because it is highly anisotropic in

spatial resolution and like its predecessor mammography requires high spatial

resolution Additionally breast tomosynthesis acquisitions and reconstructions produce

several types of artifacts The use of a cone-based method using a sphere phantom [28] is

explored to characterize the directional 3D spatial resolution of simulated images from

breast tomosynthesis A technique for removing out-of-plane artifacts of the ESFs for the

in-plane axes is investigated to yield a modified MTF in a method that separates artifact

information from resolution information

II2 Materials and Methods

II2i Image Simulation

Breast tomosynthesis images were simulated by using a virtual imaging system

depicted in Figure 12 A volumetric breast phantom was voxelized as a rectangular mass

of uniform breast equivalent tissue of 4 cm thickness embedded with fifteen evenly

spaced plastic sphere inserts of 12 mm diameter The spheres were placed in a grid

formation within the central plane of the phantom The x-ray fluence was modeled from

a 28 kVp beam incident upon an indirect flat-panel detector with 200 micro m pixel size

Twenty-three projections within an angular range of 44deg were simulated using cascaded

systems analysis to generate characteristic 2D noise and spatial blurring [29] Each

30

projection was simulated to have an exposure of 174 mR with a fluence of 79 times 105

photonsmm-2 A standard filtered backprojection technique based on the Feldkamp

reconstruction algorithm [29] was used to reconstruct the projections and produce a

volumetric dataset with an isotropic voxel size of 200 micro m

Figure 12 Depiction of the virtual image system

II2ii Uncorrected MTF

To enable comparison of multiple spheres the reconstructed volume was

initially homogenized by performing a background subtraction based on a portion of the

volume devoid of spheres The voxel values were rescaled between one and zero to

eliminate negative values

31

The volumetric data were segmented to extract individual regions of interest

(ROIs) each containing a single sphere The ROIs extended along the full range of the z-

axis A thresholded ROI was generated by determining the exterior and interior voxels

relative to the sphere in the ROI The threshold value was set at 45 of the maximum

voxel value prior to thresholding The exterior and interior voxel values were then set to

values of 0 and 1 respectively Using the thresholded volume the center of mass was

calculated to determine the centroid The voxel values from the original ROI were

subsequently tabulated with the associated distances azimuthal angles and polar

angles relative to the centroid

Conical regions were prescribed along the positive and negative directions along

the three major axes extending from the centroid of the sphere as depicted in Figure 13

The axes about which the extent of the cone angle was delineated were defined with

the azimuthal and polar angles

Voxels with centers within the angular range of the cone were considered for

generating the edge spread function (ESF) To improve regularity of the distance

sampling interval the ESF values were rebinned to discrete distances corresponding to a

fraction of the voxel size Only voxels with distances ranging from the voxel size (ie

200 micro m) to the maximum distance were considered The ESFs from multiple spheres

were averaged together for each of the three major axes to produce an averaged ESF

which was further smoothed utilizing a Gaussian filter

32

Figure 13 Example of 30-degree cone prescribed along z axis of the sphere

The resulting ESF was then differentiated using the central difference method to

produce the line spread function (LSF) A Hanning filter with the same length as the LSF

was applied to zero out the tails of the LSF The presampled MTF was subsequently

computed as the amplitude of the Fourier transform of the LSF The MTF was

normalized with respect to the maximum value occurring within the range of the cutoff

frequency Binning size and conical range for the ESF were considered for maximizing

accuracy and minimizing noise of the MTF verified by comparison against the

theoretical MTF as determined in the previous section

II2iii Theoretical Directional MTF

The theoretical 3D MTF was calculated using a priori knowledge of the transfer

function of the virtual imaging system described in the previous section A phantom

was created with a set of point objects in a uniform and noise-free background with the

objects spanning across the volume of the breast [29] Twenty-one realizations were

33

generated from the reconstructed images of the point objects to yield a set of 3D point

spread functions (PSFs) The 3D fast Fourier transform (FFT) was performed for each 3D

PSF and averaged to give an ldquoexpectationrdquo 3D MTF [29] The theoretical directional

MTFs in the three major spatial axes were determined by line profiles along each of the

corresponding spatial frequency axes in the 3D MTF An additional theoretical MTF for

each direction was determined by using the application of conical regions along the axes

in frequency-space to take into account the contributions of MTF information from other

planes

II2iv Modified MTF

The tomosynthesis reconstruction is known to have edge enhancements which

affect the overall MTF by shifting the peaks of the MTF toward the higher frequencies

[23] The presence of this artifact complicates the interpretation of the actual spatial

resolution of the images Several steps were performed to remove the artifact

contribution to the resolution information particularly for the in-plane x and y

directions with the assumption that resolution information was contained immediately

near the edge

For the x-direction averaged ESF only values that were detected to be inside the

edge of the sphere were considered Those values were previously determined via

thresholding for calculating the centroid The ESF information corresponding to these

values was inversed and flipped about the detected edge to produce a symmetric

34

modified ESF The modified MTF was subsequently calculated from this modified ESF

as described in the previous section

For the y-direction averaged ESF an upward trend was found in the initial part

of the ESF This section was detrended with a polynomial fit and subtracted to produce a

flatter curve in that region The resulting detrended ESF was used to calculate the y axis

modified MTF

Figure 14 Photograph of the imaging system with the acrylic sphere phantom

embedded in oil

II2v Preliminary Experimental Validation

A clinical breast tomosynthesis system (Mammomat Inspiration Siemens AG

Munich Germany) was used to perform a preliminary evaluation of the cone-based

MTF technique The phantom for the experiment consisted of a single acrylic ball of 075

in diameter (SmallParts Seattle WA) suspended by a 0029 in diameter plastic filament

35

(Omniflex Zebco Tulsa OK) in an acrylic frame filled up to 4 in with vegetable oil

(Target Brands Inc Minneapolis MN) The system and phantom are shown in Figure

14 Twenty-five projections with an angular range of 44deg were acquired and subsequently

reconstructed to produce a volume with a voxel size of 01times01times10 mm3 The voxels were

reformatted to have an isotropic size of 01 mm The uncorrected ESF LSF and MTF

were calculated as described in the previous section

II3 Results

II3i Reconstruction

The reconstructed volume is shown in Figure 15 Notice the edge enhancement

along the x-direction as indicated by the sharp shadowing artifacts on either side of the

spheres The background was effectively homogenized using the background

subtraction technique This also took account of the curved edges of the breast phantom

With the close spacing of the spheres in the phantom the shadows along the x direction

for the fifteen spheres overlap with each other As the nine centrally located spheres

experience this effect the same way they were used for determining the ESF

A 3D rendering of the ROI containing a sphere shown in Figure 16 indicates the

anisotropic resolution of the reconstruction Note that the sphere is not accurately

reconstructed and has an oblong shape especially along the z axis Cross sectional views

of the ROI also in Figure 16 clearly demonstrate the edge enhancement causing a

shadow artifact in the x direction caused by the incomplete angular sampling of

36

tomosynthesis The sampling also introduces the triangular reconstruction of the sphere

as seen in the x-z plane Note the gradual edge drop-off in the z direction much beyond

the sphere radius

Figure 15 View of the central slice of the breast phantom reconstruction before (top)

and after (bottom) background subtraction The z axis is through the page

37

Figure 16 3D rendering of the ROI volume (left) and cross-sectional views of the most

centrally located sphere with centroid indicated with red circle (right)

II3ii Theoretical MTF

The theoretical MTFs for x y and z directions as determined from the line

profiles of the 3D MTF are shown in Figure 17 The theoretical MTF in the x direction

has a maximum value that is toward higher frequencies Its 10 response occurs at

about 125 cyclesmm which is at 50 of the cutoff frequency The rapid increase from

the zero-frequency intercept to the peak corresponds to the ramp filter used in filtered

backprojection which decreases the weighting of low frequency contributions due to the

incomplete angular sampling of the frequency-space The MTF does not reach a value of

0 at the zero-frequency intercept as it is very difficult to assess the zero-frequency

intercept due to the finite size of the phantom The theoretical MTF in the y direction

peaks at the zero-frequency intercept and reaches 20 proximal to the cutoff frequency

38

The 10 MTF is well beyond the cutoff frequency The theoretical MTF in the z direction

has a rapid drop-off at very low spatial frequencies indicating the lack of resolution in

that dimension

Figure 17 Theoretical 3D MTF results along the three major planes (top) and along x

y and z directions (bottom) Also note that the angular spread seen in the fx-fz plane is

equal to the angular range of 44deg for the acquisition

II3iii Uncorrected MTF

The ESF LSF and MTF using the cone-based method are shown for the x y and

z directions in Figure 18 It was found that a bin size of one-tenth the voxel size (002

mm) and a cone angle of 30deg to establish the ESF were enough to minimize noise and

maximize accuracy in the uncorrected MTFs considering the reasonable comparison of

the shapes of the MTF curves with the theoretical results in Figure 17 The LSFs are

generally noisy because differentiation of the ESF increases the amplitude of the noise

39

The data shown reflect a convolution with a smoothing Gaussian filter which was later

further corrected for in the reported MTF Nevertheless the high frequency components

of the noise are well beyond the MTF cutoff frequency of 25 cyclesmm and do not

impact the MTF results greatly

For the ESF in the x direction the shadow effect evident at the edge of the sphere

is visible as a steep decline followed by an increase Due to the finite distance range

provided by the ROI the ESF beyond the edge did not asymptotically reach the

background value The corresponding LSF demonstrates a low frequency modulation

that is indicated by the shift of 03 cyclesmm in the x direction for the peak of the MTF

The MTF exhibits a zero-frequency intercept that is non-zero unlike the theoretical MTF

and a 10 value at approximately 1 cyclesmm These features may be a direct

consequence of MTF information ldquocontaminationrdquo from y and z directions Furthermore

the ESF in the y direction demonstrates a reasonably shaped curve except for the slight

upward trend within the radius of the sphere which can be attributed to the shadow

artifact overlapping with the sphere volume The associated MTF has a peak shifted by

approximately 01 cyclesmm away from the axis and a 10 MTF occurring at

approximately 15 cyclesmm Both features which are not present in the theoretical

results may also be attributed to contaminant MTF information from x and z directions

The ESF in the z direction has a drop-off that occurs at a small fraction of the cutoff

frequency similar to that demonstrated by the theoretical MTF

40

Uncorrected ESF LSF and MTF

Figure 18 Uncorrected ESF (top) LSF (middle) and MTF (bottom) for x y and z

directions

41

Figure 19 Comparisons of the directional MTFs as calculated by the sphere method

(dashed line) by theoretical line profiles (light-weight line) by theoretical cone

regions (heavy-weight line)

II3iv Comparison of Theoretical and Simulated MTFs

The theoretical MTF results obtained from line profiles through the 3D MTF and

the simulated MTFs using the cone-based technique did not match very well except for

the general shape of the curves It was assumed in the previous section that the cone-

based technique contains information from other planes Figure 19 compares MTFs in

each direction for the two methods described in the methods and an additional method

based on conical regions of the 3D MTF The latter computes the MTF by averaging

contributions of the 3D MTF using the same cone prescription method used to define the

ESFs Comparison of the curves indicate some interesting correlations aside from the

fact that using conical regions with the 3D MTF results produce more noisy MTF results

partly due to the low sampling provided by the theoretical calculations The same

conclusions regarding the z direction MTF can be confirmed regardless of either

theoretical MTF procedures The experimental x direction MTF seems to agree best with

42

the line profile method whereas the y direction MTF agrees better with the cone region

method The fact that the experimental x direction MTF has a drop-off frequency that is

lower than those of either of the theoretical MTFs in Figure 19 suggests that this might

be due to integration of the z-direction in the in-plane slices considering how slices are

essentially averages of z direction information contained within it [33]

II3v Modified MTF for x and y

Modified ESF LSF and MTF curves for x and y directions are shown in Figure

20 The modified ESF and the resulting LSF in the x direction appear symmetric as

expected from the inverse and flip operation of the interior ESF about the detected edge

The modified MTF appears with less variation than the uncorrected MTF and the MTF

peak occurs at the zero-frequency axis The correction yields a 10 MTF at about 15

cyclesmm an improvement from the uncorrected MTF but still distant from the cutoff

frequency The modified ESF in the y direction demonstrates the detrended curve within

the sphere radius after a quadratic polynomial fit The resulting modified MTF still

appears similar to the uncorrected MTF except that the peak now coincides with the

zero-frequency axis For both x and y directions the low response of the modified MTFs

at the higher frequencies suggests that the contamination from other directions is

substantial due to the angular range of the cone

43

Modified ESF LSF and MTF

Figure 20 Modified ESF (top) LSF (middle) and MTF (bottom) for x and y directions

44

II3v Preliminary Experimental Validation

Cross-sections of the reconstructed sphere volume are shown in Figure 21

Relative to the simulation reconstructions the reconstructions of the experimental

phantom images produce lower contrast and higher noise The preliminary results

shown in Figure 22 indicate that our technique can be applied to actual experimental

breast tomosynthesis reconstructions However due to the noise exhibited by the MTF

curves for the x and y directions we did not determine the modified MTFs to separate

resolution and artifact information

Figure 21 Cross sectional views of the experimental sphere image with centroid

indicated with red circle

45

Uncorrected ESF LSF and MTF for Real Image

Figure 22 ESF (top) LSF (middle) and MTF (bottom) of real image for x y

and z directions

46

II4 Discussion

II4i Evaluation of Cone-based Method

The cone-based MTF technique was introduced by Thornton and Flynn [28] for

evaluation of volumetric CT images To utilize this technique as a characterization of a

3D system spatial resolution one must first consider the validity of the assumption of

shift invariance such that the same MTF result may be obtained regardless of the

location of the sphere The study by Zhao et al [23] found that there was no shift

variance for the MTF measurements along the vertical axis but this was only considering

the in-plane resolution along one axis On the other hand this study evaluated the MTF

with images simulated with cascaded systems analysis which includes conditions of

linearity and shift invariance Additionally the MTF was calculated by averaging the

ESF from several spheres in the same volume only after performing a background

subtraction This step was essential to account for the sensitivity of centroid calculations

as well as ensuring symmetric ESFs for opposing axes of the sphere ROIs

The measurement of MTF with the cone-based technique inherently

supersamples the edge of the sphere to increase signal-to-noise-ratio (SNR) of edge

information by averaging the contributions of each voxel to the ESF [713] This method

also takes into account the discrete sampling of the voxels by accounting for various

shifts of the edge in the voxel (also known as the partial volume effect) However using

the curved surface of the sphere phantom to approximate an edge along a given

47

direction naturally leads to contamination of information from other directions aside

from the one of interest Preferably a directional ESF should be created by using a single

radial line but this would limit the available voxels to obtain edge information An ideal

situation theoretically would be to use a larger-sized sphere such that the surface is

nearly flat and perpendicular to the axes of interest This would also permit a reduction

in the angular range of the cone and thus the introduction of out-of-plane information in

the resulting MTF However sphere size is a limitation in breast tomosynthesis and the

use of a large phantom might void the assumption of shift invariance of the spatial

resolution

The choice of a sphere phantom nevertheless may be based on the clinical need

to quickly acquire a single image for MTF evaluation especially for multiple directions

without presenting extra logistical challenges The use of a wire or edge phantom

requires more precise mechanical alignment to achieve the correct set up The edge

phantom [23] would require at least two images to sample all three dimensions In the

case of the three wire phantom [2425] all three dimensions of the frame must be aligned

simultaneously with respect to the axis of rotation A similar situation would be

encountered when considering a cubic phantom with the planes normal to the axis of

interest In contrast to these phantoms the sphere eliminates the need for precise

alignment especially with respect to three spatial dimensions simultaneously A sphere

48

has ideal symmetry in all directions and can be used to evaluate MTF in any arbitrary

direction

This study unlike others [242532] did not explore the effects of physical

parameters such as scatter or contrast on the final MTF result but it demonstrated the

feasibility of using the cone-based method with an actual breast tomosynthesis image of

a sphere phantom as shown in Error Reference source not found and Error Reference

source not found These effects should be addressed in future works A further look

into deriving the principles of comparing the theoretical MTF with the experimental

MTF using the cone-based method is further warranted

II4ii Separation of Artifact and Resolution Information

The focus of this study was to develop a technique for measuring spatial

resolution of tomosynthesis images The intrinsic artifacts from tomosynthesis

reconstructions however lead to uncharacteristic MTFs and possible misinterpretation

of the effective resolution information When considering previous techniques for

calculating the presampled MTF [713152328] the analysis was performed using an

edge or a line to produce the corresponding ESF The resolution information is

essentially contained only along the edge indicated by the need to calculate the LSF In a

way the method of extracting artifact information is to focus the analysis only on the

edge part of the ESF to calculate the modified MTF This will lead to a better

understanding of the limiting size of objects that may be seen in the reconstructed 3D

49

image The presampled MTF without correction should still be analyzed to understand

the entire system response Note that the ESFs attempt to reflect information only at the

detected edge of the sphere

II5 Conclusions

The directional MTF of a simulated breast tomosynthesis reconstruction was

determined by using the cone-based MTF technique demonstrating the feasibility of a

single phantom for MTF evaluation This study further presented methods of analyzing

only the edge information in the ESF to create a modified MTF along in-slice (x and y)

axes It can provide insight into the actual spatial resolution information contained in the

image while separating the resolution information from the information introduced by

artifacts caused by the reconstruction and insufficient volumetric sampling The idea of

separating the resolution and artifacts from the measured ESF are expected to facilitate

the interpretation of MTF measurements in breast tomosynthesis Similar methods may

be applied to characterize the resolution of other 3D imaging modalities

50

References

1 Garmer M Hannigs SP Jaumlger HJ et al ldquoDigital Radiography Versus

Conventional Radiology in Chest Imaging Diagnostic Performance of a Large-

Area Silicon Flat-Panel Detector in a Clinical CT-Controlled Studyrdquo American

Journal of Roentgenology Volume 74 75-80 (2000)

2 Cowen AR Kengyelics SM and Davies AG ldquoSolid-state flat-panel digital

radiography detectors and their physical imaging characteristics rdquoClinical

Radiology Volume 63 487-498 (2008)

3 Chotas HG Dobbins III JT and Ravin CE ldquoPrinciples of Digital

Radiography with Large-Area Electronically Readable Detectors A Review of

the Basicsrdquo Radiology Volume 210 Number 3 595-599 (1999)

4 Flynn MJ and Samei E Experimental comparison of noise and resolution for

2k and 4k storage phosphor radiography systems Medical Physics Volume 26

Number 8 1612-1623 (1999)

5 Rong XJ Shaw CC Liu X Lemacks MR and Thompson SK

ldquoComparison of an amorphous siliconcesium iodide flat-panel digital chest

radiography system with screenfilm and computed radiography systems ndash A

contrast-detail phantom studyrdquo Medical Physics Volume 28 Number 11 2328-

2335 (2001)

6 Ranger NT Samei E Dobbins III JT and Ravin CE Measurement of the

detective quantum efficiency in digital detectors consistent with the IEC 62220-1

standard Practical considerations regarding the choice of filter material

Medical Physics Volume 30 Number 7 2305-2311 (2005)

7 Samei E Buhr E Granfors P Vandenbroucke D and Wang X Comparison

of edge analysis techniques for the determination of the MTF of digital

radiographic systems Physics in Medicine and Biology Volume 50 3613-3625

(2005)

8 Samei E and Flynn MJ An experimental comparison of detector performance

for computed radiography systems Medical Physics Volume 29 Number 4 447-

459 (2002)

51

9 Samei E and Flynn MJ An experimental comparison of detector performance

for direct and indirect digital radiography systems Medical Physics Volume 30

Number 4 608-622 (2003)

10 Samei E Ranger NT MacKenzie A Honey ID Dobbins III JT and Ravin

CE Effective DQE (eDQE) and speed of digital radiographic systems An

experimental methodology Medical Physics Volume 36 Number 8 3806-3817

(2009)

11 Samei E Ranger NT MacKenzie A Honey ID Dobbins III JT and Ravin

CE Detector or System Extending the Concept of Detective Quantum

Efficiency to Characterize the Performance of Digital Radiographic Imaging

Systems Radiology Volume 249 Number 3 926-937 (2008)

12 ldquoIEC 62220-1 Medical Electrical Equipment ndash Characteristics of Digital X-Ray

Imaging Devices ndash Part 1 Determination of the Detective Quantum Efficiencyrdquo

International Electrotechnical Commission Geneva Switzerland (2003)

13 Samei E Ranger NT Dobbins III JT and Chen Y Intercomparison of

methods for image quality characterization I Modulation transfer function

Medical Physics Volume 33 Number 5 1454-1465 (2006)

14 Dobbins III JT Samei E Ranger NT and Chen Y Intercomparison of

methods for image quality characterization II Noise power spectrum Medical

Physics Volume 33 Number 5 1466-1475 (2006)

15 Samei E Flynn MJ and Reimann DA A method for measuring the

presampled MTF of digital radiographic systems using an edge test device

Medical Physics Volume 25 Number 1 102-113 (1998)

16 Nagel HD ldquoAluminum equivalence of materials used in diagnostic radiology

and its dependence on beam qualityrdquo Physics in Medicine and Biology Volume

31 Number 12 1381-1399 (1986)

17 Niklason LT Christian BT Niklason LE et al ldquoDigital Tomosynthesis in

Breast Imagingrdquo Radiology Volume 205 399-406 (1997)

18 Gur D ldquoTomosynthesis Potential Clinical Role in Breast Imagingrdquo American

Journal of Roentgenology Volume 189 614-615 (2007)

52

19 Park JM Franken Jr EA Garg M Fajardo LL and Niklason LT ldquoBreast

Tomosynthesis Present Considerations and Future Applicationsrdquo

RadioGraphics Volume 27 S231-S240 (2007)

20 Good WF Abrams GS Catullo VJ Chough DM Ganott MA Hakim

CM and Gur D ldquoDigital Breast Tomosynthesis A Pilot Observer Studyrdquo

American Journal of Roentgenology Volume 190 865-869 (2008)

21 Hu Y-H Zhao W Mertelmeier T and Ludwig J ldquoImage Artifact in Digital

Breast Tomosynthesis and Its Dependence on System and Reconstruction

Parametersrdquo IWDM 2008 LNCS 5116 628-634 (2008)

22 Chen Y Lo JY Ranger NT Samei E Dobbins III JT ldquoMethodology of

NEQ(f) analysis for optimization and comparison of digital breast tomosynthesis

acquisition techniques and reconstruction algorithmsrdquo Proceedings of SPIE

Volume 6510 65101I (2007)

23 Zhao B Zhou J Hu Y-H Mertelmeier T Ludwig J and Zhao W

ldquoExperimental validation of a three-dimensional linear system model for breast

tomosynthesisrdquo Medical Physics Volume 36 Number 1 240-251 (2009)

24 Madhav P Brzymialkiewicz CN Cutler SJ Bowsher JE and Tornai MP

ldquoCharacterizing the MTF in 3D for a Quantized SPECT Camera Having Arbitrary

Trajectoriesrdquo 2005 IEEE Nuclear Science Symposium Conference Record 1722-

1726 (2005)

25 Madhav P McKinley RL Samei E Bowsher JE and Tornai MP ldquoA Novel

Method to Characterize the MTF in 3D for Computed Mammotomographyrdquo

Proceedings of SPIE Volume 6142 61421Y (2006)

26 Hu Y-H Zhao B and Zhao W ldquoImage artifacts in digital breast

tomosynthesis Investigation of the effects of system geometry and

reconstruction parameters using a linear system approachrdquo Medical Physics

Volume 35 Number 12 5242-5252 (2008)

27 Seifert A and Flynn MJ ldquoResolving power of 3D x-ray microtomography

systemsrdquo Proceedings of SPIE Volume 4682 407-413 (2002)

28 Thornton MM and Flynn MJ Measurement of the spatial resolution of a

clinical volumetric computed tomography scanner using a sphere phantom

Proceedings of SPIE Volume 6142 61421Z (2006)

53

29 Baek J Pelc NJ ldquoUse of sphere phantoms to measure the 3D MTF of FDK

reconstructionsrdquo Proceedings of SPIE Volume 7961 79610D (2011)

30 Richard S and Samei E ldquoQuantitative imaging in breast tomosynthesis and CT

Comparison of detection and estimation task performancerdquo Medical Physics

Volume 37 Number 6 2627-2637 (2010)

31 Chen Y Lo JY and Dobbins III JT ldquoImpulse response analysis for several

digital tomosynthesis mammography reconstruction algorithmsrdquo Proceedings of

SPIE Volume 5745 541-549 (2005)

32 Zhao B and Zhao W ldquoThree-dimensional linear system analysis for breast

tomosynthesisrdquo Medical Physics Volume 35 Number 12 5219-5232 (2008)

33 Wu G Mainprize JG Boone JM and Yaffe MJ ldquoEvaluation of scatter

effects on image quality for breast tomosynthesisrdquo Medical Physics Volume 36

Number 10 4425-4432 (2009)

Page 5: Development and Evaluation of 2D and 3D Image Quality ...

v

qualities RQA5 and RQA9 All three DR systems demonstrated similar modulation

transfer functions (MTFs) at most frequency ranges while the DRX-1 showed lower

values near the cutoff of approximately 35 cyclesmm At each exposure the Pixium

4600 and DRX-1C demonstrated similar noise power spectrum (NPS) curves that

indicated better noise performance than the DRX-1 Zero-frequency DQEs for Pixium

4600 DRX-1C and DRX-1 were approximately 63 74 and 38 for RQA5 and 42

50 and 28 for RQA9 respectively In terms of DQE performance the DRX-1C image

receptor was found to be superior to the Pixium 4600 and DRX-1

In the second chapter the directional spatial resolution of simulated breast

tomosynthesis images was determined using a cone-based technique and a sphere

phantom Projections were simulated for a voxelized breast phantom with 12 mm

diameter sphere inserts using a fluence modeled from a 28 kVp beam incident upon an

indirect flat-panel detector with 200 micro m pixel size Characteristic noise and blurring for

each projection were added using cascaded systems analysis The projections were

reconstructed using a standard filtered backprojection technique producing a 3D

volume with an isotropic voxel size of 200 micro m Regions of interest (ROIs) that

completely encompassed single spheres were extracted and conical regions were

prescribed along the three axes extending from the centroid Voxels within a cone were

used to form an edge spread function (ESF) from which the directional MTF was

calculated A bin size of 002 mm and a conical range of 30 degrees were found optimal

vi

for maximizing accuracy and minimizing noise of the MTF A method for removing out-

of-plane artifacts of the ESFs along in-plane axes was investigated and yielded a

modified MTF The idea of separating the effective resolution and artifacts from the

measured ESF are expected to facilitate the interpretation of MTF measurements in

breast tomosynthesis Similar methods may be applied to characterize the spatial

resolution of other 3D imaging modalities

vii

Contents

Abstract iv

List of Tables x

List of Figures xi

Acknowledgements xiii

I Evaluation of 2D Digital Image Receptors 1

I1 Introduction 1

I2 Materials and Methods 3

I2i Detectors 3

I2ii Beam Characterization 3

I2iia X-ray Techniques 3

I2iib Data Linearization 4

I2iic Spectral Simulation 5

I2iii DQE Measurements 6

I2iiia Modulation Transfer Function 6

I2iiib Noise Power Spectrum 7

I2iiic DQE Calculation 8

I3 Results 9

I3i Data Linearization 9

I3ii Spectral Simulation 9

I3iii Modulation Transfer Function 12

viii

I3iv Noise Power Spectrum 12

I3v Detective Quantum Efficiency 19

I4 Discussion 20

I4i Comparisons of Detectors 20

I4ii Comparisons of Filtrations 21

I4iii Implications of Wireless DR 26

I5 Conclusions 26

II Directional MTF for Breast Tomosynthesis 28

II1 Introduction 28

II2 Materials and Methods 29

II2i Image Simulation 29

II2ii Uncorrected MTF 30

II2iii Theoretical Directional MTF 32

II2iv Modified MTF 33

II2v Preliminary Experimental Validation 34

II3 Results 35

II3i Reconstruction 35

II3ii Theoretical MTF 37

II3iii Uncorrected MTF 38

II3iv Comparison of Theoretical and Simulated MTFs 41

II3v Modified MTF for x and y 42

II3v Preliminary Experimental Validation 44

ix

II4 Discussion 46

II4i Evaluation of Cone-based Method 46

II4ii Separation of Artifact and Resolution Information 48

II5 Conclusions 49

References 50

x

List of Tables

Table 1 Physical Characteristics of Digital Image Receptors 4

Table 2 Beam Qualities and Required Filtrations 5

Table 3 Spectral Simulation Results 11

Table 4 Experimental MTF frequency locations for 1 mR exposure 22

Table 5 Estimated DQE values for 1 mR exposure by frequency bins 22

xi

List of Figures

Figure 1 MTF images for DRX-1C detector with radio-opaque edge test device with

arrows indicating the horizontal (left) and vertical (right) directions 7

Figure 2 NNPS image for DRX-1C detector indicating the top left ROI that served as the

reference for normalizing other ROIs in the image The ROI array was formed along the

directions indicated by the arrows The heel effect visible along the vertical axis of the

detector is an example of small variation in signal across the image 8

Figure 3 Original (left) and linearized (right) system responses for Pixium 4600 The

linearized system responses were measured from actual images The offsets are small

with respect to the slope sufficient enough for zero-offset conditions 10

Figure 4 Spectral simulations for RQA5 (top) and RQA9 (bottom) conditions Note the

similarities of spectral shapes of the normalized spectra (right) Also note the significant

differences in fluence between filtrations in the simulated spectra (left) 11

Figure 5 MTF results by detector (columns) and beam quality (rows) 13

Figure 6 Plots of MTF for RQA5 (top) and RQA9 (bottom) showing the relationships

between detectors (blue red and green) and by filtration (solid and dashed) 14

Figure 7 NNPS results by detector (columns) and beam quality (rows) 15

Figure 8 Plots of NNPS for RQA5 (top) and RQA9 (bottom) at 1 mR exposure showing

the relationships between detectors (blue red and green) and by filtration (solid and

dashed) 16

Figure 9 DQE results by detector (columns) and beam quality (rows) 17

Figure 10 Plots of DQE for RQA5 (top) and RQA9 (bottom) at 1 mR exposure showing

the relationships between detectors (blue red and green) and by filtration (solid and

dashed) 18

Figure 11 DRX1-C NNPS images at 1 mR for RQA5 with IEC filtration (left) and

alternative filtration (right) Images are equally windowed at 45 and leveled at 980 24

Figure 12 Depiction of the virtual image system 30

xii

Figure 13 Example of 30-degree cone prescribed along z axis of the sphere 32

Figure 14 Photograph of the imaging system with the acrylic sphere phantom

embedded in oil 34

Figure 15 View of the central slice of the breast phantom reconstruction before (top) and

after (bottom) background subtraction The z axis is through the page 36

Figure 16 3D rendering of the ROI volume (left) and cross-sectional views of the most

centrally located sphere with centroid indicated with red circle (right) 37

Figure 17 Theoretical 3D MTF results along the three major planes (top) and along x y

and z directions (bottom) Also note that the angular spread seen in the fx-fz plane is

equal to the angular range of 44deg for the acquisition 38

Figure 18 Uncorrected ESF (top) LSF (middle) and MTF (bottom) for x y and z

directions 40

Figure 19 Comparisons of the directional MTFs as calculated by the sphere method

(dashed line) by theoretical line profiles (light-weight line) by theoretical cone regions

(heavy-weight line) 41

Figure 20 Modified ESF (top) LSF (middle) and MTF (bottom) for x and y directions 43

Figure 21 Cross sectional views of the experimental sphere image with centroid

indicated with red circle 44

Figure 22 ESF (top) LSF (middle) and MTF (bottom) of real image for x y and z

directions 45

xiii

Acknowledgements

I would like to thank Ian Yorkston Mark Purdum and Van Huston of

Carestream Health Inc (Rochester NY) for their help with digital detector

measurements I would also like to thank Olav Christianson Samuel Richard Brian

Harrawood and Max Amurao for their assistance with collecting data and analyzing

results Special thanks go to my committee members for their helpful insights and

suggestions for this thesis Last but not least I want to express deep appreciation for the

support and mentorship provided by my advisor Dr Ehsan Samei

1

I Evaluation of 2D Digital Image Receptors

I1 Introduction

In the past decade many areas of radiological practice have seen a conversion

from screen films to the storage phosphor cassettes of computed radiography (CR) to the

active-matrix flat-panel detectors of digital radiography (DR) Both CR and DR are

digital systems that offer many potential benefits including but not limited to better

image quality wider dynamic range quicker readout lower radiation dose and higher

throughput [1-3] Even with advances in DR technologies such as improved detective

quantum efficiency (DQE) the primary radiographic system of today continues to be CR

A major obstacle to completely accepting DR is the high capital cost of acquiring an

entire system per examination room while also providing capability for portable

applications Recently manufacturers like Carestream Health Fuji and Toshiba have

introduced wireless digital image receptors that can serve as replacements for CR

cassettes As these are new technologies a further investigation to characterize these

detectors is warranted

In the case of radiographic receptors DQE has historically been the metric of

choice [4] because it indicates the ability of the image receptor to convert incident x-ray

photons into useable signal ndash essentially a measure of signal-to-noise ratio (SNR)

efficiency and overall system performance [23] DQE is observed across a range of

spatial frequencies for evaluating how the detector depicts small and large objects [3]

2

DQE metrics have been used in numerous studies to characterize CR phosphor-screens

as well as indirect and direct digital detectors [4-11] The importance of this highly

quantitative metric may be implied by the introduction of a DQE measurement standard

by the International Electrotechnical Commission (IEC) [12]

The standard measurement methodology of the International Electrotechnical

Commission (IEC) pertains to the image quality of 2D digital radiographic detectors

While the IEC formalism is well-developed some of the components that it requires are

not necessarily the most optimal for characterizing DQE This has been explored in

previous studies in terms of filtration material purity beam limitations and region of

interest (ROI) configuration [1314] To reduce the variability in the radiographic output

across various x-ray tubes due to inherent filtration differences the IEC formalism

prescribes specific additional aluminum filtration to attain radiation beam qualities

based on target half value layers (HVL) Achieving and verifying the desired HVL

however requires applying a substantial amount of aluminum at the exit window of the

x-ray tube which is often directed toward the ground This can be a logistical

inconvenience and can increase the risk of damage to the image receptor and

measurement equipment Similar beam qualities on the other hand may be attained

more conveniently using a thinner lighter filtration combination utilizing a higher Z

number material Care is warranted however as a previous study [6] had indicated that

the choice of filtration material could impact the DQE

3

The purpose of this study was two-fold First we aimed to evaluate and compare

two wireless image receptors with a conventional flat-panel detector on the basis of DQE

performance Second we compared DQE results using the IEC-prescribed filtration with

an alternative filtration For the latter an optimum filtration composition was

determined and compared with the IEC filtration on the basis of DQE

I2 Materials and Methods

I2i Detectors

The physical characteristics of the three digital image receptors evaluated in this

study are listed in Table 1 The Pixium 4600 was a conventional digital flat-panel The

DRX-1C and DRX-1 were both wireless digital cassettes that were tethered for the

purposes of this study All detectors were FDA approved and available commercially

Each detector was calibrated according to its manufacturer specifications to correct for

gain offset and bad pixels They were all dedicated for non-clinical laboratory research

purposes and hence could be operated under service settings that permitted acquisition

of raw (ie for processing) images

I2ii Beam Characterization

I2iia X-ray Techniques

All measurements for this study were taken with a well-characterized standard

radiographic system (Super80CP Philips Healthcare Andover MA) The x-ray tube had

an inherent filtration of 27 mm Al Free in-air exposures were measured using

4

Table 1 Physical Characteristics of Digital Image Receptors

Manufacturer Detector

Detector

type

Detector

material

Pixel pitch

(size) Array size

Imaging

area

Trixell

(Moirans France)

Pixium

4600 Indirect

CsITl

(CsI) 0143 mm

3121times3121

4 subpanels 45times45 cm2

Carestream Health Inc

(Rochester NY)

DRX-1C

(wireless) Indirect

CsITl

(CsI) 0139 mm

2560times3072

single panel 35times43 cm2

Carestream Health Inc

(Rochester NY)

DRX-1

(wireless) Indirect

G2O2STb

(GOS) 0139 mm

2560times3072

single panel 35times43 cm2

calibrated radiation meters (Mult-O-Meter Type 407 Unfors Instruments AB Billdal

Sweden) at 183 cm source-to-chamber-distance (SCD) The SCD also corresponded to

same plane as the image receptor surface The x-ray output was made to conform to IEC

beam quality definitions [1215] on the basis of half value layer (HVL) and peak

kilovoltage setting using an aluminum filtration (type-1100 99 purity) and an

alternative filtration consisting of copper (UNS C11000 999 purity) and aluminum

(type-1100 99 purity) The IEC radiation quality numbers (RQA) used in this study are

summarized in Table 2 HVLs were determined by iteratively adding successive

thicknesses of aluminum until reaching reduced exposure levels within a tolerance of

0485-0515 [12] As for the alternative filtration the aluminum was placed downstream

of the copper filter to attenuate characteristic radiation peaks from copper at

approximately 9 keV

I2iib Data Linearization

The system response function was determined for each detector and filtration

combination by acquiring flat-field images at increasing photon fluence until just before

5

Table 2 Beam Qualities and Required Filtrations

IEC Radiation

Quality Number

Peak

kilovoltage

Required

HVL

Required IEC

Filtration

Actual IEC

Filtration

Alternative

Filtration

RQA5 70 kVp 71 mm Al 21 mm Al 21 mm Al 05 mm Cu +

10 mm Al

RQA9 120 kVp 115 mm Al 42 mm Al 40 mm Al 104 mm Cu +

10 mm Al

For reasons of convenience these will be referred to as RQA5A RQA5C RQA9A and RQA9C

saturation levels To avoid the influence of detector backscatter on exposure

measurements a relationship for each filtration was first determined for two radiation

meters A target meter was placed at the central axis and a reference meter was placed at

the edge of the light field (large enough to cover the detectors) The reference meter

served as a surrogate for the target meter to avoid direct exposure measurements in the

plane of the image receptor Exposure relationships were determined before each

measurement set (ie detector and filtration combination) to account for changes in

temperature pressure and humidity The system response function was calculated by

using a regression of ADU (pixel value) versus exposure Images acquired for each

series were then converted to achieve a linear response with zero offset and scaled to

achieve high quantization (adequate dynamic range) Linearization of the detector

responses ensured that zero exposure corresponded to zero pixel value

I2iic Spectral Simulation

The effects of additional filtration on x-ray output spectra were observed with

spectral simulation software (XSPECT V40 Henry Ford Hospital Detroit MI) To more

6

adequately describe the performance of a typical X-ray generator inherent filtration of 3

mm oil 148 mm Pyrex glass and 2 mm aluminum was input into the simulation in

addition to the filters of interest The ideal signal to noise ratio squared or incident

photon fluence per exposure (q) was estimated for each filtration by integrating the

energy-dependent photon counts per unit exposure over all energy bins

I2iii DQE Measurements

The assessment of the linearized images followed the formalism described by

IEC 62220-1 for measuring the DQE [12] For this study the normal exposure level XN

was set at 1 mR to the detector surface as measured at the central axis perpendicular to

the anode-cathode axis

I2iiia Modulation Transfer Function

Spatial resolution was characterized by evaluating the presampled modulation

transfer function (MTF) along directions parallel (vertical) and perpendicular

(horizontal) to the anode-cathode axis using the angled-edge method [6-1013] A radio-

opaque edge test device [7] was placed in the center of the field at a pitch of

approximately 301 (about 2deg) to the axis perpendicular to that being measured as

shown in Figure 1 External lead apertures were not used [6] instead the internal

collimation from the radiographic unit was used to collimate the beam to the detector

area Raw images were acquired of the edge with the normal exposure level XN of 1 mR

at the detector face The procedure of calculating the MTF followed previously described

7

methods [6-1013] The edge spread function (ESF) was determined along lines crossing

the edge of the angled test device The derivative of the ESF was calculated to form the

line spread function (LSF) to which a Hanning filter was applied The MTF was then

calculated as the fast Fourier transform (FFT) of the LSF and normalized at the zero-

frequency axis To conform to IEC guidelines the MTF was resampled into frequency

steps of 005 cyclesmm [12]

Figure 1 MTF images for DRX-1C detector with radio-opaque edge test device with

arrows indicating the horizontal (left) and vertical (right) directions

I2iiib Noise Power Spectrum

Noise amplitude and texture were characterized by determining the normalized

noise power spectrum (NNPS) which was evaluated with flat field exposures at

approximate exposure levels of XN2 XN and 2XN (05 10 and 20 mR) to the image

receptor surface Analysis of the flat-field images followed previously defined methods

[41415] using over 4 million independent pixels with regions of interest (ROIs) of size

8

128x128 The NNPS images were detrended using a quadratic (second order)

background subtraction Small variations in exposure across ROIs were corrected by

normalizing pixel values of each ROI to the mean value in the top left ROI as shown in

Figure 2 The NNPS was then calculated with the 2D FFT including the zero-frequency

axes corresponding to the horizontal and vertical directions The results were then

resampled using 005 frequency bins according to IEC guidelines [12]

Figure 2 NNPS image for DRX-1C detector indicating the top left ROI that served as

the reference for normalizing other ROIs in the image The ROI array was formed

along the directions indicated by the arrows The heel effect visible along the vertical

axis of the detector is an example of small variation in signal across the image

I2iiic DQE Calculation

The DQE was calculated using the following relationship [615]

9

where the frequency-dependent MTF and NNPS were determined as described in

previous sections X was the exposure value in mR corresponding to the NNPS image

and q was the ideal signal to noise ratio squared in units of photonsmiddotmm-2middotmR-1 as

estimated from the spectral simulations

I3 Results

I3i Data Linearization

The detectors in this study provided raw ADU (or pixel) values in a linear scale

The data were converted using the following system conversion function

where Q(ij) is the raw image data m and b are slope and intercept parameters obtained

from linear regression of the system response function and I(ij) is the linearized scaled

data The factor of 1000 was found to scale I(ij) such that the maximum value was a

large 16-bit number Figure 3 shows the original and linearized system responses for the

Pixium 4600 Note that the y-intercepts of the regressions for the linearized responses

are negligible (lt 01) with respect to the slopes a sufficient condition for zero offset

considerations

I3ii Spectral Simulation

The spectral simulations of the IEC filtrations and alternative filtrations indicate

many similarities in their effective energies HVLs and overall shapes of normalized

spectra Results are summarized in Table 3

10

Pixium 4600 Original System

Response

Pixium 4600 Linearized System

Response R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 3 Original (left) and linearized (right) system responses for Pixium 4600 The

linearized system responses were measured from actual images The offsets are small

with respect to the slope sufficient enough for zero-offset conditions

y = 13971x - 13236

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x - 00106Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 13576x + 28292

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

7000

0000 1000 2000 3000 4000 5000

AD

U

Exposure (mR)

y = 99997x - 00067Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0000 1000 2000 3000 4000 5000

AD

U

Exposure (mR)

y = 13644x + 16167Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x + 00044

Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 13845x + 13541

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x - 00177

Rsup2= 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

11

Table 3 Spectral Simulation Results

Beam Quality Filtration

Mean Energy

(kV)

Photon Fluence

(mRmm2)

RQA5A 21 mm Al 5243 259543

RQA5C 05 mm Cu + 10 mm Al 5214 259554

diff 055 0004

RQA9A 40 mm Al 7619 273281

RQA9C 104 mm Cu + 10 mm Al 7579 273964

diff 052 025

Figure 4 Spectral simulations for RQA5 (top) and RQA9 (bottom) conditions Note

the similarities of spectral shapes of the normalized spectra (right) Also note the

significant differences in fluence between filtrations in the simulated spectra (left)

00E+00

50E+04

10E+05

15E+05

20E+05

25E+05

30E+05

35E+05

40E+05

45E+05

0 20 40 60 80

ph

oto

ns

mA

s-1

cm

-2

keV

RQA5 Spectra Comparison

21 mm Al

05 mm Cu + 10 mm Al

00

02

04

06

08

10

12

0 20 40 60 80

keV

RQA5 Normalized Spectra Comparison

21 mm Al

05 mm Cu +

10 mm Al

00E+00

50E+05

10E+06

15E+06

20E+06

25E+06

30E+06

35E+06

40E+06

45E+06

50E+06

0 50 100 150

ph

oto

ns

mA

s-1

cm

-2

keV

RQA9 Spectra Comparison

40 mm Al

104 mm Cu +

10 mm Al

00

02

04

06

08

10

12

0 50 100 150

keV

RQA9 Normalized Spectra Comparison

40 mm Al104 mm Cu + 10 mm Al

12

I3iii Modulation Transfer Function

The limiting spatial resolutions of the systems were indicated by the cutoff

frequencies which were approximately 35 cyclesmm for all three detectors The spatial

resolutions also demonstrated a good degree of isotropy as confirmed by the close

alignment of MTF curves between vertical and horizontal directions differentiated in

Figure 5 by dashed and solid lines respectively The MTF curves for the Pixium 4600

and DRX-1C were nearly equal to each other whereas the DRX-1 MTF curve showed a

more rapid decrease at high frequencies as shown in Figure 6 This difference may be

due to the differences in the inherent optical properties of the scintillating materials

where finer image details are provided by structured CsI more than by granulated GOS

There were no significant differences in MTF curves across beam qualities and filtrations

as shown by the curve comparisons in Figure 6 although the alternative filtration

produced slightly higher MTF curves as seen in Figure 4 Table 4 lists the experimental

specific spatial frequencies for varying levels of MTF

I3iv Noise Power Spectrum

The noise characteristics are indicated by the NNPS curves shown in Figure 7

The noise was similar for both horizontal and vertical directions As exposure increased

the NNPS decreased consistent with the characteristics of Poisson noise describing the

relationship between signal and noise in the presence of increased photon fluence At

13

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 5 MTF results by detector (columns) and beam quality (rows)

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

horizontal

vertical

14

Figure 6 Plots of MTF for RQA5 (top) and RQA9 (bottom) showing the relationships

between detectors (blue red and green) and by filtration (solid and dashed)

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm-1)

MTF

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm-1)

MTF

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

15

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 7 NNPS results by detector (columns) and beam quality (rows)

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

05 mR - horizontal

05 mR - vertical

10 mR - horizontal

10 mR - vertical

20 mR - horizontal

20 mR - vertical

16

Figure 8 Plots of NNPS for RQA5 (top) and RQA9 (bottom) at 1 mR exposure

showing the relationships between detectors (blue red and green) and by filtration

(solid and dashed)

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm-1)

NNPS (1 mR)

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm-1)

NNPS (1 mR)

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

17

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 9 DQE results by detector (columns) and beam quality (rows)

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

05 mR - horizontal

05 mR - vertical

10 mR - horizontal

10 mR - vertical

20 mR - horizontal

20 mR - vertical

18

Figure 10 Plots of DQE for RQA5 (top) and RQA9 (bottom) at 1 mR exposure showing

the relationships between detectors (blue red and green) and by filtration (solid and

dashed)

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm-1)

DQE (1 mR)

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm-1)

DQE

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

19

higher frequencies the NNPS curves of the Pixium 4600 and DRX-1 diverge slightly for

the different directions illustrating increased noise in the readout direction (vertical)

Differences in the noise characteristics were more apparent among detectors as

shown for 1 mR in Figure 8 The NNPS curve for the DRX-1 was higher in magnitude

across the entire frequency range than either the Pixium 4600 or DRX-1C which both

seemed to demonstrate reasonably similar NNPS curves The higher magnitude noise of

the DRX-1 indicates higher relative noise content overall Closer inspection of the NNPS

curves of the Pixium 4600 and DRX-1C detectors in Figure 7 revealed differences in the

spacing between the three exposure levels The gaps between the Pixium 4600 NNPS

curves do not correspond to the factor of two differences between each exposure level

especially at low- to mid- spatial frequencies suggesting a higher level of fixed pattern

noise additional noise with increasing exposure levels due to ineffective gain map

corrections Between filtration schemes the differences in NNPS curves for a given beam

quality were not substantial as shown in Figure 7

I3v Detective Quantum Efficiency

The DQE results are shown in Figure 9 DQE curves across exposure levels were

almost collinear except for Pixium 4600 and in general could be inferred from the

NNPS results Additionally the DQE curves demonstrated a relatively linear response

with spatial frequencies as expected for flat-panel detectors [9] Differences in DQE

among detectors were consistent for the most part with the type of scintillating material

20

As depicted for 1 mR exposure in Figure 10 differences between Pixium 4600 and DRX-

1C DQE curves correspond to the differences in their NNPS curves DRX-1 DQE curves

were consistently lower than either the Pixium 4600 or DRX-1C curves The DQE curves

for the alternative filtration were consistently higher than those for the IEC filtration

and the most noticeable differences were near the zero-frequency axis These effects can

be both attributed to ineffective gain map correction DQE values for 1 mR exposure are

listed in Table 5

I4 Discussion

I4i Comparisons of Detectors

The limiting spatial resolutions of all three detectors were almost exactly the

same considering that their pixel areas were similar in size The decrease in high-

frequency MTF of the DRX-1 compared to the other detectors is probably a result of

increased optical blurring due to the differences in the powdered structure of GOS

versus the needle-like structure of CsI [2] The fact that the DRX-1C and Pixium 4600

have comparable MTFs suggests similar scintillator thicknesses assuming that the

materials were processed alike

The noise of the three detectors demonstrated similar trends with each other The

higher NNPS curves of the DRX-1 detector are probably due also to the scintillating

material and its operation in converting photons into signal The conversion process is

less efficient because of the less favorable stopping power of the GOS compared to CsI

21

especially with higher energy beams The noise of the Pixium 4600 and DRX-1C were

similar except for the spacing between exposures The DRX-1C NNPS curve spacing is

consistent with a factor of two difference in exposure levels but the Pixium 4600 has a

smaller spacing The 05 mR NNPS curve of the Pixium 4600 is closer to that of the 05

mR NNPS curve of the DRX-1C This demonstrates that at higher exposures the Pixium

4600 produces a larger amount of additional noise beyond that explained by simple

stochastic effects It suggests bad performance in the gain map corrections

The DQE results indicate SNR properties of each detector The Pixium 4600 and

DRX-1C are comparable for the most part with the DRX-1C performing slightly better

The DRX-1 as predicted from MTF and NNPS results has a DQE much lower than

either of the previous two This is a reflection of the detection properties as provided by

its scintillator material The DQE of the DRX-1 however is comparable to CR image

receptors [2] The mid-frequency dips in the DQE for Pixium 4600 may be due to the

optical properties of the CsI phosphor layer which can affect the MTF in this manner

Because the DQE is calculated by squaring the MTF this effect at the mid-range

frequencies becomes more apparent The dips may also be further evidence of bad gain

map corrections

I4ii Comparisons of Filtrations

The alternative filtration closely matches for the most part the IEC-based

filtration for MTF NNPS and DQEs at RQA5 but not at RQA9 The filters do not have

22

Table 4 Experimental MTF frequency locations for 1 mR exposure

Detector Filtration

50 MTF

(mm-1)

40 MTF

(mm-1)

30 MTF

(mm-1)

20 MTF

(mm-1)

10 MTF

(mm-1)

Pixium

4600

RQA5A 115 145 185 245 330

RQA5C 125 155 195 250 345

RQA9A 110 175 175 235 330

RQA9C 125 155 195 255 345

DRX-1C

RQA5A 120 150 185 245 350

RQA5C 125 155 195 255 355

RQA9A 120 150 190 250 355

RQA9C 130 160 210 265 360

DRX-1

RQA5A 110 135 160 205 280

RQA5C 110 135 170 210 285

RQA9A 105 125 155 195 270

RQA9C 110 135 165 210 285

Table 5 Estimated DQE values for 1 mR exposure by frequency bins

Detector Filtration DQE(00 mm-1) DQE(10 mm-1) DQE(20 mm-1) DQE(30 mm-1)

Pixium

4600

RQA5A 62 42 32 21

RQA5C 63 45 36 25

RQA9A 41 27 30 13

RQA9C 43 33 27 19

DRX-1C

RQA5A 72 52 35 21

RQA5C 76 55 41 24

RQA9A 49 33 23 15

RQA9C 51 40 31 20

DRX-1

RQA5A 38 24 12 4

RQA5C 38 25 14 5

RQA9A 28 18 9 4

RQA9C 28 19 12 5

DQE values at the zero-frequency axis were estimated by the intercept of a linear fit of low-frequency data

but excluding most proximal to the axis due to large fluctuations Other estimated values are grouped into

frequency bins due to the noisiness of the data

23

considerable differences in the spatial resolutions of the detectors as expected The noise

responses for each filtration were also similar except at the lower frequencies of the

NNPS especially near the zero-frequency axis There observing the NNPS responses at

RQA5 for Pixium 4600 and DRX-1C in Figure 8 the NNPS for the IEC-based filtration

(solid lines) tend to drop faster than the NNPS for the alternative filtration This

subsequently appears as a drop in DQE near the zero-frequency axis shown for those

detectors in Figure 10 Overall as indicated in Table 5 the DQEs of the two filtrations

while similar in trend indicate that the alternative filtration increases the DQE by a

small amount of 3-5 Part of this may be explained by the slightly higher beam

energy which may be more optimal for the energy response of the detectors or may

weigh the pixel responses slightly considering that they are energy-integrating types

The most probable explanation is the gain map correction for the alternative filtration

where fixed pattern noise is more sufficiently reduced

A previous study [6] had discussed the choice of filter material in the analysis of

DQE when achieving the beam conditions defined by IEC It found that visible

nonuniformities were present with the higher purity aluminum filter (type-11999 alloy)

The low frequency mottle in the flat-field images for NPS measurements were also

attributed to structured noise from the grain size in the IEC-based filter with an

attenuating thickness that would reveal nonuniformities The mottle in the current study

was only observable under very narrow windowing as shown in Figure 11 Such low

24

frequency artifacts which are not readily noticeable may also be caused by shading

artifacts inverse square law or even the heel effect A possible method to correct for this

is a subtraction method by taking the average of the flat-field images for an exposure

level and then subtracting that from each of them This would remove nonuniformities

that were not corrected using a suboptimal gain map calibration

Figure 11 DRX1-C NNPS images at 1 mR for RQA5 with IEC filtration (left) and

alternative filtration (right) Images are equally windowed at 45 and leveled at 980

One convenient aspect of the copper and aluminum filtration is that it requires

much less tube current to achieve the same amount of exposure at the detector than the

much thicker aluminum filtration As shown in the non-normalized spectra in Figure 2

the exiting photon fluence exiting the copper and aluminum filtration is substantially

higher than that of the IEC-specified filtration This is due to the smaller total filtration

25

attenuation For extensive DQE analysis multiple sets of exposures may be acquired

before tube overheating becomes a concern

One limitation to the comparison of the two filtrations is that calibration

procedures specified copper and aluminum filtration at 80 kVp (for all detectors 05 mm

Cu and 10 mm Al) This may have influenced the results in favor of the alternative

filtration A further investigation involving the calibration procedures and performing

DQE measurements is encouraged Another factor may be influenced by the fact that the

tests were performed at 70 kVp and 120 kVp different from the recommended

calibration tube potential Clearly there would be differences in the linear attenuation

coefficients of the filters and different energy responses of the detectors themselves This

must be considered when interpreting DQE results The current results support a

previous study decades ago that described filtration of different material types in terms

of an aluminum equivalent [16] The results show that the two filtration schemes are

essentially equivalent when considering beam qualities and spatial resolutions The

NNPS and DQE results can be seen as close enough where their small differences are

insignificant when performing quality assurance tests in a clinical setting Overall our

results indicate that the alternative filtration with copper and aluminum may be more

convenient to use than the current IEC standard filtration

26

I4iii Implications of Wireless DR

This study has shown that wireless image receptors can have the same DQE

performance if not better than conventional flat-panel detectors They operate on the

same basic physical principles the new features offered by the DRX-1C and DRX-1 are

wireless communication with the workstation and electronics packaging technology

The latter feature may pose limitations for these units in terms of possible degradation

in the detectors in routine clinical conditions A consideration for future work would be

to longitudinally track DQE performance of the wireless detectors over time while being

utilized in a clinical environment In the end one must consider risks versus benefits of

choosing portable DR technology over CR one of which includes the cost and fragility

of DR detectors

The DQE performance of one wireless system is just as good as or better than

conventional systems as seen by the DRX-1C performance compared to the Pixium

4600 Wireless systems can also reduce the need for CR readers especially in portable

applications in other regions of the world (eg military hospitals developing countries)

However while DQE performance indicates the physical performance of the detector

system it is still unknown how it relates to observer performance

I5 Conclusions

Two wireless image receptors DRX-1C and DRX-1 were evaluated and

compared with the conventional DR flat-panel Pixium 4600 in terms of DQE

27

performance along with MTF and NNPS performances The detectors have similar

resolution properties although the DRX-1 is inferior at higher spatial frequencies The

NNPS and DQE results both indicate that the DRX-1C is superior to the DRX-1 and

comparable if not better to the Pixium 4600

The results from the filtration comparison indicate no substantial differences

between the IEC-based filtration and the copper-based alternative filtration Only slight

differences were found in the low frequency components of the NNPS and the DQE due

to the inherent nonuniformities of the IEC specified filtration Given the similarity of the

results and low attenuation advantage of the copper and aluminum filter its use is

encouraged

28

II Directional MTF for Breast Tomosynthesis

II1 Introduction

Breast tomosynthesis is an emerging 3D imaging modality that has potential use

for screening and diagnosis of breast cancer Breast tomosynthesis along with other 3D

techniques is preferable to planar imaging methods (eg mammography) because they

reduce anatomical noise by removing overlying structures above and below the plane of

an image slice [17-20] Recent advances in detectors and computer technology have

made digital tomosynthesis feasible

An image quality metric of particular importance in breast tomosynthesis is

spatial resolution Resolution is important to know in order to assess small-detail

structures such as microcalcifications A descriptive metric for characterizing spatial

resolution in the Fourier (or frequency) domain is the modulation transfer function

(MTF) Affected by reconstruction filters [21] the limited angular projections involved in

breast tomosynthesis results in highly anisotropic (or nonuniform) resolution Many

studies have looked only at characterizing the in-plane spatial resolution (ie in an

individual slice) with an elevated angled edge phantom [2223] A few studies have

looked at characterizing a more comprehensive 3D spatial resolution by using a

phantom with angled wires or tubes [24-26] However such studies require precise

mechanical alignment of the phantoms Several studies have explored a method using a

29

sphere phantom for the directional 3D MTF evaluation for microtomography [27] and

multi-slice CT [2829] This method has not yet been extended to breast tomosynthesis

This chapter focuses on breast tomosynthesis because it is highly anisotropic in

spatial resolution and like its predecessor mammography requires high spatial

resolution Additionally breast tomosynthesis acquisitions and reconstructions produce

several types of artifacts The use of a cone-based method using a sphere phantom [28] is

explored to characterize the directional 3D spatial resolution of simulated images from

breast tomosynthesis A technique for removing out-of-plane artifacts of the ESFs for the

in-plane axes is investigated to yield a modified MTF in a method that separates artifact

information from resolution information

II2 Materials and Methods

II2i Image Simulation

Breast tomosynthesis images were simulated by using a virtual imaging system

depicted in Figure 12 A volumetric breast phantom was voxelized as a rectangular mass

of uniform breast equivalent tissue of 4 cm thickness embedded with fifteen evenly

spaced plastic sphere inserts of 12 mm diameter The spheres were placed in a grid

formation within the central plane of the phantom The x-ray fluence was modeled from

a 28 kVp beam incident upon an indirect flat-panel detector with 200 micro m pixel size

Twenty-three projections within an angular range of 44deg were simulated using cascaded

systems analysis to generate characteristic 2D noise and spatial blurring [29] Each

30

projection was simulated to have an exposure of 174 mR with a fluence of 79 times 105

photonsmm-2 A standard filtered backprojection technique based on the Feldkamp

reconstruction algorithm [29] was used to reconstruct the projections and produce a

volumetric dataset with an isotropic voxel size of 200 micro m

Figure 12 Depiction of the virtual image system

II2ii Uncorrected MTF

To enable comparison of multiple spheres the reconstructed volume was

initially homogenized by performing a background subtraction based on a portion of the

volume devoid of spheres The voxel values were rescaled between one and zero to

eliminate negative values

31

The volumetric data were segmented to extract individual regions of interest

(ROIs) each containing a single sphere The ROIs extended along the full range of the z-

axis A thresholded ROI was generated by determining the exterior and interior voxels

relative to the sphere in the ROI The threshold value was set at 45 of the maximum

voxel value prior to thresholding The exterior and interior voxel values were then set to

values of 0 and 1 respectively Using the thresholded volume the center of mass was

calculated to determine the centroid The voxel values from the original ROI were

subsequently tabulated with the associated distances azimuthal angles and polar

angles relative to the centroid

Conical regions were prescribed along the positive and negative directions along

the three major axes extending from the centroid of the sphere as depicted in Figure 13

The axes about which the extent of the cone angle was delineated were defined with

the azimuthal and polar angles

Voxels with centers within the angular range of the cone were considered for

generating the edge spread function (ESF) To improve regularity of the distance

sampling interval the ESF values were rebinned to discrete distances corresponding to a

fraction of the voxel size Only voxels with distances ranging from the voxel size (ie

200 micro m) to the maximum distance were considered The ESFs from multiple spheres

were averaged together for each of the three major axes to produce an averaged ESF

which was further smoothed utilizing a Gaussian filter

32

Figure 13 Example of 30-degree cone prescribed along z axis of the sphere

The resulting ESF was then differentiated using the central difference method to

produce the line spread function (LSF) A Hanning filter with the same length as the LSF

was applied to zero out the tails of the LSF The presampled MTF was subsequently

computed as the amplitude of the Fourier transform of the LSF The MTF was

normalized with respect to the maximum value occurring within the range of the cutoff

frequency Binning size and conical range for the ESF were considered for maximizing

accuracy and minimizing noise of the MTF verified by comparison against the

theoretical MTF as determined in the previous section

II2iii Theoretical Directional MTF

The theoretical 3D MTF was calculated using a priori knowledge of the transfer

function of the virtual imaging system described in the previous section A phantom

was created with a set of point objects in a uniform and noise-free background with the

objects spanning across the volume of the breast [29] Twenty-one realizations were

33

generated from the reconstructed images of the point objects to yield a set of 3D point

spread functions (PSFs) The 3D fast Fourier transform (FFT) was performed for each 3D

PSF and averaged to give an ldquoexpectationrdquo 3D MTF [29] The theoretical directional

MTFs in the three major spatial axes were determined by line profiles along each of the

corresponding spatial frequency axes in the 3D MTF An additional theoretical MTF for

each direction was determined by using the application of conical regions along the axes

in frequency-space to take into account the contributions of MTF information from other

planes

II2iv Modified MTF

The tomosynthesis reconstruction is known to have edge enhancements which

affect the overall MTF by shifting the peaks of the MTF toward the higher frequencies

[23] The presence of this artifact complicates the interpretation of the actual spatial

resolution of the images Several steps were performed to remove the artifact

contribution to the resolution information particularly for the in-plane x and y

directions with the assumption that resolution information was contained immediately

near the edge

For the x-direction averaged ESF only values that were detected to be inside the

edge of the sphere were considered Those values were previously determined via

thresholding for calculating the centroid The ESF information corresponding to these

values was inversed and flipped about the detected edge to produce a symmetric

34

modified ESF The modified MTF was subsequently calculated from this modified ESF

as described in the previous section

For the y-direction averaged ESF an upward trend was found in the initial part

of the ESF This section was detrended with a polynomial fit and subtracted to produce a

flatter curve in that region The resulting detrended ESF was used to calculate the y axis

modified MTF

Figure 14 Photograph of the imaging system with the acrylic sphere phantom

embedded in oil

II2v Preliminary Experimental Validation

A clinical breast tomosynthesis system (Mammomat Inspiration Siemens AG

Munich Germany) was used to perform a preliminary evaluation of the cone-based

MTF technique The phantom for the experiment consisted of a single acrylic ball of 075

in diameter (SmallParts Seattle WA) suspended by a 0029 in diameter plastic filament

35

(Omniflex Zebco Tulsa OK) in an acrylic frame filled up to 4 in with vegetable oil

(Target Brands Inc Minneapolis MN) The system and phantom are shown in Figure

14 Twenty-five projections with an angular range of 44deg were acquired and subsequently

reconstructed to produce a volume with a voxel size of 01times01times10 mm3 The voxels were

reformatted to have an isotropic size of 01 mm The uncorrected ESF LSF and MTF

were calculated as described in the previous section

II3 Results

II3i Reconstruction

The reconstructed volume is shown in Figure 15 Notice the edge enhancement

along the x-direction as indicated by the sharp shadowing artifacts on either side of the

spheres The background was effectively homogenized using the background

subtraction technique This also took account of the curved edges of the breast phantom

With the close spacing of the spheres in the phantom the shadows along the x direction

for the fifteen spheres overlap with each other As the nine centrally located spheres

experience this effect the same way they were used for determining the ESF

A 3D rendering of the ROI containing a sphere shown in Figure 16 indicates the

anisotropic resolution of the reconstruction Note that the sphere is not accurately

reconstructed and has an oblong shape especially along the z axis Cross sectional views

of the ROI also in Figure 16 clearly demonstrate the edge enhancement causing a

shadow artifact in the x direction caused by the incomplete angular sampling of

36

tomosynthesis The sampling also introduces the triangular reconstruction of the sphere

as seen in the x-z plane Note the gradual edge drop-off in the z direction much beyond

the sphere radius

Figure 15 View of the central slice of the breast phantom reconstruction before (top)

and after (bottom) background subtraction The z axis is through the page

37

Figure 16 3D rendering of the ROI volume (left) and cross-sectional views of the most

centrally located sphere with centroid indicated with red circle (right)

II3ii Theoretical MTF

The theoretical MTFs for x y and z directions as determined from the line

profiles of the 3D MTF are shown in Figure 17 The theoretical MTF in the x direction

has a maximum value that is toward higher frequencies Its 10 response occurs at

about 125 cyclesmm which is at 50 of the cutoff frequency The rapid increase from

the zero-frequency intercept to the peak corresponds to the ramp filter used in filtered

backprojection which decreases the weighting of low frequency contributions due to the

incomplete angular sampling of the frequency-space The MTF does not reach a value of

0 at the zero-frequency intercept as it is very difficult to assess the zero-frequency

intercept due to the finite size of the phantom The theoretical MTF in the y direction

peaks at the zero-frequency intercept and reaches 20 proximal to the cutoff frequency

38

The 10 MTF is well beyond the cutoff frequency The theoretical MTF in the z direction

has a rapid drop-off at very low spatial frequencies indicating the lack of resolution in

that dimension

Figure 17 Theoretical 3D MTF results along the three major planes (top) and along x

y and z directions (bottom) Also note that the angular spread seen in the fx-fz plane is

equal to the angular range of 44deg for the acquisition

II3iii Uncorrected MTF

The ESF LSF and MTF using the cone-based method are shown for the x y and

z directions in Figure 18 It was found that a bin size of one-tenth the voxel size (002

mm) and a cone angle of 30deg to establish the ESF were enough to minimize noise and

maximize accuracy in the uncorrected MTFs considering the reasonable comparison of

the shapes of the MTF curves with the theoretical results in Figure 17 The LSFs are

generally noisy because differentiation of the ESF increases the amplitude of the noise

39

The data shown reflect a convolution with a smoothing Gaussian filter which was later

further corrected for in the reported MTF Nevertheless the high frequency components

of the noise are well beyond the MTF cutoff frequency of 25 cyclesmm and do not

impact the MTF results greatly

For the ESF in the x direction the shadow effect evident at the edge of the sphere

is visible as a steep decline followed by an increase Due to the finite distance range

provided by the ROI the ESF beyond the edge did not asymptotically reach the

background value The corresponding LSF demonstrates a low frequency modulation

that is indicated by the shift of 03 cyclesmm in the x direction for the peak of the MTF

The MTF exhibits a zero-frequency intercept that is non-zero unlike the theoretical MTF

and a 10 value at approximately 1 cyclesmm These features may be a direct

consequence of MTF information ldquocontaminationrdquo from y and z directions Furthermore

the ESF in the y direction demonstrates a reasonably shaped curve except for the slight

upward trend within the radius of the sphere which can be attributed to the shadow

artifact overlapping with the sphere volume The associated MTF has a peak shifted by

approximately 01 cyclesmm away from the axis and a 10 MTF occurring at

approximately 15 cyclesmm Both features which are not present in the theoretical

results may also be attributed to contaminant MTF information from x and z directions

The ESF in the z direction has a drop-off that occurs at a small fraction of the cutoff

frequency similar to that demonstrated by the theoretical MTF

40

Uncorrected ESF LSF and MTF

Figure 18 Uncorrected ESF (top) LSF (middle) and MTF (bottom) for x y and z

directions

41

Figure 19 Comparisons of the directional MTFs as calculated by the sphere method

(dashed line) by theoretical line profiles (light-weight line) by theoretical cone

regions (heavy-weight line)

II3iv Comparison of Theoretical and Simulated MTFs

The theoretical MTF results obtained from line profiles through the 3D MTF and

the simulated MTFs using the cone-based technique did not match very well except for

the general shape of the curves It was assumed in the previous section that the cone-

based technique contains information from other planes Figure 19 compares MTFs in

each direction for the two methods described in the methods and an additional method

based on conical regions of the 3D MTF The latter computes the MTF by averaging

contributions of the 3D MTF using the same cone prescription method used to define the

ESFs Comparison of the curves indicate some interesting correlations aside from the

fact that using conical regions with the 3D MTF results produce more noisy MTF results

partly due to the low sampling provided by the theoretical calculations The same

conclusions regarding the z direction MTF can be confirmed regardless of either

theoretical MTF procedures The experimental x direction MTF seems to agree best with

42

the line profile method whereas the y direction MTF agrees better with the cone region

method The fact that the experimental x direction MTF has a drop-off frequency that is

lower than those of either of the theoretical MTFs in Figure 19 suggests that this might

be due to integration of the z-direction in the in-plane slices considering how slices are

essentially averages of z direction information contained within it [33]

II3v Modified MTF for x and y

Modified ESF LSF and MTF curves for x and y directions are shown in Figure

20 The modified ESF and the resulting LSF in the x direction appear symmetric as

expected from the inverse and flip operation of the interior ESF about the detected edge

The modified MTF appears with less variation than the uncorrected MTF and the MTF

peak occurs at the zero-frequency axis The correction yields a 10 MTF at about 15

cyclesmm an improvement from the uncorrected MTF but still distant from the cutoff

frequency The modified ESF in the y direction demonstrates the detrended curve within

the sphere radius after a quadratic polynomial fit The resulting modified MTF still

appears similar to the uncorrected MTF except that the peak now coincides with the

zero-frequency axis For both x and y directions the low response of the modified MTFs

at the higher frequencies suggests that the contamination from other directions is

substantial due to the angular range of the cone

43

Modified ESF LSF and MTF

Figure 20 Modified ESF (top) LSF (middle) and MTF (bottom) for x and y directions

44

II3v Preliminary Experimental Validation

Cross-sections of the reconstructed sphere volume are shown in Figure 21

Relative to the simulation reconstructions the reconstructions of the experimental

phantom images produce lower contrast and higher noise The preliminary results

shown in Figure 22 indicate that our technique can be applied to actual experimental

breast tomosynthesis reconstructions However due to the noise exhibited by the MTF

curves for the x and y directions we did not determine the modified MTFs to separate

resolution and artifact information

Figure 21 Cross sectional views of the experimental sphere image with centroid

indicated with red circle

45

Uncorrected ESF LSF and MTF for Real Image

Figure 22 ESF (top) LSF (middle) and MTF (bottom) of real image for x y

and z directions

46

II4 Discussion

II4i Evaluation of Cone-based Method

The cone-based MTF technique was introduced by Thornton and Flynn [28] for

evaluation of volumetric CT images To utilize this technique as a characterization of a

3D system spatial resolution one must first consider the validity of the assumption of

shift invariance such that the same MTF result may be obtained regardless of the

location of the sphere The study by Zhao et al [23] found that there was no shift

variance for the MTF measurements along the vertical axis but this was only considering

the in-plane resolution along one axis On the other hand this study evaluated the MTF

with images simulated with cascaded systems analysis which includes conditions of

linearity and shift invariance Additionally the MTF was calculated by averaging the

ESF from several spheres in the same volume only after performing a background

subtraction This step was essential to account for the sensitivity of centroid calculations

as well as ensuring symmetric ESFs for opposing axes of the sphere ROIs

The measurement of MTF with the cone-based technique inherently

supersamples the edge of the sphere to increase signal-to-noise-ratio (SNR) of edge

information by averaging the contributions of each voxel to the ESF [713] This method

also takes into account the discrete sampling of the voxels by accounting for various

shifts of the edge in the voxel (also known as the partial volume effect) However using

the curved surface of the sphere phantom to approximate an edge along a given

47

direction naturally leads to contamination of information from other directions aside

from the one of interest Preferably a directional ESF should be created by using a single

radial line but this would limit the available voxels to obtain edge information An ideal

situation theoretically would be to use a larger-sized sphere such that the surface is

nearly flat and perpendicular to the axes of interest This would also permit a reduction

in the angular range of the cone and thus the introduction of out-of-plane information in

the resulting MTF However sphere size is a limitation in breast tomosynthesis and the

use of a large phantom might void the assumption of shift invariance of the spatial

resolution

The choice of a sphere phantom nevertheless may be based on the clinical need

to quickly acquire a single image for MTF evaluation especially for multiple directions

without presenting extra logistical challenges The use of a wire or edge phantom

requires more precise mechanical alignment to achieve the correct set up The edge

phantom [23] would require at least two images to sample all three dimensions In the

case of the three wire phantom [2425] all three dimensions of the frame must be aligned

simultaneously with respect to the axis of rotation A similar situation would be

encountered when considering a cubic phantom with the planes normal to the axis of

interest In contrast to these phantoms the sphere eliminates the need for precise

alignment especially with respect to three spatial dimensions simultaneously A sphere

48

has ideal symmetry in all directions and can be used to evaluate MTF in any arbitrary

direction

This study unlike others [242532] did not explore the effects of physical

parameters such as scatter or contrast on the final MTF result but it demonstrated the

feasibility of using the cone-based method with an actual breast tomosynthesis image of

a sphere phantom as shown in Error Reference source not found and Error Reference

source not found These effects should be addressed in future works A further look

into deriving the principles of comparing the theoretical MTF with the experimental

MTF using the cone-based method is further warranted

II4ii Separation of Artifact and Resolution Information

The focus of this study was to develop a technique for measuring spatial

resolution of tomosynthesis images The intrinsic artifacts from tomosynthesis

reconstructions however lead to uncharacteristic MTFs and possible misinterpretation

of the effective resolution information When considering previous techniques for

calculating the presampled MTF [713152328] the analysis was performed using an

edge or a line to produce the corresponding ESF The resolution information is

essentially contained only along the edge indicated by the need to calculate the LSF In a

way the method of extracting artifact information is to focus the analysis only on the

edge part of the ESF to calculate the modified MTF This will lead to a better

understanding of the limiting size of objects that may be seen in the reconstructed 3D

49

image The presampled MTF without correction should still be analyzed to understand

the entire system response Note that the ESFs attempt to reflect information only at the

detected edge of the sphere

II5 Conclusions

The directional MTF of a simulated breast tomosynthesis reconstruction was

determined by using the cone-based MTF technique demonstrating the feasibility of a

single phantom for MTF evaluation This study further presented methods of analyzing

only the edge information in the ESF to create a modified MTF along in-slice (x and y)

axes It can provide insight into the actual spatial resolution information contained in the

image while separating the resolution information from the information introduced by

artifacts caused by the reconstruction and insufficient volumetric sampling The idea of

separating the resolution and artifacts from the measured ESF are expected to facilitate

the interpretation of MTF measurements in breast tomosynthesis Similar methods may

be applied to characterize the resolution of other 3D imaging modalities

50

References

1 Garmer M Hannigs SP Jaumlger HJ et al ldquoDigital Radiography Versus

Conventional Radiology in Chest Imaging Diagnostic Performance of a Large-

Area Silicon Flat-Panel Detector in a Clinical CT-Controlled Studyrdquo American

Journal of Roentgenology Volume 74 75-80 (2000)

2 Cowen AR Kengyelics SM and Davies AG ldquoSolid-state flat-panel digital

radiography detectors and their physical imaging characteristics rdquoClinical

Radiology Volume 63 487-498 (2008)

3 Chotas HG Dobbins III JT and Ravin CE ldquoPrinciples of Digital

Radiography with Large-Area Electronically Readable Detectors A Review of

the Basicsrdquo Radiology Volume 210 Number 3 595-599 (1999)

4 Flynn MJ and Samei E Experimental comparison of noise and resolution for

2k and 4k storage phosphor radiography systems Medical Physics Volume 26

Number 8 1612-1623 (1999)

5 Rong XJ Shaw CC Liu X Lemacks MR and Thompson SK

ldquoComparison of an amorphous siliconcesium iodide flat-panel digital chest

radiography system with screenfilm and computed radiography systems ndash A

contrast-detail phantom studyrdquo Medical Physics Volume 28 Number 11 2328-

2335 (2001)

6 Ranger NT Samei E Dobbins III JT and Ravin CE Measurement of the

detective quantum efficiency in digital detectors consistent with the IEC 62220-1

standard Practical considerations regarding the choice of filter material

Medical Physics Volume 30 Number 7 2305-2311 (2005)

7 Samei E Buhr E Granfors P Vandenbroucke D and Wang X Comparison

of edge analysis techniques for the determination of the MTF of digital

radiographic systems Physics in Medicine and Biology Volume 50 3613-3625

(2005)

8 Samei E and Flynn MJ An experimental comparison of detector performance

for computed radiography systems Medical Physics Volume 29 Number 4 447-

459 (2002)

51

9 Samei E and Flynn MJ An experimental comparison of detector performance

for direct and indirect digital radiography systems Medical Physics Volume 30

Number 4 608-622 (2003)

10 Samei E Ranger NT MacKenzie A Honey ID Dobbins III JT and Ravin

CE Effective DQE (eDQE) and speed of digital radiographic systems An

experimental methodology Medical Physics Volume 36 Number 8 3806-3817

(2009)

11 Samei E Ranger NT MacKenzie A Honey ID Dobbins III JT and Ravin

CE Detector or System Extending the Concept of Detective Quantum

Efficiency to Characterize the Performance of Digital Radiographic Imaging

Systems Radiology Volume 249 Number 3 926-937 (2008)

12 ldquoIEC 62220-1 Medical Electrical Equipment ndash Characteristics of Digital X-Ray

Imaging Devices ndash Part 1 Determination of the Detective Quantum Efficiencyrdquo

International Electrotechnical Commission Geneva Switzerland (2003)

13 Samei E Ranger NT Dobbins III JT and Chen Y Intercomparison of

methods for image quality characterization I Modulation transfer function

Medical Physics Volume 33 Number 5 1454-1465 (2006)

14 Dobbins III JT Samei E Ranger NT and Chen Y Intercomparison of

methods for image quality characterization II Noise power spectrum Medical

Physics Volume 33 Number 5 1466-1475 (2006)

15 Samei E Flynn MJ and Reimann DA A method for measuring the

presampled MTF of digital radiographic systems using an edge test device

Medical Physics Volume 25 Number 1 102-113 (1998)

16 Nagel HD ldquoAluminum equivalence of materials used in diagnostic radiology

and its dependence on beam qualityrdquo Physics in Medicine and Biology Volume

31 Number 12 1381-1399 (1986)

17 Niklason LT Christian BT Niklason LE et al ldquoDigital Tomosynthesis in

Breast Imagingrdquo Radiology Volume 205 399-406 (1997)

18 Gur D ldquoTomosynthesis Potential Clinical Role in Breast Imagingrdquo American

Journal of Roentgenology Volume 189 614-615 (2007)

52

19 Park JM Franken Jr EA Garg M Fajardo LL and Niklason LT ldquoBreast

Tomosynthesis Present Considerations and Future Applicationsrdquo

RadioGraphics Volume 27 S231-S240 (2007)

20 Good WF Abrams GS Catullo VJ Chough DM Ganott MA Hakim

CM and Gur D ldquoDigital Breast Tomosynthesis A Pilot Observer Studyrdquo

American Journal of Roentgenology Volume 190 865-869 (2008)

21 Hu Y-H Zhao W Mertelmeier T and Ludwig J ldquoImage Artifact in Digital

Breast Tomosynthesis and Its Dependence on System and Reconstruction

Parametersrdquo IWDM 2008 LNCS 5116 628-634 (2008)

22 Chen Y Lo JY Ranger NT Samei E Dobbins III JT ldquoMethodology of

NEQ(f) analysis for optimization and comparison of digital breast tomosynthesis

acquisition techniques and reconstruction algorithmsrdquo Proceedings of SPIE

Volume 6510 65101I (2007)

23 Zhao B Zhou J Hu Y-H Mertelmeier T Ludwig J and Zhao W

ldquoExperimental validation of a three-dimensional linear system model for breast

tomosynthesisrdquo Medical Physics Volume 36 Number 1 240-251 (2009)

24 Madhav P Brzymialkiewicz CN Cutler SJ Bowsher JE and Tornai MP

ldquoCharacterizing the MTF in 3D for a Quantized SPECT Camera Having Arbitrary

Trajectoriesrdquo 2005 IEEE Nuclear Science Symposium Conference Record 1722-

1726 (2005)

25 Madhav P McKinley RL Samei E Bowsher JE and Tornai MP ldquoA Novel

Method to Characterize the MTF in 3D for Computed Mammotomographyrdquo

Proceedings of SPIE Volume 6142 61421Y (2006)

26 Hu Y-H Zhao B and Zhao W ldquoImage artifacts in digital breast

tomosynthesis Investigation of the effects of system geometry and

reconstruction parameters using a linear system approachrdquo Medical Physics

Volume 35 Number 12 5242-5252 (2008)

27 Seifert A and Flynn MJ ldquoResolving power of 3D x-ray microtomography

systemsrdquo Proceedings of SPIE Volume 4682 407-413 (2002)

28 Thornton MM and Flynn MJ Measurement of the spatial resolution of a

clinical volumetric computed tomography scanner using a sphere phantom

Proceedings of SPIE Volume 6142 61421Z (2006)

53

29 Baek J Pelc NJ ldquoUse of sphere phantoms to measure the 3D MTF of FDK

reconstructionsrdquo Proceedings of SPIE Volume 7961 79610D (2011)

30 Richard S and Samei E ldquoQuantitative imaging in breast tomosynthesis and CT

Comparison of detection and estimation task performancerdquo Medical Physics

Volume 37 Number 6 2627-2637 (2010)

31 Chen Y Lo JY and Dobbins III JT ldquoImpulse response analysis for several

digital tomosynthesis mammography reconstruction algorithmsrdquo Proceedings of

SPIE Volume 5745 541-549 (2005)

32 Zhao B and Zhao W ldquoThree-dimensional linear system analysis for breast

tomosynthesisrdquo Medical Physics Volume 35 Number 12 5219-5232 (2008)

33 Wu G Mainprize JG Boone JM and Yaffe MJ ldquoEvaluation of scatter

effects on image quality for breast tomosynthesisrdquo Medical Physics Volume 36

Number 10 4425-4432 (2009)

Page 6: Development and Evaluation of 2D and 3D Image Quality ...

vi

for maximizing accuracy and minimizing noise of the MTF A method for removing out-

of-plane artifacts of the ESFs along in-plane axes was investigated and yielded a

modified MTF The idea of separating the effective resolution and artifacts from the

measured ESF are expected to facilitate the interpretation of MTF measurements in

breast tomosynthesis Similar methods may be applied to characterize the spatial

resolution of other 3D imaging modalities

vii

Contents

Abstract iv

List of Tables x

List of Figures xi

Acknowledgements xiii

I Evaluation of 2D Digital Image Receptors 1

I1 Introduction 1

I2 Materials and Methods 3

I2i Detectors 3

I2ii Beam Characterization 3

I2iia X-ray Techniques 3

I2iib Data Linearization 4

I2iic Spectral Simulation 5

I2iii DQE Measurements 6

I2iiia Modulation Transfer Function 6

I2iiib Noise Power Spectrum 7

I2iiic DQE Calculation 8

I3 Results 9

I3i Data Linearization 9

I3ii Spectral Simulation 9

I3iii Modulation Transfer Function 12

viii

I3iv Noise Power Spectrum 12

I3v Detective Quantum Efficiency 19

I4 Discussion 20

I4i Comparisons of Detectors 20

I4ii Comparisons of Filtrations 21

I4iii Implications of Wireless DR 26

I5 Conclusions 26

II Directional MTF for Breast Tomosynthesis 28

II1 Introduction 28

II2 Materials and Methods 29

II2i Image Simulation 29

II2ii Uncorrected MTF 30

II2iii Theoretical Directional MTF 32

II2iv Modified MTF 33

II2v Preliminary Experimental Validation 34

II3 Results 35

II3i Reconstruction 35

II3ii Theoretical MTF 37

II3iii Uncorrected MTF 38

II3iv Comparison of Theoretical and Simulated MTFs 41

II3v Modified MTF for x and y 42

II3v Preliminary Experimental Validation 44

ix

II4 Discussion 46

II4i Evaluation of Cone-based Method 46

II4ii Separation of Artifact and Resolution Information 48

II5 Conclusions 49

References 50

x

List of Tables

Table 1 Physical Characteristics of Digital Image Receptors 4

Table 2 Beam Qualities and Required Filtrations 5

Table 3 Spectral Simulation Results 11

Table 4 Experimental MTF frequency locations for 1 mR exposure 22

Table 5 Estimated DQE values for 1 mR exposure by frequency bins 22

xi

List of Figures

Figure 1 MTF images for DRX-1C detector with radio-opaque edge test device with

arrows indicating the horizontal (left) and vertical (right) directions 7

Figure 2 NNPS image for DRX-1C detector indicating the top left ROI that served as the

reference for normalizing other ROIs in the image The ROI array was formed along the

directions indicated by the arrows The heel effect visible along the vertical axis of the

detector is an example of small variation in signal across the image 8

Figure 3 Original (left) and linearized (right) system responses for Pixium 4600 The

linearized system responses were measured from actual images The offsets are small

with respect to the slope sufficient enough for zero-offset conditions 10

Figure 4 Spectral simulations for RQA5 (top) and RQA9 (bottom) conditions Note the

similarities of spectral shapes of the normalized spectra (right) Also note the significant

differences in fluence between filtrations in the simulated spectra (left) 11

Figure 5 MTF results by detector (columns) and beam quality (rows) 13

Figure 6 Plots of MTF for RQA5 (top) and RQA9 (bottom) showing the relationships

between detectors (blue red and green) and by filtration (solid and dashed) 14

Figure 7 NNPS results by detector (columns) and beam quality (rows) 15

Figure 8 Plots of NNPS for RQA5 (top) and RQA9 (bottom) at 1 mR exposure showing

the relationships between detectors (blue red and green) and by filtration (solid and

dashed) 16

Figure 9 DQE results by detector (columns) and beam quality (rows) 17

Figure 10 Plots of DQE for RQA5 (top) and RQA9 (bottom) at 1 mR exposure showing

the relationships between detectors (blue red and green) and by filtration (solid and

dashed) 18

Figure 11 DRX1-C NNPS images at 1 mR for RQA5 with IEC filtration (left) and

alternative filtration (right) Images are equally windowed at 45 and leveled at 980 24

Figure 12 Depiction of the virtual image system 30

xii

Figure 13 Example of 30-degree cone prescribed along z axis of the sphere 32

Figure 14 Photograph of the imaging system with the acrylic sphere phantom

embedded in oil 34

Figure 15 View of the central slice of the breast phantom reconstruction before (top) and

after (bottom) background subtraction The z axis is through the page 36

Figure 16 3D rendering of the ROI volume (left) and cross-sectional views of the most

centrally located sphere with centroid indicated with red circle (right) 37

Figure 17 Theoretical 3D MTF results along the three major planes (top) and along x y

and z directions (bottom) Also note that the angular spread seen in the fx-fz plane is

equal to the angular range of 44deg for the acquisition 38

Figure 18 Uncorrected ESF (top) LSF (middle) and MTF (bottom) for x y and z

directions 40

Figure 19 Comparisons of the directional MTFs as calculated by the sphere method

(dashed line) by theoretical line profiles (light-weight line) by theoretical cone regions

(heavy-weight line) 41

Figure 20 Modified ESF (top) LSF (middle) and MTF (bottom) for x and y directions 43

Figure 21 Cross sectional views of the experimental sphere image with centroid

indicated with red circle 44

Figure 22 ESF (top) LSF (middle) and MTF (bottom) of real image for x y and z

directions 45

xiii

Acknowledgements

I would like to thank Ian Yorkston Mark Purdum and Van Huston of

Carestream Health Inc (Rochester NY) for their help with digital detector

measurements I would also like to thank Olav Christianson Samuel Richard Brian

Harrawood and Max Amurao for their assistance with collecting data and analyzing

results Special thanks go to my committee members for their helpful insights and

suggestions for this thesis Last but not least I want to express deep appreciation for the

support and mentorship provided by my advisor Dr Ehsan Samei

1

I Evaluation of 2D Digital Image Receptors

I1 Introduction

In the past decade many areas of radiological practice have seen a conversion

from screen films to the storage phosphor cassettes of computed radiography (CR) to the

active-matrix flat-panel detectors of digital radiography (DR) Both CR and DR are

digital systems that offer many potential benefits including but not limited to better

image quality wider dynamic range quicker readout lower radiation dose and higher

throughput [1-3] Even with advances in DR technologies such as improved detective

quantum efficiency (DQE) the primary radiographic system of today continues to be CR

A major obstacle to completely accepting DR is the high capital cost of acquiring an

entire system per examination room while also providing capability for portable

applications Recently manufacturers like Carestream Health Fuji and Toshiba have

introduced wireless digital image receptors that can serve as replacements for CR

cassettes As these are new technologies a further investigation to characterize these

detectors is warranted

In the case of radiographic receptors DQE has historically been the metric of

choice [4] because it indicates the ability of the image receptor to convert incident x-ray

photons into useable signal ndash essentially a measure of signal-to-noise ratio (SNR)

efficiency and overall system performance [23] DQE is observed across a range of

spatial frequencies for evaluating how the detector depicts small and large objects [3]

2

DQE metrics have been used in numerous studies to characterize CR phosphor-screens

as well as indirect and direct digital detectors [4-11] The importance of this highly

quantitative metric may be implied by the introduction of a DQE measurement standard

by the International Electrotechnical Commission (IEC) [12]

The standard measurement methodology of the International Electrotechnical

Commission (IEC) pertains to the image quality of 2D digital radiographic detectors

While the IEC formalism is well-developed some of the components that it requires are

not necessarily the most optimal for characterizing DQE This has been explored in

previous studies in terms of filtration material purity beam limitations and region of

interest (ROI) configuration [1314] To reduce the variability in the radiographic output

across various x-ray tubes due to inherent filtration differences the IEC formalism

prescribes specific additional aluminum filtration to attain radiation beam qualities

based on target half value layers (HVL) Achieving and verifying the desired HVL

however requires applying a substantial amount of aluminum at the exit window of the

x-ray tube which is often directed toward the ground This can be a logistical

inconvenience and can increase the risk of damage to the image receptor and

measurement equipment Similar beam qualities on the other hand may be attained

more conveniently using a thinner lighter filtration combination utilizing a higher Z

number material Care is warranted however as a previous study [6] had indicated that

the choice of filtration material could impact the DQE

3

The purpose of this study was two-fold First we aimed to evaluate and compare

two wireless image receptors with a conventional flat-panel detector on the basis of DQE

performance Second we compared DQE results using the IEC-prescribed filtration with

an alternative filtration For the latter an optimum filtration composition was

determined and compared with the IEC filtration on the basis of DQE

I2 Materials and Methods

I2i Detectors

The physical characteristics of the three digital image receptors evaluated in this

study are listed in Table 1 The Pixium 4600 was a conventional digital flat-panel The

DRX-1C and DRX-1 were both wireless digital cassettes that were tethered for the

purposes of this study All detectors were FDA approved and available commercially

Each detector was calibrated according to its manufacturer specifications to correct for

gain offset and bad pixels They were all dedicated for non-clinical laboratory research

purposes and hence could be operated under service settings that permitted acquisition

of raw (ie for processing) images

I2ii Beam Characterization

I2iia X-ray Techniques

All measurements for this study were taken with a well-characterized standard

radiographic system (Super80CP Philips Healthcare Andover MA) The x-ray tube had

an inherent filtration of 27 mm Al Free in-air exposures were measured using

4

Table 1 Physical Characteristics of Digital Image Receptors

Manufacturer Detector

Detector

type

Detector

material

Pixel pitch

(size) Array size

Imaging

area

Trixell

(Moirans France)

Pixium

4600 Indirect

CsITl

(CsI) 0143 mm

3121times3121

4 subpanels 45times45 cm2

Carestream Health Inc

(Rochester NY)

DRX-1C

(wireless) Indirect

CsITl

(CsI) 0139 mm

2560times3072

single panel 35times43 cm2

Carestream Health Inc

(Rochester NY)

DRX-1

(wireless) Indirect

G2O2STb

(GOS) 0139 mm

2560times3072

single panel 35times43 cm2

calibrated radiation meters (Mult-O-Meter Type 407 Unfors Instruments AB Billdal

Sweden) at 183 cm source-to-chamber-distance (SCD) The SCD also corresponded to

same plane as the image receptor surface The x-ray output was made to conform to IEC

beam quality definitions [1215] on the basis of half value layer (HVL) and peak

kilovoltage setting using an aluminum filtration (type-1100 99 purity) and an

alternative filtration consisting of copper (UNS C11000 999 purity) and aluminum

(type-1100 99 purity) The IEC radiation quality numbers (RQA) used in this study are

summarized in Table 2 HVLs were determined by iteratively adding successive

thicknesses of aluminum until reaching reduced exposure levels within a tolerance of

0485-0515 [12] As for the alternative filtration the aluminum was placed downstream

of the copper filter to attenuate characteristic radiation peaks from copper at

approximately 9 keV

I2iib Data Linearization

The system response function was determined for each detector and filtration

combination by acquiring flat-field images at increasing photon fluence until just before

5

Table 2 Beam Qualities and Required Filtrations

IEC Radiation

Quality Number

Peak

kilovoltage

Required

HVL

Required IEC

Filtration

Actual IEC

Filtration

Alternative

Filtration

RQA5 70 kVp 71 mm Al 21 mm Al 21 mm Al 05 mm Cu +

10 mm Al

RQA9 120 kVp 115 mm Al 42 mm Al 40 mm Al 104 mm Cu +

10 mm Al

For reasons of convenience these will be referred to as RQA5A RQA5C RQA9A and RQA9C

saturation levels To avoid the influence of detector backscatter on exposure

measurements a relationship for each filtration was first determined for two radiation

meters A target meter was placed at the central axis and a reference meter was placed at

the edge of the light field (large enough to cover the detectors) The reference meter

served as a surrogate for the target meter to avoid direct exposure measurements in the

plane of the image receptor Exposure relationships were determined before each

measurement set (ie detector and filtration combination) to account for changes in

temperature pressure and humidity The system response function was calculated by

using a regression of ADU (pixel value) versus exposure Images acquired for each

series were then converted to achieve a linear response with zero offset and scaled to

achieve high quantization (adequate dynamic range) Linearization of the detector

responses ensured that zero exposure corresponded to zero pixel value

I2iic Spectral Simulation

The effects of additional filtration on x-ray output spectra were observed with

spectral simulation software (XSPECT V40 Henry Ford Hospital Detroit MI) To more

6

adequately describe the performance of a typical X-ray generator inherent filtration of 3

mm oil 148 mm Pyrex glass and 2 mm aluminum was input into the simulation in

addition to the filters of interest The ideal signal to noise ratio squared or incident

photon fluence per exposure (q) was estimated for each filtration by integrating the

energy-dependent photon counts per unit exposure over all energy bins

I2iii DQE Measurements

The assessment of the linearized images followed the formalism described by

IEC 62220-1 for measuring the DQE [12] For this study the normal exposure level XN

was set at 1 mR to the detector surface as measured at the central axis perpendicular to

the anode-cathode axis

I2iiia Modulation Transfer Function

Spatial resolution was characterized by evaluating the presampled modulation

transfer function (MTF) along directions parallel (vertical) and perpendicular

(horizontal) to the anode-cathode axis using the angled-edge method [6-1013] A radio-

opaque edge test device [7] was placed in the center of the field at a pitch of

approximately 301 (about 2deg) to the axis perpendicular to that being measured as

shown in Figure 1 External lead apertures were not used [6] instead the internal

collimation from the radiographic unit was used to collimate the beam to the detector

area Raw images were acquired of the edge with the normal exposure level XN of 1 mR

at the detector face The procedure of calculating the MTF followed previously described

7

methods [6-1013] The edge spread function (ESF) was determined along lines crossing

the edge of the angled test device The derivative of the ESF was calculated to form the

line spread function (LSF) to which a Hanning filter was applied The MTF was then

calculated as the fast Fourier transform (FFT) of the LSF and normalized at the zero-

frequency axis To conform to IEC guidelines the MTF was resampled into frequency

steps of 005 cyclesmm [12]

Figure 1 MTF images for DRX-1C detector with radio-opaque edge test device with

arrows indicating the horizontal (left) and vertical (right) directions

I2iiib Noise Power Spectrum

Noise amplitude and texture were characterized by determining the normalized

noise power spectrum (NNPS) which was evaluated with flat field exposures at

approximate exposure levels of XN2 XN and 2XN (05 10 and 20 mR) to the image

receptor surface Analysis of the flat-field images followed previously defined methods

[41415] using over 4 million independent pixels with regions of interest (ROIs) of size

8

128x128 The NNPS images were detrended using a quadratic (second order)

background subtraction Small variations in exposure across ROIs were corrected by

normalizing pixel values of each ROI to the mean value in the top left ROI as shown in

Figure 2 The NNPS was then calculated with the 2D FFT including the zero-frequency

axes corresponding to the horizontal and vertical directions The results were then

resampled using 005 frequency bins according to IEC guidelines [12]

Figure 2 NNPS image for DRX-1C detector indicating the top left ROI that served as

the reference for normalizing other ROIs in the image The ROI array was formed

along the directions indicated by the arrows The heel effect visible along the vertical

axis of the detector is an example of small variation in signal across the image

I2iiic DQE Calculation

The DQE was calculated using the following relationship [615]

9

where the frequency-dependent MTF and NNPS were determined as described in

previous sections X was the exposure value in mR corresponding to the NNPS image

and q was the ideal signal to noise ratio squared in units of photonsmiddotmm-2middotmR-1 as

estimated from the spectral simulations

I3 Results

I3i Data Linearization

The detectors in this study provided raw ADU (or pixel) values in a linear scale

The data were converted using the following system conversion function

where Q(ij) is the raw image data m and b are slope and intercept parameters obtained

from linear regression of the system response function and I(ij) is the linearized scaled

data The factor of 1000 was found to scale I(ij) such that the maximum value was a

large 16-bit number Figure 3 shows the original and linearized system responses for the

Pixium 4600 Note that the y-intercepts of the regressions for the linearized responses

are negligible (lt 01) with respect to the slopes a sufficient condition for zero offset

considerations

I3ii Spectral Simulation

The spectral simulations of the IEC filtrations and alternative filtrations indicate

many similarities in their effective energies HVLs and overall shapes of normalized

spectra Results are summarized in Table 3

10

Pixium 4600 Original System

Response

Pixium 4600 Linearized System

Response R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 3 Original (left) and linearized (right) system responses for Pixium 4600 The

linearized system responses were measured from actual images The offsets are small

with respect to the slope sufficient enough for zero-offset conditions

y = 13971x - 13236

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x - 00106Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 13576x + 28292

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

7000

0000 1000 2000 3000 4000 5000

AD

U

Exposure (mR)

y = 99997x - 00067Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0000 1000 2000 3000 4000 5000

AD

U

Exposure (mR)

y = 13644x + 16167Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x + 00044

Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 13845x + 13541

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x - 00177

Rsup2= 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

11

Table 3 Spectral Simulation Results

Beam Quality Filtration

Mean Energy

(kV)

Photon Fluence

(mRmm2)

RQA5A 21 mm Al 5243 259543

RQA5C 05 mm Cu + 10 mm Al 5214 259554

diff 055 0004

RQA9A 40 mm Al 7619 273281

RQA9C 104 mm Cu + 10 mm Al 7579 273964

diff 052 025

Figure 4 Spectral simulations for RQA5 (top) and RQA9 (bottom) conditions Note

the similarities of spectral shapes of the normalized spectra (right) Also note the

significant differences in fluence between filtrations in the simulated spectra (left)

00E+00

50E+04

10E+05

15E+05

20E+05

25E+05

30E+05

35E+05

40E+05

45E+05

0 20 40 60 80

ph

oto

ns

mA

s-1

cm

-2

keV

RQA5 Spectra Comparison

21 mm Al

05 mm Cu + 10 mm Al

00

02

04

06

08

10

12

0 20 40 60 80

keV

RQA5 Normalized Spectra Comparison

21 mm Al

05 mm Cu +

10 mm Al

00E+00

50E+05

10E+06

15E+06

20E+06

25E+06

30E+06

35E+06

40E+06

45E+06

50E+06

0 50 100 150

ph

oto

ns

mA

s-1

cm

-2

keV

RQA9 Spectra Comparison

40 mm Al

104 mm Cu +

10 mm Al

00

02

04

06

08

10

12

0 50 100 150

keV

RQA9 Normalized Spectra Comparison

40 mm Al104 mm Cu + 10 mm Al

12

I3iii Modulation Transfer Function

The limiting spatial resolutions of the systems were indicated by the cutoff

frequencies which were approximately 35 cyclesmm for all three detectors The spatial

resolutions also demonstrated a good degree of isotropy as confirmed by the close

alignment of MTF curves between vertical and horizontal directions differentiated in

Figure 5 by dashed and solid lines respectively The MTF curves for the Pixium 4600

and DRX-1C were nearly equal to each other whereas the DRX-1 MTF curve showed a

more rapid decrease at high frequencies as shown in Figure 6 This difference may be

due to the differences in the inherent optical properties of the scintillating materials

where finer image details are provided by structured CsI more than by granulated GOS

There were no significant differences in MTF curves across beam qualities and filtrations

as shown by the curve comparisons in Figure 6 although the alternative filtration

produced slightly higher MTF curves as seen in Figure 4 Table 4 lists the experimental

specific spatial frequencies for varying levels of MTF

I3iv Noise Power Spectrum

The noise characteristics are indicated by the NNPS curves shown in Figure 7

The noise was similar for both horizontal and vertical directions As exposure increased

the NNPS decreased consistent with the characteristics of Poisson noise describing the

relationship between signal and noise in the presence of increased photon fluence At

13

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 5 MTF results by detector (columns) and beam quality (rows)

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

horizontal

vertical

14

Figure 6 Plots of MTF for RQA5 (top) and RQA9 (bottom) showing the relationships

between detectors (blue red and green) and by filtration (solid and dashed)

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm-1)

MTF

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm-1)

MTF

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

15

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 7 NNPS results by detector (columns) and beam quality (rows)

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

05 mR - horizontal

05 mR - vertical

10 mR - horizontal

10 mR - vertical

20 mR - horizontal

20 mR - vertical

16

Figure 8 Plots of NNPS for RQA5 (top) and RQA9 (bottom) at 1 mR exposure

showing the relationships between detectors (blue red and green) and by filtration

(solid and dashed)

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm-1)

NNPS (1 mR)

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm-1)

NNPS (1 mR)

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

17

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 9 DQE results by detector (columns) and beam quality (rows)

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

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03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

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enl2-v

00

01

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03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

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enl1-v

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enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

05 mR - horizontal

05 mR - vertical

10 mR - horizontal

10 mR - vertical

20 mR - horizontal

20 mR - vertical

18

Figure 10 Plots of DQE for RQA5 (top) and RQA9 (bottom) at 1 mR exposure showing

the relationships between detectors (blue red and green) and by filtration (solid and

dashed)

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm-1)

DQE (1 mR)

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm-1)

DQE

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

19

higher frequencies the NNPS curves of the Pixium 4600 and DRX-1 diverge slightly for

the different directions illustrating increased noise in the readout direction (vertical)

Differences in the noise characteristics were more apparent among detectors as

shown for 1 mR in Figure 8 The NNPS curve for the DRX-1 was higher in magnitude

across the entire frequency range than either the Pixium 4600 or DRX-1C which both

seemed to demonstrate reasonably similar NNPS curves The higher magnitude noise of

the DRX-1 indicates higher relative noise content overall Closer inspection of the NNPS

curves of the Pixium 4600 and DRX-1C detectors in Figure 7 revealed differences in the

spacing between the three exposure levels The gaps between the Pixium 4600 NNPS

curves do not correspond to the factor of two differences between each exposure level

especially at low- to mid- spatial frequencies suggesting a higher level of fixed pattern

noise additional noise with increasing exposure levels due to ineffective gain map

corrections Between filtration schemes the differences in NNPS curves for a given beam

quality were not substantial as shown in Figure 7

I3v Detective Quantum Efficiency

The DQE results are shown in Figure 9 DQE curves across exposure levels were

almost collinear except for Pixium 4600 and in general could be inferred from the

NNPS results Additionally the DQE curves demonstrated a relatively linear response

with spatial frequencies as expected for flat-panel detectors [9] Differences in DQE

among detectors were consistent for the most part with the type of scintillating material

20

As depicted for 1 mR exposure in Figure 10 differences between Pixium 4600 and DRX-

1C DQE curves correspond to the differences in their NNPS curves DRX-1 DQE curves

were consistently lower than either the Pixium 4600 or DRX-1C curves The DQE curves

for the alternative filtration were consistently higher than those for the IEC filtration

and the most noticeable differences were near the zero-frequency axis These effects can

be both attributed to ineffective gain map correction DQE values for 1 mR exposure are

listed in Table 5

I4 Discussion

I4i Comparisons of Detectors

The limiting spatial resolutions of all three detectors were almost exactly the

same considering that their pixel areas were similar in size The decrease in high-

frequency MTF of the DRX-1 compared to the other detectors is probably a result of

increased optical blurring due to the differences in the powdered structure of GOS

versus the needle-like structure of CsI [2] The fact that the DRX-1C and Pixium 4600

have comparable MTFs suggests similar scintillator thicknesses assuming that the

materials were processed alike

The noise of the three detectors demonstrated similar trends with each other The

higher NNPS curves of the DRX-1 detector are probably due also to the scintillating

material and its operation in converting photons into signal The conversion process is

less efficient because of the less favorable stopping power of the GOS compared to CsI

21

especially with higher energy beams The noise of the Pixium 4600 and DRX-1C were

similar except for the spacing between exposures The DRX-1C NNPS curve spacing is

consistent with a factor of two difference in exposure levels but the Pixium 4600 has a

smaller spacing The 05 mR NNPS curve of the Pixium 4600 is closer to that of the 05

mR NNPS curve of the DRX-1C This demonstrates that at higher exposures the Pixium

4600 produces a larger amount of additional noise beyond that explained by simple

stochastic effects It suggests bad performance in the gain map corrections

The DQE results indicate SNR properties of each detector The Pixium 4600 and

DRX-1C are comparable for the most part with the DRX-1C performing slightly better

The DRX-1 as predicted from MTF and NNPS results has a DQE much lower than

either of the previous two This is a reflection of the detection properties as provided by

its scintillator material The DQE of the DRX-1 however is comparable to CR image

receptors [2] The mid-frequency dips in the DQE for Pixium 4600 may be due to the

optical properties of the CsI phosphor layer which can affect the MTF in this manner

Because the DQE is calculated by squaring the MTF this effect at the mid-range

frequencies becomes more apparent The dips may also be further evidence of bad gain

map corrections

I4ii Comparisons of Filtrations

The alternative filtration closely matches for the most part the IEC-based

filtration for MTF NNPS and DQEs at RQA5 but not at RQA9 The filters do not have

22

Table 4 Experimental MTF frequency locations for 1 mR exposure

Detector Filtration

50 MTF

(mm-1)

40 MTF

(mm-1)

30 MTF

(mm-1)

20 MTF

(mm-1)

10 MTF

(mm-1)

Pixium

4600

RQA5A 115 145 185 245 330

RQA5C 125 155 195 250 345

RQA9A 110 175 175 235 330

RQA9C 125 155 195 255 345

DRX-1C

RQA5A 120 150 185 245 350

RQA5C 125 155 195 255 355

RQA9A 120 150 190 250 355

RQA9C 130 160 210 265 360

DRX-1

RQA5A 110 135 160 205 280

RQA5C 110 135 170 210 285

RQA9A 105 125 155 195 270

RQA9C 110 135 165 210 285

Table 5 Estimated DQE values for 1 mR exposure by frequency bins

Detector Filtration DQE(00 mm-1) DQE(10 mm-1) DQE(20 mm-1) DQE(30 mm-1)

Pixium

4600

RQA5A 62 42 32 21

RQA5C 63 45 36 25

RQA9A 41 27 30 13

RQA9C 43 33 27 19

DRX-1C

RQA5A 72 52 35 21

RQA5C 76 55 41 24

RQA9A 49 33 23 15

RQA9C 51 40 31 20

DRX-1

RQA5A 38 24 12 4

RQA5C 38 25 14 5

RQA9A 28 18 9 4

RQA9C 28 19 12 5

DQE values at the zero-frequency axis were estimated by the intercept of a linear fit of low-frequency data

but excluding most proximal to the axis due to large fluctuations Other estimated values are grouped into

frequency bins due to the noisiness of the data

23

considerable differences in the spatial resolutions of the detectors as expected The noise

responses for each filtration were also similar except at the lower frequencies of the

NNPS especially near the zero-frequency axis There observing the NNPS responses at

RQA5 for Pixium 4600 and DRX-1C in Figure 8 the NNPS for the IEC-based filtration

(solid lines) tend to drop faster than the NNPS for the alternative filtration This

subsequently appears as a drop in DQE near the zero-frequency axis shown for those

detectors in Figure 10 Overall as indicated in Table 5 the DQEs of the two filtrations

while similar in trend indicate that the alternative filtration increases the DQE by a

small amount of 3-5 Part of this may be explained by the slightly higher beam

energy which may be more optimal for the energy response of the detectors or may

weigh the pixel responses slightly considering that they are energy-integrating types

The most probable explanation is the gain map correction for the alternative filtration

where fixed pattern noise is more sufficiently reduced

A previous study [6] had discussed the choice of filter material in the analysis of

DQE when achieving the beam conditions defined by IEC It found that visible

nonuniformities were present with the higher purity aluminum filter (type-11999 alloy)

The low frequency mottle in the flat-field images for NPS measurements were also

attributed to structured noise from the grain size in the IEC-based filter with an

attenuating thickness that would reveal nonuniformities The mottle in the current study

was only observable under very narrow windowing as shown in Figure 11 Such low

24

frequency artifacts which are not readily noticeable may also be caused by shading

artifacts inverse square law or even the heel effect A possible method to correct for this

is a subtraction method by taking the average of the flat-field images for an exposure

level and then subtracting that from each of them This would remove nonuniformities

that were not corrected using a suboptimal gain map calibration

Figure 11 DRX1-C NNPS images at 1 mR for RQA5 with IEC filtration (left) and

alternative filtration (right) Images are equally windowed at 45 and leveled at 980

One convenient aspect of the copper and aluminum filtration is that it requires

much less tube current to achieve the same amount of exposure at the detector than the

much thicker aluminum filtration As shown in the non-normalized spectra in Figure 2

the exiting photon fluence exiting the copper and aluminum filtration is substantially

higher than that of the IEC-specified filtration This is due to the smaller total filtration

25

attenuation For extensive DQE analysis multiple sets of exposures may be acquired

before tube overheating becomes a concern

One limitation to the comparison of the two filtrations is that calibration

procedures specified copper and aluminum filtration at 80 kVp (for all detectors 05 mm

Cu and 10 mm Al) This may have influenced the results in favor of the alternative

filtration A further investigation involving the calibration procedures and performing

DQE measurements is encouraged Another factor may be influenced by the fact that the

tests were performed at 70 kVp and 120 kVp different from the recommended

calibration tube potential Clearly there would be differences in the linear attenuation

coefficients of the filters and different energy responses of the detectors themselves This

must be considered when interpreting DQE results The current results support a

previous study decades ago that described filtration of different material types in terms

of an aluminum equivalent [16] The results show that the two filtration schemes are

essentially equivalent when considering beam qualities and spatial resolutions The

NNPS and DQE results can be seen as close enough where their small differences are

insignificant when performing quality assurance tests in a clinical setting Overall our

results indicate that the alternative filtration with copper and aluminum may be more

convenient to use than the current IEC standard filtration

26

I4iii Implications of Wireless DR

This study has shown that wireless image receptors can have the same DQE

performance if not better than conventional flat-panel detectors They operate on the

same basic physical principles the new features offered by the DRX-1C and DRX-1 are

wireless communication with the workstation and electronics packaging technology

The latter feature may pose limitations for these units in terms of possible degradation

in the detectors in routine clinical conditions A consideration for future work would be

to longitudinally track DQE performance of the wireless detectors over time while being

utilized in a clinical environment In the end one must consider risks versus benefits of

choosing portable DR technology over CR one of which includes the cost and fragility

of DR detectors

The DQE performance of one wireless system is just as good as or better than

conventional systems as seen by the DRX-1C performance compared to the Pixium

4600 Wireless systems can also reduce the need for CR readers especially in portable

applications in other regions of the world (eg military hospitals developing countries)

However while DQE performance indicates the physical performance of the detector

system it is still unknown how it relates to observer performance

I5 Conclusions

Two wireless image receptors DRX-1C and DRX-1 were evaluated and

compared with the conventional DR flat-panel Pixium 4600 in terms of DQE

27

performance along with MTF and NNPS performances The detectors have similar

resolution properties although the DRX-1 is inferior at higher spatial frequencies The

NNPS and DQE results both indicate that the DRX-1C is superior to the DRX-1 and

comparable if not better to the Pixium 4600

The results from the filtration comparison indicate no substantial differences

between the IEC-based filtration and the copper-based alternative filtration Only slight

differences were found in the low frequency components of the NNPS and the DQE due

to the inherent nonuniformities of the IEC specified filtration Given the similarity of the

results and low attenuation advantage of the copper and aluminum filter its use is

encouraged

28

II Directional MTF for Breast Tomosynthesis

II1 Introduction

Breast tomosynthesis is an emerging 3D imaging modality that has potential use

for screening and diagnosis of breast cancer Breast tomosynthesis along with other 3D

techniques is preferable to planar imaging methods (eg mammography) because they

reduce anatomical noise by removing overlying structures above and below the plane of

an image slice [17-20] Recent advances in detectors and computer technology have

made digital tomosynthesis feasible

An image quality metric of particular importance in breast tomosynthesis is

spatial resolution Resolution is important to know in order to assess small-detail

structures such as microcalcifications A descriptive metric for characterizing spatial

resolution in the Fourier (or frequency) domain is the modulation transfer function

(MTF) Affected by reconstruction filters [21] the limited angular projections involved in

breast tomosynthesis results in highly anisotropic (or nonuniform) resolution Many

studies have looked only at characterizing the in-plane spatial resolution (ie in an

individual slice) with an elevated angled edge phantom [2223] A few studies have

looked at characterizing a more comprehensive 3D spatial resolution by using a

phantom with angled wires or tubes [24-26] However such studies require precise

mechanical alignment of the phantoms Several studies have explored a method using a

29

sphere phantom for the directional 3D MTF evaluation for microtomography [27] and

multi-slice CT [2829] This method has not yet been extended to breast tomosynthesis

This chapter focuses on breast tomosynthesis because it is highly anisotropic in

spatial resolution and like its predecessor mammography requires high spatial

resolution Additionally breast tomosynthesis acquisitions and reconstructions produce

several types of artifacts The use of a cone-based method using a sphere phantom [28] is

explored to characterize the directional 3D spatial resolution of simulated images from

breast tomosynthesis A technique for removing out-of-plane artifacts of the ESFs for the

in-plane axes is investigated to yield a modified MTF in a method that separates artifact

information from resolution information

II2 Materials and Methods

II2i Image Simulation

Breast tomosynthesis images were simulated by using a virtual imaging system

depicted in Figure 12 A volumetric breast phantom was voxelized as a rectangular mass

of uniform breast equivalent tissue of 4 cm thickness embedded with fifteen evenly

spaced plastic sphere inserts of 12 mm diameter The spheres were placed in a grid

formation within the central plane of the phantom The x-ray fluence was modeled from

a 28 kVp beam incident upon an indirect flat-panel detector with 200 micro m pixel size

Twenty-three projections within an angular range of 44deg were simulated using cascaded

systems analysis to generate characteristic 2D noise and spatial blurring [29] Each

30

projection was simulated to have an exposure of 174 mR with a fluence of 79 times 105

photonsmm-2 A standard filtered backprojection technique based on the Feldkamp

reconstruction algorithm [29] was used to reconstruct the projections and produce a

volumetric dataset with an isotropic voxel size of 200 micro m

Figure 12 Depiction of the virtual image system

II2ii Uncorrected MTF

To enable comparison of multiple spheres the reconstructed volume was

initially homogenized by performing a background subtraction based on a portion of the

volume devoid of spheres The voxel values were rescaled between one and zero to

eliminate negative values

31

The volumetric data were segmented to extract individual regions of interest

(ROIs) each containing a single sphere The ROIs extended along the full range of the z-

axis A thresholded ROI was generated by determining the exterior and interior voxels

relative to the sphere in the ROI The threshold value was set at 45 of the maximum

voxel value prior to thresholding The exterior and interior voxel values were then set to

values of 0 and 1 respectively Using the thresholded volume the center of mass was

calculated to determine the centroid The voxel values from the original ROI were

subsequently tabulated with the associated distances azimuthal angles and polar

angles relative to the centroid

Conical regions were prescribed along the positive and negative directions along

the three major axes extending from the centroid of the sphere as depicted in Figure 13

The axes about which the extent of the cone angle was delineated were defined with

the azimuthal and polar angles

Voxels with centers within the angular range of the cone were considered for

generating the edge spread function (ESF) To improve regularity of the distance

sampling interval the ESF values were rebinned to discrete distances corresponding to a

fraction of the voxel size Only voxels with distances ranging from the voxel size (ie

200 micro m) to the maximum distance were considered The ESFs from multiple spheres

were averaged together for each of the three major axes to produce an averaged ESF

which was further smoothed utilizing a Gaussian filter

32

Figure 13 Example of 30-degree cone prescribed along z axis of the sphere

The resulting ESF was then differentiated using the central difference method to

produce the line spread function (LSF) A Hanning filter with the same length as the LSF

was applied to zero out the tails of the LSF The presampled MTF was subsequently

computed as the amplitude of the Fourier transform of the LSF The MTF was

normalized with respect to the maximum value occurring within the range of the cutoff

frequency Binning size and conical range for the ESF were considered for maximizing

accuracy and minimizing noise of the MTF verified by comparison against the

theoretical MTF as determined in the previous section

II2iii Theoretical Directional MTF

The theoretical 3D MTF was calculated using a priori knowledge of the transfer

function of the virtual imaging system described in the previous section A phantom

was created with a set of point objects in a uniform and noise-free background with the

objects spanning across the volume of the breast [29] Twenty-one realizations were

33

generated from the reconstructed images of the point objects to yield a set of 3D point

spread functions (PSFs) The 3D fast Fourier transform (FFT) was performed for each 3D

PSF and averaged to give an ldquoexpectationrdquo 3D MTF [29] The theoretical directional

MTFs in the three major spatial axes were determined by line profiles along each of the

corresponding spatial frequency axes in the 3D MTF An additional theoretical MTF for

each direction was determined by using the application of conical regions along the axes

in frequency-space to take into account the contributions of MTF information from other

planes

II2iv Modified MTF

The tomosynthesis reconstruction is known to have edge enhancements which

affect the overall MTF by shifting the peaks of the MTF toward the higher frequencies

[23] The presence of this artifact complicates the interpretation of the actual spatial

resolution of the images Several steps were performed to remove the artifact

contribution to the resolution information particularly for the in-plane x and y

directions with the assumption that resolution information was contained immediately

near the edge

For the x-direction averaged ESF only values that were detected to be inside the

edge of the sphere were considered Those values were previously determined via

thresholding for calculating the centroid The ESF information corresponding to these

values was inversed and flipped about the detected edge to produce a symmetric

34

modified ESF The modified MTF was subsequently calculated from this modified ESF

as described in the previous section

For the y-direction averaged ESF an upward trend was found in the initial part

of the ESF This section was detrended with a polynomial fit and subtracted to produce a

flatter curve in that region The resulting detrended ESF was used to calculate the y axis

modified MTF

Figure 14 Photograph of the imaging system with the acrylic sphere phantom

embedded in oil

II2v Preliminary Experimental Validation

A clinical breast tomosynthesis system (Mammomat Inspiration Siemens AG

Munich Germany) was used to perform a preliminary evaluation of the cone-based

MTF technique The phantom for the experiment consisted of a single acrylic ball of 075

in diameter (SmallParts Seattle WA) suspended by a 0029 in diameter plastic filament

35

(Omniflex Zebco Tulsa OK) in an acrylic frame filled up to 4 in with vegetable oil

(Target Brands Inc Minneapolis MN) The system and phantom are shown in Figure

14 Twenty-five projections with an angular range of 44deg were acquired and subsequently

reconstructed to produce a volume with a voxel size of 01times01times10 mm3 The voxels were

reformatted to have an isotropic size of 01 mm The uncorrected ESF LSF and MTF

were calculated as described in the previous section

II3 Results

II3i Reconstruction

The reconstructed volume is shown in Figure 15 Notice the edge enhancement

along the x-direction as indicated by the sharp shadowing artifacts on either side of the

spheres The background was effectively homogenized using the background

subtraction technique This also took account of the curved edges of the breast phantom

With the close spacing of the spheres in the phantom the shadows along the x direction

for the fifteen spheres overlap with each other As the nine centrally located spheres

experience this effect the same way they were used for determining the ESF

A 3D rendering of the ROI containing a sphere shown in Figure 16 indicates the

anisotropic resolution of the reconstruction Note that the sphere is not accurately

reconstructed and has an oblong shape especially along the z axis Cross sectional views

of the ROI also in Figure 16 clearly demonstrate the edge enhancement causing a

shadow artifact in the x direction caused by the incomplete angular sampling of

36

tomosynthesis The sampling also introduces the triangular reconstruction of the sphere

as seen in the x-z plane Note the gradual edge drop-off in the z direction much beyond

the sphere radius

Figure 15 View of the central slice of the breast phantom reconstruction before (top)

and after (bottom) background subtraction The z axis is through the page

37

Figure 16 3D rendering of the ROI volume (left) and cross-sectional views of the most

centrally located sphere with centroid indicated with red circle (right)

II3ii Theoretical MTF

The theoretical MTFs for x y and z directions as determined from the line

profiles of the 3D MTF are shown in Figure 17 The theoretical MTF in the x direction

has a maximum value that is toward higher frequencies Its 10 response occurs at

about 125 cyclesmm which is at 50 of the cutoff frequency The rapid increase from

the zero-frequency intercept to the peak corresponds to the ramp filter used in filtered

backprojection which decreases the weighting of low frequency contributions due to the

incomplete angular sampling of the frequency-space The MTF does not reach a value of

0 at the zero-frequency intercept as it is very difficult to assess the zero-frequency

intercept due to the finite size of the phantom The theoretical MTF in the y direction

peaks at the zero-frequency intercept and reaches 20 proximal to the cutoff frequency

38

The 10 MTF is well beyond the cutoff frequency The theoretical MTF in the z direction

has a rapid drop-off at very low spatial frequencies indicating the lack of resolution in

that dimension

Figure 17 Theoretical 3D MTF results along the three major planes (top) and along x

y and z directions (bottom) Also note that the angular spread seen in the fx-fz plane is

equal to the angular range of 44deg for the acquisition

II3iii Uncorrected MTF

The ESF LSF and MTF using the cone-based method are shown for the x y and

z directions in Figure 18 It was found that a bin size of one-tenth the voxel size (002

mm) and a cone angle of 30deg to establish the ESF were enough to minimize noise and

maximize accuracy in the uncorrected MTFs considering the reasonable comparison of

the shapes of the MTF curves with the theoretical results in Figure 17 The LSFs are

generally noisy because differentiation of the ESF increases the amplitude of the noise

39

The data shown reflect a convolution with a smoothing Gaussian filter which was later

further corrected for in the reported MTF Nevertheless the high frequency components

of the noise are well beyond the MTF cutoff frequency of 25 cyclesmm and do not

impact the MTF results greatly

For the ESF in the x direction the shadow effect evident at the edge of the sphere

is visible as a steep decline followed by an increase Due to the finite distance range

provided by the ROI the ESF beyond the edge did not asymptotically reach the

background value The corresponding LSF demonstrates a low frequency modulation

that is indicated by the shift of 03 cyclesmm in the x direction for the peak of the MTF

The MTF exhibits a zero-frequency intercept that is non-zero unlike the theoretical MTF

and a 10 value at approximately 1 cyclesmm These features may be a direct

consequence of MTF information ldquocontaminationrdquo from y and z directions Furthermore

the ESF in the y direction demonstrates a reasonably shaped curve except for the slight

upward trend within the radius of the sphere which can be attributed to the shadow

artifact overlapping with the sphere volume The associated MTF has a peak shifted by

approximately 01 cyclesmm away from the axis and a 10 MTF occurring at

approximately 15 cyclesmm Both features which are not present in the theoretical

results may also be attributed to contaminant MTF information from x and z directions

The ESF in the z direction has a drop-off that occurs at a small fraction of the cutoff

frequency similar to that demonstrated by the theoretical MTF

40

Uncorrected ESF LSF and MTF

Figure 18 Uncorrected ESF (top) LSF (middle) and MTF (bottom) for x y and z

directions

41

Figure 19 Comparisons of the directional MTFs as calculated by the sphere method

(dashed line) by theoretical line profiles (light-weight line) by theoretical cone

regions (heavy-weight line)

II3iv Comparison of Theoretical and Simulated MTFs

The theoretical MTF results obtained from line profiles through the 3D MTF and

the simulated MTFs using the cone-based technique did not match very well except for

the general shape of the curves It was assumed in the previous section that the cone-

based technique contains information from other planes Figure 19 compares MTFs in

each direction for the two methods described in the methods and an additional method

based on conical regions of the 3D MTF The latter computes the MTF by averaging

contributions of the 3D MTF using the same cone prescription method used to define the

ESFs Comparison of the curves indicate some interesting correlations aside from the

fact that using conical regions with the 3D MTF results produce more noisy MTF results

partly due to the low sampling provided by the theoretical calculations The same

conclusions regarding the z direction MTF can be confirmed regardless of either

theoretical MTF procedures The experimental x direction MTF seems to agree best with

42

the line profile method whereas the y direction MTF agrees better with the cone region

method The fact that the experimental x direction MTF has a drop-off frequency that is

lower than those of either of the theoretical MTFs in Figure 19 suggests that this might

be due to integration of the z-direction in the in-plane slices considering how slices are

essentially averages of z direction information contained within it [33]

II3v Modified MTF for x and y

Modified ESF LSF and MTF curves for x and y directions are shown in Figure

20 The modified ESF and the resulting LSF in the x direction appear symmetric as

expected from the inverse and flip operation of the interior ESF about the detected edge

The modified MTF appears with less variation than the uncorrected MTF and the MTF

peak occurs at the zero-frequency axis The correction yields a 10 MTF at about 15

cyclesmm an improvement from the uncorrected MTF but still distant from the cutoff

frequency The modified ESF in the y direction demonstrates the detrended curve within

the sphere radius after a quadratic polynomial fit The resulting modified MTF still

appears similar to the uncorrected MTF except that the peak now coincides with the

zero-frequency axis For both x and y directions the low response of the modified MTFs

at the higher frequencies suggests that the contamination from other directions is

substantial due to the angular range of the cone

43

Modified ESF LSF and MTF

Figure 20 Modified ESF (top) LSF (middle) and MTF (bottom) for x and y directions

44

II3v Preliminary Experimental Validation

Cross-sections of the reconstructed sphere volume are shown in Figure 21

Relative to the simulation reconstructions the reconstructions of the experimental

phantom images produce lower contrast and higher noise The preliminary results

shown in Figure 22 indicate that our technique can be applied to actual experimental

breast tomosynthesis reconstructions However due to the noise exhibited by the MTF

curves for the x and y directions we did not determine the modified MTFs to separate

resolution and artifact information

Figure 21 Cross sectional views of the experimental sphere image with centroid

indicated with red circle

45

Uncorrected ESF LSF and MTF for Real Image

Figure 22 ESF (top) LSF (middle) and MTF (bottom) of real image for x y

and z directions

46

II4 Discussion

II4i Evaluation of Cone-based Method

The cone-based MTF technique was introduced by Thornton and Flynn [28] for

evaluation of volumetric CT images To utilize this technique as a characterization of a

3D system spatial resolution one must first consider the validity of the assumption of

shift invariance such that the same MTF result may be obtained regardless of the

location of the sphere The study by Zhao et al [23] found that there was no shift

variance for the MTF measurements along the vertical axis but this was only considering

the in-plane resolution along one axis On the other hand this study evaluated the MTF

with images simulated with cascaded systems analysis which includes conditions of

linearity and shift invariance Additionally the MTF was calculated by averaging the

ESF from several spheres in the same volume only after performing a background

subtraction This step was essential to account for the sensitivity of centroid calculations

as well as ensuring symmetric ESFs for opposing axes of the sphere ROIs

The measurement of MTF with the cone-based technique inherently

supersamples the edge of the sphere to increase signal-to-noise-ratio (SNR) of edge

information by averaging the contributions of each voxel to the ESF [713] This method

also takes into account the discrete sampling of the voxels by accounting for various

shifts of the edge in the voxel (also known as the partial volume effect) However using

the curved surface of the sphere phantom to approximate an edge along a given

47

direction naturally leads to contamination of information from other directions aside

from the one of interest Preferably a directional ESF should be created by using a single

radial line but this would limit the available voxels to obtain edge information An ideal

situation theoretically would be to use a larger-sized sphere such that the surface is

nearly flat and perpendicular to the axes of interest This would also permit a reduction

in the angular range of the cone and thus the introduction of out-of-plane information in

the resulting MTF However sphere size is a limitation in breast tomosynthesis and the

use of a large phantom might void the assumption of shift invariance of the spatial

resolution

The choice of a sphere phantom nevertheless may be based on the clinical need

to quickly acquire a single image for MTF evaluation especially for multiple directions

without presenting extra logistical challenges The use of a wire or edge phantom

requires more precise mechanical alignment to achieve the correct set up The edge

phantom [23] would require at least two images to sample all three dimensions In the

case of the three wire phantom [2425] all three dimensions of the frame must be aligned

simultaneously with respect to the axis of rotation A similar situation would be

encountered when considering a cubic phantom with the planes normal to the axis of

interest In contrast to these phantoms the sphere eliminates the need for precise

alignment especially with respect to three spatial dimensions simultaneously A sphere

48

has ideal symmetry in all directions and can be used to evaluate MTF in any arbitrary

direction

This study unlike others [242532] did not explore the effects of physical

parameters such as scatter or contrast on the final MTF result but it demonstrated the

feasibility of using the cone-based method with an actual breast tomosynthesis image of

a sphere phantom as shown in Error Reference source not found and Error Reference

source not found These effects should be addressed in future works A further look

into deriving the principles of comparing the theoretical MTF with the experimental

MTF using the cone-based method is further warranted

II4ii Separation of Artifact and Resolution Information

The focus of this study was to develop a technique for measuring spatial

resolution of tomosynthesis images The intrinsic artifacts from tomosynthesis

reconstructions however lead to uncharacteristic MTFs and possible misinterpretation

of the effective resolution information When considering previous techniques for

calculating the presampled MTF [713152328] the analysis was performed using an

edge or a line to produce the corresponding ESF The resolution information is

essentially contained only along the edge indicated by the need to calculate the LSF In a

way the method of extracting artifact information is to focus the analysis only on the

edge part of the ESF to calculate the modified MTF This will lead to a better

understanding of the limiting size of objects that may be seen in the reconstructed 3D

49

image The presampled MTF without correction should still be analyzed to understand

the entire system response Note that the ESFs attempt to reflect information only at the

detected edge of the sphere

II5 Conclusions

The directional MTF of a simulated breast tomosynthesis reconstruction was

determined by using the cone-based MTF technique demonstrating the feasibility of a

single phantom for MTF evaluation This study further presented methods of analyzing

only the edge information in the ESF to create a modified MTF along in-slice (x and y)

axes It can provide insight into the actual spatial resolution information contained in the

image while separating the resolution information from the information introduced by

artifacts caused by the reconstruction and insufficient volumetric sampling The idea of

separating the resolution and artifacts from the measured ESF are expected to facilitate

the interpretation of MTF measurements in breast tomosynthesis Similar methods may

be applied to characterize the resolution of other 3D imaging modalities

50

References

1 Garmer M Hannigs SP Jaumlger HJ et al ldquoDigital Radiography Versus

Conventional Radiology in Chest Imaging Diagnostic Performance of a Large-

Area Silicon Flat-Panel Detector in a Clinical CT-Controlled Studyrdquo American

Journal of Roentgenology Volume 74 75-80 (2000)

2 Cowen AR Kengyelics SM and Davies AG ldquoSolid-state flat-panel digital

radiography detectors and their physical imaging characteristics rdquoClinical

Radiology Volume 63 487-498 (2008)

3 Chotas HG Dobbins III JT and Ravin CE ldquoPrinciples of Digital

Radiography with Large-Area Electronically Readable Detectors A Review of

the Basicsrdquo Radiology Volume 210 Number 3 595-599 (1999)

4 Flynn MJ and Samei E Experimental comparison of noise and resolution for

2k and 4k storage phosphor radiography systems Medical Physics Volume 26

Number 8 1612-1623 (1999)

5 Rong XJ Shaw CC Liu X Lemacks MR and Thompson SK

ldquoComparison of an amorphous siliconcesium iodide flat-panel digital chest

radiography system with screenfilm and computed radiography systems ndash A

contrast-detail phantom studyrdquo Medical Physics Volume 28 Number 11 2328-

2335 (2001)

6 Ranger NT Samei E Dobbins III JT and Ravin CE Measurement of the

detective quantum efficiency in digital detectors consistent with the IEC 62220-1

standard Practical considerations regarding the choice of filter material

Medical Physics Volume 30 Number 7 2305-2311 (2005)

7 Samei E Buhr E Granfors P Vandenbroucke D and Wang X Comparison

of edge analysis techniques for the determination of the MTF of digital

radiographic systems Physics in Medicine and Biology Volume 50 3613-3625

(2005)

8 Samei E and Flynn MJ An experimental comparison of detector performance

for computed radiography systems Medical Physics Volume 29 Number 4 447-

459 (2002)

51

9 Samei E and Flynn MJ An experimental comparison of detector performance

for direct and indirect digital radiography systems Medical Physics Volume 30

Number 4 608-622 (2003)

10 Samei E Ranger NT MacKenzie A Honey ID Dobbins III JT and Ravin

CE Effective DQE (eDQE) and speed of digital radiographic systems An

experimental methodology Medical Physics Volume 36 Number 8 3806-3817

(2009)

11 Samei E Ranger NT MacKenzie A Honey ID Dobbins III JT and Ravin

CE Detector or System Extending the Concept of Detective Quantum

Efficiency to Characterize the Performance of Digital Radiographic Imaging

Systems Radiology Volume 249 Number 3 926-937 (2008)

12 ldquoIEC 62220-1 Medical Electrical Equipment ndash Characteristics of Digital X-Ray

Imaging Devices ndash Part 1 Determination of the Detective Quantum Efficiencyrdquo

International Electrotechnical Commission Geneva Switzerland (2003)

13 Samei E Ranger NT Dobbins III JT and Chen Y Intercomparison of

methods for image quality characterization I Modulation transfer function

Medical Physics Volume 33 Number 5 1454-1465 (2006)

14 Dobbins III JT Samei E Ranger NT and Chen Y Intercomparison of

methods for image quality characterization II Noise power spectrum Medical

Physics Volume 33 Number 5 1466-1475 (2006)

15 Samei E Flynn MJ and Reimann DA A method for measuring the

presampled MTF of digital radiographic systems using an edge test device

Medical Physics Volume 25 Number 1 102-113 (1998)

16 Nagel HD ldquoAluminum equivalence of materials used in diagnostic radiology

and its dependence on beam qualityrdquo Physics in Medicine and Biology Volume

31 Number 12 1381-1399 (1986)

17 Niklason LT Christian BT Niklason LE et al ldquoDigital Tomosynthesis in

Breast Imagingrdquo Radiology Volume 205 399-406 (1997)

18 Gur D ldquoTomosynthesis Potential Clinical Role in Breast Imagingrdquo American

Journal of Roentgenology Volume 189 614-615 (2007)

52

19 Park JM Franken Jr EA Garg M Fajardo LL and Niklason LT ldquoBreast

Tomosynthesis Present Considerations and Future Applicationsrdquo

RadioGraphics Volume 27 S231-S240 (2007)

20 Good WF Abrams GS Catullo VJ Chough DM Ganott MA Hakim

CM and Gur D ldquoDigital Breast Tomosynthesis A Pilot Observer Studyrdquo

American Journal of Roentgenology Volume 190 865-869 (2008)

21 Hu Y-H Zhao W Mertelmeier T and Ludwig J ldquoImage Artifact in Digital

Breast Tomosynthesis and Its Dependence on System and Reconstruction

Parametersrdquo IWDM 2008 LNCS 5116 628-634 (2008)

22 Chen Y Lo JY Ranger NT Samei E Dobbins III JT ldquoMethodology of

NEQ(f) analysis for optimization and comparison of digital breast tomosynthesis

acquisition techniques and reconstruction algorithmsrdquo Proceedings of SPIE

Volume 6510 65101I (2007)

23 Zhao B Zhou J Hu Y-H Mertelmeier T Ludwig J and Zhao W

ldquoExperimental validation of a three-dimensional linear system model for breast

tomosynthesisrdquo Medical Physics Volume 36 Number 1 240-251 (2009)

24 Madhav P Brzymialkiewicz CN Cutler SJ Bowsher JE and Tornai MP

ldquoCharacterizing the MTF in 3D for a Quantized SPECT Camera Having Arbitrary

Trajectoriesrdquo 2005 IEEE Nuclear Science Symposium Conference Record 1722-

1726 (2005)

25 Madhav P McKinley RL Samei E Bowsher JE and Tornai MP ldquoA Novel

Method to Characterize the MTF in 3D for Computed Mammotomographyrdquo

Proceedings of SPIE Volume 6142 61421Y (2006)

26 Hu Y-H Zhao B and Zhao W ldquoImage artifacts in digital breast

tomosynthesis Investigation of the effects of system geometry and

reconstruction parameters using a linear system approachrdquo Medical Physics

Volume 35 Number 12 5242-5252 (2008)

27 Seifert A and Flynn MJ ldquoResolving power of 3D x-ray microtomography

systemsrdquo Proceedings of SPIE Volume 4682 407-413 (2002)

28 Thornton MM and Flynn MJ Measurement of the spatial resolution of a

clinical volumetric computed tomography scanner using a sphere phantom

Proceedings of SPIE Volume 6142 61421Z (2006)

53

29 Baek J Pelc NJ ldquoUse of sphere phantoms to measure the 3D MTF of FDK

reconstructionsrdquo Proceedings of SPIE Volume 7961 79610D (2011)

30 Richard S and Samei E ldquoQuantitative imaging in breast tomosynthesis and CT

Comparison of detection and estimation task performancerdquo Medical Physics

Volume 37 Number 6 2627-2637 (2010)

31 Chen Y Lo JY and Dobbins III JT ldquoImpulse response analysis for several

digital tomosynthesis mammography reconstruction algorithmsrdquo Proceedings of

SPIE Volume 5745 541-549 (2005)

32 Zhao B and Zhao W ldquoThree-dimensional linear system analysis for breast

tomosynthesisrdquo Medical Physics Volume 35 Number 12 5219-5232 (2008)

33 Wu G Mainprize JG Boone JM and Yaffe MJ ldquoEvaluation of scatter

effects on image quality for breast tomosynthesisrdquo Medical Physics Volume 36

Number 10 4425-4432 (2009)

Page 7: Development and Evaluation of 2D and 3D Image Quality ...

vii

Contents

Abstract iv

List of Tables x

List of Figures xi

Acknowledgements xiii

I Evaluation of 2D Digital Image Receptors 1

I1 Introduction 1

I2 Materials and Methods 3

I2i Detectors 3

I2ii Beam Characterization 3

I2iia X-ray Techniques 3

I2iib Data Linearization 4

I2iic Spectral Simulation 5

I2iii DQE Measurements 6

I2iiia Modulation Transfer Function 6

I2iiib Noise Power Spectrum 7

I2iiic DQE Calculation 8

I3 Results 9

I3i Data Linearization 9

I3ii Spectral Simulation 9

I3iii Modulation Transfer Function 12

viii

I3iv Noise Power Spectrum 12

I3v Detective Quantum Efficiency 19

I4 Discussion 20

I4i Comparisons of Detectors 20

I4ii Comparisons of Filtrations 21

I4iii Implications of Wireless DR 26

I5 Conclusions 26

II Directional MTF for Breast Tomosynthesis 28

II1 Introduction 28

II2 Materials and Methods 29

II2i Image Simulation 29

II2ii Uncorrected MTF 30

II2iii Theoretical Directional MTF 32

II2iv Modified MTF 33

II2v Preliminary Experimental Validation 34

II3 Results 35

II3i Reconstruction 35

II3ii Theoretical MTF 37

II3iii Uncorrected MTF 38

II3iv Comparison of Theoretical and Simulated MTFs 41

II3v Modified MTF for x and y 42

II3v Preliminary Experimental Validation 44

ix

II4 Discussion 46

II4i Evaluation of Cone-based Method 46

II4ii Separation of Artifact and Resolution Information 48

II5 Conclusions 49

References 50

x

List of Tables

Table 1 Physical Characteristics of Digital Image Receptors 4

Table 2 Beam Qualities and Required Filtrations 5

Table 3 Spectral Simulation Results 11

Table 4 Experimental MTF frequency locations for 1 mR exposure 22

Table 5 Estimated DQE values for 1 mR exposure by frequency bins 22

xi

List of Figures

Figure 1 MTF images for DRX-1C detector with radio-opaque edge test device with

arrows indicating the horizontal (left) and vertical (right) directions 7

Figure 2 NNPS image for DRX-1C detector indicating the top left ROI that served as the

reference for normalizing other ROIs in the image The ROI array was formed along the

directions indicated by the arrows The heel effect visible along the vertical axis of the

detector is an example of small variation in signal across the image 8

Figure 3 Original (left) and linearized (right) system responses for Pixium 4600 The

linearized system responses were measured from actual images The offsets are small

with respect to the slope sufficient enough for zero-offset conditions 10

Figure 4 Spectral simulations for RQA5 (top) and RQA9 (bottom) conditions Note the

similarities of spectral shapes of the normalized spectra (right) Also note the significant

differences in fluence between filtrations in the simulated spectra (left) 11

Figure 5 MTF results by detector (columns) and beam quality (rows) 13

Figure 6 Plots of MTF for RQA5 (top) and RQA9 (bottom) showing the relationships

between detectors (blue red and green) and by filtration (solid and dashed) 14

Figure 7 NNPS results by detector (columns) and beam quality (rows) 15

Figure 8 Plots of NNPS for RQA5 (top) and RQA9 (bottom) at 1 mR exposure showing

the relationships between detectors (blue red and green) and by filtration (solid and

dashed) 16

Figure 9 DQE results by detector (columns) and beam quality (rows) 17

Figure 10 Plots of DQE for RQA5 (top) and RQA9 (bottom) at 1 mR exposure showing

the relationships between detectors (blue red and green) and by filtration (solid and

dashed) 18

Figure 11 DRX1-C NNPS images at 1 mR for RQA5 with IEC filtration (left) and

alternative filtration (right) Images are equally windowed at 45 and leveled at 980 24

Figure 12 Depiction of the virtual image system 30

xii

Figure 13 Example of 30-degree cone prescribed along z axis of the sphere 32

Figure 14 Photograph of the imaging system with the acrylic sphere phantom

embedded in oil 34

Figure 15 View of the central slice of the breast phantom reconstruction before (top) and

after (bottom) background subtraction The z axis is through the page 36

Figure 16 3D rendering of the ROI volume (left) and cross-sectional views of the most

centrally located sphere with centroid indicated with red circle (right) 37

Figure 17 Theoretical 3D MTF results along the three major planes (top) and along x y

and z directions (bottom) Also note that the angular spread seen in the fx-fz plane is

equal to the angular range of 44deg for the acquisition 38

Figure 18 Uncorrected ESF (top) LSF (middle) and MTF (bottom) for x y and z

directions 40

Figure 19 Comparisons of the directional MTFs as calculated by the sphere method

(dashed line) by theoretical line profiles (light-weight line) by theoretical cone regions

(heavy-weight line) 41

Figure 20 Modified ESF (top) LSF (middle) and MTF (bottom) for x and y directions 43

Figure 21 Cross sectional views of the experimental sphere image with centroid

indicated with red circle 44

Figure 22 ESF (top) LSF (middle) and MTF (bottom) of real image for x y and z

directions 45

xiii

Acknowledgements

I would like to thank Ian Yorkston Mark Purdum and Van Huston of

Carestream Health Inc (Rochester NY) for their help with digital detector

measurements I would also like to thank Olav Christianson Samuel Richard Brian

Harrawood and Max Amurao for their assistance with collecting data and analyzing

results Special thanks go to my committee members for their helpful insights and

suggestions for this thesis Last but not least I want to express deep appreciation for the

support and mentorship provided by my advisor Dr Ehsan Samei

1

I Evaluation of 2D Digital Image Receptors

I1 Introduction

In the past decade many areas of radiological practice have seen a conversion

from screen films to the storage phosphor cassettes of computed radiography (CR) to the

active-matrix flat-panel detectors of digital radiography (DR) Both CR and DR are

digital systems that offer many potential benefits including but not limited to better

image quality wider dynamic range quicker readout lower radiation dose and higher

throughput [1-3] Even with advances in DR technologies such as improved detective

quantum efficiency (DQE) the primary radiographic system of today continues to be CR

A major obstacle to completely accepting DR is the high capital cost of acquiring an

entire system per examination room while also providing capability for portable

applications Recently manufacturers like Carestream Health Fuji and Toshiba have

introduced wireless digital image receptors that can serve as replacements for CR

cassettes As these are new technologies a further investigation to characterize these

detectors is warranted

In the case of radiographic receptors DQE has historically been the metric of

choice [4] because it indicates the ability of the image receptor to convert incident x-ray

photons into useable signal ndash essentially a measure of signal-to-noise ratio (SNR)

efficiency and overall system performance [23] DQE is observed across a range of

spatial frequencies for evaluating how the detector depicts small and large objects [3]

2

DQE metrics have been used in numerous studies to characterize CR phosphor-screens

as well as indirect and direct digital detectors [4-11] The importance of this highly

quantitative metric may be implied by the introduction of a DQE measurement standard

by the International Electrotechnical Commission (IEC) [12]

The standard measurement methodology of the International Electrotechnical

Commission (IEC) pertains to the image quality of 2D digital radiographic detectors

While the IEC formalism is well-developed some of the components that it requires are

not necessarily the most optimal for characterizing DQE This has been explored in

previous studies in terms of filtration material purity beam limitations and region of

interest (ROI) configuration [1314] To reduce the variability in the radiographic output

across various x-ray tubes due to inherent filtration differences the IEC formalism

prescribes specific additional aluminum filtration to attain radiation beam qualities

based on target half value layers (HVL) Achieving and verifying the desired HVL

however requires applying a substantial amount of aluminum at the exit window of the

x-ray tube which is often directed toward the ground This can be a logistical

inconvenience and can increase the risk of damage to the image receptor and

measurement equipment Similar beam qualities on the other hand may be attained

more conveniently using a thinner lighter filtration combination utilizing a higher Z

number material Care is warranted however as a previous study [6] had indicated that

the choice of filtration material could impact the DQE

3

The purpose of this study was two-fold First we aimed to evaluate and compare

two wireless image receptors with a conventional flat-panel detector on the basis of DQE

performance Second we compared DQE results using the IEC-prescribed filtration with

an alternative filtration For the latter an optimum filtration composition was

determined and compared with the IEC filtration on the basis of DQE

I2 Materials and Methods

I2i Detectors

The physical characteristics of the three digital image receptors evaluated in this

study are listed in Table 1 The Pixium 4600 was a conventional digital flat-panel The

DRX-1C and DRX-1 were both wireless digital cassettes that were tethered for the

purposes of this study All detectors were FDA approved and available commercially

Each detector was calibrated according to its manufacturer specifications to correct for

gain offset and bad pixels They were all dedicated for non-clinical laboratory research

purposes and hence could be operated under service settings that permitted acquisition

of raw (ie for processing) images

I2ii Beam Characterization

I2iia X-ray Techniques

All measurements for this study were taken with a well-characterized standard

radiographic system (Super80CP Philips Healthcare Andover MA) The x-ray tube had

an inherent filtration of 27 mm Al Free in-air exposures were measured using

4

Table 1 Physical Characteristics of Digital Image Receptors

Manufacturer Detector

Detector

type

Detector

material

Pixel pitch

(size) Array size

Imaging

area

Trixell

(Moirans France)

Pixium

4600 Indirect

CsITl

(CsI) 0143 mm

3121times3121

4 subpanels 45times45 cm2

Carestream Health Inc

(Rochester NY)

DRX-1C

(wireless) Indirect

CsITl

(CsI) 0139 mm

2560times3072

single panel 35times43 cm2

Carestream Health Inc

(Rochester NY)

DRX-1

(wireless) Indirect

G2O2STb

(GOS) 0139 mm

2560times3072

single panel 35times43 cm2

calibrated radiation meters (Mult-O-Meter Type 407 Unfors Instruments AB Billdal

Sweden) at 183 cm source-to-chamber-distance (SCD) The SCD also corresponded to

same plane as the image receptor surface The x-ray output was made to conform to IEC

beam quality definitions [1215] on the basis of half value layer (HVL) and peak

kilovoltage setting using an aluminum filtration (type-1100 99 purity) and an

alternative filtration consisting of copper (UNS C11000 999 purity) and aluminum

(type-1100 99 purity) The IEC radiation quality numbers (RQA) used in this study are

summarized in Table 2 HVLs were determined by iteratively adding successive

thicknesses of aluminum until reaching reduced exposure levels within a tolerance of

0485-0515 [12] As for the alternative filtration the aluminum was placed downstream

of the copper filter to attenuate characteristic radiation peaks from copper at

approximately 9 keV

I2iib Data Linearization

The system response function was determined for each detector and filtration

combination by acquiring flat-field images at increasing photon fluence until just before

5

Table 2 Beam Qualities and Required Filtrations

IEC Radiation

Quality Number

Peak

kilovoltage

Required

HVL

Required IEC

Filtration

Actual IEC

Filtration

Alternative

Filtration

RQA5 70 kVp 71 mm Al 21 mm Al 21 mm Al 05 mm Cu +

10 mm Al

RQA9 120 kVp 115 mm Al 42 mm Al 40 mm Al 104 mm Cu +

10 mm Al

For reasons of convenience these will be referred to as RQA5A RQA5C RQA9A and RQA9C

saturation levels To avoid the influence of detector backscatter on exposure

measurements a relationship for each filtration was first determined for two radiation

meters A target meter was placed at the central axis and a reference meter was placed at

the edge of the light field (large enough to cover the detectors) The reference meter

served as a surrogate for the target meter to avoid direct exposure measurements in the

plane of the image receptor Exposure relationships were determined before each

measurement set (ie detector and filtration combination) to account for changes in

temperature pressure and humidity The system response function was calculated by

using a regression of ADU (pixel value) versus exposure Images acquired for each

series were then converted to achieve a linear response with zero offset and scaled to

achieve high quantization (adequate dynamic range) Linearization of the detector

responses ensured that zero exposure corresponded to zero pixel value

I2iic Spectral Simulation

The effects of additional filtration on x-ray output spectra were observed with

spectral simulation software (XSPECT V40 Henry Ford Hospital Detroit MI) To more

6

adequately describe the performance of a typical X-ray generator inherent filtration of 3

mm oil 148 mm Pyrex glass and 2 mm aluminum was input into the simulation in

addition to the filters of interest The ideal signal to noise ratio squared or incident

photon fluence per exposure (q) was estimated for each filtration by integrating the

energy-dependent photon counts per unit exposure over all energy bins

I2iii DQE Measurements

The assessment of the linearized images followed the formalism described by

IEC 62220-1 for measuring the DQE [12] For this study the normal exposure level XN

was set at 1 mR to the detector surface as measured at the central axis perpendicular to

the anode-cathode axis

I2iiia Modulation Transfer Function

Spatial resolution was characterized by evaluating the presampled modulation

transfer function (MTF) along directions parallel (vertical) and perpendicular

(horizontal) to the anode-cathode axis using the angled-edge method [6-1013] A radio-

opaque edge test device [7] was placed in the center of the field at a pitch of

approximately 301 (about 2deg) to the axis perpendicular to that being measured as

shown in Figure 1 External lead apertures were not used [6] instead the internal

collimation from the radiographic unit was used to collimate the beam to the detector

area Raw images were acquired of the edge with the normal exposure level XN of 1 mR

at the detector face The procedure of calculating the MTF followed previously described

7

methods [6-1013] The edge spread function (ESF) was determined along lines crossing

the edge of the angled test device The derivative of the ESF was calculated to form the

line spread function (LSF) to which a Hanning filter was applied The MTF was then

calculated as the fast Fourier transform (FFT) of the LSF and normalized at the zero-

frequency axis To conform to IEC guidelines the MTF was resampled into frequency

steps of 005 cyclesmm [12]

Figure 1 MTF images for DRX-1C detector with radio-opaque edge test device with

arrows indicating the horizontal (left) and vertical (right) directions

I2iiib Noise Power Spectrum

Noise amplitude and texture were characterized by determining the normalized

noise power spectrum (NNPS) which was evaluated with flat field exposures at

approximate exposure levels of XN2 XN and 2XN (05 10 and 20 mR) to the image

receptor surface Analysis of the flat-field images followed previously defined methods

[41415] using over 4 million independent pixels with regions of interest (ROIs) of size

8

128x128 The NNPS images were detrended using a quadratic (second order)

background subtraction Small variations in exposure across ROIs were corrected by

normalizing pixel values of each ROI to the mean value in the top left ROI as shown in

Figure 2 The NNPS was then calculated with the 2D FFT including the zero-frequency

axes corresponding to the horizontal and vertical directions The results were then

resampled using 005 frequency bins according to IEC guidelines [12]

Figure 2 NNPS image for DRX-1C detector indicating the top left ROI that served as

the reference for normalizing other ROIs in the image The ROI array was formed

along the directions indicated by the arrows The heel effect visible along the vertical

axis of the detector is an example of small variation in signal across the image

I2iiic DQE Calculation

The DQE was calculated using the following relationship [615]

9

where the frequency-dependent MTF and NNPS were determined as described in

previous sections X was the exposure value in mR corresponding to the NNPS image

and q was the ideal signal to noise ratio squared in units of photonsmiddotmm-2middotmR-1 as

estimated from the spectral simulations

I3 Results

I3i Data Linearization

The detectors in this study provided raw ADU (or pixel) values in a linear scale

The data were converted using the following system conversion function

where Q(ij) is the raw image data m and b are slope and intercept parameters obtained

from linear regression of the system response function and I(ij) is the linearized scaled

data The factor of 1000 was found to scale I(ij) such that the maximum value was a

large 16-bit number Figure 3 shows the original and linearized system responses for the

Pixium 4600 Note that the y-intercepts of the regressions for the linearized responses

are negligible (lt 01) with respect to the slopes a sufficient condition for zero offset

considerations

I3ii Spectral Simulation

The spectral simulations of the IEC filtrations and alternative filtrations indicate

many similarities in their effective energies HVLs and overall shapes of normalized

spectra Results are summarized in Table 3

10

Pixium 4600 Original System

Response

Pixium 4600 Linearized System

Response R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 3 Original (left) and linearized (right) system responses for Pixium 4600 The

linearized system responses were measured from actual images The offsets are small

with respect to the slope sufficient enough for zero-offset conditions

y = 13971x - 13236

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x - 00106Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 13576x + 28292

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

7000

0000 1000 2000 3000 4000 5000

AD

U

Exposure (mR)

y = 99997x - 00067Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0000 1000 2000 3000 4000 5000

AD

U

Exposure (mR)

y = 13644x + 16167Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x + 00044

Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 13845x + 13541

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x - 00177

Rsup2= 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

11

Table 3 Spectral Simulation Results

Beam Quality Filtration

Mean Energy

(kV)

Photon Fluence

(mRmm2)

RQA5A 21 mm Al 5243 259543

RQA5C 05 mm Cu + 10 mm Al 5214 259554

diff 055 0004

RQA9A 40 mm Al 7619 273281

RQA9C 104 mm Cu + 10 mm Al 7579 273964

diff 052 025

Figure 4 Spectral simulations for RQA5 (top) and RQA9 (bottom) conditions Note

the similarities of spectral shapes of the normalized spectra (right) Also note the

significant differences in fluence between filtrations in the simulated spectra (left)

00E+00

50E+04

10E+05

15E+05

20E+05

25E+05

30E+05

35E+05

40E+05

45E+05

0 20 40 60 80

ph

oto

ns

mA

s-1

cm

-2

keV

RQA5 Spectra Comparison

21 mm Al

05 mm Cu + 10 mm Al

00

02

04

06

08

10

12

0 20 40 60 80

keV

RQA5 Normalized Spectra Comparison

21 mm Al

05 mm Cu +

10 mm Al

00E+00

50E+05

10E+06

15E+06

20E+06

25E+06

30E+06

35E+06

40E+06

45E+06

50E+06

0 50 100 150

ph

oto

ns

mA

s-1

cm

-2

keV

RQA9 Spectra Comparison

40 mm Al

104 mm Cu +

10 mm Al

00

02

04

06

08

10

12

0 50 100 150

keV

RQA9 Normalized Spectra Comparison

40 mm Al104 mm Cu + 10 mm Al

12

I3iii Modulation Transfer Function

The limiting spatial resolutions of the systems were indicated by the cutoff

frequencies which were approximately 35 cyclesmm for all three detectors The spatial

resolutions also demonstrated a good degree of isotropy as confirmed by the close

alignment of MTF curves between vertical and horizontal directions differentiated in

Figure 5 by dashed and solid lines respectively The MTF curves for the Pixium 4600

and DRX-1C were nearly equal to each other whereas the DRX-1 MTF curve showed a

more rapid decrease at high frequencies as shown in Figure 6 This difference may be

due to the differences in the inherent optical properties of the scintillating materials

where finer image details are provided by structured CsI more than by granulated GOS

There were no significant differences in MTF curves across beam qualities and filtrations

as shown by the curve comparisons in Figure 6 although the alternative filtration

produced slightly higher MTF curves as seen in Figure 4 Table 4 lists the experimental

specific spatial frequencies for varying levels of MTF

I3iv Noise Power Spectrum

The noise characteristics are indicated by the NNPS curves shown in Figure 7

The noise was similar for both horizontal and vertical directions As exposure increased

the NNPS decreased consistent with the characteristics of Poisson noise describing the

relationship between signal and noise in the presence of increased photon fluence At

13

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 5 MTF results by detector (columns) and beam quality (rows)

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

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00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

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10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

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00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

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MTF

Spatial Freq (mm)

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vert

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MTF

Spatial Freq (mm)

MTF

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MTF

Spatial Freq (mm)

MTF

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vert

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MTF

Spatial Freq (mm)

MTF

horiz

vert

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MTF

Spatial Freq (mm)

MTF

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vert

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MTF

Spatial Freq (mm)

MTF

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vert

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MTF

Spatial Freq (mm)

MTF

horiz

vert

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06

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00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

horizontal

vertical

14

Figure 6 Plots of MTF for RQA5 (top) and RQA9 (bottom) showing the relationships

between detectors (blue red and green) and by filtration (solid and dashed)

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm-1)

MTF

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm-1)

MTF

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

15

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 7 NNPS results by detector (columns) and beam quality (rows)

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

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enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

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enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

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1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

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1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

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1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

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1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

05 mR - horizontal

05 mR - vertical

10 mR - horizontal

10 mR - vertical

20 mR - horizontal

20 mR - vertical

16

Figure 8 Plots of NNPS for RQA5 (top) and RQA9 (bottom) at 1 mR exposure

showing the relationships between detectors (blue red and green) and by filtration

(solid and dashed)

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm-1)

NNPS (1 mR)

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm-1)

NNPS (1 mR)

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

17

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 9 DQE results by detector (columns) and beam quality (rows)

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DQE

Spatial Freq (mm)

DQE

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Spatial Freq (mm)

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Spatial Freq (mm)

DQE

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Spatial Freq (mm)

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DQE

Spatial Freq (mm)

DQE

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DQE

Spatial Freq (mm)

DQE

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DQE

Spatial Freq (mm)

DQE

enl0-h

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enl2-h

enl2-v

05 mR - horizontal

05 mR - vertical

10 mR - horizontal

10 mR - vertical

20 mR - horizontal

20 mR - vertical

18

Figure 10 Plots of DQE for RQA5 (top) and RQA9 (bottom) at 1 mR exposure showing

the relationships between detectors (blue red and green) and by filtration (solid and

dashed)

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm-1)

DQE (1 mR)

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

00

01

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04

05

06

07

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00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm-1)

DQE

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

19

higher frequencies the NNPS curves of the Pixium 4600 and DRX-1 diverge slightly for

the different directions illustrating increased noise in the readout direction (vertical)

Differences in the noise characteristics were more apparent among detectors as

shown for 1 mR in Figure 8 The NNPS curve for the DRX-1 was higher in magnitude

across the entire frequency range than either the Pixium 4600 or DRX-1C which both

seemed to demonstrate reasonably similar NNPS curves The higher magnitude noise of

the DRX-1 indicates higher relative noise content overall Closer inspection of the NNPS

curves of the Pixium 4600 and DRX-1C detectors in Figure 7 revealed differences in the

spacing between the three exposure levels The gaps between the Pixium 4600 NNPS

curves do not correspond to the factor of two differences between each exposure level

especially at low- to mid- spatial frequencies suggesting a higher level of fixed pattern

noise additional noise with increasing exposure levels due to ineffective gain map

corrections Between filtration schemes the differences in NNPS curves for a given beam

quality were not substantial as shown in Figure 7

I3v Detective Quantum Efficiency

The DQE results are shown in Figure 9 DQE curves across exposure levels were

almost collinear except for Pixium 4600 and in general could be inferred from the

NNPS results Additionally the DQE curves demonstrated a relatively linear response

with spatial frequencies as expected for flat-panel detectors [9] Differences in DQE

among detectors were consistent for the most part with the type of scintillating material

20

As depicted for 1 mR exposure in Figure 10 differences between Pixium 4600 and DRX-

1C DQE curves correspond to the differences in their NNPS curves DRX-1 DQE curves

were consistently lower than either the Pixium 4600 or DRX-1C curves The DQE curves

for the alternative filtration were consistently higher than those for the IEC filtration

and the most noticeable differences were near the zero-frequency axis These effects can

be both attributed to ineffective gain map correction DQE values for 1 mR exposure are

listed in Table 5

I4 Discussion

I4i Comparisons of Detectors

The limiting spatial resolutions of all three detectors were almost exactly the

same considering that their pixel areas were similar in size The decrease in high-

frequency MTF of the DRX-1 compared to the other detectors is probably a result of

increased optical blurring due to the differences in the powdered structure of GOS

versus the needle-like structure of CsI [2] The fact that the DRX-1C and Pixium 4600

have comparable MTFs suggests similar scintillator thicknesses assuming that the

materials were processed alike

The noise of the three detectors demonstrated similar trends with each other The

higher NNPS curves of the DRX-1 detector are probably due also to the scintillating

material and its operation in converting photons into signal The conversion process is

less efficient because of the less favorable stopping power of the GOS compared to CsI

21

especially with higher energy beams The noise of the Pixium 4600 and DRX-1C were

similar except for the spacing between exposures The DRX-1C NNPS curve spacing is

consistent with a factor of two difference in exposure levels but the Pixium 4600 has a

smaller spacing The 05 mR NNPS curve of the Pixium 4600 is closer to that of the 05

mR NNPS curve of the DRX-1C This demonstrates that at higher exposures the Pixium

4600 produces a larger amount of additional noise beyond that explained by simple

stochastic effects It suggests bad performance in the gain map corrections

The DQE results indicate SNR properties of each detector The Pixium 4600 and

DRX-1C are comparable for the most part with the DRX-1C performing slightly better

The DRX-1 as predicted from MTF and NNPS results has a DQE much lower than

either of the previous two This is a reflection of the detection properties as provided by

its scintillator material The DQE of the DRX-1 however is comparable to CR image

receptors [2] The mid-frequency dips in the DQE for Pixium 4600 may be due to the

optical properties of the CsI phosphor layer which can affect the MTF in this manner

Because the DQE is calculated by squaring the MTF this effect at the mid-range

frequencies becomes more apparent The dips may also be further evidence of bad gain

map corrections

I4ii Comparisons of Filtrations

The alternative filtration closely matches for the most part the IEC-based

filtration for MTF NNPS and DQEs at RQA5 but not at RQA9 The filters do not have

22

Table 4 Experimental MTF frequency locations for 1 mR exposure

Detector Filtration

50 MTF

(mm-1)

40 MTF

(mm-1)

30 MTF

(mm-1)

20 MTF

(mm-1)

10 MTF

(mm-1)

Pixium

4600

RQA5A 115 145 185 245 330

RQA5C 125 155 195 250 345

RQA9A 110 175 175 235 330

RQA9C 125 155 195 255 345

DRX-1C

RQA5A 120 150 185 245 350

RQA5C 125 155 195 255 355

RQA9A 120 150 190 250 355

RQA9C 130 160 210 265 360

DRX-1

RQA5A 110 135 160 205 280

RQA5C 110 135 170 210 285

RQA9A 105 125 155 195 270

RQA9C 110 135 165 210 285

Table 5 Estimated DQE values for 1 mR exposure by frequency bins

Detector Filtration DQE(00 mm-1) DQE(10 mm-1) DQE(20 mm-1) DQE(30 mm-1)

Pixium

4600

RQA5A 62 42 32 21

RQA5C 63 45 36 25

RQA9A 41 27 30 13

RQA9C 43 33 27 19

DRX-1C

RQA5A 72 52 35 21

RQA5C 76 55 41 24

RQA9A 49 33 23 15

RQA9C 51 40 31 20

DRX-1

RQA5A 38 24 12 4

RQA5C 38 25 14 5

RQA9A 28 18 9 4

RQA9C 28 19 12 5

DQE values at the zero-frequency axis were estimated by the intercept of a linear fit of low-frequency data

but excluding most proximal to the axis due to large fluctuations Other estimated values are grouped into

frequency bins due to the noisiness of the data

23

considerable differences in the spatial resolutions of the detectors as expected The noise

responses for each filtration were also similar except at the lower frequencies of the

NNPS especially near the zero-frequency axis There observing the NNPS responses at

RQA5 for Pixium 4600 and DRX-1C in Figure 8 the NNPS for the IEC-based filtration

(solid lines) tend to drop faster than the NNPS for the alternative filtration This

subsequently appears as a drop in DQE near the zero-frequency axis shown for those

detectors in Figure 10 Overall as indicated in Table 5 the DQEs of the two filtrations

while similar in trend indicate that the alternative filtration increases the DQE by a

small amount of 3-5 Part of this may be explained by the slightly higher beam

energy which may be more optimal for the energy response of the detectors or may

weigh the pixel responses slightly considering that they are energy-integrating types

The most probable explanation is the gain map correction for the alternative filtration

where fixed pattern noise is more sufficiently reduced

A previous study [6] had discussed the choice of filter material in the analysis of

DQE when achieving the beam conditions defined by IEC It found that visible

nonuniformities were present with the higher purity aluminum filter (type-11999 alloy)

The low frequency mottle in the flat-field images for NPS measurements were also

attributed to structured noise from the grain size in the IEC-based filter with an

attenuating thickness that would reveal nonuniformities The mottle in the current study

was only observable under very narrow windowing as shown in Figure 11 Such low

24

frequency artifacts which are not readily noticeable may also be caused by shading

artifacts inverse square law or even the heel effect A possible method to correct for this

is a subtraction method by taking the average of the flat-field images for an exposure

level and then subtracting that from each of them This would remove nonuniformities

that were not corrected using a suboptimal gain map calibration

Figure 11 DRX1-C NNPS images at 1 mR for RQA5 with IEC filtration (left) and

alternative filtration (right) Images are equally windowed at 45 and leveled at 980

One convenient aspect of the copper and aluminum filtration is that it requires

much less tube current to achieve the same amount of exposure at the detector than the

much thicker aluminum filtration As shown in the non-normalized spectra in Figure 2

the exiting photon fluence exiting the copper and aluminum filtration is substantially

higher than that of the IEC-specified filtration This is due to the smaller total filtration

25

attenuation For extensive DQE analysis multiple sets of exposures may be acquired

before tube overheating becomes a concern

One limitation to the comparison of the two filtrations is that calibration

procedures specified copper and aluminum filtration at 80 kVp (for all detectors 05 mm

Cu and 10 mm Al) This may have influenced the results in favor of the alternative

filtration A further investigation involving the calibration procedures and performing

DQE measurements is encouraged Another factor may be influenced by the fact that the

tests were performed at 70 kVp and 120 kVp different from the recommended

calibration tube potential Clearly there would be differences in the linear attenuation

coefficients of the filters and different energy responses of the detectors themselves This

must be considered when interpreting DQE results The current results support a

previous study decades ago that described filtration of different material types in terms

of an aluminum equivalent [16] The results show that the two filtration schemes are

essentially equivalent when considering beam qualities and spatial resolutions The

NNPS and DQE results can be seen as close enough where their small differences are

insignificant when performing quality assurance tests in a clinical setting Overall our

results indicate that the alternative filtration with copper and aluminum may be more

convenient to use than the current IEC standard filtration

26

I4iii Implications of Wireless DR

This study has shown that wireless image receptors can have the same DQE

performance if not better than conventional flat-panel detectors They operate on the

same basic physical principles the new features offered by the DRX-1C and DRX-1 are

wireless communication with the workstation and electronics packaging technology

The latter feature may pose limitations for these units in terms of possible degradation

in the detectors in routine clinical conditions A consideration for future work would be

to longitudinally track DQE performance of the wireless detectors over time while being

utilized in a clinical environment In the end one must consider risks versus benefits of

choosing portable DR technology over CR one of which includes the cost and fragility

of DR detectors

The DQE performance of one wireless system is just as good as or better than

conventional systems as seen by the DRX-1C performance compared to the Pixium

4600 Wireless systems can also reduce the need for CR readers especially in portable

applications in other regions of the world (eg military hospitals developing countries)

However while DQE performance indicates the physical performance of the detector

system it is still unknown how it relates to observer performance

I5 Conclusions

Two wireless image receptors DRX-1C and DRX-1 were evaluated and

compared with the conventional DR flat-panel Pixium 4600 in terms of DQE

27

performance along with MTF and NNPS performances The detectors have similar

resolution properties although the DRX-1 is inferior at higher spatial frequencies The

NNPS and DQE results both indicate that the DRX-1C is superior to the DRX-1 and

comparable if not better to the Pixium 4600

The results from the filtration comparison indicate no substantial differences

between the IEC-based filtration and the copper-based alternative filtration Only slight

differences were found in the low frequency components of the NNPS and the DQE due

to the inherent nonuniformities of the IEC specified filtration Given the similarity of the

results and low attenuation advantage of the copper and aluminum filter its use is

encouraged

28

II Directional MTF for Breast Tomosynthesis

II1 Introduction

Breast tomosynthesis is an emerging 3D imaging modality that has potential use

for screening and diagnosis of breast cancer Breast tomosynthesis along with other 3D

techniques is preferable to planar imaging methods (eg mammography) because they

reduce anatomical noise by removing overlying structures above and below the plane of

an image slice [17-20] Recent advances in detectors and computer technology have

made digital tomosynthesis feasible

An image quality metric of particular importance in breast tomosynthesis is

spatial resolution Resolution is important to know in order to assess small-detail

structures such as microcalcifications A descriptive metric for characterizing spatial

resolution in the Fourier (or frequency) domain is the modulation transfer function

(MTF) Affected by reconstruction filters [21] the limited angular projections involved in

breast tomosynthesis results in highly anisotropic (or nonuniform) resolution Many

studies have looked only at characterizing the in-plane spatial resolution (ie in an

individual slice) with an elevated angled edge phantom [2223] A few studies have

looked at characterizing a more comprehensive 3D spatial resolution by using a

phantom with angled wires or tubes [24-26] However such studies require precise

mechanical alignment of the phantoms Several studies have explored a method using a

29

sphere phantom for the directional 3D MTF evaluation for microtomography [27] and

multi-slice CT [2829] This method has not yet been extended to breast tomosynthesis

This chapter focuses on breast tomosynthesis because it is highly anisotropic in

spatial resolution and like its predecessor mammography requires high spatial

resolution Additionally breast tomosynthesis acquisitions and reconstructions produce

several types of artifacts The use of a cone-based method using a sphere phantom [28] is

explored to characterize the directional 3D spatial resolution of simulated images from

breast tomosynthesis A technique for removing out-of-plane artifacts of the ESFs for the

in-plane axes is investigated to yield a modified MTF in a method that separates artifact

information from resolution information

II2 Materials and Methods

II2i Image Simulation

Breast tomosynthesis images were simulated by using a virtual imaging system

depicted in Figure 12 A volumetric breast phantom was voxelized as a rectangular mass

of uniform breast equivalent tissue of 4 cm thickness embedded with fifteen evenly

spaced plastic sphere inserts of 12 mm diameter The spheres were placed in a grid

formation within the central plane of the phantom The x-ray fluence was modeled from

a 28 kVp beam incident upon an indirect flat-panel detector with 200 micro m pixel size

Twenty-three projections within an angular range of 44deg were simulated using cascaded

systems analysis to generate characteristic 2D noise and spatial blurring [29] Each

30

projection was simulated to have an exposure of 174 mR with a fluence of 79 times 105

photonsmm-2 A standard filtered backprojection technique based on the Feldkamp

reconstruction algorithm [29] was used to reconstruct the projections and produce a

volumetric dataset with an isotropic voxel size of 200 micro m

Figure 12 Depiction of the virtual image system

II2ii Uncorrected MTF

To enable comparison of multiple spheres the reconstructed volume was

initially homogenized by performing a background subtraction based on a portion of the

volume devoid of spheres The voxel values were rescaled between one and zero to

eliminate negative values

31

The volumetric data were segmented to extract individual regions of interest

(ROIs) each containing a single sphere The ROIs extended along the full range of the z-

axis A thresholded ROI was generated by determining the exterior and interior voxels

relative to the sphere in the ROI The threshold value was set at 45 of the maximum

voxel value prior to thresholding The exterior and interior voxel values were then set to

values of 0 and 1 respectively Using the thresholded volume the center of mass was

calculated to determine the centroid The voxel values from the original ROI were

subsequently tabulated with the associated distances azimuthal angles and polar

angles relative to the centroid

Conical regions were prescribed along the positive and negative directions along

the three major axes extending from the centroid of the sphere as depicted in Figure 13

The axes about which the extent of the cone angle was delineated were defined with

the azimuthal and polar angles

Voxels with centers within the angular range of the cone were considered for

generating the edge spread function (ESF) To improve regularity of the distance

sampling interval the ESF values were rebinned to discrete distances corresponding to a

fraction of the voxel size Only voxels with distances ranging from the voxel size (ie

200 micro m) to the maximum distance were considered The ESFs from multiple spheres

were averaged together for each of the three major axes to produce an averaged ESF

which was further smoothed utilizing a Gaussian filter

32

Figure 13 Example of 30-degree cone prescribed along z axis of the sphere

The resulting ESF was then differentiated using the central difference method to

produce the line spread function (LSF) A Hanning filter with the same length as the LSF

was applied to zero out the tails of the LSF The presampled MTF was subsequently

computed as the amplitude of the Fourier transform of the LSF The MTF was

normalized with respect to the maximum value occurring within the range of the cutoff

frequency Binning size and conical range for the ESF were considered for maximizing

accuracy and minimizing noise of the MTF verified by comparison against the

theoretical MTF as determined in the previous section

II2iii Theoretical Directional MTF

The theoretical 3D MTF was calculated using a priori knowledge of the transfer

function of the virtual imaging system described in the previous section A phantom

was created with a set of point objects in a uniform and noise-free background with the

objects spanning across the volume of the breast [29] Twenty-one realizations were

33

generated from the reconstructed images of the point objects to yield a set of 3D point

spread functions (PSFs) The 3D fast Fourier transform (FFT) was performed for each 3D

PSF and averaged to give an ldquoexpectationrdquo 3D MTF [29] The theoretical directional

MTFs in the three major spatial axes were determined by line profiles along each of the

corresponding spatial frequency axes in the 3D MTF An additional theoretical MTF for

each direction was determined by using the application of conical regions along the axes

in frequency-space to take into account the contributions of MTF information from other

planes

II2iv Modified MTF

The tomosynthesis reconstruction is known to have edge enhancements which

affect the overall MTF by shifting the peaks of the MTF toward the higher frequencies

[23] The presence of this artifact complicates the interpretation of the actual spatial

resolution of the images Several steps were performed to remove the artifact

contribution to the resolution information particularly for the in-plane x and y

directions with the assumption that resolution information was contained immediately

near the edge

For the x-direction averaged ESF only values that were detected to be inside the

edge of the sphere were considered Those values were previously determined via

thresholding for calculating the centroid The ESF information corresponding to these

values was inversed and flipped about the detected edge to produce a symmetric

34

modified ESF The modified MTF was subsequently calculated from this modified ESF

as described in the previous section

For the y-direction averaged ESF an upward trend was found in the initial part

of the ESF This section was detrended with a polynomial fit and subtracted to produce a

flatter curve in that region The resulting detrended ESF was used to calculate the y axis

modified MTF

Figure 14 Photograph of the imaging system with the acrylic sphere phantom

embedded in oil

II2v Preliminary Experimental Validation

A clinical breast tomosynthesis system (Mammomat Inspiration Siemens AG

Munich Germany) was used to perform a preliminary evaluation of the cone-based

MTF technique The phantom for the experiment consisted of a single acrylic ball of 075

in diameter (SmallParts Seattle WA) suspended by a 0029 in diameter plastic filament

35

(Omniflex Zebco Tulsa OK) in an acrylic frame filled up to 4 in with vegetable oil

(Target Brands Inc Minneapolis MN) The system and phantom are shown in Figure

14 Twenty-five projections with an angular range of 44deg were acquired and subsequently

reconstructed to produce a volume with a voxel size of 01times01times10 mm3 The voxels were

reformatted to have an isotropic size of 01 mm The uncorrected ESF LSF and MTF

were calculated as described in the previous section

II3 Results

II3i Reconstruction

The reconstructed volume is shown in Figure 15 Notice the edge enhancement

along the x-direction as indicated by the sharp shadowing artifacts on either side of the

spheres The background was effectively homogenized using the background

subtraction technique This also took account of the curved edges of the breast phantom

With the close spacing of the spheres in the phantom the shadows along the x direction

for the fifteen spheres overlap with each other As the nine centrally located spheres

experience this effect the same way they were used for determining the ESF

A 3D rendering of the ROI containing a sphere shown in Figure 16 indicates the

anisotropic resolution of the reconstruction Note that the sphere is not accurately

reconstructed and has an oblong shape especially along the z axis Cross sectional views

of the ROI also in Figure 16 clearly demonstrate the edge enhancement causing a

shadow artifact in the x direction caused by the incomplete angular sampling of

36

tomosynthesis The sampling also introduces the triangular reconstruction of the sphere

as seen in the x-z plane Note the gradual edge drop-off in the z direction much beyond

the sphere radius

Figure 15 View of the central slice of the breast phantom reconstruction before (top)

and after (bottom) background subtraction The z axis is through the page

37

Figure 16 3D rendering of the ROI volume (left) and cross-sectional views of the most

centrally located sphere with centroid indicated with red circle (right)

II3ii Theoretical MTF

The theoretical MTFs for x y and z directions as determined from the line

profiles of the 3D MTF are shown in Figure 17 The theoretical MTF in the x direction

has a maximum value that is toward higher frequencies Its 10 response occurs at

about 125 cyclesmm which is at 50 of the cutoff frequency The rapid increase from

the zero-frequency intercept to the peak corresponds to the ramp filter used in filtered

backprojection which decreases the weighting of low frequency contributions due to the

incomplete angular sampling of the frequency-space The MTF does not reach a value of

0 at the zero-frequency intercept as it is very difficult to assess the zero-frequency

intercept due to the finite size of the phantom The theoretical MTF in the y direction

peaks at the zero-frequency intercept and reaches 20 proximal to the cutoff frequency

38

The 10 MTF is well beyond the cutoff frequency The theoretical MTF in the z direction

has a rapid drop-off at very low spatial frequencies indicating the lack of resolution in

that dimension

Figure 17 Theoretical 3D MTF results along the three major planes (top) and along x

y and z directions (bottom) Also note that the angular spread seen in the fx-fz plane is

equal to the angular range of 44deg for the acquisition

II3iii Uncorrected MTF

The ESF LSF and MTF using the cone-based method are shown for the x y and

z directions in Figure 18 It was found that a bin size of one-tenth the voxel size (002

mm) and a cone angle of 30deg to establish the ESF were enough to minimize noise and

maximize accuracy in the uncorrected MTFs considering the reasonable comparison of

the shapes of the MTF curves with the theoretical results in Figure 17 The LSFs are

generally noisy because differentiation of the ESF increases the amplitude of the noise

39

The data shown reflect a convolution with a smoothing Gaussian filter which was later

further corrected for in the reported MTF Nevertheless the high frequency components

of the noise are well beyond the MTF cutoff frequency of 25 cyclesmm and do not

impact the MTF results greatly

For the ESF in the x direction the shadow effect evident at the edge of the sphere

is visible as a steep decline followed by an increase Due to the finite distance range

provided by the ROI the ESF beyond the edge did not asymptotically reach the

background value The corresponding LSF demonstrates a low frequency modulation

that is indicated by the shift of 03 cyclesmm in the x direction for the peak of the MTF

The MTF exhibits a zero-frequency intercept that is non-zero unlike the theoretical MTF

and a 10 value at approximately 1 cyclesmm These features may be a direct

consequence of MTF information ldquocontaminationrdquo from y and z directions Furthermore

the ESF in the y direction demonstrates a reasonably shaped curve except for the slight

upward trend within the radius of the sphere which can be attributed to the shadow

artifact overlapping with the sphere volume The associated MTF has a peak shifted by

approximately 01 cyclesmm away from the axis and a 10 MTF occurring at

approximately 15 cyclesmm Both features which are not present in the theoretical

results may also be attributed to contaminant MTF information from x and z directions

The ESF in the z direction has a drop-off that occurs at a small fraction of the cutoff

frequency similar to that demonstrated by the theoretical MTF

40

Uncorrected ESF LSF and MTF

Figure 18 Uncorrected ESF (top) LSF (middle) and MTF (bottom) for x y and z

directions

41

Figure 19 Comparisons of the directional MTFs as calculated by the sphere method

(dashed line) by theoretical line profiles (light-weight line) by theoretical cone

regions (heavy-weight line)

II3iv Comparison of Theoretical and Simulated MTFs

The theoretical MTF results obtained from line profiles through the 3D MTF and

the simulated MTFs using the cone-based technique did not match very well except for

the general shape of the curves It was assumed in the previous section that the cone-

based technique contains information from other planes Figure 19 compares MTFs in

each direction for the two methods described in the methods and an additional method

based on conical regions of the 3D MTF The latter computes the MTF by averaging

contributions of the 3D MTF using the same cone prescription method used to define the

ESFs Comparison of the curves indicate some interesting correlations aside from the

fact that using conical regions with the 3D MTF results produce more noisy MTF results

partly due to the low sampling provided by the theoretical calculations The same

conclusions regarding the z direction MTF can be confirmed regardless of either

theoretical MTF procedures The experimental x direction MTF seems to agree best with

42

the line profile method whereas the y direction MTF agrees better with the cone region

method The fact that the experimental x direction MTF has a drop-off frequency that is

lower than those of either of the theoretical MTFs in Figure 19 suggests that this might

be due to integration of the z-direction in the in-plane slices considering how slices are

essentially averages of z direction information contained within it [33]

II3v Modified MTF for x and y

Modified ESF LSF and MTF curves for x and y directions are shown in Figure

20 The modified ESF and the resulting LSF in the x direction appear symmetric as

expected from the inverse and flip operation of the interior ESF about the detected edge

The modified MTF appears with less variation than the uncorrected MTF and the MTF

peak occurs at the zero-frequency axis The correction yields a 10 MTF at about 15

cyclesmm an improvement from the uncorrected MTF but still distant from the cutoff

frequency The modified ESF in the y direction demonstrates the detrended curve within

the sphere radius after a quadratic polynomial fit The resulting modified MTF still

appears similar to the uncorrected MTF except that the peak now coincides with the

zero-frequency axis For both x and y directions the low response of the modified MTFs

at the higher frequencies suggests that the contamination from other directions is

substantial due to the angular range of the cone

43

Modified ESF LSF and MTF

Figure 20 Modified ESF (top) LSF (middle) and MTF (bottom) for x and y directions

44

II3v Preliminary Experimental Validation

Cross-sections of the reconstructed sphere volume are shown in Figure 21

Relative to the simulation reconstructions the reconstructions of the experimental

phantom images produce lower contrast and higher noise The preliminary results

shown in Figure 22 indicate that our technique can be applied to actual experimental

breast tomosynthesis reconstructions However due to the noise exhibited by the MTF

curves for the x and y directions we did not determine the modified MTFs to separate

resolution and artifact information

Figure 21 Cross sectional views of the experimental sphere image with centroid

indicated with red circle

45

Uncorrected ESF LSF and MTF for Real Image

Figure 22 ESF (top) LSF (middle) and MTF (bottom) of real image for x y

and z directions

46

II4 Discussion

II4i Evaluation of Cone-based Method

The cone-based MTF technique was introduced by Thornton and Flynn [28] for

evaluation of volumetric CT images To utilize this technique as a characterization of a

3D system spatial resolution one must first consider the validity of the assumption of

shift invariance such that the same MTF result may be obtained regardless of the

location of the sphere The study by Zhao et al [23] found that there was no shift

variance for the MTF measurements along the vertical axis but this was only considering

the in-plane resolution along one axis On the other hand this study evaluated the MTF

with images simulated with cascaded systems analysis which includes conditions of

linearity and shift invariance Additionally the MTF was calculated by averaging the

ESF from several spheres in the same volume only after performing a background

subtraction This step was essential to account for the sensitivity of centroid calculations

as well as ensuring symmetric ESFs for opposing axes of the sphere ROIs

The measurement of MTF with the cone-based technique inherently

supersamples the edge of the sphere to increase signal-to-noise-ratio (SNR) of edge

information by averaging the contributions of each voxel to the ESF [713] This method

also takes into account the discrete sampling of the voxels by accounting for various

shifts of the edge in the voxel (also known as the partial volume effect) However using

the curved surface of the sphere phantom to approximate an edge along a given

47

direction naturally leads to contamination of information from other directions aside

from the one of interest Preferably a directional ESF should be created by using a single

radial line but this would limit the available voxels to obtain edge information An ideal

situation theoretically would be to use a larger-sized sphere such that the surface is

nearly flat and perpendicular to the axes of interest This would also permit a reduction

in the angular range of the cone and thus the introduction of out-of-plane information in

the resulting MTF However sphere size is a limitation in breast tomosynthesis and the

use of a large phantom might void the assumption of shift invariance of the spatial

resolution

The choice of a sphere phantom nevertheless may be based on the clinical need

to quickly acquire a single image for MTF evaluation especially for multiple directions

without presenting extra logistical challenges The use of a wire or edge phantom

requires more precise mechanical alignment to achieve the correct set up The edge

phantom [23] would require at least two images to sample all three dimensions In the

case of the three wire phantom [2425] all three dimensions of the frame must be aligned

simultaneously with respect to the axis of rotation A similar situation would be

encountered when considering a cubic phantom with the planes normal to the axis of

interest In contrast to these phantoms the sphere eliminates the need for precise

alignment especially with respect to three spatial dimensions simultaneously A sphere

48

has ideal symmetry in all directions and can be used to evaluate MTF in any arbitrary

direction

This study unlike others [242532] did not explore the effects of physical

parameters such as scatter or contrast on the final MTF result but it demonstrated the

feasibility of using the cone-based method with an actual breast tomosynthesis image of

a sphere phantom as shown in Error Reference source not found and Error Reference

source not found These effects should be addressed in future works A further look

into deriving the principles of comparing the theoretical MTF with the experimental

MTF using the cone-based method is further warranted

II4ii Separation of Artifact and Resolution Information

The focus of this study was to develop a technique for measuring spatial

resolution of tomosynthesis images The intrinsic artifacts from tomosynthesis

reconstructions however lead to uncharacteristic MTFs and possible misinterpretation

of the effective resolution information When considering previous techniques for

calculating the presampled MTF [713152328] the analysis was performed using an

edge or a line to produce the corresponding ESF The resolution information is

essentially contained only along the edge indicated by the need to calculate the LSF In a

way the method of extracting artifact information is to focus the analysis only on the

edge part of the ESF to calculate the modified MTF This will lead to a better

understanding of the limiting size of objects that may be seen in the reconstructed 3D

49

image The presampled MTF without correction should still be analyzed to understand

the entire system response Note that the ESFs attempt to reflect information only at the

detected edge of the sphere

II5 Conclusions

The directional MTF of a simulated breast tomosynthesis reconstruction was

determined by using the cone-based MTF technique demonstrating the feasibility of a

single phantom for MTF evaluation This study further presented methods of analyzing

only the edge information in the ESF to create a modified MTF along in-slice (x and y)

axes It can provide insight into the actual spatial resolution information contained in the

image while separating the resolution information from the information introduced by

artifacts caused by the reconstruction and insufficient volumetric sampling The idea of

separating the resolution and artifacts from the measured ESF are expected to facilitate

the interpretation of MTF measurements in breast tomosynthesis Similar methods may

be applied to characterize the resolution of other 3D imaging modalities

50

References

1 Garmer M Hannigs SP Jaumlger HJ et al ldquoDigital Radiography Versus

Conventional Radiology in Chest Imaging Diagnostic Performance of a Large-

Area Silicon Flat-Panel Detector in a Clinical CT-Controlled Studyrdquo American

Journal of Roentgenology Volume 74 75-80 (2000)

2 Cowen AR Kengyelics SM and Davies AG ldquoSolid-state flat-panel digital

radiography detectors and their physical imaging characteristics rdquoClinical

Radiology Volume 63 487-498 (2008)

3 Chotas HG Dobbins III JT and Ravin CE ldquoPrinciples of Digital

Radiography with Large-Area Electronically Readable Detectors A Review of

the Basicsrdquo Radiology Volume 210 Number 3 595-599 (1999)

4 Flynn MJ and Samei E Experimental comparison of noise and resolution for

2k and 4k storage phosphor radiography systems Medical Physics Volume 26

Number 8 1612-1623 (1999)

5 Rong XJ Shaw CC Liu X Lemacks MR and Thompson SK

ldquoComparison of an amorphous siliconcesium iodide flat-panel digital chest

radiography system with screenfilm and computed radiography systems ndash A

contrast-detail phantom studyrdquo Medical Physics Volume 28 Number 11 2328-

2335 (2001)

6 Ranger NT Samei E Dobbins III JT and Ravin CE Measurement of the

detective quantum efficiency in digital detectors consistent with the IEC 62220-1

standard Practical considerations regarding the choice of filter material

Medical Physics Volume 30 Number 7 2305-2311 (2005)

7 Samei E Buhr E Granfors P Vandenbroucke D and Wang X Comparison

of edge analysis techniques for the determination of the MTF of digital

radiographic systems Physics in Medicine and Biology Volume 50 3613-3625

(2005)

8 Samei E and Flynn MJ An experimental comparison of detector performance

for computed radiography systems Medical Physics Volume 29 Number 4 447-

459 (2002)

51

9 Samei E and Flynn MJ An experimental comparison of detector performance

for direct and indirect digital radiography systems Medical Physics Volume 30

Number 4 608-622 (2003)

10 Samei E Ranger NT MacKenzie A Honey ID Dobbins III JT and Ravin

CE Effective DQE (eDQE) and speed of digital radiographic systems An

experimental methodology Medical Physics Volume 36 Number 8 3806-3817

(2009)

11 Samei E Ranger NT MacKenzie A Honey ID Dobbins III JT and Ravin

CE Detector or System Extending the Concept of Detective Quantum

Efficiency to Characterize the Performance of Digital Radiographic Imaging

Systems Radiology Volume 249 Number 3 926-937 (2008)

12 ldquoIEC 62220-1 Medical Electrical Equipment ndash Characteristics of Digital X-Ray

Imaging Devices ndash Part 1 Determination of the Detective Quantum Efficiencyrdquo

International Electrotechnical Commission Geneva Switzerland (2003)

13 Samei E Ranger NT Dobbins III JT and Chen Y Intercomparison of

methods for image quality characterization I Modulation transfer function

Medical Physics Volume 33 Number 5 1454-1465 (2006)

14 Dobbins III JT Samei E Ranger NT and Chen Y Intercomparison of

methods for image quality characterization II Noise power spectrum Medical

Physics Volume 33 Number 5 1466-1475 (2006)

15 Samei E Flynn MJ and Reimann DA A method for measuring the

presampled MTF of digital radiographic systems using an edge test device

Medical Physics Volume 25 Number 1 102-113 (1998)

16 Nagel HD ldquoAluminum equivalence of materials used in diagnostic radiology

and its dependence on beam qualityrdquo Physics in Medicine and Biology Volume

31 Number 12 1381-1399 (1986)

17 Niklason LT Christian BT Niklason LE et al ldquoDigital Tomosynthesis in

Breast Imagingrdquo Radiology Volume 205 399-406 (1997)

18 Gur D ldquoTomosynthesis Potential Clinical Role in Breast Imagingrdquo American

Journal of Roentgenology Volume 189 614-615 (2007)

52

19 Park JM Franken Jr EA Garg M Fajardo LL and Niklason LT ldquoBreast

Tomosynthesis Present Considerations and Future Applicationsrdquo

RadioGraphics Volume 27 S231-S240 (2007)

20 Good WF Abrams GS Catullo VJ Chough DM Ganott MA Hakim

CM and Gur D ldquoDigital Breast Tomosynthesis A Pilot Observer Studyrdquo

American Journal of Roentgenology Volume 190 865-869 (2008)

21 Hu Y-H Zhao W Mertelmeier T and Ludwig J ldquoImage Artifact in Digital

Breast Tomosynthesis and Its Dependence on System and Reconstruction

Parametersrdquo IWDM 2008 LNCS 5116 628-634 (2008)

22 Chen Y Lo JY Ranger NT Samei E Dobbins III JT ldquoMethodology of

NEQ(f) analysis for optimization and comparison of digital breast tomosynthesis

acquisition techniques and reconstruction algorithmsrdquo Proceedings of SPIE

Volume 6510 65101I (2007)

23 Zhao B Zhou J Hu Y-H Mertelmeier T Ludwig J and Zhao W

ldquoExperimental validation of a three-dimensional linear system model for breast

tomosynthesisrdquo Medical Physics Volume 36 Number 1 240-251 (2009)

24 Madhav P Brzymialkiewicz CN Cutler SJ Bowsher JE and Tornai MP

ldquoCharacterizing the MTF in 3D for a Quantized SPECT Camera Having Arbitrary

Trajectoriesrdquo 2005 IEEE Nuclear Science Symposium Conference Record 1722-

1726 (2005)

25 Madhav P McKinley RL Samei E Bowsher JE and Tornai MP ldquoA Novel

Method to Characterize the MTF in 3D for Computed Mammotomographyrdquo

Proceedings of SPIE Volume 6142 61421Y (2006)

26 Hu Y-H Zhao B and Zhao W ldquoImage artifacts in digital breast

tomosynthesis Investigation of the effects of system geometry and

reconstruction parameters using a linear system approachrdquo Medical Physics

Volume 35 Number 12 5242-5252 (2008)

27 Seifert A and Flynn MJ ldquoResolving power of 3D x-ray microtomography

systemsrdquo Proceedings of SPIE Volume 4682 407-413 (2002)

28 Thornton MM and Flynn MJ Measurement of the spatial resolution of a

clinical volumetric computed tomography scanner using a sphere phantom

Proceedings of SPIE Volume 6142 61421Z (2006)

53

29 Baek J Pelc NJ ldquoUse of sphere phantoms to measure the 3D MTF of FDK

reconstructionsrdquo Proceedings of SPIE Volume 7961 79610D (2011)

30 Richard S and Samei E ldquoQuantitative imaging in breast tomosynthesis and CT

Comparison of detection and estimation task performancerdquo Medical Physics

Volume 37 Number 6 2627-2637 (2010)

31 Chen Y Lo JY and Dobbins III JT ldquoImpulse response analysis for several

digital tomosynthesis mammography reconstruction algorithmsrdquo Proceedings of

SPIE Volume 5745 541-549 (2005)

32 Zhao B and Zhao W ldquoThree-dimensional linear system analysis for breast

tomosynthesisrdquo Medical Physics Volume 35 Number 12 5219-5232 (2008)

33 Wu G Mainprize JG Boone JM and Yaffe MJ ldquoEvaluation of scatter

effects on image quality for breast tomosynthesisrdquo Medical Physics Volume 36

Number 10 4425-4432 (2009)

Page 8: Development and Evaluation of 2D and 3D Image Quality ...

viii

I3iv Noise Power Spectrum 12

I3v Detective Quantum Efficiency 19

I4 Discussion 20

I4i Comparisons of Detectors 20

I4ii Comparisons of Filtrations 21

I4iii Implications of Wireless DR 26

I5 Conclusions 26

II Directional MTF for Breast Tomosynthesis 28

II1 Introduction 28

II2 Materials and Methods 29

II2i Image Simulation 29

II2ii Uncorrected MTF 30

II2iii Theoretical Directional MTF 32

II2iv Modified MTF 33

II2v Preliminary Experimental Validation 34

II3 Results 35

II3i Reconstruction 35

II3ii Theoretical MTF 37

II3iii Uncorrected MTF 38

II3iv Comparison of Theoretical and Simulated MTFs 41

II3v Modified MTF for x and y 42

II3v Preliminary Experimental Validation 44

ix

II4 Discussion 46

II4i Evaluation of Cone-based Method 46

II4ii Separation of Artifact and Resolution Information 48

II5 Conclusions 49

References 50

x

List of Tables

Table 1 Physical Characteristics of Digital Image Receptors 4

Table 2 Beam Qualities and Required Filtrations 5

Table 3 Spectral Simulation Results 11

Table 4 Experimental MTF frequency locations for 1 mR exposure 22

Table 5 Estimated DQE values for 1 mR exposure by frequency bins 22

xi

List of Figures

Figure 1 MTF images for DRX-1C detector with radio-opaque edge test device with

arrows indicating the horizontal (left) and vertical (right) directions 7

Figure 2 NNPS image for DRX-1C detector indicating the top left ROI that served as the

reference for normalizing other ROIs in the image The ROI array was formed along the

directions indicated by the arrows The heel effect visible along the vertical axis of the

detector is an example of small variation in signal across the image 8

Figure 3 Original (left) and linearized (right) system responses for Pixium 4600 The

linearized system responses were measured from actual images The offsets are small

with respect to the slope sufficient enough for zero-offset conditions 10

Figure 4 Spectral simulations for RQA5 (top) and RQA9 (bottom) conditions Note the

similarities of spectral shapes of the normalized spectra (right) Also note the significant

differences in fluence between filtrations in the simulated spectra (left) 11

Figure 5 MTF results by detector (columns) and beam quality (rows) 13

Figure 6 Plots of MTF for RQA5 (top) and RQA9 (bottom) showing the relationships

between detectors (blue red and green) and by filtration (solid and dashed) 14

Figure 7 NNPS results by detector (columns) and beam quality (rows) 15

Figure 8 Plots of NNPS for RQA5 (top) and RQA9 (bottom) at 1 mR exposure showing

the relationships between detectors (blue red and green) and by filtration (solid and

dashed) 16

Figure 9 DQE results by detector (columns) and beam quality (rows) 17

Figure 10 Plots of DQE for RQA5 (top) and RQA9 (bottom) at 1 mR exposure showing

the relationships between detectors (blue red and green) and by filtration (solid and

dashed) 18

Figure 11 DRX1-C NNPS images at 1 mR for RQA5 with IEC filtration (left) and

alternative filtration (right) Images are equally windowed at 45 and leveled at 980 24

Figure 12 Depiction of the virtual image system 30

xii

Figure 13 Example of 30-degree cone prescribed along z axis of the sphere 32

Figure 14 Photograph of the imaging system with the acrylic sphere phantom

embedded in oil 34

Figure 15 View of the central slice of the breast phantom reconstruction before (top) and

after (bottom) background subtraction The z axis is through the page 36

Figure 16 3D rendering of the ROI volume (left) and cross-sectional views of the most

centrally located sphere with centroid indicated with red circle (right) 37

Figure 17 Theoretical 3D MTF results along the three major planes (top) and along x y

and z directions (bottom) Also note that the angular spread seen in the fx-fz plane is

equal to the angular range of 44deg for the acquisition 38

Figure 18 Uncorrected ESF (top) LSF (middle) and MTF (bottom) for x y and z

directions 40

Figure 19 Comparisons of the directional MTFs as calculated by the sphere method

(dashed line) by theoretical line profiles (light-weight line) by theoretical cone regions

(heavy-weight line) 41

Figure 20 Modified ESF (top) LSF (middle) and MTF (bottom) for x and y directions 43

Figure 21 Cross sectional views of the experimental sphere image with centroid

indicated with red circle 44

Figure 22 ESF (top) LSF (middle) and MTF (bottom) of real image for x y and z

directions 45

xiii

Acknowledgements

I would like to thank Ian Yorkston Mark Purdum and Van Huston of

Carestream Health Inc (Rochester NY) for their help with digital detector

measurements I would also like to thank Olav Christianson Samuel Richard Brian

Harrawood and Max Amurao for their assistance with collecting data and analyzing

results Special thanks go to my committee members for their helpful insights and

suggestions for this thesis Last but not least I want to express deep appreciation for the

support and mentorship provided by my advisor Dr Ehsan Samei

1

I Evaluation of 2D Digital Image Receptors

I1 Introduction

In the past decade many areas of radiological practice have seen a conversion

from screen films to the storage phosphor cassettes of computed radiography (CR) to the

active-matrix flat-panel detectors of digital radiography (DR) Both CR and DR are

digital systems that offer many potential benefits including but not limited to better

image quality wider dynamic range quicker readout lower radiation dose and higher

throughput [1-3] Even with advances in DR technologies such as improved detective

quantum efficiency (DQE) the primary radiographic system of today continues to be CR

A major obstacle to completely accepting DR is the high capital cost of acquiring an

entire system per examination room while also providing capability for portable

applications Recently manufacturers like Carestream Health Fuji and Toshiba have

introduced wireless digital image receptors that can serve as replacements for CR

cassettes As these are new technologies a further investigation to characterize these

detectors is warranted

In the case of radiographic receptors DQE has historically been the metric of

choice [4] because it indicates the ability of the image receptor to convert incident x-ray

photons into useable signal ndash essentially a measure of signal-to-noise ratio (SNR)

efficiency and overall system performance [23] DQE is observed across a range of

spatial frequencies for evaluating how the detector depicts small and large objects [3]

2

DQE metrics have been used in numerous studies to characterize CR phosphor-screens

as well as indirect and direct digital detectors [4-11] The importance of this highly

quantitative metric may be implied by the introduction of a DQE measurement standard

by the International Electrotechnical Commission (IEC) [12]

The standard measurement methodology of the International Electrotechnical

Commission (IEC) pertains to the image quality of 2D digital radiographic detectors

While the IEC formalism is well-developed some of the components that it requires are

not necessarily the most optimal for characterizing DQE This has been explored in

previous studies in terms of filtration material purity beam limitations and region of

interest (ROI) configuration [1314] To reduce the variability in the radiographic output

across various x-ray tubes due to inherent filtration differences the IEC formalism

prescribes specific additional aluminum filtration to attain radiation beam qualities

based on target half value layers (HVL) Achieving and verifying the desired HVL

however requires applying a substantial amount of aluminum at the exit window of the

x-ray tube which is often directed toward the ground This can be a logistical

inconvenience and can increase the risk of damage to the image receptor and

measurement equipment Similar beam qualities on the other hand may be attained

more conveniently using a thinner lighter filtration combination utilizing a higher Z

number material Care is warranted however as a previous study [6] had indicated that

the choice of filtration material could impact the DQE

3

The purpose of this study was two-fold First we aimed to evaluate and compare

two wireless image receptors with a conventional flat-panel detector on the basis of DQE

performance Second we compared DQE results using the IEC-prescribed filtration with

an alternative filtration For the latter an optimum filtration composition was

determined and compared with the IEC filtration on the basis of DQE

I2 Materials and Methods

I2i Detectors

The physical characteristics of the three digital image receptors evaluated in this

study are listed in Table 1 The Pixium 4600 was a conventional digital flat-panel The

DRX-1C and DRX-1 were both wireless digital cassettes that were tethered for the

purposes of this study All detectors were FDA approved and available commercially

Each detector was calibrated according to its manufacturer specifications to correct for

gain offset and bad pixels They were all dedicated for non-clinical laboratory research

purposes and hence could be operated under service settings that permitted acquisition

of raw (ie for processing) images

I2ii Beam Characterization

I2iia X-ray Techniques

All measurements for this study were taken with a well-characterized standard

radiographic system (Super80CP Philips Healthcare Andover MA) The x-ray tube had

an inherent filtration of 27 mm Al Free in-air exposures were measured using

4

Table 1 Physical Characteristics of Digital Image Receptors

Manufacturer Detector

Detector

type

Detector

material

Pixel pitch

(size) Array size

Imaging

area

Trixell

(Moirans France)

Pixium

4600 Indirect

CsITl

(CsI) 0143 mm

3121times3121

4 subpanels 45times45 cm2

Carestream Health Inc

(Rochester NY)

DRX-1C

(wireless) Indirect

CsITl

(CsI) 0139 mm

2560times3072

single panel 35times43 cm2

Carestream Health Inc

(Rochester NY)

DRX-1

(wireless) Indirect

G2O2STb

(GOS) 0139 mm

2560times3072

single panel 35times43 cm2

calibrated radiation meters (Mult-O-Meter Type 407 Unfors Instruments AB Billdal

Sweden) at 183 cm source-to-chamber-distance (SCD) The SCD also corresponded to

same plane as the image receptor surface The x-ray output was made to conform to IEC

beam quality definitions [1215] on the basis of half value layer (HVL) and peak

kilovoltage setting using an aluminum filtration (type-1100 99 purity) and an

alternative filtration consisting of copper (UNS C11000 999 purity) and aluminum

(type-1100 99 purity) The IEC radiation quality numbers (RQA) used in this study are

summarized in Table 2 HVLs were determined by iteratively adding successive

thicknesses of aluminum until reaching reduced exposure levels within a tolerance of

0485-0515 [12] As for the alternative filtration the aluminum was placed downstream

of the copper filter to attenuate characteristic radiation peaks from copper at

approximately 9 keV

I2iib Data Linearization

The system response function was determined for each detector and filtration

combination by acquiring flat-field images at increasing photon fluence until just before

5

Table 2 Beam Qualities and Required Filtrations

IEC Radiation

Quality Number

Peak

kilovoltage

Required

HVL

Required IEC

Filtration

Actual IEC

Filtration

Alternative

Filtration

RQA5 70 kVp 71 mm Al 21 mm Al 21 mm Al 05 mm Cu +

10 mm Al

RQA9 120 kVp 115 mm Al 42 mm Al 40 mm Al 104 mm Cu +

10 mm Al

For reasons of convenience these will be referred to as RQA5A RQA5C RQA9A and RQA9C

saturation levels To avoid the influence of detector backscatter on exposure

measurements a relationship for each filtration was first determined for two radiation

meters A target meter was placed at the central axis and a reference meter was placed at

the edge of the light field (large enough to cover the detectors) The reference meter

served as a surrogate for the target meter to avoid direct exposure measurements in the

plane of the image receptor Exposure relationships were determined before each

measurement set (ie detector and filtration combination) to account for changes in

temperature pressure and humidity The system response function was calculated by

using a regression of ADU (pixel value) versus exposure Images acquired for each

series were then converted to achieve a linear response with zero offset and scaled to

achieve high quantization (adequate dynamic range) Linearization of the detector

responses ensured that zero exposure corresponded to zero pixel value

I2iic Spectral Simulation

The effects of additional filtration on x-ray output spectra were observed with

spectral simulation software (XSPECT V40 Henry Ford Hospital Detroit MI) To more

6

adequately describe the performance of a typical X-ray generator inherent filtration of 3

mm oil 148 mm Pyrex glass and 2 mm aluminum was input into the simulation in

addition to the filters of interest The ideal signal to noise ratio squared or incident

photon fluence per exposure (q) was estimated for each filtration by integrating the

energy-dependent photon counts per unit exposure over all energy bins

I2iii DQE Measurements

The assessment of the linearized images followed the formalism described by

IEC 62220-1 for measuring the DQE [12] For this study the normal exposure level XN

was set at 1 mR to the detector surface as measured at the central axis perpendicular to

the anode-cathode axis

I2iiia Modulation Transfer Function

Spatial resolution was characterized by evaluating the presampled modulation

transfer function (MTF) along directions parallel (vertical) and perpendicular

(horizontal) to the anode-cathode axis using the angled-edge method [6-1013] A radio-

opaque edge test device [7] was placed in the center of the field at a pitch of

approximately 301 (about 2deg) to the axis perpendicular to that being measured as

shown in Figure 1 External lead apertures were not used [6] instead the internal

collimation from the radiographic unit was used to collimate the beam to the detector

area Raw images were acquired of the edge with the normal exposure level XN of 1 mR

at the detector face The procedure of calculating the MTF followed previously described

7

methods [6-1013] The edge spread function (ESF) was determined along lines crossing

the edge of the angled test device The derivative of the ESF was calculated to form the

line spread function (LSF) to which a Hanning filter was applied The MTF was then

calculated as the fast Fourier transform (FFT) of the LSF and normalized at the zero-

frequency axis To conform to IEC guidelines the MTF was resampled into frequency

steps of 005 cyclesmm [12]

Figure 1 MTF images for DRX-1C detector with radio-opaque edge test device with

arrows indicating the horizontal (left) and vertical (right) directions

I2iiib Noise Power Spectrum

Noise amplitude and texture were characterized by determining the normalized

noise power spectrum (NNPS) which was evaluated with flat field exposures at

approximate exposure levels of XN2 XN and 2XN (05 10 and 20 mR) to the image

receptor surface Analysis of the flat-field images followed previously defined methods

[41415] using over 4 million independent pixels with regions of interest (ROIs) of size

8

128x128 The NNPS images were detrended using a quadratic (second order)

background subtraction Small variations in exposure across ROIs were corrected by

normalizing pixel values of each ROI to the mean value in the top left ROI as shown in

Figure 2 The NNPS was then calculated with the 2D FFT including the zero-frequency

axes corresponding to the horizontal and vertical directions The results were then

resampled using 005 frequency bins according to IEC guidelines [12]

Figure 2 NNPS image for DRX-1C detector indicating the top left ROI that served as

the reference for normalizing other ROIs in the image The ROI array was formed

along the directions indicated by the arrows The heel effect visible along the vertical

axis of the detector is an example of small variation in signal across the image

I2iiic DQE Calculation

The DQE was calculated using the following relationship [615]

9

where the frequency-dependent MTF and NNPS were determined as described in

previous sections X was the exposure value in mR corresponding to the NNPS image

and q was the ideal signal to noise ratio squared in units of photonsmiddotmm-2middotmR-1 as

estimated from the spectral simulations

I3 Results

I3i Data Linearization

The detectors in this study provided raw ADU (or pixel) values in a linear scale

The data were converted using the following system conversion function

where Q(ij) is the raw image data m and b are slope and intercept parameters obtained

from linear regression of the system response function and I(ij) is the linearized scaled

data The factor of 1000 was found to scale I(ij) such that the maximum value was a

large 16-bit number Figure 3 shows the original and linearized system responses for the

Pixium 4600 Note that the y-intercepts of the regressions for the linearized responses

are negligible (lt 01) with respect to the slopes a sufficient condition for zero offset

considerations

I3ii Spectral Simulation

The spectral simulations of the IEC filtrations and alternative filtrations indicate

many similarities in their effective energies HVLs and overall shapes of normalized

spectra Results are summarized in Table 3

10

Pixium 4600 Original System

Response

Pixium 4600 Linearized System

Response R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 3 Original (left) and linearized (right) system responses for Pixium 4600 The

linearized system responses were measured from actual images The offsets are small

with respect to the slope sufficient enough for zero-offset conditions

y = 13971x - 13236

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x - 00106Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 13576x + 28292

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

7000

0000 1000 2000 3000 4000 5000

AD

U

Exposure (mR)

y = 99997x - 00067Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0000 1000 2000 3000 4000 5000

AD

U

Exposure (mR)

y = 13644x + 16167Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x + 00044

Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 13845x + 13541

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x - 00177

Rsup2= 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

11

Table 3 Spectral Simulation Results

Beam Quality Filtration

Mean Energy

(kV)

Photon Fluence

(mRmm2)

RQA5A 21 mm Al 5243 259543

RQA5C 05 mm Cu + 10 mm Al 5214 259554

diff 055 0004

RQA9A 40 mm Al 7619 273281

RQA9C 104 mm Cu + 10 mm Al 7579 273964

diff 052 025

Figure 4 Spectral simulations for RQA5 (top) and RQA9 (bottom) conditions Note

the similarities of spectral shapes of the normalized spectra (right) Also note the

significant differences in fluence between filtrations in the simulated spectra (left)

00E+00

50E+04

10E+05

15E+05

20E+05

25E+05

30E+05

35E+05

40E+05

45E+05

0 20 40 60 80

ph

oto

ns

mA

s-1

cm

-2

keV

RQA5 Spectra Comparison

21 mm Al

05 mm Cu + 10 mm Al

00

02

04

06

08

10

12

0 20 40 60 80

keV

RQA5 Normalized Spectra Comparison

21 mm Al

05 mm Cu +

10 mm Al

00E+00

50E+05

10E+06

15E+06

20E+06

25E+06

30E+06

35E+06

40E+06

45E+06

50E+06

0 50 100 150

ph

oto

ns

mA

s-1

cm

-2

keV

RQA9 Spectra Comparison

40 mm Al

104 mm Cu +

10 mm Al

00

02

04

06

08

10

12

0 50 100 150

keV

RQA9 Normalized Spectra Comparison

40 mm Al104 mm Cu + 10 mm Al

12

I3iii Modulation Transfer Function

The limiting spatial resolutions of the systems were indicated by the cutoff

frequencies which were approximately 35 cyclesmm for all three detectors The spatial

resolutions also demonstrated a good degree of isotropy as confirmed by the close

alignment of MTF curves between vertical and horizontal directions differentiated in

Figure 5 by dashed and solid lines respectively The MTF curves for the Pixium 4600

and DRX-1C were nearly equal to each other whereas the DRX-1 MTF curve showed a

more rapid decrease at high frequencies as shown in Figure 6 This difference may be

due to the differences in the inherent optical properties of the scintillating materials

where finer image details are provided by structured CsI more than by granulated GOS

There were no significant differences in MTF curves across beam qualities and filtrations

as shown by the curve comparisons in Figure 6 although the alternative filtration

produced slightly higher MTF curves as seen in Figure 4 Table 4 lists the experimental

specific spatial frequencies for varying levels of MTF

I3iv Noise Power Spectrum

The noise characteristics are indicated by the NNPS curves shown in Figure 7

The noise was similar for both horizontal and vertical directions As exposure increased

the NNPS decreased consistent with the characteristics of Poisson noise describing the

relationship between signal and noise in the presence of increased photon fluence At

13

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 5 MTF results by detector (columns) and beam quality (rows)

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

horizontal

vertical

14

Figure 6 Plots of MTF for RQA5 (top) and RQA9 (bottom) showing the relationships

between detectors (blue red and green) and by filtration (solid and dashed)

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm-1)

MTF

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm-1)

MTF

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

15

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 7 NNPS results by detector (columns) and beam quality (rows)

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

05 mR - horizontal

05 mR - vertical

10 mR - horizontal

10 mR - vertical

20 mR - horizontal

20 mR - vertical

16

Figure 8 Plots of NNPS for RQA5 (top) and RQA9 (bottom) at 1 mR exposure

showing the relationships between detectors (blue red and green) and by filtration

(solid and dashed)

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm-1)

NNPS (1 mR)

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm-1)

NNPS (1 mR)

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

17

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 9 DQE results by detector (columns) and beam quality (rows)

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

05 mR - horizontal

05 mR - vertical

10 mR - horizontal

10 mR - vertical

20 mR - horizontal

20 mR - vertical

18

Figure 10 Plots of DQE for RQA5 (top) and RQA9 (bottom) at 1 mR exposure showing

the relationships between detectors (blue red and green) and by filtration (solid and

dashed)

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm-1)

DQE (1 mR)

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm-1)

DQE

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

19

higher frequencies the NNPS curves of the Pixium 4600 and DRX-1 diverge slightly for

the different directions illustrating increased noise in the readout direction (vertical)

Differences in the noise characteristics were more apparent among detectors as

shown for 1 mR in Figure 8 The NNPS curve for the DRX-1 was higher in magnitude

across the entire frequency range than either the Pixium 4600 or DRX-1C which both

seemed to demonstrate reasonably similar NNPS curves The higher magnitude noise of

the DRX-1 indicates higher relative noise content overall Closer inspection of the NNPS

curves of the Pixium 4600 and DRX-1C detectors in Figure 7 revealed differences in the

spacing between the three exposure levels The gaps between the Pixium 4600 NNPS

curves do not correspond to the factor of two differences between each exposure level

especially at low- to mid- spatial frequencies suggesting a higher level of fixed pattern

noise additional noise with increasing exposure levels due to ineffective gain map

corrections Between filtration schemes the differences in NNPS curves for a given beam

quality were not substantial as shown in Figure 7

I3v Detective Quantum Efficiency

The DQE results are shown in Figure 9 DQE curves across exposure levels were

almost collinear except for Pixium 4600 and in general could be inferred from the

NNPS results Additionally the DQE curves demonstrated a relatively linear response

with spatial frequencies as expected for flat-panel detectors [9] Differences in DQE

among detectors were consistent for the most part with the type of scintillating material

20

As depicted for 1 mR exposure in Figure 10 differences between Pixium 4600 and DRX-

1C DQE curves correspond to the differences in their NNPS curves DRX-1 DQE curves

were consistently lower than either the Pixium 4600 or DRX-1C curves The DQE curves

for the alternative filtration were consistently higher than those for the IEC filtration

and the most noticeable differences were near the zero-frequency axis These effects can

be both attributed to ineffective gain map correction DQE values for 1 mR exposure are

listed in Table 5

I4 Discussion

I4i Comparisons of Detectors

The limiting spatial resolutions of all three detectors were almost exactly the

same considering that their pixel areas were similar in size The decrease in high-

frequency MTF of the DRX-1 compared to the other detectors is probably a result of

increased optical blurring due to the differences in the powdered structure of GOS

versus the needle-like structure of CsI [2] The fact that the DRX-1C and Pixium 4600

have comparable MTFs suggests similar scintillator thicknesses assuming that the

materials were processed alike

The noise of the three detectors demonstrated similar trends with each other The

higher NNPS curves of the DRX-1 detector are probably due also to the scintillating

material and its operation in converting photons into signal The conversion process is

less efficient because of the less favorable stopping power of the GOS compared to CsI

21

especially with higher energy beams The noise of the Pixium 4600 and DRX-1C were

similar except for the spacing between exposures The DRX-1C NNPS curve spacing is

consistent with a factor of two difference in exposure levels but the Pixium 4600 has a

smaller spacing The 05 mR NNPS curve of the Pixium 4600 is closer to that of the 05

mR NNPS curve of the DRX-1C This demonstrates that at higher exposures the Pixium

4600 produces a larger amount of additional noise beyond that explained by simple

stochastic effects It suggests bad performance in the gain map corrections

The DQE results indicate SNR properties of each detector The Pixium 4600 and

DRX-1C are comparable for the most part with the DRX-1C performing slightly better

The DRX-1 as predicted from MTF and NNPS results has a DQE much lower than

either of the previous two This is a reflection of the detection properties as provided by

its scintillator material The DQE of the DRX-1 however is comparable to CR image

receptors [2] The mid-frequency dips in the DQE for Pixium 4600 may be due to the

optical properties of the CsI phosphor layer which can affect the MTF in this manner

Because the DQE is calculated by squaring the MTF this effect at the mid-range

frequencies becomes more apparent The dips may also be further evidence of bad gain

map corrections

I4ii Comparisons of Filtrations

The alternative filtration closely matches for the most part the IEC-based

filtration for MTF NNPS and DQEs at RQA5 but not at RQA9 The filters do not have

22

Table 4 Experimental MTF frequency locations for 1 mR exposure

Detector Filtration

50 MTF

(mm-1)

40 MTF

(mm-1)

30 MTF

(mm-1)

20 MTF

(mm-1)

10 MTF

(mm-1)

Pixium

4600

RQA5A 115 145 185 245 330

RQA5C 125 155 195 250 345

RQA9A 110 175 175 235 330

RQA9C 125 155 195 255 345

DRX-1C

RQA5A 120 150 185 245 350

RQA5C 125 155 195 255 355

RQA9A 120 150 190 250 355

RQA9C 130 160 210 265 360

DRX-1

RQA5A 110 135 160 205 280

RQA5C 110 135 170 210 285

RQA9A 105 125 155 195 270

RQA9C 110 135 165 210 285

Table 5 Estimated DQE values for 1 mR exposure by frequency bins

Detector Filtration DQE(00 mm-1) DQE(10 mm-1) DQE(20 mm-1) DQE(30 mm-1)

Pixium

4600

RQA5A 62 42 32 21

RQA5C 63 45 36 25

RQA9A 41 27 30 13

RQA9C 43 33 27 19

DRX-1C

RQA5A 72 52 35 21

RQA5C 76 55 41 24

RQA9A 49 33 23 15

RQA9C 51 40 31 20

DRX-1

RQA5A 38 24 12 4

RQA5C 38 25 14 5

RQA9A 28 18 9 4

RQA9C 28 19 12 5

DQE values at the zero-frequency axis were estimated by the intercept of a linear fit of low-frequency data

but excluding most proximal to the axis due to large fluctuations Other estimated values are grouped into

frequency bins due to the noisiness of the data

23

considerable differences in the spatial resolutions of the detectors as expected The noise

responses for each filtration were also similar except at the lower frequencies of the

NNPS especially near the zero-frequency axis There observing the NNPS responses at

RQA5 for Pixium 4600 and DRX-1C in Figure 8 the NNPS for the IEC-based filtration

(solid lines) tend to drop faster than the NNPS for the alternative filtration This

subsequently appears as a drop in DQE near the zero-frequency axis shown for those

detectors in Figure 10 Overall as indicated in Table 5 the DQEs of the two filtrations

while similar in trend indicate that the alternative filtration increases the DQE by a

small amount of 3-5 Part of this may be explained by the slightly higher beam

energy which may be more optimal for the energy response of the detectors or may

weigh the pixel responses slightly considering that they are energy-integrating types

The most probable explanation is the gain map correction for the alternative filtration

where fixed pattern noise is more sufficiently reduced

A previous study [6] had discussed the choice of filter material in the analysis of

DQE when achieving the beam conditions defined by IEC It found that visible

nonuniformities were present with the higher purity aluminum filter (type-11999 alloy)

The low frequency mottle in the flat-field images for NPS measurements were also

attributed to structured noise from the grain size in the IEC-based filter with an

attenuating thickness that would reveal nonuniformities The mottle in the current study

was only observable under very narrow windowing as shown in Figure 11 Such low

24

frequency artifacts which are not readily noticeable may also be caused by shading

artifacts inverse square law or even the heel effect A possible method to correct for this

is a subtraction method by taking the average of the flat-field images for an exposure

level and then subtracting that from each of them This would remove nonuniformities

that were not corrected using a suboptimal gain map calibration

Figure 11 DRX1-C NNPS images at 1 mR for RQA5 with IEC filtration (left) and

alternative filtration (right) Images are equally windowed at 45 and leveled at 980

One convenient aspect of the copper and aluminum filtration is that it requires

much less tube current to achieve the same amount of exposure at the detector than the

much thicker aluminum filtration As shown in the non-normalized spectra in Figure 2

the exiting photon fluence exiting the copper and aluminum filtration is substantially

higher than that of the IEC-specified filtration This is due to the smaller total filtration

25

attenuation For extensive DQE analysis multiple sets of exposures may be acquired

before tube overheating becomes a concern

One limitation to the comparison of the two filtrations is that calibration

procedures specified copper and aluminum filtration at 80 kVp (for all detectors 05 mm

Cu and 10 mm Al) This may have influenced the results in favor of the alternative

filtration A further investigation involving the calibration procedures and performing

DQE measurements is encouraged Another factor may be influenced by the fact that the

tests were performed at 70 kVp and 120 kVp different from the recommended

calibration tube potential Clearly there would be differences in the linear attenuation

coefficients of the filters and different energy responses of the detectors themselves This

must be considered when interpreting DQE results The current results support a

previous study decades ago that described filtration of different material types in terms

of an aluminum equivalent [16] The results show that the two filtration schemes are

essentially equivalent when considering beam qualities and spatial resolutions The

NNPS and DQE results can be seen as close enough where their small differences are

insignificant when performing quality assurance tests in a clinical setting Overall our

results indicate that the alternative filtration with copper and aluminum may be more

convenient to use than the current IEC standard filtration

26

I4iii Implications of Wireless DR

This study has shown that wireless image receptors can have the same DQE

performance if not better than conventional flat-panel detectors They operate on the

same basic physical principles the new features offered by the DRX-1C and DRX-1 are

wireless communication with the workstation and electronics packaging technology

The latter feature may pose limitations for these units in terms of possible degradation

in the detectors in routine clinical conditions A consideration for future work would be

to longitudinally track DQE performance of the wireless detectors over time while being

utilized in a clinical environment In the end one must consider risks versus benefits of

choosing portable DR technology over CR one of which includes the cost and fragility

of DR detectors

The DQE performance of one wireless system is just as good as or better than

conventional systems as seen by the DRX-1C performance compared to the Pixium

4600 Wireless systems can also reduce the need for CR readers especially in portable

applications in other regions of the world (eg military hospitals developing countries)

However while DQE performance indicates the physical performance of the detector

system it is still unknown how it relates to observer performance

I5 Conclusions

Two wireless image receptors DRX-1C and DRX-1 were evaluated and

compared with the conventional DR flat-panel Pixium 4600 in terms of DQE

27

performance along with MTF and NNPS performances The detectors have similar

resolution properties although the DRX-1 is inferior at higher spatial frequencies The

NNPS and DQE results both indicate that the DRX-1C is superior to the DRX-1 and

comparable if not better to the Pixium 4600

The results from the filtration comparison indicate no substantial differences

between the IEC-based filtration and the copper-based alternative filtration Only slight

differences were found in the low frequency components of the NNPS and the DQE due

to the inherent nonuniformities of the IEC specified filtration Given the similarity of the

results and low attenuation advantage of the copper and aluminum filter its use is

encouraged

28

II Directional MTF for Breast Tomosynthesis

II1 Introduction

Breast tomosynthesis is an emerging 3D imaging modality that has potential use

for screening and diagnosis of breast cancer Breast tomosynthesis along with other 3D

techniques is preferable to planar imaging methods (eg mammography) because they

reduce anatomical noise by removing overlying structures above and below the plane of

an image slice [17-20] Recent advances in detectors and computer technology have

made digital tomosynthesis feasible

An image quality metric of particular importance in breast tomosynthesis is

spatial resolution Resolution is important to know in order to assess small-detail

structures such as microcalcifications A descriptive metric for characterizing spatial

resolution in the Fourier (or frequency) domain is the modulation transfer function

(MTF) Affected by reconstruction filters [21] the limited angular projections involved in

breast tomosynthesis results in highly anisotropic (or nonuniform) resolution Many

studies have looked only at characterizing the in-plane spatial resolution (ie in an

individual slice) with an elevated angled edge phantom [2223] A few studies have

looked at characterizing a more comprehensive 3D spatial resolution by using a

phantom with angled wires or tubes [24-26] However such studies require precise

mechanical alignment of the phantoms Several studies have explored a method using a

29

sphere phantom for the directional 3D MTF evaluation for microtomography [27] and

multi-slice CT [2829] This method has not yet been extended to breast tomosynthesis

This chapter focuses on breast tomosynthesis because it is highly anisotropic in

spatial resolution and like its predecessor mammography requires high spatial

resolution Additionally breast tomosynthesis acquisitions and reconstructions produce

several types of artifacts The use of a cone-based method using a sphere phantom [28] is

explored to characterize the directional 3D spatial resolution of simulated images from

breast tomosynthesis A technique for removing out-of-plane artifacts of the ESFs for the

in-plane axes is investigated to yield a modified MTF in a method that separates artifact

information from resolution information

II2 Materials and Methods

II2i Image Simulation

Breast tomosynthesis images were simulated by using a virtual imaging system

depicted in Figure 12 A volumetric breast phantom was voxelized as a rectangular mass

of uniform breast equivalent tissue of 4 cm thickness embedded with fifteen evenly

spaced plastic sphere inserts of 12 mm diameter The spheres were placed in a grid

formation within the central plane of the phantom The x-ray fluence was modeled from

a 28 kVp beam incident upon an indirect flat-panel detector with 200 micro m pixel size

Twenty-three projections within an angular range of 44deg were simulated using cascaded

systems analysis to generate characteristic 2D noise and spatial blurring [29] Each

30

projection was simulated to have an exposure of 174 mR with a fluence of 79 times 105

photonsmm-2 A standard filtered backprojection technique based on the Feldkamp

reconstruction algorithm [29] was used to reconstruct the projections and produce a

volumetric dataset with an isotropic voxel size of 200 micro m

Figure 12 Depiction of the virtual image system

II2ii Uncorrected MTF

To enable comparison of multiple spheres the reconstructed volume was

initially homogenized by performing a background subtraction based on a portion of the

volume devoid of spheres The voxel values were rescaled between one and zero to

eliminate negative values

31

The volumetric data were segmented to extract individual regions of interest

(ROIs) each containing a single sphere The ROIs extended along the full range of the z-

axis A thresholded ROI was generated by determining the exterior and interior voxels

relative to the sphere in the ROI The threshold value was set at 45 of the maximum

voxel value prior to thresholding The exterior and interior voxel values were then set to

values of 0 and 1 respectively Using the thresholded volume the center of mass was

calculated to determine the centroid The voxel values from the original ROI were

subsequently tabulated with the associated distances azimuthal angles and polar

angles relative to the centroid

Conical regions were prescribed along the positive and negative directions along

the three major axes extending from the centroid of the sphere as depicted in Figure 13

The axes about which the extent of the cone angle was delineated were defined with

the azimuthal and polar angles

Voxels with centers within the angular range of the cone were considered for

generating the edge spread function (ESF) To improve regularity of the distance

sampling interval the ESF values were rebinned to discrete distances corresponding to a

fraction of the voxel size Only voxels with distances ranging from the voxel size (ie

200 micro m) to the maximum distance were considered The ESFs from multiple spheres

were averaged together for each of the three major axes to produce an averaged ESF

which was further smoothed utilizing a Gaussian filter

32

Figure 13 Example of 30-degree cone prescribed along z axis of the sphere

The resulting ESF was then differentiated using the central difference method to

produce the line spread function (LSF) A Hanning filter with the same length as the LSF

was applied to zero out the tails of the LSF The presampled MTF was subsequently

computed as the amplitude of the Fourier transform of the LSF The MTF was

normalized with respect to the maximum value occurring within the range of the cutoff

frequency Binning size and conical range for the ESF were considered for maximizing

accuracy and minimizing noise of the MTF verified by comparison against the

theoretical MTF as determined in the previous section

II2iii Theoretical Directional MTF

The theoretical 3D MTF was calculated using a priori knowledge of the transfer

function of the virtual imaging system described in the previous section A phantom

was created with a set of point objects in a uniform and noise-free background with the

objects spanning across the volume of the breast [29] Twenty-one realizations were

33

generated from the reconstructed images of the point objects to yield a set of 3D point

spread functions (PSFs) The 3D fast Fourier transform (FFT) was performed for each 3D

PSF and averaged to give an ldquoexpectationrdquo 3D MTF [29] The theoretical directional

MTFs in the three major spatial axes were determined by line profiles along each of the

corresponding spatial frequency axes in the 3D MTF An additional theoretical MTF for

each direction was determined by using the application of conical regions along the axes

in frequency-space to take into account the contributions of MTF information from other

planes

II2iv Modified MTF

The tomosynthesis reconstruction is known to have edge enhancements which

affect the overall MTF by shifting the peaks of the MTF toward the higher frequencies

[23] The presence of this artifact complicates the interpretation of the actual spatial

resolution of the images Several steps were performed to remove the artifact

contribution to the resolution information particularly for the in-plane x and y

directions with the assumption that resolution information was contained immediately

near the edge

For the x-direction averaged ESF only values that were detected to be inside the

edge of the sphere were considered Those values were previously determined via

thresholding for calculating the centroid The ESF information corresponding to these

values was inversed and flipped about the detected edge to produce a symmetric

34

modified ESF The modified MTF was subsequently calculated from this modified ESF

as described in the previous section

For the y-direction averaged ESF an upward trend was found in the initial part

of the ESF This section was detrended with a polynomial fit and subtracted to produce a

flatter curve in that region The resulting detrended ESF was used to calculate the y axis

modified MTF

Figure 14 Photograph of the imaging system with the acrylic sphere phantom

embedded in oil

II2v Preliminary Experimental Validation

A clinical breast tomosynthesis system (Mammomat Inspiration Siemens AG

Munich Germany) was used to perform a preliminary evaluation of the cone-based

MTF technique The phantom for the experiment consisted of a single acrylic ball of 075

in diameter (SmallParts Seattle WA) suspended by a 0029 in diameter plastic filament

35

(Omniflex Zebco Tulsa OK) in an acrylic frame filled up to 4 in with vegetable oil

(Target Brands Inc Minneapolis MN) The system and phantom are shown in Figure

14 Twenty-five projections with an angular range of 44deg were acquired and subsequently

reconstructed to produce a volume with a voxel size of 01times01times10 mm3 The voxels were

reformatted to have an isotropic size of 01 mm The uncorrected ESF LSF and MTF

were calculated as described in the previous section

II3 Results

II3i Reconstruction

The reconstructed volume is shown in Figure 15 Notice the edge enhancement

along the x-direction as indicated by the sharp shadowing artifacts on either side of the

spheres The background was effectively homogenized using the background

subtraction technique This also took account of the curved edges of the breast phantom

With the close spacing of the spheres in the phantom the shadows along the x direction

for the fifteen spheres overlap with each other As the nine centrally located spheres

experience this effect the same way they were used for determining the ESF

A 3D rendering of the ROI containing a sphere shown in Figure 16 indicates the

anisotropic resolution of the reconstruction Note that the sphere is not accurately

reconstructed and has an oblong shape especially along the z axis Cross sectional views

of the ROI also in Figure 16 clearly demonstrate the edge enhancement causing a

shadow artifact in the x direction caused by the incomplete angular sampling of

36

tomosynthesis The sampling also introduces the triangular reconstruction of the sphere

as seen in the x-z plane Note the gradual edge drop-off in the z direction much beyond

the sphere radius

Figure 15 View of the central slice of the breast phantom reconstruction before (top)

and after (bottom) background subtraction The z axis is through the page

37

Figure 16 3D rendering of the ROI volume (left) and cross-sectional views of the most

centrally located sphere with centroid indicated with red circle (right)

II3ii Theoretical MTF

The theoretical MTFs for x y and z directions as determined from the line

profiles of the 3D MTF are shown in Figure 17 The theoretical MTF in the x direction

has a maximum value that is toward higher frequencies Its 10 response occurs at

about 125 cyclesmm which is at 50 of the cutoff frequency The rapid increase from

the zero-frequency intercept to the peak corresponds to the ramp filter used in filtered

backprojection which decreases the weighting of low frequency contributions due to the

incomplete angular sampling of the frequency-space The MTF does not reach a value of

0 at the zero-frequency intercept as it is very difficult to assess the zero-frequency

intercept due to the finite size of the phantom The theoretical MTF in the y direction

peaks at the zero-frequency intercept and reaches 20 proximal to the cutoff frequency

38

The 10 MTF is well beyond the cutoff frequency The theoretical MTF in the z direction

has a rapid drop-off at very low spatial frequencies indicating the lack of resolution in

that dimension

Figure 17 Theoretical 3D MTF results along the three major planes (top) and along x

y and z directions (bottom) Also note that the angular spread seen in the fx-fz plane is

equal to the angular range of 44deg for the acquisition

II3iii Uncorrected MTF

The ESF LSF and MTF using the cone-based method are shown for the x y and

z directions in Figure 18 It was found that a bin size of one-tenth the voxel size (002

mm) and a cone angle of 30deg to establish the ESF were enough to minimize noise and

maximize accuracy in the uncorrected MTFs considering the reasonable comparison of

the shapes of the MTF curves with the theoretical results in Figure 17 The LSFs are

generally noisy because differentiation of the ESF increases the amplitude of the noise

39

The data shown reflect a convolution with a smoothing Gaussian filter which was later

further corrected for in the reported MTF Nevertheless the high frequency components

of the noise are well beyond the MTF cutoff frequency of 25 cyclesmm and do not

impact the MTF results greatly

For the ESF in the x direction the shadow effect evident at the edge of the sphere

is visible as a steep decline followed by an increase Due to the finite distance range

provided by the ROI the ESF beyond the edge did not asymptotically reach the

background value The corresponding LSF demonstrates a low frequency modulation

that is indicated by the shift of 03 cyclesmm in the x direction for the peak of the MTF

The MTF exhibits a zero-frequency intercept that is non-zero unlike the theoretical MTF

and a 10 value at approximately 1 cyclesmm These features may be a direct

consequence of MTF information ldquocontaminationrdquo from y and z directions Furthermore

the ESF in the y direction demonstrates a reasonably shaped curve except for the slight

upward trend within the radius of the sphere which can be attributed to the shadow

artifact overlapping with the sphere volume The associated MTF has a peak shifted by

approximately 01 cyclesmm away from the axis and a 10 MTF occurring at

approximately 15 cyclesmm Both features which are not present in the theoretical

results may also be attributed to contaminant MTF information from x and z directions

The ESF in the z direction has a drop-off that occurs at a small fraction of the cutoff

frequency similar to that demonstrated by the theoretical MTF

40

Uncorrected ESF LSF and MTF

Figure 18 Uncorrected ESF (top) LSF (middle) and MTF (bottom) for x y and z

directions

41

Figure 19 Comparisons of the directional MTFs as calculated by the sphere method

(dashed line) by theoretical line profiles (light-weight line) by theoretical cone

regions (heavy-weight line)

II3iv Comparison of Theoretical and Simulated MTFs

The theoretical MTF results obtained from line profiles through the 3D MTF and

the simulated MTFs using the cone-based technique did not match very well except for

the general shape of the curves It was assumed in the previous section that the cone-

based technique contains information from other planes Figure 19 compares MTFs in

each direction for the two methods described in the methods and an additional method

based on conical regions of the 3D MTF The latter computes the MTF by averaging

contributions of the 3D MTF using the same cone prescription method used to define the

ESFs Comparison of the curves indicate some interesting correlations aside from the

fact that using conical regions with the 3D MTF results produce more noisy MTF results

partly due to the low sampling provided by the theoretical calculations The same

conclusions regarding the z direction MTF can be confirmed regardless of either

theoretical MTF procedures The experimental x direction MTF seems to agree best with

42

the line profile method whereas the y direction MTF agrees better with the cone region

method The fact that the experimental x direction MTF has a drop-off frequency that is

lower than those of either of the theoretical MTFs in Figure 19 suggests that this might

be due to integration of the z-direction in the in-plane slices considering how slices are

essentially averages of z direction information contained within it [33]

II3v Modified MTF for x and y

Modified ESF LSF and MTF curves for x and y directions are shown in Figure

20 The modified ESF and the resulting LSF in the x direction appear symmetric as

expected from the inverse and flip operation of the interior ESF about the detected edge

The modified MTF appears with less variation than the uncorrected MTF and the MTF

peak occurs at the zero-frequency axis The correction yields a 10 MTF at about 15

cyclesmm an improvement from the uncorrected MTF but still distant from the cutoff

frequency The modified ESF in the y direction demonstrates the detrended curve within

the sphere radius after a quadratic polynomial fit The resulting modified MTF still

appears similar to the uncorrected MTF except that the peak now coincides with the

zero-frequency axis For both x and y directions the low response of the modified MTFs

at the higher frequencies suggests that the contamination from other directions is

substantial due to the angular range of the cone

43

Modified ESF LSF and MTF

Figure 20 Modified ESF (top) LSF (middle) and MTF (bottom) for x and y directions

44

II3v Preliminary Experimental Validation

Cross-sections of the reconstructed sphere volume are shown in Figure 21

Relative to the simulation reconstructions the reconstructions of the experimental

phantom images produce lower contrast and higher noise The preliminary results

shown in Figure 22 indicate that our technique can be applied to actual experimental

breast tomosynthesis reconstructions However due to the noise exhibited by the MTF

curves for the x and y directions we did not determine the modified MTFs to separate

resolution and artifact information

Figure 21 Cross sectional views of the experimental sphere image with centroid

indicated with red circle

45

Uncorrected ESF LSF and MTF for Real Image

Figure 22 ESF (top) LSF (middle) and MTF (bottom) of real image for x y

and z directions

46

II4 Discussion

II4i Evaluation of Cone-based Method

The cone-based MTF technique was introduced by Thornton and Flynn [28] for

evaluation of volumetric CT images To utilize this technique as a characterization of a

3D system spatial resolution one must first consider the validity of the assumption of

shift invariance such that the same MTF result may be obtained regardless of the

location of the sphere The study by Zhao et al [23] found that there was no shift

variance for the MTF measurements along the vertical axis but this was only considering

the in-plane resolution along one axis On the other hand this study evaluated the MTF

with images simulated with cascaded systems analysis which includes conditions of

linearity and shift invariance Additionally the MTF was calculated by averaging the

ESF from several spheres in the same volume only after performing a background

subtraction This step was essential to account for the sensitivity of centroid calculations

as well as ensuring symmetric ESFs for opposing axes of the sphere ROIs

The measurement of MTF with the cone-based technique inherently

supersamples the edge of the sphere to increase signal-to-noise-ratio (SNR) of edge

information by averaging the contributions of each voxel to the ESF [713] This method

also takes into account the discrete sampling of the voxels by accounting for various

shifts of the edge in the voxel (also known as the partial volume effect) However using

the curved surface of the sphere phantom to approximate an edge along a given

47

direction naturally leads to contamination of information from other directions aside

from the one of interest Preferably a directional ESF should be created by using a single

radial line but this would limit the available voxels to obtain edge information An ideal

situation theoretically would be to use a larger-sized sphere such that the surface is

nearly flat and perpendicular to the axes of interest This would also permit a reduction

in the angular range of the cone and thus the introduction of out-of-plane information in

the resulting MTF However sphere size is a limitation in breast tomosynthesis and the

use of a large phantom might void the assumption of shift invariance of the spatial

resolution

The choice of a sphere phantom nevertheless may be based on the clinical need

to quickly acquire a single image for MTF evaluation especially for multiple directions

without presenting extra logistical challenges The use of a wire or edge phantom

requires more precise mechanical alignment to achieve the correct set up The edge

phantom [23] would require at least two images to sample all three dimensions In the

case of the three wire phantom [2425] all three dimensions of the frame must be aligned

simultaneously with respect to the axis of rotation A similar situation would be

encountered when considering a cubic phantom with the planes normal to the axis of

interest In contrast to these phantoms the sphere eliminates the need for precise

alignment especially with respect to three spatial dimensions simultaneously A sphere

48

has ideal symmetry in all directions and can be used to evaluate MTF in any arbitrary

direction

This study unlike others [242532] did not explore the effects of physical

parameters such as scatter or contrast on the final MTF result but it demonstrated the

feasibility of using the cone-based method with an actual breast tomosynthesis image of

a sphere phantom as shown in Error Reference source not found and Error Reference

source not found These effects should be addressed in future works A further look

into deriving the principles of comparing the theoretical MTF with the experimental

MTF using the cone-based method is further warranted

II4ii Separation of Artifact and Resolution Information

The focus of this study was to develop a technique for measuring spatial

resolution of tomosynthesis images The intrinsic artifacts from tomosynthesis

reconstructions however lead to uncharacteristic MTFs and possible misinterpretation

of the effective resolution information When considering previous techniques for

calculating the presampled MTF [713152328] the analysis was performed using an

edge or a line to produce the corresponding ESF The resolution information is

essentially contained only along the edge indicated by the need to calculate the LSF In a

way the method of extracting artifact information is to focus the analysis only on the

edge part of the ESF to calculate the modified MTF This will lead to a better

understanding of the limiting size of objects that may be seen in the reconstructed 3D

49

image The presampled MTF without correction should still be analyzed to understand

the entire system response Note that the ESFs attempt to reflect information only at the

detected edge of the sphere

II5 Conclusions

The directional MTF of a simulated breast tomosynthesis reconstruction was

determined by using the cone-based MTF technique demonstrating the feasibility of a

single phantom for MTF evaluation This study further presented methods of analyzing

only the edge information in the ESF to create a modified MTF along in-slice (x and y)

axes It can provide insight into the actual spatial resolution information contained in the

image while separating the resolution information from the information introduced by

artifacts caused by the reconstruction and insufficient volumetric sampling The idea of

separating the resolution and artifacts from the measured ESF are expected to facilitate

the interpretation of MTF measurements in breast tomosynthesis Similar methods may

be applied to characterize the resolution of other 3D imaging modalities

50

References

1 Garmer M Hannigs SP Jaumlger HJ et al ldquoDigital Radiography Versus

Conventional Radiology in Chest Imaging Diagnostic Performance of a Large-

Area Silicon Flat-Panel Detector in a Clinical CT-Controlled Studyrdquo American

Journal of Roentgenology Volume 74 75-80 (2000)

2 Cowen AR Kengyelics SM and Davies AG ldquoSolid-state flat-panel digital

radiography detectors and their physical imaging characteristics rdquoClinical

Radiology Volume 63 487-498 (2008)

3 Chotas HG Dobbins III JT and Ravin CE ldquoPrinciples of Digital

Radiography with Large-Area Electronically Readable Detectors A Review of

the Basicsrdquo Radiology Volume 210 Number 3 595-599 (1999)

4 Flynn MJ and Samei E Experimental comparison of noise and resolution for

2k and 4k storage phosphor radiography systems Medical Physics Volume 26

Number 8 1612-1623 (1999)

5 Rong XJ Shaw CC Liu X Lemacks MR and Thompson SK

ldquoComparison of an amorphous siliconcesium iodide flat-panel digital chest

radiography system with screenfilm and computed radiography systems ndash A

contrast-detail phantom studyrdquo Medical Physics Volume 28 Number 11 2328-

2335 (2001)

6 Ranger NT Samei E Dobbins III JT and Ravin CE Measurement of the

detective quantum efficiency in digital detectors consistent with the IEC 62220-1

standard Practical considerations regarding the choice of filter material

Medical Physics Volume 30 Number 7 2305-2311 (2005)

7 Samei E Buhr E Granfors P Vandenbroucke D and Wang X Comparison

of edge analysis techniques for the determination of the MTF of digital

radiographic systems Physics in Medicine and Biology Volume 50 3613-3625

(2005)

8 Samei E and Flynn MJ An experimental comparison of detector performance

for computed radiography systems Medical Physics Volume 29 Number 4 447-

459 (2002)

51

9 Samei E and Flynn MJ An experimental comparison of detector performance

for direct and indirect digital radiography systems Medical Physics Volume 30

Number 4 608-622 (2003)

10 Samei E Ranger NT MacKenzie A Honey ID Dobbins III JT and Ravin

CE Effective DQE (eDQE) and speed of digital radiographic systems An

experimental methodology Medical Physics Volume 36 Number 8 3806-3817

(2009)

11 Samei E Ranger NT MacKenzie A Honey ID Dobbins III JT and Ravin

CE Detector or System Extending the Concept of Detective Quantum

Efficiency to Characterize the Performance of Digital Radiographic Imaging

Systems Radiology Volume 249 Number 3 926-937 (2008)

12 ldquoIEC 62220-1 Medical Electrical Equipment ndash Characteristics of Digital X-Ray

Imaging Devices ndash Part 1 Determination of the Detective Quantum Efficiencyrdquo

International Electrotechnical Commission Geneva Switzerland (2003)

13 Samei E Ranger NT Dobbins III JT and Chen Y Intercomparison of

methods for image quality characterization I Modulation transfer function

Medical Physics Volume 33 Number 5 1454-1465 (2006)

14 Dobbins III JT Samei E Ranger NT and Chen Y Intercomparison of

methods for image quality characterization II Noise power spectrum Medical

Physics Volume 33 Number 5 1466-1475 (2006)

15 Samei E Flynn MJ and Reimann DA A method for measuring the

presampled MTF of digital radiographic systems using an edge test device

Medical Physics Volume 25 Number 1 102-113 (1998)

16 Nagel HD ldquoAluminum equivalence of materials used in diagnostic radiology

and its dependence on beam qualityrdquo Physics in Medicine and Biology Volume

31 Number 12 1381-1399 (1986)

17 Niklason LT Christian BT Niklason LE et al ldquoDigital Tomosynthesis in

Breast Imagingrdquo Radiology Volume 205 399-406 (1997)

18 Gur D ldquoTomosynthesis Potential Clinical Role in Breast Imagingrdquo American

Journal of Roentgenology Volume 189 614-615 (2007)

52

19 Park JM Franken Jr EA Garg M Fajardo LL and Niklason LT ldquoBreast

Tomosynthesis Present Considerations and Future Applicationsrdquo

RadioGraphics Volume 27 S231-S240 (2007)

20 Good WF Abrams GS Catullo VJ Chough DM Ganott MA Hakim

CM and Gur D ldquoDigital Breast Tomosynthesis A Pilot Observer Studyrdquo

American Journal of Roentgenology Volume 190 865-869 (2008)

21 Hu Y-H Zhao W Mertelmeier T and Ludwig J ldquoImage Artifact in Digital

Breast Tomosynthesis and Its Dependence on System and Reconstruction

Parametersrdquo IWDM 2008 LNCS 5116 628-634 (2008)

22 Chen Y Lo JY Ranger NT Samei E Dobbins III JT ldquoMethodology of

NEQ(f) analysis for optimization and comparison of digital breast tomosynthesis

acquisition techniques and reconstruction algorithmsrdquo Proceedings of SPIE

Volume 6510 65101I (2007)

23 Zhao B Zhou J Hu Y-H Mertelmeier T Ludwig J and Zhao W

ldquoExperimental validation of a three-dimensional linear system model for breast

tomosynthesisrdquo Medical Physics Volume 36 Number 1 240-251 (2009)

24 Madhav P Brzymialkiewicz CN Cutler SJ Bowsher JE and Tornai MP

ldquoCharacterizing the MTF in 3D for a Quantized SPECT Camera Having Arbitrary

Trajectoriesrdquo 2005 IEEE Nuclear Science Symposium Conference Record 1722-

1726 (2005)

25 Madhav P McKinley RL Samei E Bowsher JE and Tornai MP ldquoA Novel

Method to Characterize the MTF in 3D for Computed Mammotomographyrdquo

Proceedings of SPIE Volume 6142 61421Y (2006)

26 Hu Y-H Zhao B and Zhao W ldquoImage artifacts in digital breast

tomosynthesis Investigation of the effects of system geometry and

reconstruction parameters using a linear system approachrdquo Medical Physics

Volume 35 Number 12 5242-5252 (2008)

27 Seifert A and Flynn MJ ldquoResolving power of 3D x-ray microtomography

systemsrdquo Proceedings of SPIE Volume 4682 407-413 (2002)

28 Thornton MM and Flynn MJ Measurement of the spatial resolution of a

clinical volumetric computed tomography scanner using a sphere phantom

Proceedings of SPIE Volume 6142 61421Z (2006)

53

29 Baek J Pelc NJ ldquoUse of sphere phantoms to measure the 3D MTF of FDK

reconstructionsrdquo Proceedings of SPIE Volume 7961 79610D (2011)

30 Richard S and Samei E ldquoQuantitative imaging in breast tomosynthesis and CT

Comparison of detection and estimation task performancerdquo Medical Physics

Volume 37 Number 6 2627-2637 (2010)

31 Chen Y Lo JY and Dobbins III JT ldquoImpulse response analysis for several

digital tomosynthesis mammography reconstruction algorithmsrdquo Proceedings of

SPIE Volume 5745 541-549 (2005)

32 Zhao B and Zhao W ldquoThree-dimensional linear system analysis for breast

tomosynthesisrdquo Medical Physics Volume 35 Number 12 5219-5232 (2008)

33 Wu G Mainprize JG Boone JM and Yaffe MJ ldquoEvaluation of scatter

effects on image quality for breast tomosynthesisrdquo Medical Physics Volume 36

Number 10 4425-4432 (2009)

Page 9: Development and Evaluation of 2D and 3D Image Quality ...

ix

II4 Discussion 46

II4i Evaluation of Cone-based Method 46

II4ii Separation of Artifact and Resolution Information 48

II5 Conclusions 49

References 50

x

List of Tables

Table 1 Physical Characteristics of Digital Image Receptors 4

Table 2 Beam Qualities and Required Filtrations 5

Table 3 Spectral Simulation Results 11

Table 4 Experimental MTF frequency locations for 1 mR exposure 22

Table 5 Estimated DQE values for 1 mR exposure by frequency bins 22

xi

List of Figures

Figure 1 MTF images for DRX-1C detector with radio-opaque edge test device with

arrows indicating the horizontal (left) and vertical (right) directions 7

Figure 2 NNPS image for DRX-1C detector indicating the top left ROI that served as the

reference for normalizing other ROIs in the image The ROI array was formed along the

directions indicated by the arrows The heel effect visible along the vertical axis of the

detector is an example of small variation in signal across the image 8

Figure 3 Original (left) and linearized (right) system responses for Pixium 4600 The

linearized system responses were measured from actual images The offsets are small

with respect to the slope sufficient enough for zero-offset conditions 10

Figure 4 Spectral simulations for RQA5 (top) and RQA9 (bottom) conditions Note the

similarities of spectral shapes of the normalized spectra (right) Also note the significant

differences in fluence between filtrations in the simulated spectra (left) 11

Figure 5 MTF results by detector (columns) and beam quality (rows) 13

Figure 6 Plots of MTF for RQA5 (top) and RQA9 (bottom) showing the relationships

between detectors (blue red and green) and by filtration (solid and dashed) 14

Figure 7 NNPS results by detector (columns) and beam quality (rows) 15

Figure 8 Plots of NNPS for RQA5 (top) and RQA9 (bottom) at 1 mR exposure showing

the relationships between detectors (blue red and green) and by filtration (solid and

dashed) 16

Figure 9 DQE results by detector (columns) and beam quality (rows) 17

Figure 10 Plots of DQE for RQA5 (top) and RQA9 (bottom) at 1 mR exposure showing

the relationships between detectors (blue red and green) and by filtration (solid and

dashed) 18

Figure 11 DRX1-C NNPS images at 1 mR for RQA5 with IEC filtration (left) and

alternative filtration (right) Images are equally windowed at 45 and leveled at 980 24

Figure 12 Depiction of the virtual image system 30

xii

Figure 13 Example of 30-degree cone prescribed along z axis of the sphere 32

Figure 14 Photograph of the imaging system with the acrylic sphere phantom

embedded in oil 34

Figure 15 View of the central slice of the breast phantom reconstruction before (top) and

after (bottom) background subtraction The z axis is through the page 36

Figure 16 3D rendering of the ROI volume (left) and cross-sectional views of the most

centrally located sphere with centroid indicated with red circle (right) 37

Figure 17 Theoretical 3D MTF results along the three major planes (top) and along x y

and z directions (bottom) Also note that the angular spread seen in the fx-fz plane is

equal to the angular range of 44deg for the acquisition 38

Figure 18 Uncorrected ESF (top) LSF (middle) and MTF (bottom) for x y and z

directions 40

Figure 19 Comparisons of the directional MTFs as calculated by the sphere method

(dashed line) by theoretical line profiles (light-weight line) by theoretical cone regions

(heavy-weight line) 41

Figure 20 Modified ESF (top) LSF (middle) and MTF (bottom) for x and y directions 43

Figure 21 Cross sectional views of the experimental sphere image with centroid

indicated with red circle 44

Figure 22 ESF (top) LSF (middle) and MTF (bottom) of real image for x y and z

directions 45

xiii

Acknowledgements

I would like to thank Ian Yorkston Mark Purdum and Van Huston of

Carestream Health Inc (Rochester NY) for their help with digital detector

measurements I would also like to thank Olav Christianson Samuel Richard Brian

Harrawood and Max Amurao for their assistance with collecting data and analyzing

results Special thanks go to my committee members for their helpful insights and

suggestions for this thesis Last but not least I want to express deep appreciation for the

support and mentorship provided by my advisor Dr Ehsan Samei

1

I Evaluation of 2D Digital Image Receptors

I1 Introduction

In the past decade many areas of radiological practice have seen a conversion

from screen films to the storage phosphor cassettes of computed radiography (CR) to the

active-matrix flat-panel detectors of digital radiography (DR) Both CR and DR are

digital systems that offer many potential benefits including but not limited to better

image quality wider dynamic range quicker readout lower radiation dose and higher

throughput [1-3] Even with advances in DR technologies such as improved detective

quantum efficiency (DQE) the primary radiographic system of today continues to be CR

A major obstacle to completely accepting DR is the high capital cost of acquiring an

entire system per examination room while also providing capability for portable

applications Recently manufacturers like Carestream Health Fuji and Toshiba have

introduced wireless digital image receptors that can serve as replacements for CR

cassettes As these are new technologies a further investigation to characterize these

detectors is warranted

In the case of radiographic receptors DQE has historically been the metric of

choice [4] because it indicates the ability of the image receptor to convert incident x-ray

photons into useable signal ndash essentially a measure of signal-to-noise ratio (SNR)

efficiency and overall system performance [23] DQE is observed across a range of

spatial frequencies for evaluating how the detector depicts small and large objects [3]

2

DQE metrics have been used in numerous studies to characterize CR phosphor-screens

as well as indirect and direct digital detectors [4-11] The importance of this highly

quantitative metric may be implied by the introduction of a DQE measurement standard

by the International Electrotechnical Commission (IEC) [12]

The standard measurement methodology of the International Electrotechnical

Commission (IEC) pertains to the image quality of 2D digital radiographic detectors

While the IEC formalism is well-developed some of the components that it requires are

not necessarily the most optimal for characterizing DQE This has been explored in

previous studies in terms of filtration material purity beam limitations and region of

interest (ROI) configuration [1314] To reduce the variability in the radiographic output

across various x-ray tubes due to inherent filtration differences the IEC formalism

prescribes specific additional aluminum filtration to attain radiation beam qualities

based on target half value layers (HVL) Achieving and verifying the desired HVL

however requires applying a substantial amount of aluminum at the exit window of the

x-ray tube which is often directed toward the ground This can be a logistical

inconvenience and can increase the risk of damage to the image receptor and

measurement equipment Similar beam qualities on the other hand may be attained

more conveniently using a thinner lighter filtration combination utilizing a higher Z

number material Care is warranted however as a previous study [6] had indicated that

the choice of filtration material could impact the DQE

3

The purpose of this study was two-fold First we aimed to evaluate and compare

two wireless image receptors with a conventional flat-panel detector on the basis of DQE

performance Second we compared DQE results using the IEC-prescribed filtration with

an alternative filtration For the latter an optimum filtration composition was

determined and compared with the IEC filtration on the basis of DQE

I2 Materials and Methods

I2i Detectors

The physical characteristics of the three digital image receptors evaluated in this

study are listed in Table 1 The Pixium 4600 was a conventional digital flat-panel The

DRX-1C and DRX-1 were both wireless digital cassettes that were tethered for the

purposes of this study All detectors were FDA approved and available commercially

Each detector was calibrated according to its manufacturer specifications to correct for

gain offset and bad pixels They were all dedicated for non-clinical laboratory research

purposes and hence could be operated under service settings that permitted acquisition

of raw (ie for processing) images

I2ii Beam Characterization

I2iia X-ray Techniques

All measurements for this study were taken with a well-characterized standard

radiographic system (Super80CP Philips Healthcare Andover MA) The x-ray tube had

an inherent filtration of 27 mm Al Free in-air exposures were measured using

4

Table 1 Physical Characteristics of Digital Image Receptors

Manufacturer Detector

Detector

type

Detector

material

Pixel pitch

(size) Array size

Imaging

area

Trixell

(Moirans France)

Pixium

4600 Indirect

CsITl

(CsI) 0143 mm

3121times3121

4 subpanels 45times45 cm2

Carestream Health Inc

(Rochester NY)

DRX-1C

(wireless) Indirect

CsITl

(CsI) 0139 mm

2560times3072

single panel 35times43 cm2

Carestream Health Inc

(Rochester NY)

DRX-1

(wireless) Indirect

G2O2STb

(GOS) 0139 mm

2560times3072

single panel 35times43 cm2

calibrated radiation meters (Mult-O-Meter Type 407 Unfors Instruments AB Billdal

Sweden) at 183 cm source-to-chamber-distance (SCD) The SCD also corresponded to

same plane as the image receptor surface The x-ray output was made to conform to IEC

beam quality definitions [1215] on the basis of half value layer (HVL) and peak

kilovoltage setting using an aluminum filtration (type-1100 99 purity) and an

alternative filtration consisting of copper (UNS C11000 999 purity) and aluminum

(type-1100 99 purity) The IEC radiation quality numbers (RQA) used in this study are

summarized in Table 2 HVLs were determined by iteratively adding successive

thicknesses of aluminum until reaching reduced exposure levels within a tolerance of

0485-0515 [12] As for the alternative filtration the aluminum was placed downstream

of the copper filter to attenuate characteristic radiation peaks from copper at

approximately 9 keV

I2iib Data Linearization

The system response function was determined for each detector and filtration

combination by acquiring flat-field images at increasing photon fluence until just before

5

Table 2 Beam Qualities and Required Filtrations

IEC Radiation

Quality Number

Peak

kilovoltage

Required

HVL

Required IEC

Filtration

Actual IEC

Filtration

Alternative

Filtration

RQA5 70 kVp 71 mm Al 21 mm Al 21 mm Al 05 mm Cu +

10 mm Al

RQA9 120 kVp 115 mm Al 42 mm Al 40 mm Al 104 mm Cu +

10 mm Al

For reasons of convenience these will be referred to as RQA5A RQA5C RQA9A and RQA9C

saturation levels To avoid the influence of detector backscatter on exposure

measurements a relationship for each filtration was first determined for two radiation

meters A target meter was placed at the central axis and a reference meter was placed at

the edge of the light field (large enough to cover the detectors) The reference meter

served as a surrogate for the target meter to avoid direct exposure measurements in the

plane of the image receptor Exposure relationships were determined before each

measurement set (ie detector and filtration combination) to account for changes in

temperature pressure and humidity The system response function was calculated by

using a regression of ADU (pixel value) versus exposure Images acquired for each

series were then converted to achieve a linear response with zero offset and scaled to

achieve high quantization (adequate dynamic range) Linearization of the detector

responses ensured that zero exposure corresponded to zero pixel value

I2iic Spectral Simulation

The effects of additional filtration on x-ray output spectra were observed with

spectral simulation software (XSPECT V40 Henry Ford Hospital Detroit MI) To more

6

adequately describe the performance of a typical X-ray generator inherent filtration of 3

mm oil 148 mm Pyrex glass and 2 mm aluminum was input into the simulation in

addition to the filters of interest The ideal signal to noise ratio squared or incident

photon fluence per exposure (q) was estimated for each filtration by integrating the

energy-dependent photon counts per unit exposure over all energy bins

I2iii DQE Measurements

The assessment of the linearized images followed the formalism described by

IEC 62220-1 for measuring the DQE [12] For this study the normal exposure level XN

was set at 1 mR to the detector surface as measured at the central axis perpendicular to

the anode-cathode axis

I2iiia Modulation Transfer Function

Spatial resolution was characterized by evaluating the presampled modulation

transfer function (MTF) along directions parallel (vertical) and perpendicular

(horizontal) to the anode-cathode axis using the angled-edge method [6-1013] A radio-

opaque edge test device [7] was placed in the center of the field at a pitch of

approximately 301 (about 2deg) to the axis perpendicular to that being measured as

shown in Figure 1 External lead apertures were not used [6] instead the internal

collimation from the radiographic unit was used to collimate the beam to the detector

area Raw images were acquired of the edge with the normal exposure level XN of 1 mR

at the detector face The procedure of calculating the MTF followed previously described

7

methods [6-1013] The edge spread function (ESF) was determined along lines crossing

the edge of the angled test device The derivative of the ESF was calculated to form the

line spread function (LSF) to which a Hanning filter was applied The MTF was then

calculated as the fast Fourier transform (FFT) of the LSF and normalized at the zero-

frequency axis To conform to IEC guidelines the MTF was resampled into frequency

steps of 005 cyclesmm [12]

Figure 1 MTF images for DRX-1C detector with radio-opaque edge test device with

arrows indicating the horizontal (left) and vertical (right) directions

I2iiib Noise Power Spectrum

Noise amplitude and texture were characterized by determining the normalized

noise power spectrum (NNPS) which was evaluated with flat field exposures at

approximate exposure levels of XN2 XN and 2XN (05 10 and 20 mR) to the image

receptor surface Analysis of the flat-field images followed previously defined methods

[41415] using over 4 million independent pixels with regions of interest (ROIs) of size

8

128x128 The NNPS images were detrended using a quadratic (second order)

background subtraction Small variations in exposure across ROIs were corrected by

normalizing pixel values of each ROI to the mean value in the top left ROI as shown in

Figure 2 The NNPS was then calculated with the 2D FFT including the zero-frequency

axes corresponding to the horizontal and vertical directions The results were then

resampled using 005 frequency bins according to IEC guidelines [12]

Figure 2 NNPS image for DRX-1C detector indicating the top left ROI that served as

the reference for normalizing other ROIs in the image The ROI array was formed

along the directions indicated by the arrows The heel effect visible along the vertical

axis of the detector is an example of small variation in signal across the image

I2iiic DQE Calculation

The DQE was calculated using the following relationship [615]

9

where the frequency-dependent MTF and NNPS were determined as described in

previous sections X was the exposure value in mR corresponding to the NNPS image

and q was the ideal signal to noise ratio squared in units of photonsmiddotmm-2middotmR-1 as

estimated from the spectral simulations

I3 Results

I3i Data Linearization

The detectors in this study provided raw ADU (or pixel) values in a linear scale

The data were converted using the following system conversion function

where Q(ij) is the raw image data m and b are slope and intercept parameters obtained

from linear regression of the system response function and I(ij) is the linearized scaled

data The factor of 1000 was found to scale I(ij) such that the maximum value was a

large 16-bit number Figure 3 shows the original and linearized system responses for the

Pixium 4600 Note that the y-intercepts of the regressions for the linearized responses

are negligible (lt 01) with respect to the slopes a sufficient condition for zero offset

considerations

I3ii Spectral Simulation

The spectral simulations of the IEC filtrations and alternative filtrations indicate

many similarities in their effective energies HVLs and overall shapes of normalized

spectra Results are summarized in Table 3

10

Pixium 4600 Original System

Response

Pixium 4600 Linearized System

Response R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 3 Original (left) and linearized (right) system responses for Pixium 4600 The

linearized system responses were measured from actual images The offsets are small

with respect to the slope sufficient enough for zero-offset conditions

y = 13971x - 13236

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x - 00106Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 13576x + 28292

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

7000

0000 1000 2000 3000 4000 5000

AD

U

Exposure (mR)

y = 99997x - 00067Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0000 1000 2000 3000 4000 5000

AD

U

Exposure (mR)

y = 13644x + 16167Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x + 00044

Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 13845x + 13541

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x - 00177

Rsup2= 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

11

Table 3 Spectral Simulation Results

Beam Quality Filtration

Mean Energy

(kV)

Photon Fluence

(mRmm2)

RQA5A 21 mm Al 5243 259543

RQA5C 05 mm Cu + 10 mm Al 5214 259554

diff 055 0004

RQA9A 40 mm Al 7619 273281

RQA9C 104 mm Cu + 10 mm Al 7579 273964

diff 052 025

Figure 4 Spectral simulations for RQA5 (top) and RQA9 (bottom) conditions Note

the similarities of spectral shapes of the normalized spectra (right) Also note the

significant differences in fluence between filtrations in the simulated spectra (left)

00E+00

50E+04

10E+05

15E+05

20E+05

25E+05

30E+05

35E+05

40E+05

45E+05

0 20 40 60 80

ph

oto

ns

mA

s-1

cm

-2

keV

RQA5 Spectra Comparison

21 mm Al

05 mm Cu + 10 mm Al

00

02

04

06

08

10

12

0 20 40 60 80

keV

RQA5 Normalized Spectra Comparison

21 mm Al

05 mm Cu +

10 mm Al

00E+00

50E+05

10E+06

15E+06

20E+06

25E+06

30E+06

35E+06

40E+06

45E+06

50E+06

0 50 100 150

ph

oto

ns

mA

s-1

cm

-2

keV

RQA9 Spectra Comparison

40 mm Al

104 mm Cu +

10 mm Al

00

02

04

06

08

10

12

0 50 100 150

keV

RQA9 Normalized Spectra Comparison

40 mm Al104 mm Cu + 10 mm Al

12

I3iii Modulation Transfer Function

The limiting spatial resolutions of the systems were indicated by the cutoff

frequencies which were approximately 35 cyclesmm for all three detectors The spatial

resolutions also demonstrated a good degree of isotropy as confirmed by the close

alignment of MTF curves between vertical and horizontal directions differentiated in

Figure 5 by dashed and solid lines respectively The MTF curves for the Pixium 4600

and DRX-1C were nearly equal to each other whereas the DRX-1 MTF curve showed a

more rapid decrease at high frequencies as shown in Figure 6 This difference may be

due to the differences in the inherent optical properties of the scintillating materials

where finer image details are provided by structured CsI more than by granulated GOS

There were no significant differences in MTF curves across beam qualities and filtrations

as shown by the curve comparisons in Figure 6 although the alternative filtration

produced slightly higher MTF curves as seen in Figure 4 Table 4 lists the experimental

specific spatial frequencies for varying levels of MTF

I3iv Noise Power Spectrum

The noise characteristics are indicated by the NNPS curves shown in Figure 7

The noise was similar for both horizontal and vertical directions As exposure increased

the NNPS decreased consistent with the characteristics of Poisson noise describing the

relationship between signal and noise in the presence of increased photon fluence At

13

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 5 MTF results by detector (columns) and beam quality (rows)

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

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14

Figure 6 Plots of MTF for RQA5 (top) and RQA9 (bottom) showing the relationships

between detectors (blue red and green) and by filtration (solid and dashed)

00

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15

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

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A9C

Figure 7 NNPS results by detector (columns) and beam quality (rows)

1E-7

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Spatial Freq (mm)

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16

Figure 8 Plots of NNPS for RQA5 (top) and RQA9 (bottom) at 1 mR exposure

showing the relationships between detectors (blue red and green) and by filtration

(solid and dashed)

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17

Pixium 4600 DRX-1C DRX-1 R

QA

5A

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Figure 9 DQE results by detector (columns) and beam quality (rows)

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18

Figure 10 Plots of DQE for RQA5 (top) and RQA9 (bottom) at 1 mR exposure showing

the relationships between detectors (blue red and green) and by filtration (solid and

dashed)

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19

higher frequencies the NNPS curves of the Pixium 4600 and DRX-1 diverge slightly for

the different directions illustrating increased noise in the readout direction (vertical)

Differences in the noise characteristics were more apparent among detectors as

shown for 1 mR in Figure 8 The NNPS curve for the DRX-1 was higher in magnitude

across the entire frequency range than either the Pixium 4600 or DRX-1C which both

seemed to demonstrate reasonably similar NNPS curves The higher magnitude noise of

the DRX-1 indicates higher relative noise content overall Closer inspection of the NNPS

curves of the Pixium 4600 and DRX-1C detectors in Figure 7 revealed differences in the

spacing between the three exposure levels The gaps between the Pixium 4600 NNPS

curves do not correspond to the factor of two differences between each exposure level

especially at low- to mid- spatial frequencies suggesting a higher level of fixed pattern

noise additional noise with increasing exposure levels due to ineffective gain map

corrections Between filtration schemes the differences in NNPS curves for a given beam

quality were not substantial as shown in Figure 7

I3v Detective Quantum Efficiency

The DQE results are shown in Figure 9 DQE curves across exposure levels were

almost collinear except for Pixium 4600 and in general could be inferred from the

NNPS results Additionally the DQE curves demonstrated a relatively linear response

with spatial frequencies as expected for flat-panel detectors [9] Differences in DQE

among detectors were consistent for the most part with the type of scintillating material

20

As depicted for 1 mR exposure in Figure 10 differences between Pixium 4600 and DRX-

1C DQE curves correspond to the differences in their NNPS curves DRX-1 DQE curves

were consistently lower than either the Pixium 4600 or DRX-1C curves The DQE curves

for the alternative filtration were consistently higher than those for the IEC filtration

and the most noticeable differences were near the zero-frequency axis These effects can

be both attributed to ineffective gain map correction DQE values for 1 mR exposure are

listed in Table 5

I4 Discussion

I4i Comparisons of Detectors

The limiting spatial resolutions of all three detectors were almost exactly the

same considering that their pixel areas were similar in size The decrease in high-

frequency MTF of the DRX-1 compared to the other detectors is probably a result of

increased optical blurring due to the differences in the powdered structure of GOS

versus the needle-like structure of CsI [2] The fact that the DRX-1C and Pixium 4600

have comparable MTFs suggests similar scintillator thicknesses assuming that the

materials were processed alike

The noise of the three detectors demonstrated similar trends with each other The

higher NNPS curves of the DRX-1 detector are probably due also to the scintillating

material and its operation in converting photons into signal The conversion process is

less efficient because of the less favorable stopping power of the GOS compared to CsI

21

especially with higher energy beams The noise of the Pixium 4600 and DRX-1C were

similar except for the spacing between exposures The DRX-1C NNPS curve spacing is

consistent with a factor of two difference in exposure levels but the Pixium 4600 has a

smaller spacing The 05 mR NNPS curve of the Pixium 4600 is closer to that of the 05

mR NNPS curve of the DRX-1C This demonstrates that at higher exposures the Pixium

4600 produces a larger amount of additional noise beyond that explained by simple

stochastic effects It suggests bad performance in the gain map corrections

The DQE results indicate SNR properties of each detector The Pixium 4600 and

DRX-1C are comparable for the most part with the DRX-1C performing slightly better

The DRX-1 as predicted from MTF and NNPS results has a DQE much lower than

either of the previous two This is a reflection of the detection properties as provided by

its scintillator material The DQE of the DRX-1 however is comparable to CR image

receptors [2] The mid-frequency dips in the DQE for Pixium 4600 may be due to the

optical properties of the CsI phosphor layer which can affect the MTF in this manner

Because the DQE is calculated by squaring the MTF this effect at the mid-range

frequencies becomes more apparent The dips may also be further evidence of bad gain

map corrections

I4ii Comparisons of Filtrations

The alternative filtration closely matches for the most part the IEC-based

filtration for MTF NNPS and DQEs at RQA5 but not at RQA9 The filters do not have

22

Table 4 Experimental MTF frequency locations for 1 mR exposure

Detector Filtration

50 MTF

(mm-1)

40 MTF

(mm-1)

30 MTF

(mm-1)

20 MTF

(mm-1)

10 MTF

(mm-1)

Pixium

4600

RQA5A 115 145 185 245 330

RQA5C 125 155 195 250 345

RQA9A 110 175 175 235 330

RQA9C 125 155 195 255 345

DRX-1C

RQA5A 120 150 185 245 350

RQA5C 125 155 195 255 355

RQA9A 120 150 190 250 355

RQA9C 130 160 210 265 360

DRX-1

RQA5A 110 135 160 205 280

RQA5C 110 135 170 210 285

RQA9A 105 125 155 195 270

RQA9C 110 135 165 210 285

Table 5 Estimated DQE values for 1 mR exposure by frequency bins

Detector Filtration DQE(00 mm-1) DQE(10 mm-1) DQE(20 mm-1) DQE(30 mm-1)

Pixium

4600

RQA5A 62 42 32 21

RQA5C 63 45 36 25

RQA9A 41 27 30 13

RQA9C 43 33 27 19

DRX-1C

RQA5A 72 52 35 21

RQA5C 76 55 41 24

RQA9A 49 33 23 15

RQA9C 51 40 31 20

DRX-1

RQA5A 38 24 12 4

RQA5C 38 25 14 5

RQA9A 28 18 9 4

RQA9C 28 19 12 5

DQE values at the zero-frequency axis were estimated by the intercept of a linear fit of low-frequency data

but excluding most proximal to the axis due to large fluctuations Other estimated values are grouped into

frequency bins due to the noisiness of the data

23

considerable differences in the spatial resolutions of the detectors as expected The noise

responses for each filtration were also similar except at the lower frequencies of the

NNPS especially near the zero-frequency axis There observing the NNPS responses at

RQA5 for Pixium 4600 and DRX-1C in Figure 8 the NNPS for the IEC-based filtration

(solid lines) tend to drop faster than the NNPS for the alternative filtration This

subsequently appears as a drop in DQE near the zero-frequency axis shown for those

detectors in Figure 10 Overall as indicated in Table 5 the DQEs of the two filtrations

while similar in trend indicate that the alternative filtration increases the DQE by a

small amount of 3-5 Part of this may be explained by the slightly higher beam

energy which may be more optimal for the energy response of the detectors or may

weigh the pixel responses slightly considering that they are energy-integrating types

The most probable explanation is the gain map correction for the alternative filtration

where fixed pattern noise is more sufficiently reduced

A previous study [6] had discussed the choice of filter material in the analysis of

DQE when achieving the beam conditions defined by IEC It found that visible

nonuniformities were present with the higher purity aluminum filter (type-11999 alloy)

The low frequency mottle in the flat-field images for NPS measurements were also

attributed to structured noise from the grain size in the IEC-based filter with an

attenuating thickness that would reveal nonuniformities The mottle in the current study

was only observable under very narrow windowing as shown in Figure 11 Such low

24

frequency artifacts which are not readily noticeable may also be caused by shading

artifacts inverse square law or even the heel effect A possible method to correct for this

is a subtraction method by taking the average of the flat-field images for an exposure

level and then subtracting that from each of them This would remove nonuniformities

that were not corrected using a suboptimal gain map calibration

Figure 11 DRX1-C NNPS images at 1 mR for RQA5 with IEC filtration (left) and

alternative filtration (right) Images are equally windowed at 45 and leveled at 980

One convenient aspect of the copper and aluminum filtration is that it requires

much less tube current to achieve the same amount of exposure at the detector than the

much thicker aluminum filtration As shown in the non-normalized spectra in Figure 2

the exiting photon fluence exiting the copper and aluminum filtration is substantially

higher than that of the IEC-specified filtration This is due to the smaller total filtration

25

attenuation For extensive DQE analysis multiple sets of exposures may be acquired

before tube overheating becomes a concern

One limitation to the comparison of the two filtrations is that calibration

procedures specified copper and aluminum filtration at 80 kVp (for all detectors 05 mm

Cu and 10 mm Al) This may have influenced the results in favor of the alternative

filtration A further investigation involving the calibration procedures and performing

DQE measurements is encouraged Another factor may be influenced by the fact that the

tests were performed at 70 kVp and 120 kVp different from the recommended

calibration tube potential Clearly there would be differences in the linear attenuation

coefficients of the filters and different energy responses of the detectors themselves This

must be considered when interpreting DQE results The current results support a

previous study decades ago that described filtration of different material types in terms

of an aluminum equivalent [16] The results show that the two filtration schemes are

essentially equivalent when considering beam qualities and spatial resolutions The

NNPS and DQE results can be seen as close enough where their small differences are

insignificant when performing quality assurance tests in a clinical setting Overall our

results indicate that the alternative filtration with copper and aluminum may be more

convenient to use than the current IEC standard filtration

26

I4iii Implications of Wireless DR

This study has shown that wireless image receptors can have the same DQE

performance if not better than conventional flat-panel detectors They operate on the

same basic physical principles the new features offered by the DRX-1C and DRX-1 are

wireless communication with the workstation and electronics packaging technology

The latter feature may pose limitations for these units in terms of possible degradation

in the detectors in routine clinical conditions A consideration for future work would be

to longitudinally track DQE performance of the wireless detectors over time while being

utilized in a clinical environment In the end one must consider risks versus benefits of

choosing portable DR technology over CR one of which includes the cost and fragility

of DR detectors

The DQE performance of one wireless system is just as good as or better than

conventional systems as seen by the DRX-1C performance compared to the Pixium

4600 Wireless systems can also reduce the need for CR readers especially in portable

applications in other regions of the world (eg military hospitals developing countries)

However while DQE performance indicates the physical performance of the detector

system it is still unknown how it relates to observer performance

I5 Conclusions

Two wireless image receptors DRX-1C and DRX-1 were evaluated and

compared with the conventional DR flat-panel Pixium 4600 in terms of DQE

27

performance along with MTF and NNPS performances The detectors have similar

resolution properties although the DRX-1 is inferior at higher spatial frequencies The

NNPS and DQE results both indicate that the DRX-1C is superior to the DRX-1 and

comparable if not better to the Pixium 4600

The results from the filtration comparison indicate no substantial differences

between the IEC-based filtration and the copper-based alternative filtration Only slight

differences were found in the low frequency components of the NNPS and the DQE due

to the inherent nonuniformities of the IEC specified filtration Given the similarity of the

results and low attenuation advantage of the copper and aluminum filter its use is

encouraged

28

II Directional MTF for Breast Tomosynthesis

II1 Introduction

Breast tomosynthesis is an emerging 3D imaging modality that has potential use

for screening and diagnosis of breast cancer Breast tomosynthesis along with other 3D

techniques is preferable to planar imaging methods (eg mammography) because they

reduce anatomical noise by removing overlying structures above and below the plane of

an image slice [17-20] Recent advances in detectors and computer technology have

made digital tomosynthesis feasible

An image quality metric of particular importance in breast tomosynthesis is

spatial resolution Resolution is important to know in order to assess small-detail

structures such as microcalcifications A descriptive metric for characterizing spatial

resolution in the Fourier (or frequency) domain is the modulation transfer function

(MTF) Affected by reconstruction filters [21] the limited angular projections involved in

breast tomosynthesis results in highly anisotropic (or nonuniform) resolution Many

studies have looked only at characterizing the in-plane spatial resolution (ie in an

individual slice) with an elevated angled edge phantom [2223] A few studies have

looked at characterizing a more comprehensive 3D spatial resolution by using a

phantom with angled wires or tubes [24-26] However such studies require precise

mechanical alignment of the phantoms Several studies have explored a method using a

29

sphere phantom for the directional 3D MTF evaluation for microtomography [27] and

multi-slice CT [2829] This method has not yet been extended to breast tomosynthesis

This chapter focuses on breast tomosynthesis because it is highly anisotropic in

spatial resolution and like its predecessor mammography requires high spatial

resolution Additionally breast tomosynthesis acquisitions and reconstructions produce

several types of artifacts The use of a cone-based method using a sphere phantom [28] is

explored to characterize the directional 3D spatial resolution of simulated images from

breast tomosynthesis A technique for removing out-of-plane artifacts of the ESFs for the

in-plane axes is investigated to yield a modified MTF in a method that separates artifact

information from resolution information

II2 Materials and Methods

II2i Image Simulation

Breast tomosynthesis images were simulated by using a virtual imaging system

depicted in Figure 12 A volumetric breast phantom was voxelized as a rectangular mass

of uniform breast equivalent tissue of 4 cm thickness embedded with fifteen evenly

spaced plastic sphere inserts of 12 mm diameter The spheres were placed in a grid

formation within the central plane of the phantom The x-ray fluence was modeled from

a 28 kVp beam incident upon an indirect flat-panel detector with 200 micro m pixel size

Twenty-three projections within an angular range of 44deg were simulated using cascaded

systems analysis to generate characteristic 2D noise and spatial blurring [29] Each

30

projection was simulated to have an exposure of 174 mR with a fluence of 79 times 105

photonsmm-2 A standard filtered backprojection technique based on the Feldkamp

reconstruction algorithm [29] was used to reconstruct the projections and produce a

volumetric dataset with an isotropic voxel size of 200 micro m

Figure 12 Depiction of the virtual image system

II2ii Uncorrected MTF

To enable comparison of multiple spheres the reconstructed volume was

initially homogenized by performing a background subtraction based on a portion of the

volume devoid of spheres The voxel values were rescaled between one and zero to

eliminate negative values

31

The volumetric data were segmented to extract individual regions of interest

(ROIs) each containing a single sphere The ROIs extended along the full range of the z-

axis A thresholded ROI was generated by determining the exterior and interior voxels

relative to the sphere in the ROI The threshold value was set at 45 of the maximum

voxel value prior to thresholding The exterior and interior voxel values were then set to

values of 0 and 1 respectively Using the thresholded volume the center of mass was

calculated to determine the centroid The voxel values from the original ROI were

subsequently tabulated with the associated distances azimuthal angles and polar

angles relative to the centroid

Conical regions were prescribed along the positive and negative directions along

the three major axes extending from the centroid of the sphere as depicted in Figure 13

The axes about which the extent of the cone angle was delineated were defined with

the azimuthal and polar angles

Voxels with centers within the angular range of the cone were considered for

generating the edge spread function (ESF) To improve regularity of the distance

sampling interval the ESF values were rebinned to discrete distances corresponding to a

fraction of the voxel size Only voxels with distances ranging from the voxel size (ie

200 micro m) to the maximum distance were considered The ESFs from multiple spheres

were averaged together for each of the three major axes to produce an averaged ESF

which was further smoothed utilizing a Gaussian filter

32

Figure 13 Example of 30-degree cone prescribed along z axis of the sphere

The resulting ESF was then differentiated using the central difference method to

produce the line spread function (LSF) A Hanning filter with the same length as the LSF

was applied to zero out the tails of the LSF The presampled MTF was subsequently

computed as the amplitude of the Fourier transform of the LSF The MTF was

normalized with respect to the maximum value occurring within the range of the cutoff

frequency Binning size and conical range for the ESF were considered for maximizing

accuracy and minimizing noise of the MTF verified by comparison against the

theoretical MTF as determined in the previous section

II2iii Theoretical Directional MTF

The theoretical 3D MTF was calculated using a priori knowledge of the transfer

function of the virtual imaging system described in the previous section A phantom

was created with a set of point objects in a uniform and noise-free background with the

objects spanning across the volume of the breast [29] Twenty-one realizations were

33

generated from the reconstructed images of the point objects to yield a set of 3D point

spread functions (PSFs) The 3D fast Fourier transform (FFT) was performed for each 3D

PSF and averaged to give an ldquoexpectationrdquo 3D MTF [29] The theoretical directional

MTFs in the three major spatial axes were determined by line profiles along each of the

corresponding spatial frequency axes in the 3D MTF An additional theoretical MTF for

each direction was determined by using the application of conical regions along the axes

in frequency-space to take into account the contributions of MTF information from other

planes

II2iv Modified MTF

The tomosynthesis reconstruction is known to have edge enhancements which

affect the overall MTF by shifting the peaks of the MTF toward the higher frequencies

[23] The presence of this artifact complicates the interpretation of the actual spatial

resolution of the images Several steps were performed to remove the artifact

contribution to the resolution information particularly for the in-plane x and y

directions with the assumption that resolution information was contained immediately

near the edge

For the x-direction averaged ESF only values that were detected to be inside the

edge of the sphere were considered Those values were previously determined via

thresholding for calculating the centroid The ESF information corresponding to these

values was inversed and flipped about the detected edge to produce a symmetric

34

modified ESF The modified MTF was subsequently calculated from this modified ESF

as described in the previous section

For the y-direction averaged ESF an upward trend was found in the initial part

of the ESF This section was detrended with a polynomial fit and subtracted to produce a

flatter curve in that region The resulting detrended ESF was used to calculate the y axis

modified MTF

Figure 14 Photograph of the imaging system with the acrylic sphere phantom

embedded in oil

II2v Preliminary Experimental Validation

A clinical breast tomosynthesis system (Mammomat Inspiration Siemens AG

Munich Germany) was used to perform a preliminary evaluation of the cone-based

MTF technique The phantom for the experiment consisted of a single acrylic ball of 075

in diameter (SmallParts Seattle WA) suspended by a 0029 in diameter plastic filament

35

(Omniflex Zebco Tulsa OK) in an acrylic frame filled up to 4 in with vegetable oil

(Target Brands Inc Minneapolis MN) The system and phantom are shown in Figure

14 Twenty-five projections with an angular range of 44deg were acquired and subsequently

reconstructed to produce a volume with a voxel size of 01times01times10 mm3 The voxels were

reformatted to have an isotropic size of 01 mm The uncorrected ESF LSF and MTF

were calculated as described in the previous section

II3 Results

II3i Reconstruction

The reconstructed volume is shown in Figure 15 Notice the edge enhancement

along the x-direction as indicated by the sharp shadowing artifacts on either side of the

spheres The background was effectively homogenized using the background

subtraction technique This also took account of the curved edges of the breast phantom

With the close spacing of the spheres in the phantom the shadows along the x direction

for the fifteen spheres overlap with each other As the nine centrally located spheres

experience this effect the same way they were used for determining the ESF

A 3D rendering of the ROI containing a sphere shown in Figure 16 indicates the

anisotropic resolution of the reconstruction Note that the sphere is not accurately

reconstructed and has an oblong shape especially along the z axis Cross sectional views

of the ROI also in Figure 16 clearly demonstrate the edge enhancement causing a

shadow artifact in the x direction caused by the incomplete angular sampling of

36

tomosynthesis The sampling also introduces the triangular reconstruction of the sphere

as seen in the x-z plane Note the gradual edge drop-off in the z direction much beyond

the sphere radius

Figure 15 View of the central slice of the breast phantom reconstruction before (top)

and after (bottom) background subtraction The z axis is through the page

37

Figure 16 3D rendering of the ROI volume (left) and cross-sectional views of the most

centrally located sphere with centroid indicated with red circle (right)

II3ii Theoretical MTF

The theoretical MTFs for x y and z directions as determined from the line

profiles of the 3D MTF are shown in Figure 17 The theoretical MTF in the x direction

has a maximum value that is toward higher frequencies Its 10 response occurs at

about 125 cyclesmm which is at 50 of the cutoff frequency The rapid increase from

the zero-frequency intercept to the peak corresponds to the ramp filter used in filtered

backprojection which decreases the weighting of low frequency contributions due to the

incomplete angular sampling of the frequency-space The MTF does not reach a value of

0 at the zero-frequency intercept as it is very difficult to assess the zero-frequency

intercept due to the finite size of the phantom The theoretical MTF in the y direction

peaks at the zero-frequency intercept and reaches 20 proximal to the cutoff frequency

38

The 10 MTF is well beyond the cutoff frequency The theoretical MTF in the z direction

has a rapid drop-off at very low spatial frequencies indicating the lack of resolution in

that dimension

Figure 17 Theoretical 3D MTF results along the three major planes (top) and along x

y and z directions (bottom) Also note that the angular spread seen in the fx-fz plane is

equal to the angular range of 44deg for the acquisition

II3iii Uncorrected MTF

The ESF LSF and MTF using the cone-based method are shown for the x y and

z directions in Figure 18 It was found that a bin size of one-tenth the voxel size (002

mm) and a cone angle of 30deg to establish the ESF were enough to minimize noise and

maximize accuracy in the uncorrected MTFs considering the reasonable comparison of

the shapes of the MTF curves with the theoretical results in Figure 17 The LSFs are

generally noisy because differentiation of the ESF increases the amplitude of the noise

39

The data shown reflect a convolution with a smoothing Gaussian filter which was later

further corrected for in the reported MTF Nevertheless the high frequency components

of the noise are well beyond the MTF cutoff frequency of 25 cyclesmm and do not

impact the MTF results greatly

For the ESF in the x direction the shadow effect evident at the edge of the sphere

is visible as a steep decline followed by an increase Due to the finite distance range

provided by the ROI the ESF beyond the edge did not asymptotically reach the

background value The corresponding LSF demonstrates a low frequency modulation

that is indicated by the shift of 03 cyclesmm in the x direction for the peak of the MTF

The MTF exhibits a zero-frequency intercept that is non-zero unlike the theoretical MTF

and a 10 value at approximately 1 cyclesmm These features may be a direct

consequence of MTF information ldquocontaminationrdquo from y and z directions Furthermore

the ESF in the y direction demonstrates a reasonably shaped curve except for the slight

upward trend within the radius of the sphere which can be attributed to the shadow

artifact overlapping with the sphere volume The associated MTF has a peak shifted by

approximately 01 cyclesmm away from the axis and a 10 MTF occurring at

approximately 15 cyclesmm Both features which are not present in the theoretical

results may also be attributed to contaminant MTF information from x and z directions

The ESF in the z direction has a drop-off that occurs at a small fraction of the cutoff

frequency similar to that demonstrated by the theoretical MTF

40

Uncorrected ESF LSF and MTF

Figure 18 Uncorrected ESF (top) LSF (middle) and MTF (bottom) for x y and z

directions

41

Figure 19 Comparisons of the directional MTFs as calculated by the sphere method

(dashed line) by theoretical line profiles (light-weight line) by theoretical cone

regions (heavy-weight line)

II3iv Comparison of Theoretical and Simulated MTFs

The theoretical MTF results obtained from line profiles through the 3D MTF and

the simulated MTFs using the cone-based technique did not match very well except for

the general shape of the curves It was assumed in the previous section that the cone-

based technique contains information from other planes Figure 19 compares MTFs in

each direction for the two methods described in the methods and an additional method

based on conical regions of the 3D MTF The latter computes the MTF by averaging

contributions of the 3D MTF using the same cone prescription method used to define the

ESFs Comparison of the curves indicate some interesting correlations aside from the

fact that using conical regions with the 3D MTF results produce more noisy MTF results

partly due to the low sampling provided by the theoretical calculations The same

conclusions regarding the z direction MTF can be confirmed regardless of either

theoretical MTF procedures The experimental x direction MTF seems to agree best with

42

the line profile method whereas the y direction MTF agrees better with the cone region

method The fact that the experimental x direction MTF has a drop-off frequency that is

lower than those of either of the theoretical MTFs in Figure 19 suggests that this might

be due to integration of the z-direction in the in-plane slices considering how slices are

essentially averages of z direction information contained within it [33]

II3v Modified MTF for x and y

Modified ESF LSF and MTF curves for x and y directions are shown in Figure

20 The modified ESF and the resulting LSF in the x direction appear symmetric as

expected from the inverse and flip operation of the interior ESF about the detected edge

The modified MTF appears with less variation than the uncorrected MTF and the MTF

peak occurs at the zero-frequency axis The correction yields a 10 MTF at about 15

cyclesmm an improvement from the uncorrected MTF but still distant from the cutoff

frequency The modified ESF in the y direction demonstrates the detrended curve within

the sphere radius after a quadratic polynomial fit The resulting modified MTF still

appears similar to the uncorrected MTF except that the peak now coincides with the

zero-frequency axis For both x and y directions the low response of the modified MTFs

at the higher frequencies suggests that the contamination from other directions is

substantial due to the angular range of the cone

43

Modified ESF LSF and MTF

Figure 20 Modified ESF (top) LSF (middle) and MTF (bottom) for x and y directions

44

II3v Preliminary Experimental Validation

Cross-sections of the reconstructed sphere volume are shown in Figure 21

Relative to the simulation reconstructions the reconstructions of the experimental

phantom images produce lower contrast and higher noise The preliminary results

shown in Figure 22 indicate that our technique can be applied to actual experimental

breast tomosynthesis reconstructions However due to the noise exhibited by the MTF

curves for the x and y directions we did not determine the modified MTFs to separate

resolution and artifact information

Figure 21 Cross sectional views of the experimental sphere image with centroid

indicated with red circle

45

Uncorrected ESF LSF and MTF for Real Image

Figure 22 ESF (top) LSF (middle) and MTF (bottom) of real image for x y

and z directions

46

II4 Discussion

II4i Evaluation of Cone-based Method

The cone-based MTF technique was introduced by Thornton and Flynn [28] for

evaluation of volumetric CT images To utilize this technique as a characterization of a

3D system spatial resolution one must first consider the validity of the assumption of

shift invariance such that the same MTF result may be obtained regardless of the

location of the sphere The study by Zhao et al [23] found that there was no shift

variance for the MTF measurements along the vertical axis but this was only considering

the in-plane resolution along one axis On the other hand this study evaluated the MTF

with images simulated with cascaded systems analysis which includes conditions of

linearity and shift invariance Additionally the MTF was calculated by averaging the

ESF from several spheres in the same volume only after performing a background

subtraction This step was essential to account for the sensitivity of centroid calculations

as well as ensuring symmetric ESFs for opposing axes of the sphere ROIs

The measurement of MTF with the cone-based technique inherently

supersamples the edge of the sphere to increase signal-to-noise-ratio (SNR) of edge

information by averaging the contributions of each voxel to the ESF [713] This method

also takes into account the discrete sampling of the voxels by accounting for various

shifts of the edge in the voxel (also known as the partial volume effect) However using

the curved surface of the sphere phantom to approximate an edge along a given

47

direction naturally leads to contamination of information from other directions aside

from the one of interest Preferably a directional ESF should be created by using a single

radial line but this would limit the available voxels to obtain edge information An ideal

situation theoretically would be to use a larger-sized sphere such that the surface is

nearly flat and perpendicular to the axes of interest This would also permit a reduction

in the angular range of the cone and thus the introduction of out-of-plane information in

the resulting MTF However sphere size is a limitation in breast tomosynthesis and the

use of a large phantom might void the assumption of shift invariance of the spatial

resolution

The choice of a sphere phantom nevertheless may be based on the clinical need

to quickly acquire a single image for MTF evaluation especially for multiple directions

without presenting extra logistical challenges The use of a wire or edge phantom

requires more precise mechanical alignment to achieve the correct set up The edge

phantom [23] would require at least two images to sample all three dimensions In the

case of the three wire phantom [2425] all three dimensions of the frame must be aligned

simultaneously with respect to the axis of rotation A similar situation would be

encountered when considering a cubic phantom with the planes normal to the axis of

interest In contrast to these phantoms the sphere eliminates the need for precise

alignment especially with respect to three spatial dimensions simultaneously A sphere

48

has ideal symmetry in all directions and can be used to evaluate MTF in any arbitrary

direction

This study unlike others [242532] did not explore the effects of physical

parameters such as scatter or contrast on the final MTF result but it demonstrated the

feasibility of using the cone-based method with an actual breast tomosynthesis image of

a sphere phantom as shown in Error Reference source not found and Error Reference

source not found These effects should be addressed in future works A further look

into deriving the principles of comparing the theoretical MTF with the experimental

MTF using the cone-based method is further warranted

II4ii Separation of Artifact and Resolution Information

The focus of this study was to develop a technique for measuring spatial

resolution of tomosynthesis images The intrinsic artifacts from tomosynthesis

reconstructions however lead to uncharacteristic MTFs and possible misinterpretation

of the effective resolution information When considering previous techniques for

calculating the presampled MTF [713152328] the analysis was performed using an

edge or a line to produce the corresponding ESF The resolution information is

essentially contained only along the edge indicated by the need to calculate the LSF In a

way the method of extracting artifact information is to focus the analysis only on the

edge part of the ESF to calculate the modified MTF This will lead to a better

understanding of the limiting size of objects that may be seen in the reconstructed 3D

49

image The presampled MTF without correction should still be analyzed to understand

the entire system response Note that the ESFs attempt to reflect information only at the

detected edge of the sphere

II5 Conclusions

The directional MTF of a simulated breast tomosynthesis reconstruction was

determined by using the cone-based MTF technique demonstrating the feasibility of a

single phantom for MTF evaluation This study further presented methods of analyzing

only the edge information in the ESF to create a modified MTF along in-slice (x and y)

axes It can provide insight into the actual spatial resolution information contained in the

image while separating the resolution information from the information introduced by

artifacts caused by the reconstruction and insufficient volumetric sampling The idea of

separating the resolution and artifacts from the measured ESF are expected to facilitate

the interpretation of MTF measurements in breast tomosynthesis Similar methods may

be applied to characterize the resolution of other 3D imaging modalities

50

References

1 Garmer M Hannigs SP Jaumlger HJ et al ldquoDigital Radiography Versus

Conventional Radiology in Chest Imaging Diagnostic Performance of a Large-

Area Silicon Flat-Panel Detector in a Clinical CT-Controlled Studyrdquo American

Journal of Roentgenology Volume 74 75-80 (2000)

2 Cowen AR Kengyelics SM and Davies AG ldquoSolid-state flat-panel digital

radiography detectors and their physical imaging characteristics rdquoClinical

Radiology Volume 63 487-498 (2008)

3 Chotas HG Dobbins III JT and Ravin CE ldquoPrinciples of Digital

Radiography with Large-Area Electronically Readable Detectors A Review of

the Basicsrdquo Radiology Volume 210 Number 3 595-599 (1999)

4 Flynn MJ and Samei E Experimental comparison of noise and resolution for

2k and 4k storage phosphor radiography systems Medical Physics Volume 26

Number 8 1612-1623 (1999)

5 Rong XJ Shaw CC Liu X Lemacks MR and Thompson SK

ldquoComparison of an amorphous siliconcesium iodide flat-panel digital chest

radiography system with screenfilm and computed radiography systems ndash A

contrast-detail phantom studyrdquo Medical Physics Volume 28 Number 11 2328-

2335 (2001)

6 Ranger NT Samei E Dobbins III JT and Ravin CE Measurement of the

detective quantum efficiency in digital detectors consistent with the IEC 62220-1

standard Practical considerations regarding the choice of filter material

Medical Physics Volume 30 Number 7 2305-2311 (2005)

7 Samei E Buhr E Granfors P Vandenbroucke D and Wang X Comparison

of edge analysis techniques for the determination of the MTF of digital

radiographic systems Physics in Medicine and Biology Volume 50 3613-3625

(2005)

8 Samei E and Flynn MJ An experimental comparison of detector performance

for computed radiography systems Medical Physics Volume 29 Number 4 447-

459 (2002)

51

9 Samei E and Flynn MJ An experimental comparison of detector performance

for direct and indirect digital radiography systems Medical Physics Volume 30

Number 4 608-622 (2003)

10 Samei E Ranger NT MacKenzie A Honey ID Dobbins III JT and Ravin

CE Effective DQE (eDQE) and speed of digital radiographic systems An

experimental methodology Medical Physics Volume 36 Number 8 3806-3817

(2009)

11 Samei E Ranger NT MacKenzie A Honey ID Dobbins III JT and Ravin

CE Detector or System Extending the Concept of Detective Quantum

Efficiency to Characterize the Performance of Digital Radiographic Imaging

Systems Radiology Volume 249 Number 3 926-937 (2008)

12 ldquoIEC 62220-1 Medical Electrical Equipment ndash Characteristics of Digital X-Ray

Imaging Devices ndash Part 1 Determination of the Detective Quantum Efficiencyrdquo

International Electrotechnical Commission Geneva Switzerland (2003)

13 Samei E Ranger NT Dobbins III JT and Chen Y Intercomparison of

methods for image quality characterization I Modulation transfer function

Medical Physics Volume 33 Number 5 1454-1465 (2006)

14 Dobbins III JT Samei E Ranger NT and Chen Y Intercomparison of

methods for image quality characterization II Noise power spectrum Medical

Physics Volume 33 Number 5 1466-1475 (2006)

15 Samei E Flynn MJ and Reimann DA A method for measuring the

presampled MTF of digital radiographic systems using an edge test device

Medical Physics Volume 25 Number 1 102-113 (1998)

16 Nagel HD ldquoAluminum equivalence of materials used in diagnostic radiology

and its dependence on beam qualityrdquo Physics in Medicine and Biology Volume

31 Number 12 1381-1399 (1986)

17 Niklason LT Christian BT Niklason LE et al ldquoDigital Tomosynthesis in

Breast Imagingrdquo Radiology Volume 205 399-406 (1997)

18 Gur D ldquoTomosynthesis Potential Clinical Role in Breast Imagingrdquo American

Journal of Roentgenology Volume 189 614-615 (2007)

52

19 Park JM Franken Jr EA Garg M Fajardo LL and Niklason LT ldquoBreast

Tomosynthesis Present Considerations and Future Applicationsrdquo

RadioGraphics Volume 27 S231-S240 (2007)

20 Good WF Abrams GS Catullo VJ Chough DM Ganott MA Hakim

CM and Gur D ldquoDigital Breast Tomosynthesis A Pilot Observer Studyrdquo

American Journal of Roentgenology Volume 190 865-869 (2008)

21 Hu Y-H Zhao W Mertelmeier T and Ludwig J ldquoImage Artifact in Digital

Breast Tomosynthesis and Its Dependence on System and Reconstruction

Parametersrdquo IWDM 2008 LNCS 5116 628-634 (2008)

22 Chen Y Lo JY Ranger NT Samei E Dobbins III JT ldquoMethodology of

NEQ(f) analysis for optimization and comparison of digital breast tomosynthesis

acquisition techniques and reconstruction algorithmsrdquo Proceedings of SPIE

Volume 6510 65101I (2007)

23 Zhao B Zhou J Hu Y-H Mertelmeier T Ludwig J and Zhao W

ldquoExperimental validation of a three-dimensional linear system model for breast

tomosynthesisrdquo Medical Physics Volume 36 Number 1 240-251 (2009)

24 Madhav P Brzymialkiewicz CN Cutler SJ Bowsher JE and Tornai MP

ldquoCharacterizing the MTF in 3D for a Quantized SPECT Camera Having Arbitrary

Trajectoriesrdquo 2005 IEEE Nuclear Science Symposium Conference Record 1722-

1726 (2005)

25 Madhav P McKinley RL Samei E Bowsher JE and Tornai MP ldquoA Novel

Method to Characterize the MTF in 3D for Computed Mammotomographyrdquo

Proceedings of SPIE Volume 6142 61421Y (2006)

26 Hu Y-H Zhao B and Zhao W ldquoImage artifacts in digital breast

tomosynthesis Investigation of the effects of system geometry and

reconstruction parameters using a linear system approachrdquo Medical Physics

Volume 35 Number 12 5242-5252 (2008)

27 Seifert A and Flynn MJ ldquoResolving power of 3D x-ray microtomography

systemsrdquo Proceedings of SPIE Volume 4682 407-413 (2002)

28 Thornton MM and Flynn MJ Measurement of the spatial resolution of a

clinical volumetric computed tomography scanner using a sphere phantom

Proceedings of SPIE Volume 6142 61421Z (2006)

53

29 Baek J Pelc NJ ldquoUse of sphere phantoms to measure the 3D MTF of FDK

reconstructionsrdquo Proceedings of SPIE Volume 7961 79610D (2011)

30 Richard S and Samei E ldquoQuantitative imaging in breast tomosynthesis and CT

Comparison of detection and estimation task performancerdquo Medical Physics

Volume 37 Number 6 2627-2637 (2010)

31 Chen Y Lo JY and Dobbins III JT ldquoImpulse response analysis for several

digital tomosynthesis mammography reconstruction algorithmsrdquo Proceedings of

SPIE Volume 5745 541-549 (2005)

32 Zhao B and Zhao W ldquoThree-dimensional linear system analysis for breast

tomosynthesisrdquo Medical Physics Volume 35 Number 12 5219-5232 (2008)

33 Wu G Mainprize JG Boone JM and Yaffe MJ ldquoEvaluation of scatter

effects on image quality for breast tomosynthesisrdquo Medical Physics Volume 36

Number 10 4425-4432 (2009)

Page 10: Development and Evaluation of 2D and 3D Image Quality ...

x

List of Tables

Table 1 Physical Characteristics of Digital Image Receptors 4

Table 2 Beam Qualities and Required Filtrations 5

Table 3 Spectral Simulation Results 11

Table 4 Experimental MTF frequency locations for 1 mR exposure 22

Table 5 Estimated DQE values for 1 mR exposure by frequency bins 22

xi

List of Figures

Figure 1 MTF images for DRX-1C detector with radio-opaque edge test device with

arrows indicating the horizontal (left) and vertical (right) directions 7

Figure 2 NNPS image for DRX-1C detector indicating the top left ROI that served as the

reference for normalizing other ROIs in the image The ROI array was formed along the

directions indicated by the arrows The heel effect visible along the vertical axis of the

detector is an example of small variation in signal across the image 8

Figure 3 Original (left) and linearized (right) system responses for Pixium 4600 The

linearized system responses were measured from actual images The offsets are small

with respect to the slope sufficient enough for zero-offset conditions 10

Figure 4 Spectral simulations for RQA5 (top) and RQA9 (bottom) conditions Note the

similarities of spectral shapes of the normalized spectra (right) Also note the significant

differences in fluence between filtrations in the simulated spectra (left) 11

Figure 5 MTF results by detector (columns) and beam quality (rows) 13

Figure 6 Plots of MTF for RQA5 (top) and RQA9 (bottom) showing the relationships

between detectors (blue red and green) and by filtration (solid and dashed) 14

Figure 7 NNPS results by detector (columns) and beam quality (rows) 15

Figure 8 Plots of NNPS for RQA5 (top) and RQA9 (bottom) at 1 mR exposure showing

the relationships between detectors (blue red and green) and by filtration (solid and

dashed) 16

Figure 9 DQE results by detector (columns) and beam quality (rows) 17

Figure 10 Plots of DQE for RQA5 (top) and RQA9 (bottom) at 1 mR exposure showing

the relationships between detectors (blue red and green) and by filtration (solid and

dashed) 18

Figure 11 DRX1-C NNPS images at 1 mR for RQA5 with IEC filtration (left) and

alternative filtration (right) Images are equally windowed at 45 and leveled at 980 24

Figure 12 Depiction of the virtual image system 30

xii

Figure 13 Example of 30-degree cone prescribed along z axis of the sphere 32

Figure 14 Photograph of the imaging system with the acrylic sphere phantom

embedded in oil 34

Figure 15 View of the central slice of the breast phantom reconstruction before (top) and

after (bottom) background subtraction The z axis is through the page 36

Figure 16 3D rendering of the ROI volume (left) and cross-sectional views of the most

centrally located sphere with centroid indicated with red circle (right) 37

Figure 17 Theoretical 3D MTF results along the three major planes (top) and along x y

and z directions (bottom) Also note that the angular spread seen in the fx-fz plane is

equal to the angular range of 44deg for the acquisition 38

Figure 18 Uncorrected ESF (top) LSF (middle) and MTF (bottom) for x y and z

directions 40

Figure 19 Comparisons of the directional MTFs as calculated by the sphere method

(dashed line) by theoretical line profiles (light-weight line) by theoretical cone regions

(heavy-weight line) 41

Figure 20 Modified ESF (top) LSF (middle) and MTF (bottom) for x and y directions 43

Figure 21 Cross sectional views of the experimental sphere image with centroid

indicated with red circle 44

Figure 22 ESF (top) LSF (middle) and MTF (bottom) of real image for x y and z

directions 45

xiii

Acknowledgements

I would like to thank Ian Yorkston Mark Purdum and Van Huston of

Carestream Health Inc (Rochester NY) for their help with digital detector

measurements I would also like to thank Olav Christianson Samuel Richard Brian

Harrawood and Max Amurao for their assistance with collecting data and analyzing

results Special thanks go to my committee members for their helpful insights and

suggestions for this thesis Last but not least I want to express deep appreciation for the

support and mentorship provided by my advisor Dr Ehsan Samei

1

I Evaluation of 2D Digital Image Receptors

I1 Introduction

In the past decade many areas of radiological practice have seen a conversion

from screen films to the storage phosphor cassettes of computed radiography (CR) to the

active-matrix flat-panel detectors of digital radiography (DR) Both CR and DR are

digital systems that offer many potential benefits including but not limited to better

image quality wider dynamic range quicker readout lower radiation dose and higher

throughput [1-3] Even with advances in DR technologies such as improved detective

quantum efficiency (DQE) the primary radiographic system of today continues to be CR

A major obstacle to completely accepting DR is the high capital cost of acquiring an

entire system per examination room while also providing capability for portable

applications Recently manufacturers like Carestream Health Fuji and Toshiba have

introduced wireless digital image receptors that can serve as replacements for CR

cassettes As these are new technologies a further investigation to characterize these

detectors is warranted

In the case of radiographic receptors DQE has historically been the metric of

choice [4] because it indicates the ability of the image receptor to convert incident x-ray

photons into useable signal ndash essentially a measure of signal-to-noise ratio (SNR)

efficiency and overall system performance [23] DQE is observed across a range of

spatial frequencies for evaluating how the detector depicts small and large objects [3]

2

DQE metrics have been used in numerous studies to characterize CR phosphor-screens

as well as indirect and direct digital detectors [4-11] The importance of this highly

quantitative metric may be implied by the introduction of a DQE measurement standard

by the International Electrotechnical Commission (IEC) [12]

The standard measurement methodology of the International Electrotechnical

Commission (IEC) pertains to the image quality of 2D digital radiographic detectors

While the IEC formalism is well-developed some of the components that it requires are

not necessarily the most optimal for characterizing DQE This has been explored in

previous studies in terms of filtration material purity beam limitations and region of

interest (ROI) configuration [1314] To reduce the variability in the radiographic output

across various x-ray tubes due to inherent filtration differences the IEC formalism

prescribes specific additional aluminum filtration to attain radiation beam qualities

based on target half value layers (HVL) Achieving and verifying the desired HVL

however requires applying a substantial amount of aluminum at the exit window of the

x-ray tube which is often directed toward the ground This can be a logistical

inconvenience and can increase the risk of damage to the image receptor and

measurement equipment Similar beam qualities on the other hand may be attained

more conveniently using a thinner lighter filtration combination utilizing a higher Z

number material Care is warranted however as a previous study [6] had indicated that

the choice of filtration material could impact the DQE

3

The purpose of this study was two-fold First we aimed to evaluate and compare

two wireless image receptors with a conventional flat-panel detector on the basis of DQE

performance Second we compared DQE results using the IEC-prescribed filtration with

an alternative filtration For the latter an optimum filtration composition was

determined and compared with the IEC filtration on the basis of DQE

I2 Materials and Methods

I2i Detectors

The physical characteristics of the three digital image receptors evaluated in this

study are listed in Table 1 The Pixium 4600 was a conventional digital flat-panel The

DRX-1C and DRX-1 were both wireless digital cassettes that were tethered for the

purposes of this study All detectors were FDA approved and available commercially

Each detector was calibrated according to its manufacturer specifications to correct for

gain offset and bad pixels They were all dedicated for non-clinical laboratory research

purposes and hence could be operated under service settings that permitted acquisition

of raw (ie for processing) images

I2ii Beam Characterization

I2iia X-ray Techniques

All measurements for this study were taken with a well-characterized standard

radiographic system (Super80CP Philips Healthcare Andover MA) The x-ray tube had

an inherent filtration of 27 mm Al Free in-air exposures were measured using

4

Table 1 Physical Characteristics of Digital Image Receptors

Manufacturer Detector

Detector

type

Detector

material

Pixel pitch

(size) Array size

Imaging

area

Trixell

(Moirans France)

Pixium

4600 Indirect

CsITl

(CsI) 0143 mm

3121times3121

4 subpanels 45times45 cm2

Carestream Health Inc

(Rochester NY)

DRX-1C

(wireless) Indirect

CsITl

(CsI) 0139 mm

2560times3072

single panel 35times43 cm2

Carestream Health Inc

(Rochester NY)

DRX-1

(wireless) Indirect

G2O2STb

(GOS) 0139 mm

2560times3072

single panel 35times43 cm2

calibrated radiation meters (Mult-O-Meter Type 407 Unfors Instruments AB Billdal

Sweden) at 183 cm source-to-chamber-distance (SCD) The SCD also corresponded to

same plane as the image receptor surface The x-ray output was made to conform to IEC

beam quality definitions [1215] on the basis of half value layer (HVL) and peak

kilovoltage setting using an aluminum filtration (type-1100 99 purity) and an

alternative filtration consisting of copper (UNS C11000 999 purity) and aluminum

(type-1100 99 purity) The IEC radiation quality numbers (RQA) used in this study are

summarized in Table 2 HVLs were determined by iteratively adding successive

thicknesses of aluminum until reaching reduced exposure levels within a tolerance of

0485-0515 [12] As for the alternative filtration the aluminum was placed downstream

of the copper filter to attenuate characteristic radiation peaks from copper at

approximately 9 keV

I2iib Data Linearization

The system response function was determined for each detector and filtration

combination by acquiring flat-field images at increasing photon fluence until just before

5

Table 2 Beam Qualities and Required Filtrations

IEC Radiation

Quality Number

Peak

kilovoltage

Required

HVL

Required IEC

Filtration

Actual IEC

Filtration

Alternative

Filtration

RQA5 70 kVp 71 mm Al 21 mm Al 21 mm Al 05 mm Cu +

10 mm Al

RQA9 120 kVp 115 mm Al 42 mm Al 40 mm Al 104 mm Cu +

10 mm Al

For reasons of convenience these will be referred to as RQA5A RQA5C RQA9A and RQA9C

saturation levels To avoid the influence of detector backscatter on exposure

measurements a relationship for each filtration was first determined for two radiation

meters A target meter was placed at the central axis and a reference meter was placed at

the edge of the light field (large enough to cover the detectors) The reference meter

served as a surrogate for the target meter to avoid direct exposure measurements in the

plane of the image receptor Exposure relationships were determined before each

measurement set (ie detector and filtration combination) to account for changes in

temperature pressure and humidity The system response function was calculated by

using a regression of ADU (pixel value) versus exposure Images acquired for each

series were then converted to achieve a linear response with zero offset and scaled to

achieve high quantization (adequate dynamic range) Linearization of the detector

responses ensured that zero exposure corresponded to zero pixel value

I2iic Spectral Simulation

The effects of additional filtration on x-ray output spectra were observed with

spectral simulation software (XSPECT V40 Henry Ford Hospital Detroit MI) To more

6

adequately describe the performance of a typical X-ray generator inherent filtration of 3

mm oil 148 mm Pyrex glass and 2 mm aluminum was input into the simulation in

addition to the filters of interest The ideal signal to noise ratio squared or incident

photon fluence per exposure (q) was estimated for each filtration by integrating the

energy-dependent photon counts per unit exposure over all energy bins

I2iii DQE Measurements

The assessment of the linearized images followed the formalism described by

IEC 62220-1 for measuring the DQE [12] For this study the normal exposure level XN

was set at 1 mR to the detector surface as measured at the central axis perpendicular to

the anode-cathode axis

I2iiia Modulation Transfer Function

Spatial resolution was characterized by evaluating the presampled modulation

transfer function (MTF) along directions parallel (vertical) and perpendicular

(horizontal) to the anode-cathode axis using the angled-edge method [6-1013] A radio-

opaque edge test device [7] was placed in the center of the field at a pitch of

approximately 301 (about 2deg) to the axis perpendicular to that being measured as

shown in Figure 1 External lead apertures were not used [6] instead the internal

collimation from the radiographic unit was used to collimate the beam to the detector

area Raw images were acquired of the edge with the normal exposure level XN of 1 mR

at the detector face The procedure of calculating the MTF followed previously described

7

methods [6-1013] The edge spread function (ESF) was determined along lines crossing

the edge of the angled test device The derivative of the ESF was calculated to form the

line spread function (LSF) to which a Hanning filter was applied The MTF was then

calculated as the fast Fourier transform (FFT) of the LSF and normalized at the zero-

frequency axis To conform to IEC guidelines the MTF was resampled into frequency

steps of 005 cyclesmm [12]

Figure 1 MTF images for DRX-1C detector with radio-opaque edge test device with

arrows indicating the horizontal (left) and vertical (right) directions

I2iiib Noise Power Spectrum

Noise amplitude and texture were characterized by determining the normalized

noise power spectrum (NNPS) which was evaluated with flat field exposures at

approximate exposure levels of XN2 XN and 2XN (05 10 and 20 mR) to the image

receptor surface Analysis of the flat-field images followed previously defined methods

[41415] using over 4 million independent pixels with regions of interest (ROIs) of size

8

128x128 The NNPS images were detrended using a quadratic (second order)

background subtraction Small variations in exposure across ROIs were corrected by

normalizing pixel values of each ROI to the mean value in the top left ROI as shown in

Figure 2 The NNPS was then calculated with the 2D FFT including the zero-frequency

axes corresponding to the horizontal and vertical directions The results were then

resampled using 005 frequency bins according to IEC guidelines [12]

Figure 2 NNPS image for DRX-1C detector indicating the top left ROI that served as

the reference for normalizing other ROIs in the image The ROI array was formed

along the directions indicated by the arrows The heel effect visible along the vertical

axis of the detector is an example of small variation in signal across the image

I2iiic DQE Calculation

The DQE was calculated using the following relationship [615]

9

where the frequency-dependent MTF and NNPS were determined as described in

previous sections X was the exposure value in mR corresponding to the NNPS image

and q was the ideal signal to noise ratio squared in units of photonsmiddotmm-2middotmR-1 as

estimated from the spectral simulations

I3 Results

I3i Data Linearization

The detectors in this study provided raw ADU (or pixel) values in a linear scale

The data were converted using the following system conversion function

where Q(ij) is the raw image data m and b are slope and intercept parameters obtained

from linear regression of the system response function and I(ij) is the linearized scaled

data The factor of 1000 was found to scale I(ij) such that the maximum value was a

large 16-bit number Figure 3 shows the original and linearized system responses for the

Pixium 4600 Note that the y-intercepts of the regressions for the linearized responses

are negligible (lt 01) with respect to the slopes a sufficient condition for zero offset

considerations

I3ii Spectral Simulation

The spectral simulations of the IEC filtrations and alternative filtrations indicate

many similarities in their effective energies HVLs and overall shapes of normalized

spectra Results are summarized in Table 3

10

Pixium 4600 Original System

Response

Pixium 4600 Linearized System

Response R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 3 Original (left) and linearized (right) system responses for Pixium 4600 The

linearized system responses were measured from actual images The offsets are small

with respect to the slope sufficient enough for zero-offset conditions

y = 13971x - 13236

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x - 00106Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 13576x + 28292

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

7000

0000 1000 2000 3000 4000 5000

AD

U

Exposure (mR)

y = 99997x - 00067Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0000 1000 2000 3000 4000 5000

AD

U

Exposure (mR)

y = 13644x + 16167Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x + 00044

Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 13845x + 13541

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x - 00177

Rsup2= 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

11

Table 3 Spectral Simulation Results

Beam Quality Filtration

Mean Energy

(kV)

Photon Fluence

(mRmm2)

RQA5A 21 mm Al 5243 259543

RQA5C 05 mm Cu + 10 mm Al 5214 259554

diff 055 0004

RQA9A 40 mm Al 7619 273281

RQA9C 104 mm Cu + 10 mm Al 7579 273964

diff 052 025

Figure 4 Spectral simulations for RQA5 (top) and RQA9 (bottom) conditions Note

the similarities of spectral shapes of the normalized spectra (right) Also note the

significant differences in fluence between filtrations in the simulated spectra (left)

00E+00

50E+04

10E+05

15E+05

20E+05

25E+05

30E+05

35E+05

40E+05

45E+05

0 20 40 60 80

ph

oto

ns

mA

s-1

cm

-2

keV

RQA5 Spectra Comparison

21 mm Al

05 mm Cu + 10 mm Al

00

02

04

06

08

10

12

0 20 40 60 80

keV

RQA5 Normalized Spectra Comparison

21 mm Al

05 mm Cu +

10 mm Al

00E+00

50E+05

10E+06

15E+06

20E+06

25E+06

30E+06

35E+06

40E+06

45E+06

50E+06

0 50 100 150

ph

oto

ns

mA

s-1

cm

-2

keV

RQA9 Spectra Comparison

40 mm Al

104 mm Cu +

10 mm Al

00

02

04

06

08

10

12

0 50 100 150

keV

RQA9 Normalized Spectra Comparison

40 mm Al104 mm Cu + 10 mm Al

12

I3iii Modulation Transfer Function

The limiting spatial resolutions of the systems were indicated by the cutoff

frequencies which were approximately 35 cyclesmm for all three detectors The spatial

resolutions also demonstrated a good degree of isotropy as confirmed by the close

alignment of MTF curves between vertical and horizontal directions differentiated in

Figure 5 by dashed and solid lines respectively The MTF curves for the Pixium 4600

and DRX-1C were nearly equal to each other whereas the DRX-1 MTF curve showed a

more rapid decrease at high frequencies as shown in Figure 6 This difference may be

due to the differences in the inherent optical properties of the scintillating materials

where finer image details are provided by structured CsI more than by granulated GOS

There were no significant differences in MTF curves across beam qualities and filtrations

as shown by the curve comparisons in Figure 6 although the alternative filtration

produced slightly higher MTF curves as seen in Figure 4 Table 4 lists the experimental

specific spatial frequencies for varying levels of MTF

I3iv Noise Power Spectrum

The noise characteristics are indicated by the NNPS curves shown in Figure 7

The noise was similar for both horizontal and vertical directions As exposure increased

the NNPS decreased consistent with the characteristics of Poisson noise describing the

relationship between signal and noise in the presence of increased photon fluence At

13

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 5 MTF results by detector (columns) and beam quality (rows)

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

horizontal

vertical

14

Figure 6 Plots of MTF for RQA5 (top) and RQA9 (bottom) showing the relationships

between detectors (blue red and green) and by filtration (solid and dashed)

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm-1)

MTF

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm-1)

MTF

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

15

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 7 NNPS results by detector (columns) and beam quality (rows)

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

05 mR - horizontal

05 mR - vertical

10 mR - horizontal

10 mR - vertical

20 mR - horizontal

20 mR - vertical

16

Figure 8 Plots of NNPS for RQA5 (top) and RQA9 (bottom) at 1 mR exposure

showing the relationships between detectors (blue red and green) and by filtration

(solid and dashed)

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm-1)

NNPS (1 mR)

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm-1)

NNPS (1 mR)

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

17

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 9 DQE results by detector (columns) and beam quality (rows)

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

05 mR - horizontal

05 mR - vertical

10 mR - horizontal

10 mR - vertical

20 mR - horizontal

20 mR - vertical

18

Figure 10 Plots of DQE for RQA5 (top) and RQA9 (bottom) at 1 mR exposure showing

the relationships between detectors (blue red and green) and by filtration (solid and

dashed)

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm-1)

DQE (1 mR)

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm-1)

DQE

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

19

higher frequencies the NNPS curves of the Pixium 4600 and DRX-1 diverge slightly for

the different directions illustrating increased noise in the readout direction (vertical)

Differences in the noise characteristics were more apparent among detectors as

shown for 1 mR in Figure 8 The NNPS curve for the DRX-1 was higher in magnitude

across the entire frequency range than either the Pixium 4600 or DRX-1C which both

seemed to demonstrate reasonably similar NNPS curves The higher magnitude noise of

the DRX-1 indicates higher relative noise content overall Closer inspection of the NNPS

curves of the Pixium 4600 and DRX-1C detectors in Figure 7 revealed differences in the

spacing between the three exposure levels The gaps between the Pixium 4600 NNPS

curves do not correspond to the factor of two differences between each exposure level

especially at low- to mid- spatial frequencies suggesting a higher level of fixed pattern

noise additional noise with increasing exposure levels due to ineffective gain map

corrections Between filtration schemes the differences in NNPS curves for a given beam

quality were not substantial as shown in Figure 7

I3v Detective Quantum Efficiency

The DQE results are shown in Figure 9 DQE curves across exposure levels were

almost collinear except for Pixium 4600 and in general could be inferred from the

NNPS results Additionally the DQE curves demonstrated a relatively linear response

with spatial frequencies as expected for flat-panel detectors [9] Differences in DQE

among detectors were consistent for the most part with the type of scintillating material

20

As depicted for 1 mR exposure in Figure 10 differences between Pixium 4600 and DRX-

1C DQE curves correspond to the differences in their NNPS curves DRX-1 DQE curves

were consistently lower than either the Pixium 4600 or DRX-1C curves The DQE curves

for the alternative filtration were consistently higher than those for the IEC filtration

and the most noticeable differences were near the zero-frequency axis These effects can

be both attributed to ineffective gain map correction DQE values for 1 mR exposure are

listed in Table 5

I4 Discussion

I4i Comparisons of Detectors

The limiting spatial resolutions of all three detectors were almost exactly the

same considering that their pixel areas were similar in size The decrease in high-

frequency MTF of the DRX-1 compared to the other detectors is probably a result of

increased optical blurring due to the differences in the powdered structure of GOS

versus the needle-like structure of CsI [2] The fact that the DRX-1C and Pixium 4600

have comparable MTFs suggests similar scintillator thicknesses assuming that the

materials were processed alike

The noise of the three detectors demonstrated similar trends with each other The

higher NNPS curves of the DRX-1 detector are probably due also to the scintillating

material and its operation in converting photons into signal The conversion process is

less efficient because of the less favorable stopping power of the GOS compared to CsI

21

especially with higher energy beams The noise of the Pixium 4600 and DRX-1C were

similar except for the spacing between exposures The DRX-1C NNPS curve spacing is

consistent with a factor of two difference in exposure levels but the Pixium 4600 has a

smaller spacing The 05 mR NNPS curve of the Pixium 4600 is closer to that of the 05

mR NNPS curve of the DRX-1C This demonstrates that at higher exposures the Pixium

4600 produces a larger amount of additional noise beyond that explained by simple

stochastic effects It suggests bad performance in the gain map corrections

The DQE results indicate SNR properties of each detector The Pixium 4600 and

DRX-1C are comparable for the most part with the DRX-1C performing slightly better

The DRX-1 as predicted from MTF and NNPS results has a DQE much lower than

either of the previous two This is a reflection of the detection properties as provided by

its scintillator material The DQE of the DRX-1 however is comparable to CR image

receptors [2] The mid-frequency dips in the DQE for Pixium 4600 may be due to the

optical properties of the CsI phosphor layer which can affect the MTF in this manner

Because the DQE is calculated by squaring the MTF this effect at the mid-range

frequencies becomes more apparent The dips may also be further evidence of bad gain

map corrections

I4ii Comparisons of Filtrations

The alternative filtration closely matches for the most part the IEC-based

filtration for MTF NNPS and DQEs at RQA5 but not at RQA9 The filters do not have

22

Table 4 Experimental MTF frequency locations for 1 mR exposure

Detector Filtration

50 MTF

(mm-1)

40 MTF

(mm-1)

30 MTF

(mm-1)

20 MTF

(mm-1)

10 MTF

(mm-1)

Pixium

4600

RQA5A 115 145 185 245 330

RQA5C 125 155 195 250 345

RQA9A 110 175 175 235 330

RQA9C 125 155 195 255 345

DRX-1C

RQA5A 120 150 185 245 350

RQA5C 125 155 195 255 355

RQA9A 120 150 190 250 355

RQA9C 130 160 210 265 360

DRX-1

RQA5A 110 135 160 205 280

RQA5C 110 135 170 210 285

RQA9A 105 125 155 195 270

RQA9C 110 135 165 210 285

Table 5 Estimated DQE values for 1 mR exposure by frequency bins

Detector Filtration DQE(00 mm-1) DQE(10 mm-1) DQE(20 mm-1) DQE(30 mm-1)

Pixium

4600

RQA5A 62 42 32 21

RQA5C 63 45 36 25

RQA9A 41 27 30 13

RQA9C 43 33 27 19

DRX-1C

RQA5A 72 52 35 21

RQA5C 76 55 41 24

RQA9A 49 33 23 15

RQA9C 51 40 31 20

DRX-1

RQA5A 38 24 12 4

RQA5C 38 25 14 5

RQA9A 28 18 9 4

RQA9C 28 19 12 5

DQE values at the zero-frequency axis were estimated by the intercept of a linear fit of low-frequency data

but excluding most proximal to the axis due to large fluctuations Other estimated values are grouped into

frequency bins due to the noisiness of the data

23

considerable differences in the spatial resolutions of the detectors as expected The noise

responses for each filtration were also similar except at the lower frequencies of the

NNPS especially near the zero-frequency axis There observing the NNPS responses at

RQA5 for Pixium 4600 and DRX-1C in Figure 8 the NNPS for the IEC-based filtration

(solid lines) tend to drop faster than the NNPS for the alternative filtration This

subsequently appears as a drop in DQE near the zero-frequency axis shown for those

detectors in Figure 10 Overall as indicated in Table 5 the DQEs of the two filtrations

while similar in trend indicate that the alternative filtration increases the DQE by a

small amount of 3-5 Part of this may be explained by the slightly higher beam

energy which may be more optimal for the energy response of the detectors or may

weigh the pixel responses slightly considering that they are energy-integrating types

The most probable explanation is the gain map correction for the alternative filtration

where fixed pattern noise is more sufficiently reduced

A previous study [6] had discussed the choice of filter material in the analysis of

DQE when achieving the beam conditions defined by IEC It found that visible

nonuniformities were present with the higher purity aluminum filter (type-11999 alloy)

The low frequency mottle in the flat-field images for NPS measurements were also

attributed to structured noise from the grain size in the IEC-based filter with an

attenuating thickness that would reveal nonuniformities The mottle in the current study

was only observable under very narrow windowing as shown in Figure 11 Such low

24

frequency artifacts which are not readily noticeable may also be caused by shading

artifacts inverse square law or even the heel effect A possible method to correct for this

is a subtraction method by taking the average of the flat-field images for an exposure

level and then subtracting that from each of them This would remove nonuniformities

that were not corrected using a suboptimal gain map calibration

Figure 11 DRX1-C NNPS images at 1 mR for RQA5 with IEC filtration (left) and

alternative filtration (right) Images are equally windowed at 45 and leveled at 980

One convenient aspect of the copper and aluminum filtration is that it requires

much less tube current to achieve the same amount of exposure at the detector than the

much thicker aluminum filtration As shown in the non-normalized spectra in Figure 2

the exiting photon fluence exiting the copper and aluminum filtration is substantially

higher than that of the IEC-specified filtration This is due to the smaller total filtration

25

attenuation For extensive DQE analysis multiple sets of exposures may be acquired

before tube overheating becomes a concern

One limitation to the comparison of the two filtrations is that calibration

procedures specified copper and aluminum filtration at 80 kVp (for all detectors 05 mm

Cu and 10 mm Al) This may have influenced the results in favor of the alternative

filtration A further investigation involving the calibration procedures and performing

DQE measurements is encouraged Another factor may be influenced by the fact that the

tests were performed at 70 kVp and 120 kVp different from the recommended

calibration tube potential Clearly there would be differences in the linear attenuation

coefficients of the filters and different energy responses of the detectors themselves This

must be considered when interpreting DQE results The current results support a

previous study decades ago that described filtration of different material types in terms

of an aluminum equivalent [16] The results show that the two filtration schemes are

essentially equivalent when considering beam qualities and spatial resolutions The

NNPS and DQE results can be seen as close enough where their small differences are

insignificant when performing quality assurance tests in a clinical setting Overall our

results indicate that the alternative filtration with copper and aluminum may be more

convenient to use than the current IEC standard filtration

26

I4iii Implications of Wireless DR

This study has shown that wireless image receptors can have the same DQE

performance if not better than conventional flat-panel detectors They operate on the

same basic physical principles the new features offered by the DRX-1C and DRX-1 are

wireless communication with the workstation and electronics packaging technology

The latter feature may pose limitations for these units in terms of possible degradation

in the detectors in routine clinical conditions A consideration for future work would be

to longitudinally track DQE performance of the wireless detectors over time while being

utilized in a clinical environment In the end one must consider risks versus benefits of

choosing portable DR technology over CR one of which includes the cost and fragility

of DR detectors

The DQE performance of one wireless system is just as good as or better than

conventional systems as seen by the DRX-1C performance compared to the Pixium

4600 Wireless systems can also reduce the need for CR readers especially in portable

applications in other regions of the world (eg military hospitals developing countries)

However while DQE performance indicates the physical performance of the detector

system it is still unknown how it relates to observer performance

I5 Conclusions

Two wireless image receptors DRX-1C and DRX-1 were evaluated and

compared with the conventional DR flat-panel Pixium 4600 in terms of DQE

27

performance along with MTF and NNPS performances The detectors have similar

resolution properties although the DRX-1 is inferior at higher spatial frequencies The

NNPS and DQE results both indicate that the DRX-1C is superior to the DRX-1 and

comparable if not better to the Pixium 4600

The results from the filtration comparison indicate no substantial differences

between the IEC-based filtration and the copper-based alternative filtration Only slight

differences were found in the low frequency components of the NNPS and the DQE due

to the inherent nonuniformities of the IEC specified filtration Given the similarity of the

results and low attenuation advantage of the copper and aluminum filter its use is

encouraged

28

II Directional MTF for Breast Tomosynthesis

II1 Introduction

Breast tomosynthesis is an emerging 3D imaging modality that has potential use

for screening and diagnosis of breast cancer Breast tomosynthesis along with other 3D

techniques is preferable to planar imaging methods (eg mammography) because they

reduce anatomical noise by removing overlying structures above and below the plane of

an image slice [17-20] Recent advances in detectors and computer technology have

made digital tomosynthesis feasible

An image quality metric of particular importance in breast tomosynthesis is

spatial resolution Resolution is important to know in order to assess small-detail

structures such as microcalcifications A descriptive metric for characterizing spatial

resolution in the Fourier (or frequency) domain is the modulation transfer function

(MTF) Affected by reconstruction filters [21] the limited angular projections involved in

breast tomosynthesis results in highly anisotropic (or nonuniform) resolution Many

studies have looked only at characterizing the in-plane spatial resolution (ie in an

individual slice) with an elevated angled edge phantom [2223] A few studies have

looked at characterizing a more comprehensive 3D spatial resolution by using a

phantom with angled wires or tubes [24-26] However such studies require precise

mechanical alignment of the phantoms Several studies have explored a method using a

29

sphere phantom for the directional 3D MTF evaluation for microtomography [27] and

multi-slice CT [2829] This method has not yet been extended to breast tomosynthesis

This chapter focuses on breast tomosynthesis because it is highly anisotropic in

spatial resolution and like its predecessor mammography requires high spatial

resolution Additionally breast tomosynthesis acquisitions and reconstructions produce

several types of artifacts The use of a cone-based method using a sphere phantom [28] is

explored to characterize the directional 3D spatial resolution of simulated images from

breast tomosynthesis A technique for removing out-of-plane artifacts of the ESFs for the

in-plane axes is investigated to yield a modified MTF in a method that separates artifact

information from resolution information

II2 Materials and Methods

II2i Image Simulation

Breast tomosynthesis images were simulated by using a virtual imaging system

depicted in Figure 12 A volumetric breast phantom was voxelized as a rectangular mass

of uniform breast equivalent tissue of 4 cm thickness embedded with fifteen evenly

spaced plastic sphere inserts of 12 mm diameter The spheres were placed in a grid

formation within the central plane of the phantom The x-ray fluence was modeled from

a 28 kVp beam incident upon an indirect flat-panel detector with 200 micro m pixel size

Twenty-three projections within an angular range of 44deg were simulated using cascaded

systems analysis to generate characteristic 2D noise and spatial blurring [29] Each

30

projection was simulated to have an exposure of 174 mR with a fluence of 79 times 105

photonsmm-2 A standard filtered backprojection technique based on the Feldkamp

reconstruction algorithm [29] was used to reconstruct the projections and produce a

volumetric dataset with an isotropic voxel size of 200 micro m

Figure 12 Depiction of the virtual image system

II2ii Uncorrected MTF

To enable comparison of multiple spheres the reconstructed volume was

initially homogenized by performing a background subtraction based on a portion of the

volume devoid of spheres The voxel values were rescaled between one and zero to

eliminate negative values

31

The volumetric data were segmented to extract individual regions of interest

(ROIs) each containing a single sphere The ROIs extended along the full range of the z-

axis A thresholded ROI was generated by determining the exterior and interior voxels

relative to the sphere in the ROI The threshold value was set at 45 of the maximum

voxel value prior to thresholding The exterior and interior voxel values were then set to

values of 0 and 1 respectively Using the thresholded volume the center of mass was

calculated to determine the centroid The voxel values from the original ROI were

subsequently tabulated with the associated distances azimuthal angles and polar

angles relative to the centroid

Conical regions were prescribed along the positive and negative directions along

the three major axes extending from the centroid of the sphere as depicted in Figure 13

The axes about which the extent of the cone angle was delineated were defined with

the azimuthal and polar angles

Voxels with centers within the angular range of the cone were considered for

generating the edge spread function (ESF) To improve regularity of the distance

sampling interval the ESF values were rebinned to discrete distances corresponding to a

fraction of the voxel size Only voxels with distances ranging from the voxel size (ie

200 micro m) to the maximum distance were considered The ESFs from multiple spheres

were averaged together for each of the three major axes to produce an averaged ESF

which was further smoothed utilizing a Gaussian filter

32

Figure 13 Example of 30-degree cone prescribed along z axis of the sphere

The resulting ESF was then differentiated using the central difference method to

produce the line spread function (LSF) A Hanning filter with the same length as the LSF

was applied to zero out the tails of the LSF The presampled MTF was subsequently

computed as the amplitude of the Fourier transform of the LSF The MTF was

normalized with respect to the maximum value occurring within the range of the cutoff

frequency Binning size and conical range for the ESF were considered for maximizing

accuracy and minimizing noise of the MTF verified by comparison against the

theoretical MTF as determined in the previous section

II2iii Theoretical Directional MTF

The theoretical 3D MTF was calculated using a priori knowledge of the transfer

function of the virtual imaging system described in the previous section A phantom

was created with a set of point objects in a uniform and noise-free background with the

objects spanning across the volume of the breast [29] Twenty-one realizations were

33

generated from the reconstructed images of the point objects to yield a set of 3D point

spread functions (PSFs) The 3D fast Fourier transform (FFT) was performed for each 3D

PSF and averaged to give an ldquoexpectationrdquo 3D MTF [29] The theoretical directional

MTFs in the three major spatial axes were determined by line profiles along each of the

corresponding spatial frequency axes in the 3D MTF An additional theoretical MTF for

each direction was determined by using the application of conical regions along the axes

in frequency-space to take into account the contributions of MTF information from other

planes

II2iv Modified MTF

The tomosynthesis reconstruction is known to have edge enhancements which

affect the overall MTF by shifting the peaks of the MTF toward the higher frequencies

[23] The presence of this artifact complicates the interpretation of the actual spatial

resolution of the images Several steps were performed to remove the artifact

contribution to the resolution information particularly for the in-plane x and y

directions with the assumption that resolution information was contained immediately

near the edge

For the x-direction averaged ESF only values that were detected to be inside the

edge of the sphere were considered Those values were previously determined via

thresholding for calculating the centroid The ESF information corresponding to these

values was inversed and flipped about the detected edge to produce a symmetric

34

modified ESF The modified MTF was subsequently calculated from this modified ESF

as described in the previous section

For the y-direction averaged ESF an upward trend was found in the initial part

of the ESF This section was detrended with a polynomial fit and subtracted to produce a

flatter curve in that region The resulting detrended ESF was used to calculate the y axis

modified MTF

Figure 14 Photograph of the imaging system with the acrylic sphere phantom

embedded in oil

II2v Preliminary Experimental Validation

A clinical breast tomosynthesis system (Mammomat Inspiration Siemens AG

Munich Germany) was used to perform a preliminary evaluation of the cone-based

MTF technique The phantom for the experiment consisted of a single acrylic ball of 075

in diameter (SmallParts Seattle WA) suspended by a 0029 in diameter plastic filament

35

(Omniflex Zebco Tulsa OK) in an acrylic frame filled up to 4 in with vegetable oil

(Target Brands Inc Minneapolis MN) The system and phantom are shown in Figure

14 Twenty-five projections with an angular range of 44deg were acquired and subsequently

reconstructed to produce a volume with a voxel size of 01times01times10 mm3 The voxels were

reformatted to have an isotropic size of 01 mm The uncorrected ESF LSF and MTF

were calculated as described in the previous section

II3 Results

II3i Reconstruction

The reconstructed volume is shown in Figure 15 Notice the edge enhancement

along the x-direction as indicated by the sharp shadowing artifacts on either side of the

spheres The background was effectively homogenized using the background

subtraction technique This also took account of the curved edges of the breast phantom

With the close spacing of the spheres in the phantom the shadows along the x direction

for the fifteen spheres overlap with each other As the nine centrally located spheres

experience this effect the same way they were used for determining the ESF

A 3D rendering of the ROI containing a sphere shown in Figure 16 indicates the

anisotropic resolution of the reconstruction Note that the sphere is not accurately

reconstructed and has an oblong shape especially along the z axis Cross sectional views

of the ROI also in Figure 16 clearly demonstrate the edge enhancement causing a

shadow artifact in the x direction caused by the incomplete angular sampling of

36

tomosynthesis The sampling also introduces the triangular reconstruction of the sphere

as seen in the x-z plane Note the gradual edge drop-off in the z direction much beyond

the sphere radius

Figure 15 View of the central slice of the breast phantom reconstruction before (top)

and after (bottom) background subtraction The z axis is through the page

37

Figure 16 3D rendering of the ROI volume (left) and cross-sectional views of the most

centrally located sphere with centroid indicated with red circle (right)

II3ii Theoretical MTF

The theoretical MTFs for x y and z directions as determined from the line

profiles of the 3D MTF are shown in Figure 17 The theoretical MTF in the x direction

has a maximum value that is toward higher frequencies Its 10 response occurs at

about 125 cyclesmm which is at 50 of the cutoff frequency The rapid increase from

the zero-frequency intercept to the peak corresponds to the ramp filter used in filtered

backprojection which decreases the weighting of low frequency contributions due to the

incomplete angular sampling of the frequency-space The MTF does not reach a value of

0 at the zero-frequency intercept as it is very difficult to assess the zero-frequency

intercept due to the finite size of the phantom The theoretical MTF in the y direction

peaks at the zero-frequency intercept and reaches 20 proximal to the cutoff frequency

38

The 10 MTF is well beyond the cutoff frequency The theoretical MTF in the z direction

has a rapid drop-off at very low spatial frequencies indicating the lack of resolution in

that dimension

Figure 17 Theoretical 3D MTF results along the three major planes (top) and along x

y and z directions (bottom) Also note that the angular spread seen in the fx-fz plane is

equal to the angular range of 44deg for the acquisition

II3iii Uncorrected MTF

The ESF LSF and MTF using the cone-based method are shown for the x y and

z directions in Figure 18 It was found that a bin size of one-tenth the voxel size (002

mm) and a cone angle of 30deg to establish the ESF were enough to minimize noise and

maximize accuracy in the uncorrected MTFs considering the reasonable comparison of

the shapes of the MTF curves with the theoretical results in Figure 17 The LSFs are

generally noisy because differentiation of the ESF increases the amplitude of the noise

39

The data shown reflect a convolution with a smoothing Gaussian filter which was later

further corrected for in the reported MTF Nevertheless the high frequency components

of the noise are well beyond the MTF cutoff frequency of 25 cyclesmm and do not

impact the MTF results greatly

For the ESF in the x direction the shadow effect evident at the edge of the sphere

is visible as a steep decline followed by an increase Due to the finite distance range

provided by the ROI the ESF beyond the edge did not asymptotically reach the

background value The corresponding LSF demonstrates a low frequency modulation

that is indicated by the shift of 03 cyclesmm in the x direction for the peak of the MTF

The MTF exhibits a zero-frequency intercept that is non-zero unlike the theoretical MTF

and a 10 value at approximately 1 cyclesmm These features may be a direct

consequence of MTF information ldquocontaminationrdquo from y and z directions Furthermore

the ESF in the y direction demonstrates a reasonably shaped curve except for the slight

upward trend within the radius of the sphere which can be attributed to the shadow

artifact overlapping with the sphere volume The associated MTF has a peak shifted by

approximately 01 cyclesmm away from the axis and a 10 MTF occurring at

approximately 15 cyclesmm Both features which are not present in the theoretical

results may also be attributed to contaminant MTF information from x and z directions

The ESF in the z direction has a drop-off that occurs at a small fraction of the cutoff

frequency similar to that demonstrated by the theoretical MTF

40

Uncorrected ESF LSF and MTF

Figure 18 Uncorrected ESF (top) LSF (middle) and MTF (bottom) for x y and z

directions

41

Figure 19 Comparisons of the directional MTFs as calculated by the sphere method

(dashed line) by theoretical line profiles (light-weight line) by theoretical cone

regions (heavy-weight line)

II3iv Comparison of Theoretical and Simulated MTFs

The theoretical MTF results obtained from line profiles through the 3D MTF and

the simulated MTFs using the cone-based technique did not match very well except for

the general shape of the curves It was assumed in the previous section that the cone-

based technique contains information from other planes Figure 19 compares MTFs in

each direction for the two methods described in the methods and an additional method

based on conical regions of the 3D MTF The latter computes the MTF by averaging

contributions of the 3D MTF using the same cone prescription method used to define the

ESFs Comparison of the curves indicate some interesting correlations aside from the

fact that using conical regions with the 3D MTF results produce more noisy MTF results

partly due to the low sampling provided by the theoretical calculations The same

conclusions regarding the z direction MTF can be confirmed regardless of either

theoretical MTF procedures The experimental x direction MTF seems to agree best with

42

the line profile method whereas the y direction MTF agrees better with the cone region

method The fact that the experimental x direction MTF has a drop-off frequency that is

lower than those of either of the theoretical MTFs in Figure 19 suggests that this might

be due to integration of the z-direction in the in-plane slices considering how slices are

essentially averages of z direction information contained within it [33]

II3v Modified MTF for x and y

Modified ESF LSF and MTF curves for x and y directions are shown in Figure

20 The modified ESF and the resulting LSF in the x direction appear symmetric as

expected from the inverse and flip operation of the interior ESF about the detected edge

The modified MTF appears with less variation than the uncorrected MTF and the MTF

peak occurs at the zero-frequency axis The correction yields a 10 MTF at about 15

cyclesmm an improvement from the uncorrected MTF but still distant from the cutoff

frequency The modified ESF in the y direction demonstrates the detrended curve within

the sphere radius after a quadratic polynomial fit The resulting modified MTF still

appears similar to the uncorrected MTF except that the peak now coincides with the

zero-frequency axis For both x and y directions the low response of the modified MTFs

at the higher frequencies suggests that the contamination from other directions is

substantial due to the angular range of the cone

43

Modified ESF LSF and MTF

Figure 20 Modified ESF (top) LSF (middle) and MTF (bottom) for x and y directions

44

II3v Preliminary Experimental Validation

Cross-sections of the reconstructed sphere volume are shown in Figure 21

Relative to the simulation reconstructions the reconstructions of the experimental

phantom images produce lower contrast and higher noise The preliminary results

shown in Figure 22 indicate that our technique can be applied to actual experimental

breast tomosynthesis reconstructions However due to the noise exhibited by the MTF

curves for the x and y directions we did not determine the modified MTFs to separate

resolution and artifact information

Figure 21 Cross sectional views of the experimental sphere image with centroid

indicated with red circle

45

Uncorrected ESF LSF and MTF for Real Image

Figure 22 ESF (top) LSF (middle) and MTF (bottom) of real image for x y

and z directions

46

II4 Discussion

II4i Evaluation of Cone-based Method

The cone-based MTF technique was introduced by Thornton and Flynn [28] for

evaluation of volumetric CT images To utilize this technique as a characterization of a

3D system spatial resolution one must first consider the validity of the assumption of

shift invariance such that the same MTF result may be obtained regardless of the

location of the sphere The study by Zhao et al [23] found that there was no shift

variance for the MTF measurements along the vertical axis but this was only considering

the in-plane resolution along one axis On the other hand this study evaluated the MTF

with images simulated with cascaded systems analysis which includes conditions of

linearity and shift invariance Additionally the MTF was calculated by averaging the

ESF from several spheres in the same volume only after performing a background

subtraction This step was essential to account for the sensitivity of centroid calculations

as well as ensuring symmetric ESFs for opposing axes of the sphere ROIs

The measurement of MTF with the cone-based technique inherently

supersamples the edge of the sphere to increase signal-to-noise-ratio (SNR) of edge

information by averaging the contributions of each voxel to the ESF [713] This method

also takes into account the discrete sampling of the voxels by accounting for various

shifts of the edge in the voxel (also known as the partial volume effect) However using

the curved surface of the sphere phantom to approximate an edge along a given

47

direction naturally leads to contamination of information from other directions aside

from the one of interest Preferably a directional ESF should be created by using a single

radial line but this would limit the available voxels to obtain edge information An ideal

situation theoretically would be to use a larger-sized sphere such that the surface is

nearly flat and perpendicular to the axes of interest This would also permit a reduction

in the angular range of the cone and thus the introduction of out-of-plane information in

the resulting MTF However sphere size is a limitation in breast tomosynthesis and the

use of a large phantom might void the assumption of shift invariance of the spatial

resolution

The choice of a sphere phantom nevertheless may be based on the clinical need

to quickly acquire a single image for MTF evaluation especially for multiple directions

without presenting extra logistical challenges The use of a wire or edge phantom

requires more precise mechanical alignment to achieve the correct set up The edge

phantom [23] would require at least two images to sample all three dimensions In the

case of the three wire phantom [2425] all three dimensions of the frame must be aligned

simultaneously with respect to the axis of rotation A similar situation would be

encountered when considering a cubic phantom with the planes normal to the axis of

interest In contrast to these phantoms the sphere eliminates the need for precise

alignment especially with respect to three spatial dimensions simultaneously A sphere

48

has ideal symmetry in all directions and can be used to evaluate MTF in any arbitrary

direction

This study unlike others [242532] did not explore the effects of physical

parameters such as scatter or contrast on the final MTF result but it demonstrated the

feasibility of using the cone-based method with an actual breast tomosynthesis image of

a sphere phantom as shown in Error Reference source not found and Error Reference

source not found These effects should be addressed in future works A further look

into deriving the principles of comparing the theoretical MTF with the experimental

MTF using the cone-based method is further warranted

II4ii Separation of Artifact and Resolution Information

The focus of this study was to develop a technique for measuring spatial

resolution of tomosynthesis images The intrinsic artifacts from tomosynthesis

reconstructions however lead to uncharacteristic MTFs and possible misinterpretation

of the effective resolution information When considering previous techniques for

calculating the presampled MTF [713152328] the analysis was performed using an

edge or a line to produce the corresponding ESF The resolution information is

essentially contained only along the edge indicated by the need to calculate the LSF In a

way the method of extracting artifact information is to focus the analysis only on the

edge part of the ESF to calculate the modified MTF This will lead to a better

understanding of the limiting size of objects that may be seen in the reconstructed 3D

49

image The presampled MTF without correction should still be analyzed to understand

the entire system response Note that the ESFs attempt to reflect information only at the

detected edge of the sphere

II5 Conclusions

The directional MTF of a simulated breast tomosynthesis reconstruction was

determined by using the cone-based MTF technique demonstrating the feasibility of a

single phantom for MTF evaluation This study further presented methods of analyzing

only the edge information in the ESF to create a modified MTF along in-slice (x and y)

axes It can provide insight into the actual spatial resolution information contained in the

image while separating the resolution information from the information introduced by

artifacts caused by the reconstruction and insufficient volumetric sampling The idea of

separating the resolution and artifacts from the measured ESF are expected to facilitate

the interpretation of MTF measurements in breast tomosynthesis Similar methods may

be applied to characterize the resolution of other 3D imaging modalities

50

References

1 Garmer M Hannigs SP Jaumlger HJ et al ldquoDigital Radiography Versus

Conventional Radiology in Chest Imaging Diagnostic Performance of a Large-

Area Silicon Flat-Panel Detector in a Clinical CT-Controlled Studyrdquo American

Journal of Roentgenology Volume 74 75-80 (2000)

2 Cowen AR Kengyelics SM and Davies AG ldquoSolid-state flat-panel digital

radiography detectors and their physical imaging characteristics rdquoClinical

Radiology Volume 63 487-498 (2008)

3 Chotas HG Dobbins III JT and Ravin CE ldquoPrinciples of Digital

Radiography with Large-Area Electronically Readable Detectors A Review of

the Basicsrdquo Radiology Volume 210 Number 3 595-599 (1999)

4 Flynn MJ and Samei E Experimental comparison of noise and resolution for

2k and 4k storage phosphor radiography systems Medical Physics Volume 26

Number 8 1612-1623 (1999)

5 Rong XJ Shaw CC Liu X Lemacks MR and Thompson SK

ldquoComparison of an amorphous siliconcesium iodide flat-panel digital chest

radiography system with screenfilm and computed radiography systems ndash A

contrast-detail phantom studyrdquo Medical Physics Volume 28 Number 11 2328-

2335 (2001)

6 Ranger NT Samei E Dobbins III JT and Ravin CE Measurement of the

detective quantum efficiency in digital detectors consistent with the IEC 62220-1

standard Practical considerations regarding the choice of filter material

Medical Physics Volume 30 Number 7 2305-2311 (2005)

7 Samei E Buhr E Granfors P Vandenbroucke D and Wang X Comparison

of edge analysis techniques for the determination of the MTF of digital

radiographic systems Physics in Medicine and Biology Volume 50 3613-3625

(2005)

8 Samei E and Flynn MJ An experimental comparison of detector performance

for computed radiography systems Medical Physics Volume 29 Number 4 447-

459 (2002)

51

9 Samei E and Flynn MJ An experimental comparison of detector performance

for direct and indirect digital radiography systems Medical Physics Volume 30

Number 4 608-622 (2003)

10 Samei E Ranger NT MacKenzie A Honey ID Dobbins III JT and Ravin

CE Effective DQE (eDQE) and speed of digital radiographic systems An

experimental methodology Medical Physics Volume 36 Number 8 3806-3817

(2009)

11 Samei E Ranger NT MacKenzie A Honey ID Dobbins III JT and Ravin

CE Detector or System Extending the Concept of Detective Quantum

Efficiency to Characterize the Performance of Digital Radiographic Imaging

Systems Radiology Volume 249 Number 3 926-937 (2008)

12 ldquoIEC 62220-1 Medical Electrical Equipment ndash Characteristics of Digital X-Ray

Imaging Devices ndash Part 1 Determination of the Detective Quantum Efficiencyrdquo

International Electrotechnical Commission Geneva Switzerland (2003)

13 Samei E Ranger NT Dobbins III JT and Chen Y Intercomparison of

methods for image quality characterization I Modulation transfer function

Medical Physics Volume 33 Number 5 1454-1465 (2006)

14 Dobbins III JT Samei E Ranger NT and Chen Y Intercomparison of

methods for image quality characterization II Noise power spectrum Medical

Physics Volume 33 Number 5 1466-1475 (2006)

15 Samei E Flynn MJ and Reimann DA A method for measuring the

presampled MTF of digital radiographic systems using an edge test device

Medical Physics Volume 25 Number 1 102-113 (1998)

16 Nagel HD ldquoAluminum equivalence of materials used in diagnostic radiology

and its dependence on beam qualityrdquo Physics in Medicine and Biology Volume

31 Number 12 1381-1399 (1986)

17 Niklason LT Christian BT Niklason LE et al ldquoDigital Tomosynthesis in

Breast Imagingrdquo Radiology Volume 205 399-406 (1997)

18 Gur D ldquoTomosynthesis Potential Clinical Role in Breast Imagingrdquo American

Journal of Roentgenology Volume 189 614-615 (2007)

52

19 Park JM Franken Jr EA Garg M Fajardo LL and Niklason LT ldquoBreast

Tomosynthesis Present Considerations and Future Applicationsrdquo

RadioGraphics Volume 27 S231-S240 (2007)

20 Good WF Abrams GS Catullo VJ Chough DM Ganott MA Hakim

CM and Gur D ldquoDigital Breast Tomosynthesis A Pilot Observer Studyrdquo

American Journal of Roentgenology Volume 190 865-869 (2008)

21 Hu Y-H Zhao W Mertelmeier T and Ludwig J ldquoImage Artifact in Digital

Breast Tomosynthesis and Its Dependence on System and Reconstruction

Parametersrdquo IWDM 2008 LNCS 5116 628-634 (2008)

22 Chen Y Lo JY Ranger NT Samei E Dobbins III JT ldquoMethodology of

NEQ(f) analysis for optimization and comparison of digital breast tomosynthesis

acquisition techniques and reconstruction algorithmsrdquo Proceedings of SPIE

Volume 6510 65101I (2007)

23 Zhao B Zhou J Hu Y-H Mertelmeier T Ludwig J and Zhao W

ldquoExperimental validation of a three-dimensional linear system model for breast

tomosynthesisrdquo Medical Physics Volume 36 Number 1 240-251 (2009)

24 Madhav P Brzymialkiewicz CN Cutler SJ Bowsher JE and Tornai MP

ldquoCharacterizing the MTF in 3D for a Quantized SPECT Camera Having Arbitrary

Trajectoriesrdquo 2005 IEEE Nuclear Science Symposium Conference Record 1722-

1726 (2005)

25 Madhav P McKinley RL Samei E Bowsher JE and Tornai MP ldquoA Novel

Method to Characterize the MTF in 3D for Computed Mammotomographyrdquo

Proceedings of SPIE Volume 6142 61421Y (2006)

26 Hu Y-H Zhao B and Zhao W ldquoImage artifacts in digital breast

tomosynthesis Investigation of the effects of system geometry and

reconstruction parameters using a linear system approachrdquo Medical Physics

Volume 35 Number 12 5242-5252 (2008)

27 Seifert A and Flynn MJ ldquoResolving power of 3D x-ray microtomography

systemsrdquo Proceedings of SPIE Volume 4682 407-413 (2002)

28 Thornton MM and Flynn MJ Measurement of the spatial resolution of a

clinical volumetric computed tomography scanner using a sphere phantom

Proceedings of SPIE Volume 6142 61421Z (2006)

53

29 Baek J Pelc NJ ldquoUse of sphere phantoms to measure the 3D MTF of FDK

reconstructionsrdquo Proceedings of SPIE Volume 7961 79610D (2011)

30 Richard S and Samei E ldquoQuantitative imaging in breast tomosynthesis and CT

Comparison of detection and estimation task performancerdquo Medical Physics

Volume 37 Number 6 2627-2637 (2010)

31 Chen Y Lo JY and Dobbins III JT ldquoImpulse response analysis for several

digital tomosynthesis mammography reconstruction algorithmsrdquo Proceedings of

SPIE Volume 5745 541-549 (2005)

32 Zhao B and Zhao W ldquoThree-dimensional linear system analysis for breast

tomosynthesisrdquo Medical Physics Volume 35 Number 12 5219-5232 (2008)

33 Wu G Mainprize JG Boone JM and Yaffe MJ ldquoEvaluation of scatter

effects on image quality for breast tomosynthesisrdquo Medical Physics Volume 36

Number 10 4425-4432 (2009)

Page 11: Development and Evaluation of 2D and 3D Image Quality ...

xi

List of Figures

Figure 1 MTF images for DRX-1C detector with radio-opaque edge test device with

arrows indicating the horizontal (left) and vertical (right) directions 7

Figure 2 NNPS image for DRX-1C detector indicating the top left ROI that served as the

reference for normalizing other ROIs in the image The ROI array was formed along the

directions indicated by the arrows The heel effect visible along the vertical axis of the

detector is an example of small variation in signal across the image 8

Figure 3 Original (left) and linearized (right) system responses for Pixium 4600 The

linearized system responses were measured from actual images The offsets are small

with respect to the slope sufficient enough for zero-offset conditions 10

Figure 4 Spectral simulations for RQA5 (top) and RQA9 (bottom) conditions Note the

similarities of spectral shapes of the normalized spectra (right) Also note the significant

differences in fluence between filtrations in the simulated spectra (left) 11

Figure 5 MTF results by detector (columns) and beam quality (rows) 13

Figure 6 Plots of MTF for RQA5 (top) and RQA9 (bottom) showing the relationships

between detectors (blue red and green) and by filtration (solid and dashed) 14

Figure 7 NNPS results by detector (columns) and beam quality (rows) 15

Figure 8 Plots of NNPS for RQA5 (top) and RQA9 (bottom) at 1 mR exposure showing

the relationships between detectors (blue red and green) and by filtration (solid and

dashed) 16

Figure 9 DQE results by detector (columns) and beam quality (rows) 17

Figure 10 Plots of DQE for RQA5 (top) and RQA9 (bottom) at 1 mR exposure showing

the relationships between detectors (blue red and green) and by filtration (solid and

dashed) 18

Figure 11 DRX1-C NNPS images at 1 mR for RQA5 with IEC filtration (left) and

alternative filtration (right) Images are equally windowed at 45 and leveled at 980 24

Figure 12 Depiction of the virtual image system 30

xii

Figure 13 Example of 30-degree cone prescribed along z axis of the sphere 32

Figure 14 Photograph of the imaging system with the acrylic sphere phantom

embedded in oil 34

Figure 15 View of the central slice of the breast phantom reconstruction before (top) and

after (bottom) background subtraction The z axis is through the page 36

Figure 16 3D rendering of the ROI volume (left) and cross-sectional views of the most

centrally located sphere with centroid indicated with red circle (right) 37

Figure 17 Theoretical 3D MTF results along the three major planes (top) and along x y

and z directions (bottom) Also note that the angular spread seen in the fx-fz plane is

equal to the angular range of 44deg for the acquisition 38

Figure 18 Uncorrected ESF (top) LSF (middle) and MTF (bottom) for x y and z

directions 40

Figure 19 Comparisons of the directional MTFs as calculated by the sphere method

(dashed line) by theoretical line profiles (light-weight line) by theoretical cone regions

(heavy-weight line) 41

Figure 20 Modified ESF (top) LSF (middle) and MTF (bottom) for x and y directions 43

Figure 21 Cross sectional views of the experimental sphere image with centroid

indicated with red circle 44

Figure 22 ESF (top) LSF (middle) and MTF (bottom) of real image for x y and z

directions 45

xiii

Acknowledgements

I would like to thank Ian Yorkston Mark Purdum and Van Huston of

Carestream Health Inc (Rochester NY) for their help with digital detector

measurements I would also like to thank Olav Christianson Samuel Richard Brian

Harrawood and Max Amurao for their assistance with collecting data and analyzing

results Special thanks go to my committee members for their helpful insights and

suggestions for this thesis Last but not least I want to express deep appreciation for the

support and mentorship provided by my advisor Dr Ehsan Samei

1

I Evaluation of 2D Digital Image Receptors

I1 Introduction

In the past decade many areas of radiological practice have seen a conversion

from screen films to the storage phosphor cassettes of computed radiography (CR) to the

active-matrix flat-panel detectors of digital radiography (DR) Both CR and DR are

digital systems that offer many potential benefits including but not limited to better

image quality wider dynamic range quicker readout lower radiation dose and higher

throughput [1-3] Even with advances in DR technologies such as improved detective

quantum efficiency (DQE) the primary radiographic system of today continues to be CR

A major obstacle to completely accepting DR is the high capital cost of acquiring an

entire system per examination room while also providing capability for portable

applications Recently manufacturers like Carestream Health Fuji and Toshiba have

introduced wireless digital image receptors that can serve as replacements for CR

cassettes As these are new technologies a further investigation to characterize these

detectors is warranted

In the case of radiographic receptors DQE has historically been the metric of

choice [4] because it indicates the ability of the image receptor to convert incident x-ray

photons into useable signal ndash essentially a measure of signal-to-noise ratio (SNR)

efficiency and overall system performance [23] DQE is observed across a range of

spatial frequencies for evaluating how the detector depicts small and large objects [3]

2

DQE metrics have been used in numerous studies to characterize CR phosphor-screens

as well as indirect and direct digital detectors [4-11] The importance of this highly

quantitative metric may be implied by the introduction of a DQE measurement standard

by the International Electrotechnical Commission (IEC) [12]

The standard measurement methodology of the International Electrotechnical

Commission (IEC) pertains to the image quality of 2D digital radiographic detectors

While the IEC formalism is well-developed some of the components that it requires are

not necessarily the most optimal for characterizing DQE This has been explored in

previous studies in terms of filtration material purity beam limitations and region of

interest (ROI) configuration [1314] To reduce the variability in the radiographic output

across various x-ray tubes due to inherent filtration differences the IEC formalism

prescribes specific additional aluminum filtration to attain radiation beam qualities

based on target half value layers (HVL) Achieving and verifying the desired HVL

however requires applying a substantial amount of aluminum at the exit window of the

x-ray tube which is often directed toward the ground This can be a logistical

inconvenience and can increase the risk of damage to the image receptor and

measurement equipment Similar beam qualities on the other hand may be attained

more conveniently using a thinner lighter filtration combination utilizing a higher Z

number material Care is warranted however as a previous study [6] had indicated that

the choice of filtration material could impact the DQE

3

The purpose of this study was two-fold First we aimed to evaluate and compare

two wireless image receptors with a conventional flat-panel detector on the basis of DQE

performance Second we compared DQE results using the IEC-prescribed filtration with

an alternative filtration For the latter an optimum filtration composition was

determined and compared with the IEC filtration on the basis of DQE

I2 Materials and Methods

I2i Detectors

The physical characteristics of the three digital image receptors evaluated in this

study are listed in Table 1 The Pixium 4600 was a conventional digital flat-panel The

DRX-1C and DRX-1 were both wireless digital cassettes that were tethered for the

purposes of this study All detectors were FDA approved and available commercially

Each detector was calibrated according to its manufacturer specifications to correct for

gain offset and bad pixels They were all dedicated for non-clinical laboratory research

purposes and hence could be operated under service settings that permitted acquisition

of raw (ie for processing) images

I2ii Beam Characterization

I2iia X-ray Techniques

All measurements for this study were taken with a well-characterized standard

radiographic system (Super80CP Philips Healthcare Andover MA) The x-ray tube had

an inherent filtration of 27 mm Al Free in-air exposures were measured using

4

Table 1 Physical Characteristics of Digital Image Receptors

Manufacturer Detector

Detector

type

Detector

material

Pixel pitch

(size) Array size

Imaging

area

Trixell

(Moirans France)

Pixium

4600 Indirect

CsITl

(CsI) 0143 mm

3121times3121

4 subpanels 45times45 cm2

Carestream Health Inc

(Rochester NY)

DRX-1C

(wireless) Indirect

CsITl

(CsI) 0139 mm

2560times3072

single panel 35times43 cm2

Carestream Health Inc

(Rochester NY)

DRX-1

(wireless) Indirect

G2O2STb

(GOS) 0139 mm

2560times3072

single panel 35times43 cm2

calibrated radiation meters (Mult-O-Meter Type 407 Unfors Instruments AB Billdal

Sweden) at 183 cm source-to-chamber-distance (SCD) The SCD also corresponded to

same plane as the image receptor surface The x-ray output was made to conform to IEC

beam quality definitions [1215] on the basis of half value layer (HVL) and peak

kilovoltage setting using an aluminum filtration (type-1100 99 purity) and an

alternative filtration consisting of copper (UNS C11000 999 purity) and aluminum

(type-1100 99 purity) The IEC radiation quality numbers (RQA) used in this study are

summarized in Table 2 HVLs were determined by iteratively adding successive

thicknesses of aluminum until reaching reduced exposure levels within a tolerance of

0485-0515 [12] As for the alternative filtration the aluminum was placed downstream

of the copper filter to attenuate characteristic radiation peaks from copper at

approximately 9 keV

I2iib Data Linearization

The system response function was determined for each detector and filtration

combination by acquiring flat-field images at increasing photon fluence until just before

5

Table 2 Beam Qualities and Required Filtrations

IEC Radiation

Quality Number

Peak

kilovoltage

Required

HVL

Required IEC

Filtration

Actual IEC

Filtration

Alternative

Filtration

RQA5 70 kVp 71 mm Al 21 mm Al 21 mm Al 05 mm Cu +

10 mm Al

RQA9 120 kVp 115 mm Al 42 mm Al 40 mm Al 104 mm Cu +

10 mm Al

For reasons of convenience these will be referred to as RQA5A RQA5C RQA9A and RQA9C

saturation levels To avoid the influence of detector backscatter on exposure

measurements a relationship for each filtration was first determined for two radiation

meters A target meter was placed at the central axis and a reference meter was placed at

the edge of the light field (large enough to cover the detectors) The reference meter

served as a surrogate for the target meter to avoid direct exposure measurements in the

plane of the image receptor Exposure relationships were determined before each

measurement set (ie detector and filtration combination) to account for changes in

temperature pressure and humidity The system response function was calculated by

using a regression of ADU (pixel value) versus exposure Images acquired for each

series were then converted to achieve a linear response with zero offset and scaled to

achieve high quantization (adequate dynamic range) Linearization of the detector

responses ensured that zero exposure corresponded to zero pixel value

I2iic Spectral Simulation

The effects of additional filtration on x-ray output spectra were observed with

spectral simulation software (XSPECT V40 Henry Ford Hospital Detroit MI) To more

6

adequately describe the performance of a typical X-ray generator inherent filtration of 3

mm oil 148 mm Pyrex glass and 2 mm aluminum was input into the simulation in

addition to the filters of interest The ideal signal to noise ratio squared or incident

photon fluence per exposure (q) was estimated for each filtration by integrating the

energy-dependent photon counts per unit exposure over all energy bins

I2iii DQE Measurements

The assessment of the linearized images followed the formalism described by

IEC 62220-1 for measuring the DQE [12] For this study the normal exposure level XN

was set at 1 mR to the detector surface as measured at the central axis perpendicular to

the anode-cathode axis

I2iiia Modulation Transfer Function

Spatial resolution was characterized by evaluating the presampled modulation

transfer function (MTF) along directions parallel (vertical) and perpendicular

(horizontal) to the anode-cathode axis using the angled-edge method [6-1013] A radio-

opaque edge test device [7] was placed in the center of the field at a pitch of

approximately 301 (about 2deg) to the axis perpendicular to that being measured as

shown in Figure 1 External lead apertures were not used [6] instead the internal

collimation from the radiographic unit was used to collimate the beam to the detector

area Raw images were acquired of the edge with the normal exposure level XN of 1 mR

at the detector face The procedure of calculating the MTF followed previously described

7

methods [6-1013] The edge spread function (ESF) was determined along lines crossing

the edge of the angled test device The derivative of the ESF was calculated to form the

line spread function (LSF) to which a Hanning filter was applied The MTF was then

calculated as the fast Fourier transform (FFT) of the LSF and normalized at the zero-

frequency axis To conform to IEC guidelines the MTF was resampled into frequency

steps of 005 cyclesmm [12]

Figure 1 MTF images for DRX-1C detector with radio-opaque edge test device with

arrows indicating the horizontal (left) and vertical (right) directions

I2iiib Noise Power Spectrum

Noise amplitude and texture were characterized by determining the normalized

noise power spectrum (NNPS) which was evaluated with flat field exposures at

approximate exposure levels of XN2 XN and 2XN (05 10 and 20 mR) to the image

receptor surface Analysis of the flat-field images followed previously defined methods

[41415] using over 4 million independent pixels with regions of interest (ROIs) of size

8

128x128 The NNPS images were detrended using a quadratic (second order)

background subtraction Small variations in exposure across ROIs were corrected by

normalizing pixel values of each ROI to the mean value in the top left ROI as shown in

Figure 2 The NNPS was then calculated with the 2D FFT including the zero-frequency

axes corresponding to the horizontal and vertical directions The results were then

resampled using 005 frequency bins according to IEC guidelines [12]

Figure 2 NNPS image for DRX-1C detector indicating the top left ROI that served as

the reference for normalizing other ROIs in the image The ROI array was formed

along the directions indicated by the arrows The heel effect visible along the vertical

axis of the detector is an example of small variation in signal across the image

I2iiic DQE Calculation

The DQE was calculated using the following relationship [615]

9

where the frequency-dependent MTF and NNPS were determined as described in

previous sections X was the exposure value in mR corresponding to the NNPS image

and q was the ideal signal to noise ratio squared in units of photonsmiddotmm-2middotmR-1 as

estimated from the spectral simulations

I3 Results

I3i Data Linearization

The detectors in this study provided raw ADU (or pixel) values in a linear scale

The data were converted using the following system conversion function

where Q(ij) is the raw image data m and b are slope and intercept parameters obtained

from linear regression of the system response function and I(ij) is the linearized scaled

data The factor of 1000 was found to scale I(ij) such that the maximum value was a

large 16-bit number Figure 3 shows the original and linearized system responses for the

Pixium 4600 Note that the y-intercepts of the regressions for the linearized responses

are negligible (lt 01) with respect to the slopes a sufficient condition for zero offset

considerations

I3ii Spectral Simulation

The spectral simulations of the IEC filtrations and alternative filtrations indicate

many similarities in their effective energies HVLs and overall shapes of normalized

spectra Results are summarized in Table 3

10

Pixium 4600 Original System

Response

Pixium 4600 Linearized System

Response R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 3 Original (left) and linearized (right) system responses for Pixium 4600 The

linearized system responses were measured from actual images The offsets are small

with respect to the slope sufficient enough for zero-offset conditions

y = 13971x - 13236

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x - 00106Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 13576x + 28292

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

7000

0000 1000 2000 3000 4000 5000

AD

U

Exposure (mR)

y = 99997x - 00067Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0000 1000 2000 3000 4000 5000

AD

U

Exposure (mR)

y = 13644x + 16167Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x + 00044

Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 13845x + 13541

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x - 00177

Rsup2= 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

11

Table 3 Spectral Simulation Results

Beam Quality Filtration

Mean Energy

(kV)

Photon Fluence

(mRmm2)

RQA5A 21 mm Al 5243 259543

RQA5C 05 mm Cu + 10 mm Al 5214 259554

diff 055 0004

RQA9A 40 mm Al 7619 273281

RQA9C 104 mm Cu + 10 mm Al 7579 273964

diff 052 025

Figure 4 Spectral simulations for RQA5 (top) and RQA9 (bottom) conditions Note

the similarities of spectral shapes of the normalized spectra (right) Also note the

significant differences in fluence between filtrations in the simulated spectra (left)

00E+00

50E+04

10E+05

15E+05

20E+05

25E+05

30E+05

35E+05

40E+05

45E+05

0 20 40 60 80

ph

oto

ns

mA

s-1

cm

-2

keV

RQA5 Spectra Comparison

21 mm Al

05 mm Cu + 10 mm Al

00

02

04

06

08

10

12

0 20 40 60 80

keV

RQA5 Normalized Spectra Comparison

21 mm Al

05 mm Cu +

10 mm Al

00E+00

50E+05

10E+06

15E+06

20E+06

25E+06

30E+06

35E+06

40E+06

45E+06

50E+06

0 50 100 150

ph

oto

ns

mA

s-1

cm

-2

keV

RQA9 Spectra Comparison

40 mm Al

104 mm Cu +

10 mm Al

00

02

04

06

08

10

12

0 50 100 150

keV

RQA9 Normalized Spectra Comparison

40 mm Al104 mm Cu + 10 mm Al

12

I3iii Modulation Transfer Function

The limiting spatial resolutions of the systems were indicated by the cutoff

frequencies which were approximately 35 cyclesmm for all three detectors The spatial

resolutions also demonstrated a good degree of isotropy as confirmed by the close

alignment of MTF curves between vertical and horizontal directions differentiated in

Figure 5 by dashed and solid lines respectively The MTF curves for the Pixium 4600

and DRX-1C were nearly equal to each other whereas the DRX-1 MTF curve showed a

more rapid decrease at high frequencies as shown in Figure 6 This difference may be

due to the differences in the inherent optical properties of the scintillating materials

where finer image details are provided by structured CsI more than by granulated GOS

There were no significant differences in MTF curves across beam qualities and filtrations

as shown by the curve comparisons in Figure 6 although the alternative filtration

produced slightly higher MTF curves as seen in Figure 4 Table 4 lists the experimental

specific spatial frequencies for varying levels of MTF

I3iv Noise Power Spectrum

The noise characteristics are indicated by the NNPS curves shown in Figure 7

The noise was similar for both horizontal and vertical directions As exposure increased

the NNPS decreased consistent with the characteristics of Poisson noise describing the

relationship between signal and noise in the presence of increased photon fluence At

13

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 5 MTF results by detector (columns) and beam quality (rows)

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

horizontal

vertical

14

Figure 6 Plots of MTF for RQA5 (top) and RQA9 (bottom) showing the relationships

between detectors (blue red and green) and by filtration (solid and dashed)

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm-1)

MTF

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm-1)

MTF

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

15

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 7 NNPS results by detector (columns) and beam quality (rows)

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

05 mR - horizontal

05 mR - vertical

10 mR - horizontal

10 mR - vertical

20 mR - horizontal

20 mR - vertical

16

Figure 8 Plots of NNPS for RQA5 (top) and RQA9 (bottom) at 1 mR exposure

showing the relationships between detectors (blue red and green) and by filtration

(solid and dashed)

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm-1)

NNPS (1 mR)

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm-1)

NNPS (1 mR)

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

17

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 9 DQE results by detector (columns) and beam quality (rows)

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

05 mR - horizontal

05 mR - vertical

10 mR - horizontal

10 mR - vertical

20 mR - horizontal

20 mR - vertical

18

Figure 10 Plots of DQE for RQA5 (top) and RQA9 (bottom) at 1 mR exposure showing

the relationships between detectors (blue red and green) and by filtration (solid and

dashed)

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm-1)

DQE (1 mR)

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm-1)

DQE

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

19

higher frequencies the NNPS curves of the Pixium 4600 and DRX-1 diverge slightly for

the different directions illustrating increased noise in the readout direction (vertical)

Differences in the noise characteristics were more apparent among detectors as

shown for 1 mR in Figure 8 The NNPS curve for the DRX-1 was higher in magnitude

across the entire frequency range than either the Pixium 4600 or DRX-1C which both

seemed to demonstrate reasonably similar NNPS curves The higher magnitude noise of

the DRX-1 indicates higher relative noise content overall Closer inspection of the NNPS

curves of the Pixium 4600 and DRX-1C detectors in Figure 7 revealed differences in the

spacing between the three exposure levels The gaps between the Pixium 4600 NNPS

curves do not correspond to the factor of two differences between each exposure level

especially at low- to mid- spatial frequencies suggesting a higher level of fixed pattern

noise additional noise with increasing exposure levels due to ineffective gain map

corrections Between filtration schemes the differences in NNPS curves for a given beam

quality were not substantial as shown in Figure 7

I3v Detective Quantum Efficiency

The DQE results are shown in Figure 9 DQE curves across exposure levels were

almost collinear except for Pixium 4600 and in general could be inferred from the

NNPS results Additionally the DQE curves demonstrated a relatively linear response

with spatial frequencies as expected for flat-panel detectors [9] Differences in DQE

among detectors were consistent for the most part with the type of scintillating material

20

As depicted for 1 mR exposure in Figure 10 differences between Pixium 4600 and DRX-

1C DQE curves correspond to the differences in their NNPS curves DRX-1 DQE curves

were consistently lower than either the Pixium 4600 or DRX-1C curves The DQE curves

for the alternative filtration were consistently higher than those for the IEC filtration

and the most noticeable differences were near the zero-frequency axis These effects can

be both attributed to ineffective gain map correction DQE values for 1 mR exposure are

listed in Table 5

I4 Discussion

I4i Comparisons of Detectors

The limiting spatial resolutions of all three detectors were almost exactly the

same considering that their pixel areas were similar in size The decrease in high-

frequency MTF of the DRX-1 compared to the other detectors is probably a result of

increased optical blurring due to the differences in the powdered structure of GOS

versus the needle-like structure of CsI [2] The fact that the DRX-1C and Pixium 4600

have comparable MTFs suggests similar scintillator thicknesses assuming that the

materials were processed alike

The noise of the three detectors demonstrated similar trends with each other The

higher NNPS curves of the DRX-1 detector are probably due also to the scintillating

material and its operation in converting photons into signal The conversion process is

less efficient because of the less favorable stopping power of the GOS compared to CsI

21

especially with higher energy beams The noise of the Pixium 4600 and DRX-1C were

similar except for the spacing between exposures The DRX-1C NNPS curve spacing is

consistent with a factor of two difference in exposure levels but the Pixium 4600 has a

smaller spacing The 05 mR NNPS curve of the Pixium 4600 is closer to that of the 05

mR NNPS curve of the DRX-1C This demonstrates that at higher exposures the Pixium

4600 produces a larger amount of additional noise beyond that explained by simple

stochastic effects It suggests bad performance in the gain map corrections

The DQE results indicate SNR properties of each detector The Pixium 4600 and

DRX-1C are comparable for the most part with the DRX-1C performing slightly better

The DRX-1 as predicted from MTF and NNPS results has a DQE much lower than

either of the previous two This is a reflection of the detection properties as provided by

its scintillator material The DQE of the DRX-1 however is comparable to CR image

receptors [2] The mid-frequency dips in the DQE for Pixium 4600 may be due to the

optical properties of the CsI phosphor layer which can affect the MTF in this manner

Because the DQE is calculated by squaring the MTF this effect at the mid-range

frequencies becomes more apparent The dips may also be further evidence of bad gain

map corrections

I4ii Comparisons of Filtrations

The alternative filtration closely matches for the most part the IEC-based

filtration for MTF NNPS and DQEs at RQA5 but not at RQA9 The filters do not have

22

Table 4 Experimental MTF frequency locations for 1 mR exposure

Detector Filtration

50 MTF

(mm-1)

40 MTF

(mm-1)

30 MTF

(mm-1)

20 MTF

(mm-1)

10 MTF

(mm-1)

Pixium

4600

RQA5A 115 145 185 245 330

RQA5C 125 155 195 250 345

RQA9A 110 175 175 235 330

RQA9C 125 155 195 255 345

DRX-1C

RQA5A 120 150 185 245 350

RQA5C 125 155 195 255 355

RQA9A 120 150 190 250 355

RQA9C 130 160 210 265 360

DRX-1

RQA5A 110 135 160 205 280

RQA5C 110 135 170 210 285

RQA9A 105 125 155 195 270

RQA9C 110 135 165 210 285

Table 5 Estimated DQE values for 1 mR exposure by frequency bins

Detector Filtration DQE(00 mm-1) DQE(10 mm-1) DQE(20 mm-1) DQE(30 mm-1)

Pixium

4600

RQA5A 62 42 32 21

RQA5C 63 45 36 25

RQA9A 41 27 30 13

RQA9C 43 33 27 19

DRX-1C

RQA5A 72 52 35 21

RQA5C 76 55 41 24

RQA9A 49 33 23 15

RQA9C 51 40 31 20

DRX-1

RQA5A 38 24 12 4

RQA5C 38 25 14 5

RQA9A 28 18 9 4

RQA9C 28 19 12 5

DQE values at the zero-frequency axis were estimated by the intercept of a linear fit of low-frequency data

but excluding most proximal to the axis due to large fluctuations Other estimated values are grouped into

frequency bins due to the noisiness of the data

23

considerable differences in the spatial resolutions of the detectors as expected The noise

responses for each filtration were also similar except at the lower frequencies of the

NNPS especially near the zero-frequency axis There observing the NNPS responses at

RQA5 for Pixium 4600 and DRX-1C in Figure 8 the NNPS for the IEC-based filtration

(solid lines) tend to drop faster than the NNPS for the alternative filtration This

subsequently appears as a drop in DQE near the zero-frequency axis shown for those

detectors in Figure 10 Overall as indicated in Table 5 the DQEs of the two filtrations

while similar in trend indicate that the alternative filtration increases the DQE by a

small amount of 3-5 Part of this may be explained by the slightly higher beam

energy which may be more optimal for the energy response of the detectors or may

weigh the pixel responses slightly considering that they are energy-integrating types

The most probable explanation is the gain map correction for the alternative filtration

where fixed pattern noise is more sufficiently reduced

A previous study [6] had discussed the choice of filter material in the analysis of

DQE when achieving the beam conditions defined by IEC It found that visible

nonuniformities were present with the higher purity aluminum filter (type-11999 alloy)

The low frequency mottle in the flat-field images for NPS measurements were also

attributed to structured noise from the grain size in the IEC-based filter with an

attenuating thickness that would reveal nonuniformities The mottle in the current study

was only observable under very narrow windowing as shown in Figure 11 Such low

24

frequency artifacts which are not readily noticeable may also be caused by shading

artifacts inverse square law or even the heel effect A possible method to correct for this

is a subtraction method by taking the average of the flat-field images for an exposure

level and then subtracting that from each of them This would remove nonuniformities

that were not corrected using a suboptimal gain map calibration

Figure 11 DRX1-C NNPS images at 1 mR for RQA5 with IEC filtration (left) and

alternative filtration (right) Images are equally windowed at 45 and leveled at 980

One convenient aspect of the copper and aluminum filtration is that it requires

much less tube current to achieve the same amount of exposure at the detector than the

much thicker aluminum filtration As shown in the non-normalized spectra in Figure 2

the exiting photon fluence exiting the copper and aluminum filtration is substantially

higher than that of the IEC-specified filtration This is due to the smaller total filtration

25

attenuation For extensive DQE analysis multiple sets of exposures may be acquired

before tube overheating becomes a concern

One limitation to the comparison of the two filtrations is that calibration

procedures specified copper and aluminum filtration at 80 kVp (for all detectors 05 mm

Cu and 10 mm Al) This may have influenced the results in favor of the alternative

filtration A further investigation involving the calibration procedures and performing

DQE measurements is encouraged Another factor may be influenced by the fact that the

tests were performed at 70 kVp and 120 kVp different from the recommended

calibration tube potential Clearly there would be differences in the linear attenuation

coefficients of the filters and different energy responses of the detectors themselves This

must be considered when interpreting DQE results The current results support a

previous study decades ago that described filtration of different material types in terms

of an aluminum equivalent [16] The results show that the two filtration schemes are

essentially equivalent when considering beam qualities and spatial resolutions The

NNPS and DQE results can be seen as close enough where their small differences are

insignificant when performing quality assurance tests in a clinical setting Overall our

results indicate that the alternative filtration with copper and aluminum may be more

convenient to use than the current IEC standard filtration

26

I4iii Implications of Wireless DR

This study has shown that wireless image receptors can have the same DQE

performance if not better than conventional flat-panel detectors They operate on the

same basic physical principles the new features offered by the DRX-1C and DRX-1 are

wireless communication with the workstation and electronics packaging technology

The latter feature may pose limitations for these units in terms of possible degradation

in the detectors in routine clinical conditions A consideration for future work would be

to longitudinally track DQE performance of the wireless detectors over time while being

utilized in a clinical environment In the end one must consider risks versus benefits of

choosing portable DR technology over CR one of which includes the cost and fragility

of DR detectors

The DQE performance of one wireless system is just as good as or better than

conventional systems as seen by the DRX-1C performance compared to the Pixium

4600 Wireless systems can also reduce the need for CR readers especially in portable

applications in other regions of the world (eg military hospitals developing countries)

However while DQE performance indicates the physical performance of the detector

system it is still unknown how it relates to observer performance

I5 Conclusions

Two wireless image receptors DRX-1C and DRX-1 were evaluated and

compared with the conventional DR flat-panel Pixium 4600 in terms of DQE

27

performance along with MTF and NNPS performances The detectors have similar

resolution properties although the DRX-1 is inferior at higher spatial frequencies The

NNPS and DQE results both indicate that the DRX-1C is superior to the DRX-1 and

comparable if not better to the Pixium 4600

The results from the filtration comparison indicate no substantial differences

between the IEC-based filtration and the copper-based alternative filtration Only slight

differences were found in the low frequency components of the NNPS and the DQE due

to the inherent nonuniformities of the IEC specified filtration Given the similarity of the

results and low attenuation advantage of the copper and aluminum filter its use is

encouraged

28

II Directional MTF for Breast Tomosynthesis

II1 Introduction

Breast tomosynthesis is an emerging 3D imaging modality that has potential use

for screening and diagnosis of breast cancer Breast tomosynthesis along with other 3D

techniques is preferable to planar imaging methods (eg mammography) because they

reduce anatomical noise by removing overlying structures above and below the plane of

an image slice [17-20] Recent advances in detectors and computer technology have

made digital tomosynthesis feasible

An image quality metric of particular importance in breast tomosynthesis is

spatial resolution Resolution is important to know in order to assess small-detail

structures such as microcalcifications A descriptive metric for characterizing spatial

resolution in the Fourier (or frequency) domain is the modulation transfer function

(MTF) Affected by reconstruction filters [21] the limited angular projections involved in

breast tomosynthesis results in highly anisotropic (or nonuniform) resolution Many

studies have looked only at characterizing the in-plane spatial resolution (ie in an

individual slice) with an elevated angled edge phantom [2223] A few studies have

looked at characterizing a more comprehensive 3D spatial resolution by using a

phantom with angled wires or tubes [24-26] However such studies require precise

mechanical alignment of the phantoms Several studies have explored a method using a

29

sphere phantom for the directional 3D MTF evaluation for microtomography [27] and

multi-slice CT [2829] This method has not yet been extended to breast tomosynthesis

This chapter focuses on breast tomosynthesis because it is highly anisotropic in

spatial resolution and like its predecessor mammography requires high spatial

resolution Additionally breast tomosynthesis acquisitions and reconstructions produce

several types of artifacts The use of a cone-based method using a sphere phantom [28] is

explored to characterize the directional 3D spatial resolution of simulated images from

breast tomosynthesis A technique for removing out-of-plane artifacts of the ESFs for the

in-plane axes is investigated to yield a modified MTF in a method that separates artifact

information from resolution information

II2 Materials and Methods

II2i Image Simulation

Breast tomosynthesis images were simulated by using a virtual imaging system

depicted in Figure 12 A volumetric breast phantom was voxelized as a rectangular mass

of uniform breast equivalent tissue of 4 cm thickness embedded with fifteen evenly

spaced plastic sphere inserts of 12 mm diameter The spheres were placed in a grid

formation within the central plane of the phantom The x-ray fluence was modeled from

a 28 kVp beam incident upon an indirect flat-panel detector with 200 micro m pixel size

Twenty-three projections within an angular range of 44deg were simulated using cascaded

systems analysis to generate characteristic 2D noise and spatial blurring [29] Each

30

projection was simulated to have an exposure of 174 mR with a fluence of 79 times 105

photonsmm-2 A standard filtered backprojection technique based on the Feldkamp

reconstruction algorithm [29] was used to reconstruct the projections and produce a

volumetric dataset with an isotropic voxel size of 200 micro m

Figure 12 Depiction of the virtual image system

II2ii Uncorrected MTF

To enable comparison of multiple spheres the reconstructed volume was

initially homogenized by performing a background subtraction based on a portion of the

volume devoid of spheres The voxel values were rescaled between one and zero to

eliminate negative values

31

The volumetric data were segmented to extract individual regions of interest

(ROIs) each containing a single sphere The ROIs extended along the full range of the z-

axis A thresholded ROI was generated by determining the exterior and interior voxels

relative to the sphere in the ROI The threshold value was set at 45 of the maximum

voxel value prior to thresholding The exterior and interior voxel values were then set to

values of 0 and 1 respectively Using the thresholded volume the center of mass was

calculated to determine the centroid The voxel values from the original ROI were

subsequently tabulated with the associated distances azimuthal angles and polar

angles relative to the centroid

Conical regions were prescribed along the positive and negative directions along

the three major axes extending from the centroid of the sphere as depicted in Figure 13

The axes about which the extent of the cone angle was delineated were defined with

the azimuthal and polar angles

Voxels with centers within the angular range of the cone were considered for

generating the edge spread function (ESF) To improve regularity of the distance

sampling interval the ESF values were rebinned to discrete distances corresponding to a

fraction of the voxel size Only voxels with distances ranging from the voxel size (ie

200 micro m) to the maximum distance were considered The ESFs from multiple spheres

were averaged together for each of the three major axes to produce an averaged ESF

which was further smoothed utilizing a Gaussian filter

32

Figure 13 Example of 30-degree cone prescribed along z axis of the sphere

The resulting ESF was then differentiated using the central difference method to

produce the line spread function (LSF) A Hanning filter with the same length as the LSF

was applied to zero out the tails of the LSF The presampled MTF was subsequently

computed as the amplitude of the Fourier transform of the LSF The MTF was

normalized with respect to the maximum value occurring within the range of the cutoff

frequency Binning size and conical range for the ESF were considered for maximizing

accuracy and minimizing noise of the MTF verified by comparison against the

theoretical MTF as determined in the previous section

II2iii Theoretical Directional MTF

The theoretical 3D MTF was calculated using a priori knowledge of the transfer

function of the virtual imaging system described in the previous section A phantom

was created with a set of point objects in a uniform and noise-free background with the

objects spanning across the volume of the breast [29] Twenty-one realizations were

33

generated from the reconstructed images of the point objects to yield a set of 3D point

spread functions (PSFs) The 3D fast Fourier transform (FFT) was performed for each 3D

PSF and averaged to give an ldquoexpectationrdquo 3D MTF [29] The theoretical directional

MTFs in the three major spatial axes were determined by line profiles along each of the

corresponding spatial frequency axes in the 3D MTF An additional theoretical MTF for

each direction was determined by using the application of conical regions along the axes

in frequency-space to take into account the contributions of MTF information from other

planes

II2iv Modified MTF

The tomosynthesis reconstruction is known to have edge enhancements which

affect the overall MTF by shifting the peaks of the MTF toward the higher frequencies

[23] The presence of this artifact complicates the interpretation of the actual spatial

resolution of the images Several steps were performed to remove the artifact

contribution to the resolution information particularly for the in-plane x and y

directions with the assumption that resolution information was contained immediately

near the edge

For the x-direction averaged ESF only values that were detected to be inside the

edge of the sphere were considered Those values were previously determined via

thresholding for calculating the centroid The ESF information corresponding to these

values was inversed and flipped about the detected edge to produce a symmetric

34

modified ESF The modified MTF was subsequently calculated from this modified ESF

as described in the previous section

For the y-direction averaged ESF an upward trend was found in the initial part

of the ESF This section was detrended with a polynomial fit and subtracted to produce a

flatter curve in that region The resulting detrended ESF was used to calculate the y axis

modified MTF

Figure 14 Photograph of the imaging system with the acrylic sphere phantom

embedded in oil

II2v Preliminary Experimental Validation

A clinical breast tomosynthesis system (Mammomat Inspiration Siemens AG

Munich Germany) was used to perform a preliminary evaluation of the cone-based

MTF technique The phantom for the experiment consisted of a single acrylic ball of 075

in diameter (SmallParts Seattle WA) suspended by a 0029 in diameter plastic filament

35

(Omniflex Zebco Tulsa OK) in an acrylic frame filled up to 4 in with vegetable oil

(Target Brands Inc Minneapolis MN) The system and phantom are shown in Figure

14 Twenty-five projections with an angular range of 44deg were acquired and subsequently

reconstructed to produce a volume with a voxel size of 01times01times10 mm3 The voxels were

reformatted to have an isotropic size of 01 mm The uncorrected ESF LSF and MTF

were calculated as described in the previous section

II3 Results

II3i Reconstruction

The reconstructed volume is shown in Figure 15 Notice the edge enhancement

along the x-direction as indicated by the sharp shadowing artifacts on either side of the

spheres The background was effectively homogenized using the background

subtraction technique This also took account of the curved edges of the breast phantom

With the close spacing of the spheres in the phantom the shadows along the x direction

for the fifteen spheres overlap with each other As the nine centrally located spheres

experience this effect the same way they were used for determining the ESF

A 3D rendering of the ROI containing a sphere shown in Figure 16 indicates the

anisotropic resolution of the reconstruction Note that the sphere is not accurately

reconstructed and has an oblong shape especially along the z axis Cross sectional views

of the ROI also in Figure 16 clearly demonstrate the edge enhancement causing a

shadow artifact in the x direction caused by the incomplete angular sampling of

36

tomosynthesis The sampling also introduces the triangular reconstruction of the sphere

as seen in the x-z plane Note the gradual edge drop-off in the z direction much beyond

the sphere radius

Figure 15 View of the central slice of the breast phantom reconstruction before (top)

and after (bottom) background subtraction The z axis is through the page

37

Figure 16 3D rendering of the ROI volume (left) and cross-sectional views of the most

centrally located sphere with centroid indicated with red circle (right)

II3ii Theoretical MTF

The theoretical MTFs for x y and z directions as determined from the line

profiles of the 3D MTF are shown in Figure 17 The theoretical MTF in the x direction

has a maximum value that is toward higher frequencies Its 10 response occurs at

about 125 cyclesmm which is at 50 of the cutoff frequency The rapid increase from

the zero-frequency intercept to the peak corresponds to the ramp filter used in filtered

backprojection which decreases the weighting of low frequency contributions due to the

incomplete angular sampling of the frequency-space The MTF does not reach a value of

0 at the zero-frequency intercept as it is very difficult to assess the zero-frequency

intercept due to the finite size of the phantom The theoretical MTF in the y direction

peaks at the zero-frequency intercept and reaches 20 proximal to the cutoff frequency

38

The 10 MTF is well beyond the cutoff frequency The theoretical MTF in the z direction

has a rapid drop-off at very low spatial frequencies indicating the lack of resolution in

that dimension

Figure 17 Theoretical 3D MTF results along the three major planes (top) and along x

y and z directions (bottom) Also note that the angular spread seen in the fx-fz plane is

equal to the angular range of 44deg for the acquisition

II3iii Uncorrected MTF

The ESF LSF and MTF using the cone-based method are shown for the x y and

z directions in Figure 18 It was found that a bin size of one-tenth the voxel size (002

mm) and a cone angle of 30deg to establish the ESF were enough to minimize noise and

maximize accuracy in the uncorrected MTFs considering the reasonable comparison of

the shapes of the MTF curves with the theoretical results in Figure 17 The LSFs are

generally noisy because differentiation of the ESF increases the amplitude of the noise

39

The data shown reflect a convolution with a smoothing Gaussian filter which was later

further corrected for in the reported MTF Nevertheless the high frequency components

of the noise are well beyond the MTF cutoff frequency of 25 cyclesmm and do not

impact the MTF results greatly

For the ESF in the x direction the shadow effect evident at the edge of the sphere

is visible as a steep decline followed by an increase Due to the finite distance range

provided by the ROI the ESF beyond the edge did not asymptotically reach the

background value The corresponding LSF demonstrates a low frequency modulation

that is indicated by the shift of 03 cyclesmm in the x direction for the peak of the MTF

The MTF exhibits a zero-frequency intercept that is non-zero unlike the theoretical MTF

and a 10 value at approximately 1 cyclesmm These features may be a direct

consequence of MTF information ldquocontaminationrdquo from y and z directions Furthermore

the ESF in the y direction demonstrates a reasonably shaped curve except for the slight

upward trend within the radius of the sphere which can be attributed to the shadow

artifact overlapping with the sphere volume The associated MTF has a peak shifted by

approximately 01 cyclesmm away from the axis and a 10 MTF occurring at

approximately 15 cyclesmm Both features which are not present in the theoretical

results may also be attributed to contaminant MTF information from x and z directions

The ESF in the z direction has a drop-off that occurs at a small fraction of the cutoff

frequency similar to that demonstrated by the theoretical MTF

40

Uncorrected ESF LSF and MTF

Figure 18 Uncorrected ESF (top) LSF (middle) and MTF (bottom) for x y and z

directions

41

Figure 19 Comparisons of the directional MTFs as calculated by the sphere method

(dashed line) by theoretical line profiles (light-weight line) by theoretical cone

regions (heavy-weight line)

II3iv Comparison of Theoretical and Simulated MTFs

The theoretical MTF results obtained from line profiles through the 3D MTF and

the simulated MTFs using the cone-based technique did not match very well except for

the general shape of the curves It was assumed in the previous section that the cone-

based technique contains information from other planes Figure 19 compares MTFs in

each direction for the two methods described in the methods and an additional method

based on conical regions of the 3D MTF The latter computes the MTF by averaging

contributions of the 3D MTF using the same cone prescription method used to define the

ESFs Comparison of the curves indicate some interesting correlations aside from the

fact that using conical regions with the 3D MTF results produce more noisy MTF results

partly due to the low sampling provided by the theoretical calculations The same

conclusions regarding the z direction MTF can be confirmed regardless of either

theoretical MTF procedures The experimental x direction MTF seems to agree best with

42

the line profile method whereas the y direction MTF agrees better with the cone region

method The fact that the experimental x direction MTF has a drop-off frequency that is

lower than those of either of the theoretical MTFs in Figure 19 suggests that this might

be due to integration of the z-direction in the in-plane slices considering how slices are

essentially averages of z direction information contained within it [33]

II3v Modified MTF for x and y

Modified ESF LSF and MTF curves for x and y directions are shown in Figure

20 The modified ESF and the resulting LSF in the x direction appear symmetric as

expected from the inverse and flip operation of the interior ESF about the detected edge

The modified MTF appears with less variation than the uncorrected MTF and the MTF

peak occurs at the zero-frequency axis The correction yields a 10 MTF at about 15

cyclesmm an improvement from the uncorrected MTF but still distant from the cutoff

frequency The modified ESF in the y direction demonstrates the detrended curve within

the sphere radius after a quadratic polynomial fit The resulting modified MTF still

appears similar to the uncorrected MTF except that the peak now coincides with the

zero-frequency axis For both x and y directions the low response of the modified MTFs

at the higher frequencies suggests that the contamination from other directions is

substantial due to the angular range of the cone

43

Modified ESF LSF and MTF

Figure 20 Modified ESF (top) LSF (middle) and MTF (bottom) for x and y directions

44

II3v Preliminary Experimental Validation

Cross-sections of the reconstructed sphere volume are shown in Figure 21

Relative to the simulation reconstructions the reconstructions of the experimental

phantom images produce lower contrast and higher noise The preliminary results

shown in Figure 22 indicate that our technique can be applied to actual experimental

breast tomosynthesis reconstructions However due to the noise exhibited by the MTF

curves for the x and y directions we did not determine the modified MTFs to separate

resolution and artifact information

Figure 21 Cross sectional views of the experimental sphere image with centroid

indicated with red circle

45

Uncorrected ESF LSF and MTF for Real Image

Figure 22 ESF (top) LSF (middle) and MTF (bottom) of real image for x y

and z directions

46

II4 Discussion

II4i Evaluation of Cone-based Method

The cone-based MTF technique was introduced by Thornton and Flynn [28] for

evaluation of volumetric CT images To utilize this technique as a characterization of a

3D system spatial resolution one must first consider the validity of the assumption of

shift invariance such that the same MTF result may be obtained regardless of the

location of the sphere The study by Zhao et al [23] found that there was no shift

variance for the MTF measurements along the vertical axis but this was only considering

the in-plane resolution along one axis On the other hand this study evaluated the MTF

with images simulated with cascaded systems analysis which includes conditions of

linearity and shift invariance Additionally the MTF was calculated by averaging the

ESF from several spheres in the same volume only after performing a background

subtraction This step was essential to account for the sensitivity of centroid calculations

as well as ensuring symmetric ESFs for opposing axes of the sphere ROIs

The measurement of MTF with the cone-based technique inherently

supersamples the edge of the sphere to increase signal-to-noise-ratio (SNR) of edge

information by averaging the contributions of each voxel to the ESF [713] This method

also takes into account the discrete sampling of the voxels by accounting for various

shifts of the edge in the voxel (also known as the partial volume effect) However using

the curved surface of the sphere phantom to approximate an edge along a given

47

direction naturally leads to contamination of information from other directions aside

from the one of interest Preferably a directional ESF should be created by using a single

radial line but this would limit the available voxels to obtain edge information An ideal

situation theoretically would be to use a larger-sized sphere such that the surface is

nearly flat and perpendicular to the axes of interest This would also permit a reduction

in the angular range of the cone and thus the introduction of out-of-plane information in

the resulting MTF However sphere size is a limitation in breast tomosynthesis and the

use of a large phantom might void the assumption of shift invariance of the spatial

resolution

The choice of a sphere phantom nevertheless may be based on the clinical need

to quickly acquire a single image for MTF evaluation especially for multiple directions

without presenting extra logistical challenges The use of a wire or edge phantom

requires more precise mechanical alignment to achieve the correct set up The edge

phantom [23] would require at least two images to sample all three dimensions In the

case of the three wire phantom [2425] all three dimensions of the frame must be aligned

simultaneously with respect to the axis of rotation A similar situation would be

encountered when considering a cubic phantom with the planes normal to the axis of

interest In contrast to these phantoms the sphere eliminates the need for precise

alignment especially with respect to three spatial dimensions simultaneously A sphere

48

has ideal symmetry in all directions and can be used to evaluate MTF in any arbitrary

direction

This study unlike others [242532] did not explore the effects of physical

parameters such as scatter or contrast on the final MTF result but it demonstrated the

feasibility of using the cone-based method with an actual breast tomosynthesis image of

a sphere phantom as shown in Error Reference source not found and Error Reference

source not found These effects should be addressed in future works A further look

into deriving the principles of comparing the theoretical MTF with the experimental

MTF using the cone-based method is further warranted

II4ii Separation of Artifact and Resolution Information

The focus of this study was to develop a technique for measuring spatial

resolution of tomosynthesis images The intrinsic artifacts from tomosynthesis

reconstructions however lead to uncharacteristic MTFs and possible misinterpretation

of the effective resolution information When considering previous techniques for

calculating the presampled MTF [713152328] the analysis was performed using an

edge or a line to produce the corresponding ESF The resolution information is

essentially contained only along the edge indicated by the need to calculate the LSF In a

way the method of extracting artifact information is to focus the analysis only on the

edge part of the ESF to calculate the modified MTF This will lead to a better

understanding of the limiting size of objects that may be seen in the reconstructed 3D

49

image The presampled MTF without correction should still be analyzed to understand

the entire system response Note that the ESFs attempt to reflect information only at the

detected edge of the sphere

II5 Conclusions

The directional MTF of a simulated breast tomosynthesis reconstruction was

determined by using the cone-based MTF technique demonstrating the feasibility of a

single phantom for MTF evaluation This study further presented methods of analyzing

only the edge information in the ESF to create a modified MTF along in-slice (x and y)

axes It can provide insight into the actual spatial resolution information contained in the

image while separating the resolution information from the information introduced by

artifacts caused by the reconstruction and insufficient volumetric sampling The idea of

separating the resolution and artifacts from the measured ESF are expected to facilitate

the interpretation of MTF measurements in breast tomosynthesis Similar methods may

be applied to characterize the resolution of other 3D imaging modalities

50

References

1 Garmer M Hannigs SP Jaumlger HJ et al ldquoDigital Radiography Versus

Conventional Radiology in Chest Imaging Diagnostic Performance of a Large-

Area Silicon Flat-Panel Detector in a Clinical CT-Controlled Studyrdquo American

Journal of Roentgenology Volume 74 75-80 (2000)

2 Cowen AR Kengyelics SM and Davies AG ldquoSolid-state flat-panel digital

radiography detectors and their physical imaging characteristics rdquoClinical

Radiology Volume 63 487-498 (2008)

3 Chotas HG Dobbins III JT and Ravin CE ldquoPrinciples of Digital

Radiography with Large-Area Electronically Readable Detectors A Review of

the Basicsrdquo Radiology Volume 210 Number 3 595-599 (1999)

4 Flynn MJ and Samei E Experimental comparison of noise and resolution for

2k and 4k storage phosphor radiography systems Medical Physics Volume 26

Number 8 1612-1623 (1999)

5 Rong XJ Shaw CC Liu X Lemacks MR and Thompson SK

ldquoComparison of an amorphous siliconcesium iodide flat-panel digital chest

radiography system with screenfilm and computed radiography systems ndash A

contrast-detail phantom studyrdquo Medical Physics Volume 28 Number 11 2328-

2335 (2001)

6 Ranger NT Samei E Dobbins III JT and Ravin CE Measurement of the

detective quantum efficiency in digital detectors consistent with the IEC 62220-1

standard Practical considerations regarding the choice of filter material

Medical Physics Volume 30 Number 7 2305-2311 (2005)

7 Samei E Buhr E Granfors P Vandenbroucke D and Wang X Comparison

of edge analysis techniques for the determination of the MTF of digital

radiographic systems Physics in Medicine and Biology Volume 50 3613-3625

(2005)

8 Samei E and Flynn MJ An experimental comparison of detector performance

for computed radiography systems Medical Physics Volume 29 Number 4 447-

459 (2002)

51

9 Samei E and Flynn MJ An experimental comparison of detector performance

for direct and indirect digital radiography systems Medical Physics Volume 30

Number 4 608-622 (2003)

10 Samei E Ranger NT MacKenzie A Honey ID Dobbins III JT and Ravin

CE Effective DQE (eDQE) and speed of digital radiographic systems An

experimental methodology Medical Physics Volume 36 Number 8 3806-3817

(2009)

11 Samei E Ranger NT MacKenzie A Honey ID Dobbins III JT and Ravin

CE Detector or System Extending the Concept of Detective Quantum

Efficiency to Characterize the Performance of Digital Radiographic Imaging

Systems Radiology Volume 249 Number 3 926-937 (2008)

12 ldquoIEC 62220-1 Medical Electrical Equipment ndash Characteristics of Digital X-Ray

Imaging Devices ndash Part 1 Determination of the Detective Quantum Efficiencyrdquo

International Electrotechnical Commission Geneva Switzerland (2003)

13 Samei E Ranger NT Dobbins III JT and Chen Y Intercomparison of

methods for image quality characterization I Modulation transfer function

Medical Physics Volume 33 Number 5 1454-1465 (2006)

14 Dobbins III JT Samei E Ranger NT and Chen Y Intercomparison of

methods for image quality characterization II Noise power spectrum Medical

Physics Volume 33 Number 5 1466-1475 (2006)

15 Samei E Flynn MJ and Reimann DA A method for measuring the

presampled MTF of digital radiographic systems using an edge test device

Medical Physics Volume 25 Number 1 102-113 (1998)

16 Nagel HD ldquoAluminum equivalence of materials used in diagnostic radiology

and its dependence on beam qualityrdquo Physics in Medicine and Biology Volume

31 Number 12 1381-1399 (1986)

17 Niklason LT Christian BT Niklason LE et al ldquoDigital Tomosynthesis in

Breast Imagingrdquo Radiology Volume 205 399-406 (1997)

18 Gur D ldquoTomosynthesis Potential Clinical Role in Breast Imagingrdquo American

Journal of Roentgenology Volume 189 614-615 (2007)

52

19 Park JM Franken Jr EA Garg M Fajardo LL and Niklason LT ldquoBreast

Tomosynthesis Present Considerations and Future Applicationsrdquo

RadioGraphics Volume 27 S231-S240 (2007)

20 Good WF Abrams GS Catullo VJ Chough DM Ganott MA Hakim

CM and Gur D ldquoDigital Breast Tomosynthesis A Pilot Observer Studyrdquo

American Journal of Roentgenology Volume 190 865-869 (2008)

21 Hu Y-H Zhao W Mertelmeier T and Ludwig J ldquoImage Artifact in Digital

Breast Tomosynthesis and Its Dependence on System and Reconstruction

Parametersrdquo IWDM 2008 LNCS 5116 628-634 (2008)

22 Chen Y Lo JY Ranger NT Samei E Dobbins III JT ldquoMethodology of

NEQ(f) analysis for optimization and comparison of digital breast tomosynthesis

acquisition techniques and reconstruction algorithmsrdquo Proceedings of SPIE

Volume 6510 65101I (2007)

23 Zhao B Zhou J Hu Y-H Mertelmeier T Ludwig J and Zhao W

ldquoExperimental validation of a three-dimensional linear system model for breast

tomosynthesisrdquo Medical Physics Volume 36 Number 1 240-251 (2009)

24 Madhav P Brzymialkiewicz CN Cutler SJ Bowsher JE and Tornai MP

ldquoCharacterizing the MTF in 3D for a Quantized SPECT Camera Having Arbitrary

Trajectoriesrdquo 2005 IEEE Nuclear Science Symposium Conference Record 1722-

1726 (2005)

25 Madhav P McKinley RL Samei E Bowsher JE and Tornai MP ldquoA Novel

Method to Characterize the MTF in 3D for Computed Mammotomographyrdquo

Proceedings of SPIE Volume 6142 61421Y (2006)

26 Hu Y-H Zhao B and Zhao W ldquoImage artifacts in digital breast

tomosynthesis Investigation of the effects of system geometry and

reconstruction parameters using a linear system approachrdquo Medical Physics

Volume 35 Number 12 5242-5252 (2008)

27 Seifert A and Flynn MJ ldquoResolving power of 3D x-ray microtomography

systemsrdquo Proceedings of SPIE Volume 4682 407-413 (2002)

28 Thornton MM and Flynn MJ Measurement of the spatial resolution of a

clinical volumetric computed tomography scanner using a sphere phantom

Proceedings of SPIE Volume 6142 61421Z (2006)

53

29 Baek J Pelc NJ ldquoUse of sphere phantoms to measure the 3D MTF of FDK

reconstructionsrdquo Proceedings of SPIE Volume 7961 79610D (2011)

30 Richard S and Samei E ldquoQuantitative imaging in breast tomosynthesis and CT

Comparison of detection and estimation task performancerdquo Medical Physics

Volume 37 Number 6 2627-2637 (2010)

31 Chen Y Lo JY and Dobbins III JT ldquoImpulse response analysis for several

digital tomosynthesis mammography reconstruction algorithmsrdquo Proceedings of

SPIE Volume 5745 541-549 (2005)

32 Zhao B and Zhao W ldquoThree-dimensional linear system analysis for breast

tomosynthesisrdquo Medical Physics Volume 35 Number 12 5219-5232 (2008)

33 Wu G Mainprize JG Boone JM and Yaffe MJ ldquoEvaluation of scatter

effects on image quality for breast tomosynthesisrdquo Medical Physics Volume 36

Number 10 4425-4432 (2009)

Page 12: Development and Evaluation of 2D and 3D Image Quality ...

xii

Figure 13 Example of 30-degree cone prescribed along z axis of the sphere 32

Figure 14 Photograph of the imaging system with the acrylic sphere phantom

embedded in oil 34

Figure 15 View of the central slice of the breast phantom reconstruction before (top) and

after (bottom) background subtraction The z axis is through the page 36

Figure 16 3D rendering of the ROI volume (left) and cross-sectional views of the most

centrally located sphere with centroid indicated with red circle (right) 37

Figure 17 Theoretical 3D MTF results along the three major planes (top) and along x y

and z directions (bottom) Also note that the angular spread seen in the fx-fz plane is

equal to the angular range of 44deg for the acquisition 38

Figure 18 Uncorrected ESF (top) LSF (middle) and MTF (bottom) for x y and z

directions 40

Figure 19 Comparisons of the directional MTFs as calculated by the sphere method

(dashed line) by theoretical line profiles (light-weight line) by theoretical cone regions

(heavy-weight line) 41

Figure 20 Modified ESF (top) LSF (middle) and MTF (bottom) for x and y directions 43

Figure 21 Cross sectional views of the experimental sphere image with centroid

indicated with red circle 44

Figure 22 ESF (top) LSF (middle) and MTF (bottom) of real image for x y and z

directions 45

xiii

Acknowledgements

I would like to thank Ian Yorkston Mark Purdum and Van Huston of

Carestream Health Inc (Rochester NY) for their help with digital detector

measurements I would also like to thank Olav Christianson Samuel Richard Brian

Harrawood and Max Amurao for their assistance with collecting data and analyzing

results Special thanks go to my committee members for their helpful insights and

suggestions for this thesis Last but not least I want to express deep appreciation for the

support and mentorship provided by my advisor Dr Ehsan Samei

1

I Evaluation of 2D Digital Image Receptors

I1 Introduction

In the past decade many areas of radiological practice have seen a conversion

from screen films to the storage phosphor cassettes of computed radiography (CR) to the

active-matrix flat-panel detectors of digital radiography (DR) Both CR and DR are

digital systems that offer many potential benefits including but not limited to better

image quality wider dynamic range quicker readout lower radiation dose and higher

throughput [1-3] Even with advances in DR technologies such as improved detective

quantum efficiency (DQE) the primary radiographic system of today continues to be CR

A major obstacle to completely accepting DR is the high capital cost of acquiring an

entire system per examination room while also providing capability for portable

applications Recently manufacturers like Carestream Health Fuji and Toshiba have

introduced wireless digital image receptors that can serve as replacements for CR

cassettes As these are new technologies a further investigation to characterize these

detectors is warranted

In the case of radiographic receptors DQE has historically been the metric of

choice [4] because it indicates the ability of the image receptor to convert incident x-ray

photons into useable signal ndash essentially a measure of signal-to-noise ratio (SNR)

efficiency and overall system performance [23] DQE is observed across a range of

spatial frequencies for evaluating how the detector depicts small and large objects [3]

2

DQE metrics have been used in numerous studies to characterize CR phosphor-screens

as well as indirect and direct digital detectors [4-11] The importance of this highly

quantitative metric may be implied by the introduction of a DQE measurement standard

by the International Electrotechnical Commission (IEC) [12]

The standard measurement methodology of the International Electrotechnical

Commission (IEC) pertains to the image quality of 2D digital radiographic detectors

While the IEC formalism is well-developed some of the components that it requires are

not necessarily the most optimal for characterizing DQE This has been explored in

previous studies in terms of filtration material purity beam limitations and region of

interest (ROI) configuration [1314] To reduce the variability in the radiographic output

across various x-ray tubes due to inherent filtration differences the IEC formalism

prescribes specific additional aluminum filtration to attain radiation beam qualities

based on target half value layers (HVL) Achieving and verifying the desired HVL

however requires applying a substantial amount of aluminum at the exit window of the

x-ray tube which is often directed toward the ground This can be a logistical

inconvenience and can increase the risk of damage to the image receptor and

measurement equipment Similar beam qualities on the other hand may be attained

more conveniently using a thinner lighter filtration combination utilizing a higher Z

number material Care is warranted however as a previous study [6] had indicated that

the choice of filtration material could impact the DQE

3

The purpose of this study was two-fold First we aimed to evaluate and compare

two wireless image receptors with a conventional flat-panel detector on the basis of DQE

performance Second we compared DQE results using the IEC-prescribed filtration with

an alternative filtration For the latter an optimum filtration composition was

determined and compared with the IEC filtration on the basis of DQE

I2 Materials and Methods

I2i Detectors

The physical characteristics of the three digital image receptors evaluated in this

study are listed in Table 1 The Pixium 4600 was a conventional digital flat-panel The

DRX-1C and DRX-1 were both wireless digital cassettes that were tethered for the

purposes of this study All detectors were FDA approved and available commercially

Each detector was calibrated according to its manufacturer specifications to correct for

gain offset and bad pixels They were all dedicated for non-clinical laboratory research

purposes and hence could be operated under service settings that permitted acquisition

of raw (ie for processing) images

I2ii Beam Characterization

I2iia X-ray Techniques

All measurements for this study were taken with a well-characterized standard

radiographic system (Super80CP Philips Healthcare Andover MA) The x-ray tube had

an inherent filtration of 27 mm Al Free in-air exposures were measured using

4

Table 1 Physical Characteristics of Digital Image Receptors

Manufacturer Detector

Detector

type

Detector

material

Pixel pitch

(size) Array size

Imaging

area

Trixell

(Moirans France)

Pixium

4600 Indirect

CsITl

(CsI) 0143 mm

3121times3121

4 subpanels 45times45 cm2

Carestream Health Inc

(Rochester NY)

DRX-1C

(wireless) Indirect

CsITl

(CsI) 0139 mm

2560times3072

single panel 35times43 cm2

Carestream Health Inc

(Rochester NY)

DRX-1

(wireless) Indirect

G2O2STb

(GOS) 0139 mm

2560times3072

single panel 35times43 cm2

calibrated radiation meters (Mult-O-Meter Type 407 Unfors Instruments AB Billdal

Sweden) at 183 cm source-to-chamber-distance (SCD) The SCD also corresponded to

same plane as the image receptor surface The x-ray output was made to conform to IEC

beam quality definitions [1215] on the basis of half value layer (HVL) and peak

kilovoltage setting using an aluminum filtration (type-1100 99 purity) and an

alternative filtration consisting of copper (UNS C11000 999 purity) and aluminum

(type-1100 99 purity) The IEC radiation quality numbers (RQA) used in this study are

summarized in Table 2 HVLs were determined by iteratively adding successive

thicknesses of aluminum until reaching reduced exposure levels within a tolerance of

0485-0515 [12] As for the alternative filtration the aluminum was placed downstream

of the copper filter to attenuate characteristic radiation peaks from copper at

approximately 9 keV

I2iib Data Linearization

The system response function was determined for each detector and filtration

combination by acquiring flat-field images at increasing photon fluence until just before

5

Table 2 Beam Qualities and Required Filtrations

IEC Radiation

Quality Number

Peak

kilovoltage

Required

HVL

Required IEC

Filtration

Actual IEC

Filtration

Alternative

Filtration

RQA5 70 kVp 71 mm Al 21 mm Al 21 mm Al 05 mm Cu +

10 mm Al

RQA9 120 kVp 115 mm Al 42 mm Al 40 mm Al 104 mm Cu +

10 mm Al

For reasons of convenience these will be referred to as RQA5A RQA5C RQA9A and RQA9C

saturation levels To avoid the influence of detector backscatter on exposure

measurements a relationship for each filtration was first determined for two radiation

meters A target meter was placed at the central axis and a reference meter was placed at

the edge of the light field (large enough to cover the detectors) The reference meter

served as a surrogate for the target meter to avoid direct exposure measurements in the

plane of the image receptor Exposure relationships were determined before each

measurement set (ie detector and filtration combination) to account for changes in

temperature pressure and humidity The system response function was calculated by

using a regression of ADU (pixel value) versus exposure Images acquired for each

series were then converted to achieve a linear response with zero offset and scaled to

achieve high quantization (adequate dynamic range) Linearization of the detector

responses ensured that zero exposure corresponded to zero pixel value

I2iic Spectral Simulation

The effects of additional filtration on x-ray output spectra were observed with

spectral simulation software (XSPECT V40 Henry Ford Hospital Detroit MI) To more

6

adequately describe the performance of a typical X-ray generator inherent filtration of 3

mm oil 148 mm Pyrex glass and 2 mm aluminum was input into the simulation in

addition to the filters of interest The ideal signal to noise ratio squared or incident

photon fluence per exposure (q) was estimated for each filtration by integrating the

energy-dependent photon counts per unit exposure over all energy bins

I2iii DQE Measurements

The assessment of the linearized images followed the formalism described by

IEC 62220-1 for measuring the DQE [12] For this study the normal exposure level XN

was set at 1 mR to the detector surface as measured at the central axis perpendicular to

the anode-cathode axis

I2iiia Modulation Transfer Function

Spatial resolution was characterized by evaluating the presampled modulation

transfer function (MTF) along directions parallel (vertical) and perpendicular

(horizontal) to the anode-cathode axis using the angled-edge method [6-1013] A radio-

opaque edge test device [7] was placed in the center of the field at a pitch of

approximately 301 (about 2deg) to the axis perpendicular to that being measured as

shown in Figure 1 External lead apertures were not used [6] instead the internal

collimation from the radiographic unit was used to collimate the beam to the detector

area Raw images were acquired of the edge with the normal exposure level XN of 1 mR

at the detector face The procedure of calculating the MTF followed previously described

7

methods [6-1013] The edge spread function (ESF) was determined along lines crossing

the edge of the angled test device The derivative of the ESF was calculated to form the

line spread function (LSF) to which a Hanning filter was applied The MTF was then

calculated as the fast Fourier transform (FFT) of the LSF and normalized at the zero-

frequency axis To conform to IEC guidelines the MTF was resampled into frequency

steps of 005 cyclesmm [12]

Figure 1 MTF images for DRX-1C detector with radio-opaque edge test device with

arrows indicating the horizontal (left) and vertical (right) directions

I2iiib Noise Power Spectrum

Noise amplitude and texture were characterized by determining the normalized

noise power spectrum (NNPS) which was evaluated with flat field exposures at

approximate exposure levels of XN2 XN and 2XN (05 10 and 20 mR) to the image

receptor surface Analysis of the flat-field images followed previously defined methods

[41415] using over 4 million independent pixels with regions of interest (ROIs) of size

8

128x128 The NNPS images were detrended using a quadratic (second order)

background subtraction Small variations in exposure across ROIs were corrected by

normalizing pixel values of each ROI to the mean value in the top left ROI as shown in

Figure 2 The NNPS was then calculated with the 2D FFT including the zero-frequency

axes corresponding to the horizontal and vertical directions The results were then

resampled using 005 frequency bins according to IEC guidelines [12]

Figure 2 NNPS image for DRX-1C detector indicating the top left ROI that served as

the reference for normalizing other ROIs in the image The ROI array was formed

along the directions indicated by the arrows The heel effect visible along the vertical

axis of the detector is an example of small variation in signal across the image

I2iiic DQE Calculation

The DQE was calculated using the following relationship [615]

9

where the frequency-dependent MTF and NNPS were determined as described in

previous sections X was the exposure value in mR corresponding to the NNPS image

and q was the ideal signal to noise ratio squared in units of photonsmiddotmm-2middotmR-1 as

estimated from the spectral simulations

I3 Results

I3i Data Linearization

The detectors in this study provided raw ADU (or pixel) values in a linear scale

The data were converted using the following system conversion function

where Q(ij) is the raw image data m and b are slope and intercept parameters obtained

from linear regression of the system response function and I(ij) is the linearized scaled

data The factor of 1000 was found to scale I(ij) such that the maximum value was a

large 16-bit number Figure 3 shows the original and linearized system responses for the

Pixium 4600 Note that the y-intercepts of the regressions for the linearized responses

are negligible (lt 01) with respect to the slopes a sufficient condition for zero offset

considerations

I3ii Spectral Simulation

The spectral simulations of the IEC filtrations and alternative filtrations indicate

many similarities in their effective energies HVLs and overall shapes of normalized

spectra Results are summarized in Table 3

10

Pixium 4600 Original System

Response

Pixium 4600 Linearized System

Response R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 3 Original (left) and linearized (right) system responses for Pixium 4600 The

linearized system responses were measured from actual images The offsets are small

with respect to the slope sufficient enough for zero-offset conditions

y = 13971x - 13236

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x - 00106Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 13576x + 28292

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

7000

0000 1000 2000 3000 4000 5000

AD

U

Exposure (mR)

y = 99997x - 00067Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0000 1000 2000 3000 4000 5000

AD

U

Exposure (mR)

y = 13644x + 16167Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x + 00044

Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 13845x + 13541

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x - 00177

Rsup2= 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

11

Table 3 Spectral Simulation Results

Beam Quality Filtration

Mean Energy

(kV)

Photon Fluence

(mRmm2)

RQA5A 21 mm Al 5243 259543

RQA5C 05 mm Cu + 10 mm Al 5214 259554

diff 055 0004

RQA9A 40 mm Al 7619 273281

RQA9C 104 mm Cu + 10 mm Al 7579 273964

diff 052 025

Figure 4 Spectral simulations for RQA5 (top) and RQA9 (bottom) conditions Note

the similarities of spectral shapes of the normalized spectra (right) Also note the

significant differences in fluence between filtrations in the simulated spectra (left)

00E+00

50E+04

10E+05

15E+05

20E+05

25E+05

30E+05

35E+05

40E+05

45E+05

0 20 40 60 80

ph

oto

ns

mA

s-1

cm

-2

keV

RQA5 Spectra Comparison

21 mm Al

05 mm Cu + 10 mm Al

00

02

04

06

08

10

12

0 20 40 60 80

keV

RQA5 Normalized Spectra Comparison

21 mm Al

05 mm Cu +

10 mm Al

00E+00

50E+05

10E+06

15E+06

20E+06

25E+06

30E+06

35E+06

40E+06

45E+06

50E+06

0 50 100 150

ph

oto

ns

mA

s-1

cm

-2

keV

RQA9 Spectra Comparison

40 mm Al

104 mm Cu +

10 mm Al

00

02

04

06

08

10

12

0 50 100 150

keV

RQA9 Normalized Spectra Comparison

40 mm Al104 mm Cu + 10 mm Al

12

I3iii Modulation Transfer Function

The limiting spatial resolutions of the systems were indicated by the cutoff

frequencies which were approximately 35 cyclesmm for all three detectors The spatial

resolutions also demonstrated a good degree of isotropy as confirmed by the close

alignment of MTF curves between vertical and horizontal directions differentiated in

Figure 5 by dashed and solid lines respectively The MTF curves for the Pixium 4600

and DRX-1C were nearly equal to each other whereas the DRX-1 MTF curve showed a

more rapid decrease at high frequencies as shown in Figure 6 This difference may be

due to the differences in the inherent optical properties of the scintillating materials

where finer image details are provided by structured CsI more than by granulated GOS

There were no significant differences in MTF curves across beam qualities and filtrations

as shown by the curve comparisons in Figure 6 although the alternative filtration

produced slightly higher MTF curves as seen in Figure 4 Table 4 lists the experimental

specific spatial frequencies for varying levels of MTF

I3iv Noise Power Spectrum

The noise characteristics are indicated by the NNPS curves shown in Figure 7

The noise was similar for both horizontal and vertical directions As exposure increased

the NNPS decreased consistent with the characteristics of Poisson noise describing the

relationship between signal and noise in the presence of increased photon fluence At

13

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 5 MTF results by detector (columns) and beam quality (rows)

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

horizontal

vertical

14

Figure 6 Plots of MTF for RQA5 (top) and RQA9 (bottom) showing the relationships

between detectors (blue red and green) and by filtration (solid and dashed)

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm-1)

MTF

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm-1)

MTF

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

15

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 7 NNPS results by detector (columns) and beam quality (rows)

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

05 mR - horizontal

05 mR - vertical

10 mR - horizontal

10 mR - vertical

20 mR - horizontal

20 mR - vertical

16

Figure 8 Plots of NNPS for RQA5 (top) and RQA9 (bottom) at 1 mR exposure

showing the relationships between detectors (blue red and green) and by filtration

(solid and dashed)

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm-1)

NNPS (1 mR)

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm-1)

NNPS (1 mR)

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

17

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 9 DQE results by detector (columns) and beam quality (rows)

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

05 mR - horizontal

05 mR - vertical

10 mR - horizontal

10 mR - vertical

20 mR - horizontal

20 mR - vertical

18

Figure 10 Plots of DQE for RQA5 (top) and RQA9 (bottom) at 1 mR exposure showing

the relationships between detectors (blue red and green) and by filtration (solid and

dashed)

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm-1)

DQE (1 mR)

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm-1)

DQE

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

19

higher frequencies the NNPS curves of the Pixium 4600 and DRX-1 diverge slightly for

the different directions illustrating increased noise in the readout direction (vertical)

Differences in the noise characteristics were more apparent among detectors as

shown for 1 mR in Figure 8 The NNPS curve for the DRX-1 was higher in magnitude

across the entire frequency range than either the Pixium 4600 or DRX-1C which both

seemed to demonstrate reasonably similar NNPS curves The higher magnitude noise of

the DRX-1 indicates higher relative noise content overall Closer inspection of the NNPS

curves of the Pixium 4600 and DRX-1C detectors in Figure 7 revealed differences in the

spacing between the three exposure levels The gaps between the Pixium 4600 NNPS

curves do not correspond to the factor of two differences between each exposure level

especially at low- to mid- spatial frequencies suggesting a higher level of fixed pattern

noise additional noise with increasing exposure levels due to ineffective gain map

corrections Between filtration schemes the differences in NNPS curves for a given beam

quality were not substantial as shown in Figure 7

I3v Detective Quantum Efficiency

The DQE results are shown in Figure 9 DQE curves across exposure levels were

almost collinear except for Pixium 4600 and in general could be inferred from the

NNPS results Additionally the DQE curves demonstrated a relatively linear response

with spatial frequencies as expected for flat-panel detectors [9] Differences in DQE

among detectors were consistent for the most part with the type of scintillating material

20

As depicted for 1 mR exposure in Figure 10 differences between Pixium 4600 and DRX-

1C DQE curves correspond to the differences in their NNPS curves DRX-1 DQE curves

were consistently lower than either the Pixium 4600 or DRX-1C curves The DQE curves

for the alternative filtration were consistently higher than those for the IEC filtration

and the most noticeable differences were near the zero-frequency axis These effects can

be both attributed to ineffective gain map correction DQE values for 1 mR exposure are

listed in Table 5

I4 Discussion

I4i Comparisons of Detectors

The limiting spatial resolutions of all three detectors were almost exactly the

same considering that their pixel areas were similar in size The decrease in high-

frequency MTF of the DRX-1 compared to the other detectors is probably a result of

increased optical blurring due to the differences in the powdered structure of GOS

versus the needle-like structure of CsI [2] The fact that the DRX-1C and Pixium 4600

have comparable MTFs suggests similar scintillator thicknesses assuming that the

materials were processed alike

The noise of the three detectors demonstrated similar trends with each other The

higher NNPS curves of the DRX-1 detector are probably due also to the scintillating

material and its operation in converting photons into signal The conversion process is

less efficient because of the less favorable stopping power of the GOS compared to CsI

21

especially with higher energy beams The noise of the Pixium 4600 and DRX-1C were

similar except for the spacing between exposures The DRX-1C NNPS curve spacing is

consistent with a factor of two difference in exposure levels but the Pixium 4600 has a

smaller spacing The 05 mR NNPS curve of the Pixium 4600 is closer to that of the 05

mR NNPS curve of the DRX-1C This demonstrates that at higher exposures the Pixium

4600 produces a larger amount of additional noise beyond that explained by simple

stochastic effects It suggests bad performance in the gain map corrections

The DQE results indicate SNR properties of each detector The Pixium 4600 and

DRX-1C are comparable for the most part with the DRX-1C performing slightly better

The DRX-1 as predicted from MTF and NNPS results has a DQE much lower than

either of the previous two This is a reflection of the detection properties as provided by

its scintillator material The DQE of the DRX-1 however is comparable to CR image

receptors [2] The mid-frequency dips in the DQE for Pixium 4600 may be due to the

optical properties of the CsI phosphor layer which can affect the MTF in this manner

Because the DQE is calculated by squaring the MTF this effect at the mid-range

frequencies becomes more apparent The dips may also be further evidence of bad gain

map corrections

I4ii Comparisons of Filtrations

The alternative filtration closely matches for the most part the IEC-based

filtration for MTF NNPS and DQEs at RQA5 but not at RQA9 The filters do not have

22

Table 4 Experimental MTF frequency locations for 1 mR exposure

Detector Filtration

50 MTF

(mm-1)

40 MTF

(mm-1)

30 MTF

(mm-1)

20 MTF

(mm-1)

10 MTF

(mm-1)

Pixium

4600

RQA5A 115 145 185 245 330

RQA5C 125 155 195 250 345

RQA9A 110 175 175 235 330

RQA9C 125 155 195 255 345

DRX-1C

RQA5A 120 150 185 245 350

RQA5C 125 155 195 255 355

RQA9A 120 150 190 250 355

RQA9C 130 160 210 265 360

DRX-1

RQA5A 110 135 160 205 280

RQA5C 110 135 170 210 285

RQA9A 105 125 155 195 270

RQA9C 110 135 165 210 285

Table 5 Estimated DQE values for 1 mR exposure by frequency bins

Detector Filtration DQE(00 mm-1) DQE(10 mm-1) DQE(20 mm-1) DQE(30 mm-1)

Pixium

4600

RQA5A 62 42 32 21

RQA5C 63 45 36 25

RQA9A 41 27 30 13

RQA9C 43 33 27 19

DRX-1C

RQA5A 72 52 35 21

RQA5C 76 55 41 24

RQA9A 49 33 23 15

RQA9C 51 40 31 20

DRX-1

RQA5A 38 24 12 4

RQA5C 38 25 14 5

RQA9A 28 18 9 4

RQA9C 28 19 12 5

DQE values at the zero-frequency axis were estimated by the intercept of a linear fit of low-frequency data

but excluding most proximal to the axis due to large fluctuations Other estimated values are grouped into

frequency bins due to the noisiness of the data

23

considerable differences in the spatial resolutions of the detectors as expected The noise

responses for each filtration were also similar except at the lower frequencies of the

NNPS especially near the zero-frequency axis There observing the NNPS responses at

RQA5 for Pixium 4600 and DRX-1C in Figure 8 the NNPS for the IEC-based filtration

(solid lines) tend to drop faster than the NNPS for the alternative filtration This

subsequently appears as a drop in DQE near the zero-frequency axis shown for those

detectors in Figure 10 Overall as indicated in Table 5 the DQEs of the two filtrations

while similar in trend indicate that the alternative filtration increases the DQE by a

small amount of 3-5 Part of this may be explained by the slightly higher beam

energy which may be more optimal for the energy response of the detectors or may

weigh the pixel responses slightly considering that they are energy-integrating types

The most probable explanation is the gain map correction for the alternative filtration

where fixed pattern noise is more sufficiently reduced

A previous study [6] had discussed the choice of filter material in the analysis of

DQE when achieving the beam conditions defined by IEC It found that visible

nonuniformities were present with the higher purity aluminum filter (type-11999 alloy)

The low frequency mottle in the flat-field images for NPS measurements were also

attributed to structured noise from the grain size in the IEC-based filter with an

attenuating thickness that would reveal nonuniformities The mottle in the current study

was only observable under very narrow windowing as shown in Figure 11 Such low

24

frequency artifacts which are not readily noticeable may also be caused by shading

artifacts inverse square law or even the heel effect A possible method to correct for this

is a subtraction method by taking the average of the flat-field images for an exposure

level and then subtracting that from each of them This would remove nonuniformities

that were not corrected using a suboptimal gain map calibration

Figure 11 DRX1-C NNPS images at 1 mR for RQA5 with IEC filtration (left) and

alternative filtration (right) Images are equally windowed at 45 and leveled at 980

One convenient aspect of the copper and aluminum filtration is that it requires

much less tube current to achieve the same amount of exposure at the detector than the

much thicker aluminum filtration As shown in the non-normalized spectra in Figure 2

the exiting photon fluence exiting the copper and aluminum filtration is substantially

higher than that of the IEC-specified filtration This is due to the smaller total filtration

25

attenuation For extensive DQE analysis multiple sets of exposures may be acquired

before tube overheating becomes a concern

One limitation to the comparison of the two filtrations is that calibration

procedures specified copper and aluminum filtration at 80 kVp (for all detectors 05 mm

Cu and 10 mm Al) This may have influenced the results in favor of the alternative

filtration A further investigation involving the calibration procedures and performing

DQE measurements is encouraged Another factor may be influenced by the fact that the

tests were performed at 70 kVp and 120 kVp different from the recommended

calibration tube potential Clearly there would be differences in the linear attenuation

coefficients of the filters and different energy responses of the detectors themselves This

must be considered when interpreting DQE results The current results support a

previous study decades ago that described filtration of different material types in terms

of an aluminum equivalent [16] The results show that the two filtration schemes are

essentially equivalent when considering beam qualities and spatial resolutions The

NNPS and DQE results can be seen as close enough where their small differences are

insignificant when performing quality assurance tests in a clinical setting Overall our

results indicate that the alternative filtration with copper and aluminum may be more

convenient to use than the current IEC standard filtration

26

I4iii Implications of Wireless DR

This study has shown that wireless image receptors can have the same DQE

performance if not better than conventional flat-panel detectors They operate on the

same basic physical principles the new features offered by the DRX-1C and DRX-1 are

wireless communication with the workstation and electronics packaging technology

The latter feature may pose limitations for these units in terms of possible degradation

in the detectors in routine clinical conditions A consideration for future work would be

to longitudinally track DQE performance of the wireless detectors over time while being

utilized in a clinical environment In the end one must consider risks versus benefits of

choosing portable DR technology over CR one of which includes the cost and fragility

of DR detectors

The DQE performance of one wireless system is just as good as or better than

conventional systems as seen by the DRX-1C performance compared to the Pixium

4600 Wireless systems can also reduce the need for CR readers especially in portable

applications in other regions of the world (eg military hospitals developing countries)

However while DQE performance indicates the physical performance of the detector

system it is still unknown how it relates to observer performance

I5 Conclusions

Two wireless image receptors DRX-1C and DRX-1 were evaluated and

compared with the conventional DR flat-panel Pixium 4600 in terms of DQE

27

performance along with MTF and NNPS performances The detectors have similar

resolution properties although the DRX-1 is inferior at higher spatial frequencies The

NNPS and DQE results both indicate that the DRX-1C is superior to the DRX-1 and

comparable if not better to the Pixium 4600

The results from the filtration comparison indicate no substantial differences

between the IEC-based filtration and the copper-based alternative filtration Only slight

differences were found in the low frequency components of the NNPS and the DQE due

to the inherent nonuniformities of the IEC specified filtration Given the similarity of the

results and low attenuation advantage of the copper and aluminum filter its use is

encouraged

28

II Directional MTF for Breast Tomosynthesis

II1 Introduction

Breast tomosynthesis is an emerging 3D imaging modality that has potential use

for screening and diagnosis of breast cancer Breast tomosynthesis along with other 3D

techniques is preferable to planar imaging methods (eg mammography) because they

reduce anatomical noise by removing overlying structures above and below the plane of

an image slice [17-20] Recent advances in detectors and computer technology have

made digital tomosynthesis feasible

An image quality metric of particular importance in breast tomosynthesis is

spatial resolution Resolution is important to know in order to assess small-detail

structures such as microcalcifications A descriptive metric for characterizing spatial

resolution in the Fourier (or frequency) domain is the modulation transfer function

(MTF) Affected by reconstruction filters [21] the limited angular projections involved in

breast tomosynthesis results in highly anisotropic (or nonuniform) resolution Many

studies have looked only at characterizing the in-plane spatial resolution (ie in an

individual slice) with an elevated angled edge phantom [2223] A few studies have

looked at characterizing a more comprehensive 3D spatial resolution by using a

phantom with angled wires or tubes [24-26] However such studies require precise

mechanical alignment of the phantoms Several studies have explored a method using a

29

sphere phantom for the directional 3D MTF evaluation for microtomography [27] and

multi-slice CT [2829] This method has not yet been extended to breast tomosynthesis

This chapter focuses on breast tomosynthesis because it is highly anisotropic in

spatial resolution and like its predecessor mammography requires high spatial

resolution Additionally breast tomosynthesis acquisitions and reconstructions produce

several types of artifacts The use of a cone-based method using a sphere phantom [28] is

explored to characterize the directional 3D spatial resolution of simulated images from

breast tomosynthesis A technique for removing out-of-plane artifacts of the ESFs for the

in-plane axes is investigated to yield a modified MTF in a method that separates artifact

information from resolution information

II2 Materials and Methods

II2i Image Simulation

Breast tomosynthesis images were simulated by using a virtual imaging system

depicted in Figure 12 A volumetric breast phantom was voxelized as a rectangular mass

of uniform breast equivalent tissue of 4 cm thickness embedded with fifteen evenly

spaced plastic sphere inserts of 12 mm diameter The spheres were placed in a grid

formation within the central plane of the phantom The x-ray fluence was modeled from

a 28 kVp beam incident upon an indirect flat-panel detector with 200 micro m pixel size

Twenty-three projections within an angular range of 44deg were simulated using cascaded

systems analysis to generate characteristic 2D noise and spatial blurring [29] Each

30

projection was simulated to have an exposure of 174 mR with a fluence of 79 times 105

photonsmm-2 A standard filtered backprojection technique based on the Feldkamp

reconstruction algorithm [29] was used to reconstruct the projections and produce a

volumetric dataset with an isotropic voxel size of 200 micro m

Figure 12 Depiction of the virtual image system

II2ii Uncorrected MTF

To enable comparison of multiple spheres the reconstructed volume was

initially homogenized by performing a background subtraction based on a portion of the

volume devoid of spheres The voxel values were rescaled between one and zero to

eliminate negative values

31

The volumetric data were segmented to extract individual regions of interest

(ROIs) each containing a single sphere The ROIs extended along the full range of the z-

axis A thresholded ROI was generated by determining the exterior and interior voxels

relative to the sphere in the ROI The threshold value was set at 45 of the maximum

voxel value prior to thresholding The exterior and interior voxel values were then set to

values of 0 and 1 respectively Using the thresholded volume the center of mass was

calculated to determine the centroid The voxel values from the original ROI were

subsequently tabulated with the associated distances azimuthal angles and polar

angles relative to the centroid

Conical regions were prescribed along the positive and negative directions along

the three major axes extending from the centroid of the sphere as depicted in Figure 13

The axes about which the extent of the cone angle was delineated were defined with

the azimuthal and polar angles

Voxels with centers within the angular range of the cone were considered for

generating the edge spread function (ESF) To improve regularity of the distance

sampling interval the ESF values were rebinned to discrete distances corresponding to a

fraction of the voxel size Only voxels with distances ranging from the voxel size (ie

200 micro m) to the maximum distance were considered The ESFs from multiple spheres

were averaged together for each of the three major axes to produce an averaged ESF

which was further smoothed utilizing a Gaussian filter

32

Figure 13 Example of 30-degree cone prescribed along z axis of the sphere

The resulting ESF was then differentiated using the central difference method to

produce the line spread function (LSF) A Hanning filter with the same length as the LSF

was applied to zero out the tails of the LSF The presampled MTF was subsequently

computed as the amplitude of the Fourier transform of the LSF The MTF was

normalized with respect to the maximum value occurring within the range of the cutoff

frequency Binning size and conical range for the ESF were considered for maximizing

accuracy and minimizing noise of the MTF verified by comparison against the

theoretical MTF as determined in the previous section

II2iii Theoretical Directional MTF

The theoretical 3D MTF was calculated using a priori knowledge of the transfer

function of the virtual imaging system described in the previous section A phantom

was created with a set of point objects in a uniform and noise-free background with the

objects spanning across the volume of the breast [29] Twenty-one realizations were

33

generated from the reconstructed images of the point objects to yield a set of 3D point

spread functions (PSFs) The 3D fast Fourier transform (FFT) was performed for each 3D

PSF and averaged to give an ldquoexpectationrdquo 3D MTF [29] The theoretical directional

MTFs in the three major spatial axes were determined by line profiles along each of the

corresponding spatial frequency axes in the 3D MTF An additional theoretical MTF for

each direction was determined by using the application of conical regions along the axes

in frequency-space to take into account the contributions of MTF information from other

planes

II2iv Modified MTF

The tomosynthesis reconstruction is known to have edge enhancements which

affect the overall MTF by shifting the peaks of the MTF toward the higher frequencies

[23] The presence of this artifact complicates the interpretation of the actual spatial

resolution of the images Several steps were performed to remove the artifact

contribution to the resolution information particularly for the in-plane x and y

directions with the assumption that resolution information was contained immediately

near the edge

For the x-direction averaged ESF only values that were detected to be inside the

edge of the sphere were considered Those values were previously determined via

thresholding for calculating the centroid The ESF information corresponding to these

values was inversed and flipped about the detected edge to produce a symmetric

34

modified ESF The modified MTF was subsequently calculated from this modified ESF

as described in the previous section

For the y-direction averaged ESF an upward trend was found in the initial part

of the ESF This section was detrended with a polynomial fit and subtracted to produce a

flatter curve in that region The resulting detrended ESF was used to calculate the y axis

modified MTF

Figure 14 Photograph of the imaging system with the acrylic sphere phantom

embedded in oil

II2v Preliminary Experimental Validation

A clinical breast tomosynthesis system (Mammomat Inspiration Siemens AG

Munich Germany) was used to perform a preliminary evaluation of the cone-based

MTF technique The phantom for the experiment consisted of a single acrylic ball of 075

in diameter (SmallParts Seattle WA) suspended by a 0029 in diameter plastic filament

35

(Omniflex Zebco Tulsa OK) in an acrylic frame filled up to 4 in with vegetable oil

(Target Brands Inc Minneapolis MN) The system and phantom are shown in Figure

14 Twenty-five projections with an angular range of 44deg were acquired and subsequently

reconstructed to produce a volume with a voxel size of 01times01times10 mm3 The voxels were

reformatted to have an isotropic size of 01 mm The uncorrected ESF LSF and MTF

were calculated as described in the previous section

II3 Results

II3i Reconstruction

The reconstructed volume is shown in Figure 15 Notice the edge enhancement

along the x-direction as indicated by the sharp shadowing artifacts on either side of the

spheres The background was effectively homogenized using the background

subtraction technique This also took account of the curved edges of the breast phantom

With the close spacing of the spheres in the phantom the shadows along the x direction

for the fifteen spheres overlap with each other As the nine centrally located spheres

experience this effect the same way they were used for determining the ESF

A 3D rendering of the ROI containing a sphere shown in Figure 16 indicates the

anisotropic resolution of the reconstruction Note that the sphere is not accurately

reconstructed and has an oblong shape especially along the z axis Cross sectional views

of the ROI also in Figure 16 clearly demonstrate the edge enhancement causing a

shadow artifact in the x direction caused by the incomplete angular sampling of

36

tomosynthesis The sampling also introduces the triangular reconstruction of the sphere

as seen in the x-z plane Note the gradual edge drop-off in the z direction much beyond

the sphere radius

Figure 15 View of the central slice of the breast phantom reconstruction before (top)

and after (bottom) background subtraction The z axis is through the page

37

Figure 16 3D rendering of the ROI volume (left) and cross-sectional views of the most

centrally located sphere with centroid indicated with red circle (right)

II3ii Theoretical MTF

The theoretical MTFs for x y and z directions as determined from the line

profiles of the 3D MTF are shown in Figure 17 The theoretical MTF in the x direction

has a maximum value that is toward higher frequencies Its 10 response occurs at

about 125 cyclesmm which is at 50 of the cutoff frequency The rapid increase from

the zero-frequency intercept to the peak corresponds to the ramp filter used in filtered

backprojection which decreases the weighting of low frequency contributions due to the

incomplete angular sampling of the frequency-space The MTF does not reach a value of

0 at the zero-frequency intercept as it is very difficult to assess the zero-frequency

intercept due to the finite size of the phantom The theoretical MTF in the y direction

peaks at the zero-frequency intercept and reaches 20 proximal to the cutoff frequency

38

The 10 MTF is well beyond the cutoff frequency The theoretical MTF in the z direction

has a rapid drop-off at very low spatial frequencies indicating the lack of resolution in

that dimension

Figure 17 Theoretical 3D MTF results along the three major planes (top) and along x

y and z directions (bottom) Also note that the angular spread seen in the fx-fz plane is

equal to the angular range of 44deg for the acquisition

II3iii Uncorrected MTF

The ESF LSF and MTF using the cone-based method are shown for the x y and

z directions in Figure 18 It was found that a bin size of one-tenth the voxel size (002

mm) and a cone angle of 30deg to establish the ESF were enough to minimize noise and

maximize accuracy in the uncorrected MTFs considering the reasonable comparison of

the shapes of the MTF curves with the theoretical results in Figure 17 The LSFs are

generally noisy because differentiation of the ESF increases the amplitude of the noise

39

The data shown reflect a convolution with a smoothing Gaussian filter which was later

further corrected for in the reported MTF Nevertheless the high frequency components

of the noise are well beyond the MTF cutoff frequency of 25 cyclesmm and do not

impact the MTF results greatly

For the ESF in the x direction the shadow effect evident at the edge of the sphere

is visible as a steep decline followed by an increase Due to the finite distance range

provided by the ROI the ESF beyond the edge did not asymptotically reach the

background value The corresponding LSF demonstrates a low frequency modulation

that is indicated by the shift of 03 cyclesmm in the x direction for the peak of the MTF

The MTF exhibits a zero-frequency intercept that is non-zero unlike the theoretical MTF

and a 10 value at approximately 1 cyclesmm These features may be a direct

consequence of MTF information ldquocontaminationrdquo from y and z directions Furthermore

the ESF in the y direction demonstrates a reasonably shaped curve except for the slight

upward trend within the radius of the sphere which can be attributed to the shadow

artifact overlapping with the sphere volume The associated MTF has a peak shifted by

approximately 01 cyclesmm away from the axis and a 10 MTF occurring at

approximately 15 cyclesmm Both features which are not present in the theoretical

results may also be attributed to contaminant MTF information from x and z directions

The ESF in the z direction has a drop-off that occurs at a small fraction of the cutoff

frequency similar to that demonstrated by the theoretical MTF

40

Uncorrected ESF LSF and MTF

Figure 18 Uncorrected ESF (top) LSF (middle) and MTF (bottom) for x y and z

directions

41

Figure 19 Comparisons of the directional MTFs as calculated by the sphere method

(dashed line) by theoretical line profiles (light-weight line) by theoretical cone

regions (heavy-weight line)

II3iv Comparison of Theoretical and Simulated MTFs

The theoretical MTF results obtained from line profiles through the 3D MTF and

the simulated MTFs using the cone-based technique did not match very well except for

the general shape of the curves It was assumed in the previous section that the cone-

based technique contains information from other planes Figure 19 compares MTFs in

each direction for the two methods described in the methods and an additional method

based on conical regions of the 3D MTF The latter computes the MTF by averaging

contributions of the 3D MTF using the same cone prescription method used to define the

ESFs Comparison of the curves indicate some interesting correlations aside from the

fact that using conical regions with the 3D MTF results produce more noisy MTF results

partly due to the low sampling provided by the theoretical calculations The same

conclusions regarding the z direction MTF can be confirmed regardless of either

theoretical MTF procedures The experimental x direction MTF seems to agree best with

42

the line profile method whereas the y direction MTF agrees better with the cone region

method The fact that the experimental x direction MTF has a drop-off frequency that is

lower than those of either of the theoretical MTFs in Figure 19 suggests that this might

be due to integration of the z-direction in the in-plane slices considering how slices are

essentially averages of z direction information contained within it [33]

II3v Modified MTF for x and y

Modified ESF LSF and MTF curves for x and y directions are shown in Figure

20 The modified ESF and the resulting LSF in the x direction appear symmetric as

expected from the inverse and flip operation of the interior ESF about the detected edge

The modified MTF appears with less variation than the uncorrected MTF and the MTF

peak occurs at the zero-frequency axis The correction yields a 10 MTF at about 15

cyclesmm an improvement from the uncorrected MTF but still distant from the cutoff

frequency The modified ESF in the y direction demonstrates the detrended curve within

the sphere radius after a quadratic polynomial fit The resulting modified MTF still

appears similar to the uncorrected MTF except that the peak now coincides with the

zero-frequency axis For both x and y directions the low response of the modified MTFs

at the higher frequencies suggests that the contamination from other directions is

substantial due to the angular range of the cone

43

Modified ESF LSF and MTF

Figure 20 Modified ESF (top) LSF (middle) and MTF (bottom) for x and y directions

44

II3v Preliminary Experimental Validation

Cross-sections of the reconstructed sphere volume are shown in Figure 21

Relative to the simulation reconstructions the reconstructions of the experimental

phantom images produce lower contrast and higher noise The preliminary results

shown in Figure 22 indicate that our technique can be applied to actual experimental

breast tomosynthesis reconstructions However due to the noise exhibited by the MTF

curves for the x and y directions we did not determine the modified MTFs to separate

resolution and artifact information

Figure 21 Cross sectional views of the experimental sphere image with centroid

indicated with red circle

45

Uncorrected ESF LSF and MTF for Real Image

Figure 22 ESF (top) LSF (middle) and MTF (bottom) of real image for x y

and z directions

46

II4 Discussion

II4i Evaluation of Cone-based Method

The cone-based MTF technique was introduced by Thornton and Flynn [28] for

evaluation of volumetric CT images To utilize this technique as a characterization of a

3D system spatial resolution one must first consider the validity of the assumption of

shift invariance such that the same MTF result may be obtained regardless of the

location of the sphere The study by Zhao et al [23] found that there was no shift

variance for the MTF measurements along the vertical axis but this was only considering

the in-plane resolution along one axis On the other hand this study evaluated the MTF

with images simulated with cascaded systems analysis which includes conditions of

linearity and shift invariance Additionally the MTF was calculated by averaging the

ESF from several spheres in the same volume only after performing a background

subtraction This step was essential to account for the sensitivity of centroid calculations

as well as ensuring symmetric ESFs for opposing axes of the sphere ROIs

The measurement of MTF with the cone-based technique inherently

supersamples the edge of the sphere to increase signal-to-noise-ratio (SNR) of edge

information by averaging the contributions of each voxel to the ESF [713] This method

also takes into account the discrete sampling of the voxels by accounting for various

shifts of the edge in the voxel (also known as the partial volume effect) However using

the curved surface of the sphere phantom to approximate an edge along a given

47

direction naturally leads to contamination of information from other directions aside

from the one of interest Preferably a directional ESF should be created by using a single

radial line but this would limit the available voxels to obtain edge information An ideal

situation theoretically would be to use a larger-sized sphere such that the surface is

nearly flat and perpendicular to the axes of interest This would also permit a reduction

in the angular range of the cone and thus the introduction of out-of-plane information in

the resulting MTF However sphere size is a limitation in breast tomosynthesis and the

use of a large phantom might void the assumption of shift invariance of the spatial

resolution

The choice of a sphere phantom nevertheless may be based on the clinical need

to quickly acquire a single image for MTF evaluation especially for multiple directions

without presenting extra logistical challenges The use of a wire or edge phantom

requires more precise mechanical alignment to achieve the correct set up The edge

phantom [23] would require at least two images to sample all three dimensions In the

case of the three wire phantom [2425] all three dimensions of the frame must be aligned

simultaneously with respect to the axis of rotation A similar situation would be

encountered when considering a cubic phantom with the planes normal to the axis of

interest In contrast to these phantoms the sphere eliminates the need for precise

alignment especially with respect to three spatial dimensions simultaneously A sphere

48

has ideal symmetry in all directions and can be used to evaluate MTF in any arbitrary

direction

This study unlike others [242532] did not explore the effects of physical

parameters such as scatter or contrast on the final MTF result but it demonstrated the

feasibility of using the cone-based method with an actual breast tomosynthesis image of

a sphere phantom as shown in Error Reference source not found and Error Reference

source not found These effects should be addressed in future works A further look

into deriving the principles of comparing the theoretical MTF with the experimental

MTF using the cone-based method is further warranted

II4ii Separation of Artifact and Resolution Information

The focus of this study was to develop a technique for measuring spatial

resolution of tomosynthesis images The intrinsic artifacts from tomosynthesis

reconstructions however lead to uncharacteristic MTFs and possible misinterpretation

of the effective resolution information When considering previous techniques for

calculating the presampled MTF [713152328] the analysis was performed using an

edge or a line to produce the corresponding ESF The resolution information is

essentially contained only along the edge indicated by the need to calculate the LSF In a

way the method of extracting artifact information is to focus the analysis only on the

edge part of the ESF to calculate the modified MTF This will lead to a better

understanding of the limiting size of objects that may be seen in the reconstructed 3D

49

image The presampled MTF without correction should still be analyzed to understand

the entire system response Note that the ESFs attempt to reflect information only at the

detected edge of the sphere

II5 Conclusions

The directional MTF of a simulated breast tomosynthesis reconstruction was

determined by using the cone-based MTF technique demonstrating the feasibility of a

single phantom for MTF evaluation This study further presented methods of analyzing

only the edge information in the ESF to create a modified MTF along in-slice (x and y)

axes It can provide insight into the actual spatial resolution information contained in the

image while separating the resolution information from the information introduced by

artifacts caused by the reconstruction and insufficient volumetric sampling The idea of

separating the resolution and artifacts from the measured ESF are expected to facilitate

the interpretation of MTF measurements in breast tomosynthesis Similar methods may

be applied to characterize the resolution of other 3D imaging modalities

50

References

1 Garmer M Hannigs SP Jaumlger HJ et al ldquoDigital Radiography Versus

Conventional Radiology in Chest Imaging Diagnostic Performance of a Large-

Area Silicon Flat-Panel Detector in a Clinical CT-Controlled Studyrdquo American

Journal of Roentgenology Volume 74 75-80 (2000)

2 Cowen AR Kengyelics SM and Davies AG ldquoSolid-state flat-panel digital

radiography detectors and their physical imaging characteristics rdquoClinical

Radiology Volume 63 487-498 (2008)

3 Chotas HG Dobbins III JT and Ravin CE ldquoPrinciples of Digital

Radiography with Large-Area Electronically Readable Detectors A Review of

the Basicsrdquo Radiology Volume 210 Number 3 595-599 (1999)

4 Flynn MJ and Samei E Experimental comparison of noise and resolution for

2k and 4k storage phosphor radiography systems Medical Physics Volume 26

Number 8 1612-1623 (1999)

5 Rong XJ Shaw CC Liu X Lemacks MR and Thompson SK

ldquoComparison of an amorphous siliconcesium iodide flat-panel digital chest

radiography system with screenfilm and computed radiography systems ndash A

contrast-detail phantom studyrdquo Medical Physics Volume 28 Number 11 2328-

2335 (2001)

6 Ranger NT Samei E Dobbins III JT and Ravin CE Measurement of the

detective quantum efficiency in digital detectors consistent with the IEC 62220-1

standard Practical considerations regarding the choice of filter material

Medical Physics Volume 30 Number 7 2305-2311 (2005)

7 Samei E Buhr E Granfors P Vandenbroucke D and Wang X Comparison

of edge analysis techniques for the determination of the MTF of digital

radiographic systems Physics in Medicine and Biology Volume 50 3613-3625

(2005)

8 Samei E and Flynn MJ An experimental comparison of detector performance

for computed radiography systems Medical Physics Volume 29 Number 4 447-

459 (2002)

51

9 Samei E and Flynn MJ An experimental comparison of detector performance

for direct and indirect digital radiography systems Medical Physics Volume 30

Number 4 608-622 (2003)

10 Samei E Ranger NT MacKenzie A Honey ID Dobbins III JT and Ravin

CE Effective DQE (eDQE) and speed of digital radiographic systems An

experimental methodology Medical Physics Volume 36 Number 8 3806-3817

(2009)

11 Samei E Ranger NT MacKenzie A Honey ID Dobbins III JT and Ravin

CE Detector or System Extending the Concept of Detective Quantum

Efficiency to Characterize the Performance of Digital Radiographic Imaging

Systems Radiology Volume 249 Number 3 926-937 (2008)

12 ldquoIEC 62220-1 Medical Electrical Equipment ndash Characteristics of Digital X-Ray

Imaging Devices ndash Part 1 Determination of the Detective Quantum Efficiencyrdquo

International Electrotechnical Commission Geneva Switzerland (2003)

13 Samei E Ranger NT Dobbins III JT and Chen Y Intercomparison of

methods for image quality characterization I Modulation transfer function

Medical Physics Volume 33 Number 5 1454-1465 (2006)

14 Dobbins III JT Samei E Ranger NT and Chen Y Intercomparison of

methods for image quality characterization II Noise power spectrum Medical

Physics Volume 33 Number 5 1466-1475 (2006)

15 Samei E Flynn MJ and Reimann DA A method for measuring the

presampled MTF of digital radiographic systems using an edge test device

Medical Physics Volume 25 Number 1 102-113 (1998)

16 Nagel HD ldquoAluminum equivalence of materials used in diagnostic radiology

and its dependence on beam qualityrdquo Physics in Medicine and Biology Volume

31 Number 12 1381-1399 (1986)

17 Niklason LT Christian BT Niklason LE et al ldquoDigital Tomosynthesis in

Breast Imagingrdquo Radiology Volume 205 399-406 (1997)

18 Gur D ldquoTomosynthesis Potential Clinical Role in Breast Imagingrdquo American

Journal of Roentgenology Volume 189 614-615 (2007)

52

19 Park JM Franken Jr EA Garg M Fajardo LL and Niklason LT ldquoBreast

Tomosynthesis Present Considerations and Future Applicationsrdquo

RadioGraphics Volume 27 S231-S240 (2007)

20 Good WF Abrams GS Catullo VJ Chough DM Ganott MA Hakim

CM and Gur D ldquoDigital Breast Tomosynthesis A Pilot Observer Studyrdquo

American Journal of Roentgenology Volume 190 865-869 (2008)

21 Hu Y-H Zhao W Mertelmeier T and Ludwig J ldquoImage Artifact in Digital

Breast Tomosynthesis and Its Dependence on System and Reconstruction

Parametersrdquo IWDM 2008 LNCS 5116 628-634 (2008)

22 Chen Y Lo JY Ranger NT Samei E Dobbins III JT ldquoMethodology of

NEQ(f) analysis for optimization and comparison of digital breast tomosynthesis

acquisition techniques and reconstruction algorithmsrdquo Proceedings of SPIE

Volume 6510 65101I (2007)

23 Zhao B Zhou J Hu Y-H Mertelmeier T Ludwig J and Zhao W

ldquoExperimental validation of a three-dimensional linear system model for breast

tomosynthesisrdquo Medical Physics Volume 36 Number 1 240-251 (2009)

24 Madhav P Brzymialkiewicz CN Cutler SJ Bowsher JE and Tornai MP

ldquoCharacterizing the MTF in 3D for a Quantized SPECT Camera Having Arbitrary

Trajectoriesrdquo 2005 IEEE Nuclear Science Symposium Conference Record 1722-

1726 (2005)

25 Madhav P McKinley RL Samei E Bowsher JE and Tornai MP ldquoA Novel

Method to Characterize the MTF in 3D for Computed Mammotomographyrdquo

Proceedings of SPIE Volume 6142 61421Y (2006)

26 Hu Y-H Zhao B and Zhao W ldquoImage artifacts in digital breast

tomosynthesis Investigation of the effects of system geometry and

reconstruction parameters using a linear system approachrdquo Medical Physics

Volume 35 Number 12 5242-5252 (2008)

27 Seifert A and Flynn MJ ldquoResolving power of 3D x-ray microtomography

systemsrdquo Proceedings of SPIE Volume 4682 407-413 (2002)

28 Thornton MM and Flynn MJ Measurement of the spatial resolution of a

clinical volumetric computed tomography scanner using a sphere phantom

Proceedings of SPIE Volume 6142 61421Z (2006)

53

29 Baek J Pelc NJ ldquoUse of sphere phantoms to measure the 3D MTF of FDK

reconstructionsrdquo Proceedings of SPIE Volume 7961 79610D (2011)

30 Richard S and Samei E ldquoQuantitative imaging in breast tomosynthesis and CT

Comparison of detection and estimation task performancerdquo Medical Physics

Volume 37 Number 6 2627-2637 (2010)

31 Chen Y Lo JY and Dobbins III JT ldquoImpulse response analysis for several

digital tomosynthesis mammography reconstruction algorithmsrdquo Proceedings of

SPIE Volume 5745 541-549 (2005)

32 Zhao B and Zhao W ldquoThree-dimensional linear system analysis for breast

tomosynthesisrdquo Medical Physics Volume 35 Number 12 5219-5232 (2008)

33 Wu G Mainprize JG Boone JM and Yaffe MJ ldquoEvaluation of scatter

effects on image quality for breast tomosynthesisrdquo Medical Physics Volume 36

Number 10 4425-4432 (2009)

Page 13: Development and Evaluation of 2D and 3D Image Quality ...

xiii

Acknowledgements

I would like to thank Ian Yorkston Mark Purdum and Van Huston of

Carestream Health Inc (Rochester NY) for their help with digital detector

measurements I would also like to thank Olav Christianson Samuel Richard Brian

Harrawood and Max Amurao for their assistance with collecting data and analyzing

results Special thanks go to my committee members for their helpful insights and

suggestions for this thesis Last but not least I want to express deep appreciation for the

support and mentorship provided by my advisor Dr Ehsan Samei

1

I Evaluation of 2D Digital Image Receptors

I1 Introduction

In the past decade many areas of radiological practice have seen a conversion

from screen films to the storage phosphor cassettes of computed radiography (CR) to the

active-matrix flat-panel detectors of digital radiography (DR) Both CR and DR are

digital systems that offer many potential benefits including but not limited to better

image quality wider dynamic range quicker readout lower radiation dose and higher

throughput [1-3] Even with advances in DR technologies such as improved detective

quantum efficiency (DQE) the primary radiographic system of today continues to be CR

A major obstacle to completely accepting DR is the high capital cost of acquiring an

entire system per examination room while also providing capability for portable

applications Recently manufacturers like Carestream Health Fuji and Toshiba have

introduced wireless digital image receptors that can serve as replacements for CR

cassettes As these are new technologies a further investigation to characterize these

detectors is warranted

In the case of radiographic receptors DQE has historically been the metric of

choice [4] because it indicates the ability of the image receptor to convert incident x-ray

photons into useable signal ndash essentially a measure of signal-to-noise ratio (SNR)

efficiency and overall system performance [23] DQE is observed across a range of

spatial frequencies for evaluating how the detector depicts small and large objects [3]

2

DQE metrics have been used in numerous studies to characterize CR phosphor-screens

as well as indirect and direct digital detectors [4-11] The importance of this highly

quantitative metric may be implied by the introduction of a DQE measurement standard

by the International Electrotechnical Commission (IEC) [12]

The standard measurement methodology of the International Electrotechnical

Commission (IEC) pertains to the image quality of 2D digital radiographic detectors

While the IEC formalism is well-developed some of the components that it requires are

not necessarily the most optimal for characterizing DQE This has been explored in

previous studies in terms of filtration material purity beam limitations and region of

interest (ROI) configuration [1314] To reduce the variability in the radiographic output

across various x-ray tubes due to inherent filtration differences the IEC formalism

prescribes specific additional aluminum filtration to attain radiation beam qualities

based on target half value layers (HVL) Achieving and verifying the desired HVL

however requires applying a substantial amount of aluminum at the exit window of the

x-ray tube which is often directed toward the ground This can be a logistical

inconvenience and can increase the risk of damage to the image receptor and

measurement equipment Similar beam qualities on the other hand may be attained

more conveniently using a thinner lighter filtration combination utilizing a higher Z

number material Care is warranted however as a previous study [6] had indicated that

the choice of filtration material could impact the DQE

3

The purpose of this study was two-fold First we aimed to evaluate and compare

two wireless image receptors with a conventional flat-panel detector on the basis of DQE

performance Second we compared DQE results using the IEC-prescribed filtration with

an alternative filtration For the latter an optimum filtration composition was

determined and compared with the IEC filtration on the basis of DQE

I2 Materials and Methods

I2i Detectors

The physical characteristics of the three digital image receptors evaluated in this

study are listed in Table 1 The Pixium 4600 was a conventional digital flat-panel The

DRX-1C and DRX-1 were both wireless digital cassettes that were tethered for the

purposes of this study All detectors were FDA approved and available commercially

Each detector was calibrated according to its manufacturer specifications to correct for

gain offset and bad pixels They were all dedicated for non-clinical laboratory research

purposes and hence could be operated under service settings that permitted acquisition

of raw (ie for processing) images

I2ii Beam Characterization

I2iia X-ray Techniques

All measurements for this study were taken with a well-characterized standard

radiographic system (Super80CP Philips Healthcare Andover MA) The x-ray tube had

an inherent filtration of 27 mm Al Free in-air exposures were measured using

4

Table 1 Physical Characteristics of Digital Image Receptors

Manufacturer Detector

Detector

type

Detector

material

Pixel pitch

(size) Array size

Imaging

area

Trixell

(Moirans France)

Pixium

4600 Indirect

CsITl

(CsI) 0143 mm

3121times3121

4 subpanels 45times45 cm2

Carestream Health Inc

(Rochester NY)

DRX-1C

(wireless) Indirect

CsITl

(CsI) 0139 mm

2560times3072

single panel 35times43 cm2

Carestream Health Inc

(Rochester NY)

DRX-1

(wireless) Indirect

G2O2STb

(GOS) 0139 mm

2560times3072

single panel 35times43 cm2

calibrated radiation meters (Mult-O-Meter Type 407 Unfors Instruments AB Billdal

Sweden) at 183 cm source-to-chamber-distance (SCD) The SCD also corresponded to

same plane as the image receptor surface The x-ray output was made to conform to IEC

beam quality definitions [1215] on the basis of half value layer (HVL) and peak

kilovoltage setting using an aluminum filtration (type-1100 99 purity) and an

alternative filtration consisting of copper (UNS C11000 999 purity) and aluminum

(type-1100 99 purity) The IEC radiation quality numbers (RQA) used in this study are

summarized in Table 2 HVLs were determined by iteratively adding successive

thicknesses of aluminum until reaching reduced exposure levels within a tolerance of

0485-0515 [12] As for the alternative filtration the aluminum was placed downstream

of the copper filter to attenuate characteristic radiation peaks from copper at

approximately 9 keV

I2iib Data Linearization

The system response function was determined for each detector and filtration

combination by acquiring flat-field images at increasing photon fluence until just before

5

Table 2 Beam Qualities and Required Filtrations

IEC Radiation

Quality Number

Peak

kilovoltage

Required

HVL

Required IEC

Filtration

Actual IEC

Filtration

Alternative

Filtration

RQA5 70 kVp 71 mm Al 21 mm Al 21 mm Al 05 mm Cu +

10 mm Al

RQA9 120 kVp 115 mm Al 42 mm Al 40 mm Al 104 mm Cu +

10 mm Al

For reasons of convenience these will be referred to as RQA5A RQA5C RQA9A and RQA9C

saturation levels To avoid the influence of detector backscatter on exposure

measurements a relationship for each filtration was first determined for two radiation

meters A target meter was placed at the central axis and a reference meter was placed at

the edge of the light field (large enough to cover the detectors) The reference meter

served as a surrogate for the target meter to avoid direct exposure measurements in the

plane of the image receptor Exposure relationships were determined before each

measurement set (ie detector and filtration combination) to account for changes in

temperature pressure and humidity The system response function was calculated by

using a regression of ADU (pixel value) versus exposure Images acquired for each

series were then converted to achieve a linear response with zero offset and scaled to

achieve high quantization (adequate dynamic range) Linearization of the detector

responses ensured that zero exposure corresponded to zero pixel value

I2iic Spectral Simulation

The effects of additional filtration on x-ray output spectra were observed with

spectral simulation software (XSPECT V40 Henry Ford Hospital Detroit MI) To more

6

adequately describe the performance of a typical X-ray generator inherent filtration of 3

mm oil 148 mm Pyrex glass and 2 mm aluminum was input into the simulation in

addition to the filters of interest The ideal signal to noise ratio squared or incident

photon fluence per exposure (q) was estimated for each filtration by integrating the

energy-dependent photon counts per unit exposure over all energy bins

I2iii DQE Measurements

The assessment of the linearized images followed the formalism described by

IEC 62220-1 for measuring the DQE [12] For this study the normal exposure level XN

was set at 1 mR to the detector surface as measured at the central axis perpendicular to

the anode-cathode axis

I2iiia Modulation Transfer Function

Spatial resolution was characterized by evaluating the presampled modulation

transfer function (MTF) along directions parallel (vertical) and perpendicular

(horizontal) to the anode-cathode axis using the angled-edge method [6-1013] A radio-

opaque edge test device [7] was placed in the center of the field at a pitch of

approximately 301 (about 2deg) to the axis perpendicular to that being measured as

shown in Figure 1 External lead apertures were not used [6] instead the internal

collimation from the radiographic unit was used to collimate the beam to the detector

area Raw images were acquired of the edge with the normal exposure level XN of 1 mR

at the detector face The procedure of calculating the MTF followed previously described

7

methods [6-1013] The edge spread function (ESF) was determined along lines crossing

the edge of the angled test device The derivative of the ESF was calculated to form the

line spread function (LSF) to which a Hanning filter was applied The MTF was then

calculated as the fast Fourier transform (FFT) of the LSF and normalized at the zero-

frequency axis To conform to IEC guidelines the MTF was resampled into frequency

steps of 005 cyclesmm [12]

Figure 1 MTF images for DRX-1C detector with radio-opaque edge test device with

arrows indicating the horizontal (left) and vertical (right) directions

I2iiib Noise Power Spectrum

Noise amplitude and texture were characterized by determining the normalized

noise power spectrum (NNPS) which was evaluated with flat field exposures at

approximate exposure levels of XN2 XN and 2XN (05 10 and 20 mR) to the image

receptor surface Analysis of the flat-field images followed previously defined methods

[41415] using over 4 million independent pixels with regions of interest (ROIs) of size

8

128x128 The NNPS images were detrended using a quadratic (second order)

background subtraction Small variations in exposure across ROIs were corrected by

normalizing pixel values of each ROI to the mean value in the top left ROI as shown in

Figure 2 The NNPS was then calculated with the 2D FFT including the zero-frequency

axes corresponding to the horizontal and vertical directions The results were then

resampled using 005 frequency bins according to IEC guidelines [12]

Figure 2 NNPS image for DRX-1C detector indicating the top left ROI that served as

the reference for normalizing other ROIs in the image The ROI array was formed

along the directions indicated by the arrows The heel effect visible along the vertical

axis of the detector is an example of small variation in signal across the image

I2iiic DQE Calculation

The DQE was calculated using the following relationship [615]

9

where the frequency-dependent MTF and NNPS were determined as described in

previous sections X was the exposure value in mR corresponding to the NNPS image

and q was the ideal signal to noise ratio squared in units of photonsmiddotmm-2middotmR-1 as

estimated from the spectral simulations

I3 Results

I3i Data Linearization

The detectors in this study provided raw ADU (or pixel) values in a linear scale

The data were converted using the following system conversion function

where Q(ij) is the raw image data m and b are slope and intercept parameters obtained

from linear regression of the system response function and I(ij) is the linearized scaled

data The factor of 1000 was found to scale I(ij) such that the maximum value was a

large 16-bit number Figure 3 shows the original and linearized system responses for the

Pixium 4600 Note that the y-intercepts of the regressions for the linearized responses

are negligible (lt 01) with respect to the slopes a sufficient condition for zero offset

considerations

I3ii Spectral Simulation

The spectral simulations of the IEC filtrations and alternative filtrations indicate

many similarities in their effective energies HVLs and overall shapes of normalized

spectra Results are summarized in Table 3

10

Pixium 4600 Original System

Response

Pixium 4600 Linearized System

Response R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 3 Original (left) and linearized (right) system responses for Pixium 4600 The

linearized system responses were measured from actual images The offsets are small

with respect to the slope sufficient enough for zero-offset conditions

y = 13971x - 13236

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x - 00106Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 13576x + 28292

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

7000

0000 1000 2000 3000 4000 5000

AD

U

Exposure (mR)

y = 99997x - 00067Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0000 1000 2000 3000 4000 5000

AD

U

Exposure (mR)

y = 13644x + 16167Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x + 00044

Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 13845x + 13541

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x - 00177

Rsup2= 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

11

Table 3 Spectral Simulation Results

Beam Quality Filtration

Mean Energy

(kV)

Photon Fluence

(mRmm2)

RQA5A 21 mm Al 5243 259543

RQA5C 05 mm Cu + 10 mm Al 5214 259554

diff 055 0004

RQA9A 40 mm Al 7619 273281

RQA9C 104 mm Cu + 10 mm Al 7579 273964

diff 052 025

Figure 4 Spectral simulations for RQA5 (top) and RQA9 (bottom) conditions Note

the similarities of spectral shapes of the normalized spectra (right) Also note the

significant differences in fluence between filtrations in the simulated spectra (left)

00E+00

50E+04

10E+05

15E+05

20E+05

25E+05

30E+05

35E+05

40E+05

45E+05

0 20 40 60 80

ph

oto

ns

mA

s-1

cm

-2

keV

RQA5 Spectra Comparison

21 mm Al

05 mm Cu + 10 mm Al

00

02

04

06

08

10

12

0 20 40 60 80

keV

RQA5 Normalized Spectra Comparison

21 mm Al

05 mm Cu +

10 mm Al

00E+00

50E+05

10E+06

15E+06

20E+06

25E+06

30E+06

35E+06

40E+06

45E+06

50E+06

0 50 100 150

ph

oto

ns

mA

s-1

cm

-2

keV

RQA9 Spectra Comparison

40 mm Al

104 mm Cu +

10 mm Al

00

02

04

06

08

10

12

0 50 100 150

keV

RQA9 Normalized Spectra Comparison

40 mm Al104 mm Cu + 10 mm Al

12

I3iii Modulation Transfer Function

The limiting spatial resolutions of the systems were indicated by the cutoff

frequencies which were approximately 35 cyclesmm for all three detectors The spatial

resolutions also demonstrated a good degree of isotropy as confirmed by the close

alignment of MTF curves between vertical and horizontal directions differentiated in

Figure 5 by dashed and solid lines respectively The MTF curves for the Pixium 4600

and DRX-1C were nearly equal to each other whereas the DRX-1 MTF curve showed a

more rapid decrease at high frequencies as shown in Figure 6 This difference may be

due to the differences in the inherent optical properties of the scintillating materials

where finer image details are provided by structured CsI more than by granulated GOS

There were no significant differences in MTF curves across beam qualities and filtrations

as shown by the curve comparisons in Figure 6 although the alternative filtration

produced slightly higher MTF curves as seen in Figure 4 Table 4 lists the experimental

specific spatial frequencies for varying levels of MTF

I3iv Noise Power Spectrum

The noise characteristics are indicated by the NNPS curves shown in Figure 7

The noise was similar for both horizontal and vertical directions As exposure increased

the NNPS decreased consistent with the characteristics of Poisson noise describing the

relationship between signal and noise in the presence of increased photon fluence At

13

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 5 MTF results by detector (columns) and beam quality (rows)

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

horizontal

vertical

14

Figure 6 Plots of MTF for RQA5 (top) and RQA9 (bottom) showing the relationships

between detectors (blue red and green) and by filtration (solid and dashed)

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm-1)

MTF

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm-1)

MTF

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

15

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 7 NNPS results by detector (columns) and beam quality (rows)

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

05 mR - horizontal

05 mR - vertical

10 mR - horizontal

10 mR - vertical

20 mR - horizontal

20 mR - vertical

16

Figure 8 Plots of NNPS for RQA5 (top) and RQA9 (bottom) at 1 mR exposure

showing the relationships between detectors (blue red and green) and by filtration

(solid and dashed)

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm-1)

NNPS (1 mR)

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm-1)

NNPS (1 mR)

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

17

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 9 DQE results by detector (columns) and beam quality (rows)

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

05 mR - horizontal

05 mR - vertical

10 mR - horizontal

10 mR - vertical

20 mR - horizontal

20 mR - vertical

18

Figure 10 Plots of DQE for RQA5 (top) and RQA9 (bottom) at 1 mR exposure showing

the relationships between detectors (blue red and green) and by filtration (solid and

dashed)

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm-1)

DQE (1 mR)

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm-1)

DQE

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

19

higher frequencies the NNPS curves of the Pixium 4600 and DRX-1 diverge slightly for

the different directions illustrating increased noise in the readout direction (vertical)

Differences in the noise characteristics were more apparent among detectors as

shown for 1 mR in Figure 8 The NNPS curve for the DRX-1 was higher in magnitude

across the entire frequency range than either the Pixium 4600 or DRX-1C which both

seemed to demonstrate reasonably similar NNPS curves The higher magnitude noise of

the DRX-1 indicates higher relative noise content overall Closer inspection of the NNPS

curves of the Pixium 4600 and DRX-1C detectors in Figure 7 revealed differences in the

spacing between the three exposure levels The gaps between the Pixium 4600 NNPS

curves do not correspond to the factor of two differences between each exposure level

especially at low- to mid- spatial frequencies suggesting a higher level of fixed pattern

noise additional noise with increasing exposure levels due to ineffective gain map

corrections Between filtration schemes the differences in NNPS curves for a given beam

quality were not substantial as shown in Figure 7

I3v Detective Quantum Efficiency

The DQE results are shown in Figure 9 DQE curves across exposure levels were

almost collinear except for Pixium 4600 and in general could be inferred from the

NNPS results Additionally the DQE curves demonstrated a relatively linear response

with spatial frequencies as expected for flat-panel detectors [9] Differences in DQE

among detectors were consistent for the most part with the type of scintillating material

20

As depicted for 1 mR exposure in Figure 10 differences between Pixium 4600 and DRX-

1C DQE curves correspond to the differences in their NNPS curves DRX-1 DQE curves

were consistently lower than either the Pixium 4600 or DRX-1C curves The DQE curves

for the alternative filtration were consistently higher than those for the IEC filtration

and the most noticeable differences were near the zero-frequency axis These effects can

be both attributed to ineffective gain map correction DQE values for 1 mR exposure are

listed in Table 5

I4 Discussion

I4i Comparisons of Detectors

The limiting spatial resolutions of all three detectors were almost exactly the

same considering that their pixel areas were similar in size The decrease in high-

frequency MTF of the DRX-1 compared to the other detectors is probably a result of

increased optical blurring due to the differences in the powdered structure of GOS

versus the needle-like structure of CsI [2] The fact that the DRX-1C and Pixium 4600

have comparable MTFs suggests similar scintillator thicknesses assuming that the

materials were processed alike

The noise of the three detectors demonstrated similar trends with each other The

higher NNPS curves of the DRX-1 detector are probably due also to the scintillating

material and its operation in converting photons into signal The conversion process is

less efficient because of the less favorable stopping power of the GOS compared to CsI

21

especially with higher energy beams The noise of the Pixium 4600 and DRX-1C were

similar except for the spacing between exposures The DRX-1C NNPS curve spacing is

consistent with a factor of two difference in exposure levels but the Pixium 4600 has a

smaller spacing The 05 mR NNPS curve of the Pixium 4600 is closer to that of the 05

mR NNPS curve of the DRX-1C This demonstrates that at higher exposures the Pixium

4600 produces a larger amount of additional noise beyond that explained by simple

stochastic effects It suggests bad performance in the gain map corrections

The DQE results indicate SNR properties of each detector The Pixium 4600 and

DRX-1C are comparable for the most part with the DRX-1C performing slightly better

The DRX-1 as predicted from MTF and NNPS results has a DQE much lower than

either of the previous two This is a reflection of the detection properties as provided by

its scintillator material The DQE of the DRX-1 however is comparable to CR image

receptors [2] The mid-frequency dips in the DQE for Pixium 4600 may be due to the

optical properties of the CsI phosphor layer which can affect the MTF in this manner

Because the DQE is calculated by squaring the MTF this effect at the mid-range

frequencies becomes more apparent The dips may also be further evidence of bad gain

map corrections

I4ii Comparisons of Filtrations

The alternative filtration closely matches for the most part the IEC-based

filtration for MTF NNPS and DQEs at RQA5 but not at RQA9 The filters do not have

22

Table 4 Experimental MTF frequency locations for 1 mR exposure

Detector Filtration

50 MTF

(mm-1)

40 MTF

(mm-1)

30 MTF

(mm-1)

20 MTF

(mm-1)

10 MTF

(mm-1)

Pixium

4600

RQA5A 115 145 185 245 330

RQA5C 125 155 195 250 345

RQA9A 110 175 175 235 330

RQA9C 125 155 195 255 345

DRX-1C

RQA5A 120 150 185 245 350

RQA5C 125 155 195 255 355

RQA9A 120 150 190 250 355

RQA9C 130 160 210 265 360

DRX-1

RQA5A 110 135 160 205 280

RQA5C 110 135 170 210 285

RQA9A 105 125 155 195 270

RQA9C 110 135 165 210 285

Table 5 Estimated DQE values for 1 mR exposure by frequency bins

Detector Filtration DQE(00 mm-1) DQE(10 mm-1) DQE(20 mm-1) DQE(30 mm-1)

Pixium

4600

RQA5A 62 42 32 21

RQA5C 63 45 36 25

RQA9A 41 27 30 13

RQA9C 43 33 27 19

DRX-1C

RQA5A 72 52 35 21

RQA5C 76 55 41 24

RQA9A 49 33 23 15

RQA9C 51 40 31 20

DRX-1

RQA5A 38 24 12 4

RQA5C 38 25 14 5

RQA9A 28 18 9 4

RQA9C 28 19 12 5

DQE values at the zero-frequency axis were estimated by the intercept of a linear fit of low-frequency data

but excluding most proximal to the axis due to large fluctuations Other estimated values are grouped into

frequency bins due to the noisiness of the data

23

considerable differences in the spatial resolutions of the detectors as expected The noise

responses for each filtration were also similar except at the lower frequencies of the

NNPS especially near the zero-frequency axis There observing the NNPS responses at

RQA5 for Pixium 4600 and DRX-1C in Figure 8 the NNPS for the IEC-based filtration

(solid lines) tend to drop faster than the NNPS for the alternative filtration This

subsequently appears as a drop in DQE near the zero-frequency axis shown for those

detectors in Figure 10 Overall as indicated in Table 5 the DQEs of the two filtrations

while similar in trend indicate that the alternative filtration increases the DQE by a

small amount of 3-5 Part of this may be explained by the slightly higher beam

energy which may be more optimal for the energy response of the detectors or may

weigh the pixel responses slightly considering that they are energy-integrating types

The most probable explanation is the gain map correction for the alternative filtration

where fixed pattern noise is more sufficiently reduced

A previous study [6] had discussed the choice of filter material in the analysis of

DQE when achieving the beam conditions defined by IEC It found that visible

nonuniformities were present with the higher purity aluminum filter (type-11999 alloy)

The low frequency mottle in the flat-field images for NPS measurements were also

attributed to structured noise from the grain size in the IEC-based filter with an

attenuating thickness that would reveal nonuniformities The mottle in the current study

was only observable under very narrow windowing as shown in Figure 11 Such low

24

frequency artifacts which are not readily noticeable may also be caused by shading

artifacts inverse square law or even the heel effect A possible method to correct for this

is a subtraction method by taking the average of the flat-field images for an exposure

level and then subtracting that from each of them This would remove nonuniformities

that were not corrected using a suboptimal gain map calibration

Figure 11 DRX1-C NNPS images at 1 mR for RQA5 with IEC filtration (left) and

alternative filtration (right) Images are equally windowed at 45 and leveled at 980

One convenient aspect of the copper and aluminum filtration is that it requires

much less tube current to achieve the same amount of exposure at the detector than the

much thicker aluminum filtration As shown in the non-normalized spectra in Figure 2

the exiting photon fluence exiting the copper and aluminum filtration is substantially

higher than that of the IEC-specified filtration This is due to the smaller total filtration

25

attenuation For extensive DQE analysis multiple sets of exposures may be acquired

before tube overheating becomes a concern

One limitation to the comparison of the two filtrations is that calibration

procedures specified copper and aluminum filtration at 80 kVp (for all detectors 05 mm

Cu and 10 mm Al) This may have influenced the results in favor of the alternative

filtration A further investigation involving the calibration procedures and performing

DQE measurements is encouraged Another factor may be influenced by the fact that the

tests were performed at 70 kVp and 120 kVp different from the recommended

calibration tube potential Clearly there would be differences in the linear attenuation

coefficients of the filters and different energy responses of the detectors themselves This

must be considered when interpreting DQE results The current results support a

previous study decades ago that described filtration of different material types in terms

of an aluminum equivalent [16] The results show that the two filtration schemes are

essentially equivalent when considering beam qualities and spatial resolutions The

NNPS and DQE results can be seen as close enough where their small differences are

insignificant when performing quality assurance tests in a clinical setting Overall our

results indicate that the alternative filtration with copper and aluminum may be more

convenient to use than the current IEC standard filtration

26

I4iii Implications of Wireless DR

This study has shown that wireless image receptors can have the same DQE

performance if not better than conventional flat-panel detectors They operate on the

same basic physical principles the new features offered by the DRX-1C and DRX-1 are

wireless communication with the workstation and electronics packaging technology

The latter feature may pose limitations for these units in terms of possible degradation

in the detectors in routine clinical conditions A consideration for future work would be

to longitudinally track DQE performance of the wireless detectors over time while being

utilized in a clinical environment In the end one must consider risks versus benefits of

choosing portable DR technology over CR one of which includes the cost and fragility

of DR detectors

The DQE performance of one wireless system is just as good as or better than

conventional systems as seen by the DRX-1C performance compared to the Pixium

4600 Wireless systems can also reduce the need for CR readers especially in portable

applications in other regions of the world (eg military hospitals developing countries)

However while DQE performance indicates the physical performance of the detector

system it is still unknown how it relates to observer performance

I5 Conclusions

Two wireless image receptors DRX-1C and DRX-1 were evaluated and

compared with the conventional DR flat-panel Pixium 4600 in terms of DQE

27

performance along with MTF and NNPS performances The detectors have similar

resolution properties although the DRX-1 is inferior at higher spatial frequencies The

NNPS and DQE results both indicate that the DRX-1C is superior to the DRX-1 and

comparable if not better to the Pixium 4600

The results from the filtration comparison indicate no substantial differences

between the IEC-based filtration and the copper-based alternative filtration Only slight

differences were found in the low frequency components of the NNPS and the DQE due

to the inherent nonuniformities of the IEC specified filtration Given the similarity of the

results and low attenuation advantage of the copper and aluminum filter its use is

encouraged

28

II Directional MTF for Breast Tomosynthesis

II1 Introduction

Breast tomosynthesis is an emerging 3D imaging modality that has potential use

for screening and diagnosis of breast cancer Breast tomosynthesis along with other 3D

techniques is preferable to planar imaging methods (eg mammography) because they

reduce anatomical noise by removing overlying structures above and below the plane of

an image slice [17-20] Recent advances in detectors and computer technology have

made digital tomosynthesis feasible

An image quality metric of particular importance in breast tomosynthesis is

spatial resolution Resolution is important to know in order to assess small-detail

structures such as microcalcifications A descriptive metric for characterizing spatial

resolution in the Fourier (or frequency) domain is the modulation transfer function

(MTF) Affected by reconstruction filters [21] the limited angular projections involved in

breast tomosynthesis results in highly anisotropic (or nonuniform) resolution Many

studies have looked only at characterizing the in-plane spatial resolution (ie in an

individual slice) with an elevated angled edge phantom [2223] A few studies have

looked at characterizing a more comprehensive 3D spatial resolution by using a

phantom with angled wires or tubes [24-26] However such studies require precise

mechanical alignment of the phantoms Several studies have explored a method using a

29

sphere phantom for the directional 3D MTF evaluation for microtomography [27] and

multi-slice CT [2829] This method has not yet been extended to breast tomosynthesis

This chapter focuses on breast tomosynthesis because it is highly anisotropic in

spatial resolution and like its predecessor mammography requires high spatial

resolution Additionally breast tomosynthesis acquisitions and reconstructions produce

several types of artifacts The use of a cone-based method using a sphere phantom [28] is

explored to characterize the directional 3D spatial resolution of simulated images from

breast tomosynthesis A technique for removing out-of-plane artifacts of the ESFs for the

in-plane axes is investigated to yield a modified MTF in a method that separates artifact

information from resolution information

II2 Materials and Methods

II2i Image Simulation

Breast tomosynthesis images were simulated by using a virtual imaging system

depicted in Figure 12 A volumetric breast phantom was voxelized as a rectangular mass

of uniform breast equivalent tissue of 4 cm thickness embedded with fifteen evenly

spaced plastic sphere inserts of 12 mm diameter The spheres were placed in a grid

formation within the central plane of the phantom The x-ray fluence was modeled from

a 28 kVp beam incident upon an indirect flat-panel detector with 200 micro m pixel size

Twenty-three projections within an angular range of 44deg were simulated using cascaded

systems analysis to generate characteristic 2D noise and spatial blurring [29] Each

30

projection was simulated to have an exposure of 174 mR with a fluence of 79 times 105

photonsmm-2 A standard filtered backprojection technique based on the Feldkamp

reconstruction algorithm [29] was used to reconstruct the projections and produce a

volumetric dataset with an isotropic voxel size of 200 micro m

Figure 12 Depiction of the virtual image system

II2ii Uncorrected MTF

To enable comparison of multiple spheres the reconstructed volume was

initially homogenized by performing a background subtraction based on a portion of the

volume devoid of spheres The voxel values were rescaled between one and zero to

eliminate negative values

31

The volumetric data were segmented to extract individual regions of interest

(ROIs) each containing a single sphere The ROIs extended along the full range of the z-

axis A thresholded ROI was generated by determining the exterior and interior voxels

relative to the sphere in the ROI The threshold value was set at 45 of the maximum

voxel value prior to thresholding The exterior and interior voxel values were then set to

values of 0 and 1 respectively Using the thresholded volume the center of mass was

calculated to determine the centroid The voxel values from the original ROI were

subsequently tabulated with the associated distances azimuthal angles and polar

angles relative to the centroid

Conical regions were prescribed along the positive and negative directions along

the three major axes extending from the centroid of the sphere as depicted in Figure 13

The axes about which the extent of the cone angle was delineated were defined with

the azimuthal and polar angles

Voxels with centers within the angular range of the cone were considered for

generating the edge spread function (ESF) To improve regularity of the distance

sampling interval the ESF values were rebinned to discrete distances corresponding to a

fraction of the voxel size Only voxels with distances ranging from the voxel size (ie

200 micro m) to the maximum distance were considered The ESFs from multiple spheres

were averaged together for each of the three major axes to produce an averaged ESF

which was further smoothed utilizing a Gaussian filter

32

Figure 13 Example of 30-degree cone prescribed along z axis of the sphere

The resulting ESF was then differentiated using the central difference method to

produce the line spread function (LSF) A Hanning filter with the same length as the LSF

was applied to zero out the tails of the LSF The presampled MTF was subsequently

computed as the amplitude of the Fourier transform of the LSF The MTF was

normalized with respect to the maximum value occurring within the range of the cutoff

frequency Binning size and conical range for the ESF were considered for maximizing

accuracy and minimizing noise of the MTF verified by comparison against the

theoretical MTF as determined in the previous section

II2iii Theoretical Directional MTF

The theoretical 3D MTF was calculated using a priori knowledge of the transfer

function of the virtual imaging system described in the previous section A phantom

was created with a set of point objects in a uniform and noise-free background with the

objects spanning across the volume of the breast [29] Twenty-one realizations were

33

generated from the reconstructed images of the point objects to yield a set of 3D point

spread functions (PSFs) The 3D fast Fourier transform (FFT) was performed for each 3D

PSF and averaged to give an ldquoexpectationrdquo 3D MTF [29] The theoretical directional

MTFs in the three major spatial axes were determined by line profiles along each of the

corresponding spatial frequency axes in the 3D MTF An additional theoretical MTF for

each direction was determined by using the application of conical regions along the axes

in frequency-space to take into account the contributions of MTF information from other

planes

II2iv Modified MTF

The tomosynthesis reconstruction is known to have edge enhancements which

affect the overall MTF by shifting the peaks of the MTF toward the higher frequencies

[23] The presence of this artifact complicates the interpretation of the actual spatial

resolution of the images Several steps were performed to remove the artifact

contribution to the resolution information particularly for the in-plane x and y

directions with the assumption that resolution information was contained immediately

near the edge

For the x-direction averaged ESF only values that were detected to be inside the

edge of the sphere were considered Those values were previously determined via

thresholding for calculating the centroid The ESF information corresponding to these

values was inversed and flipped about the detected edge to produce a symmetric

34

modified ESF The modified MTF was subsequently calculated from this modified ESF

as described in the previous section

For the y-direction averaged ESF an upward trend was found in the initial part

of the ESF This section was detrended with a polynomial fit and subtracted to produce a

flatter curve in that region The resulting detrended ESF was used to calculate the y axis

modified MTF

Figure 14 Photograph of the imaging system with the acrylic sphere phantom

embedded in oil

II2v Preliminary Experimental Validation

A clinical breast tomosynthesis system (Mammomat Inspiration Siemens AG

Munich Germany) was used to perform a preliminary evaluation of the cone-based

MTF technique The phantom for the experiment consisted of a single acrylic ball of 075

in diameter (SmallParts Seattle WA) suspended by a 0029 in diameter plastic filament

35

(Omniflex Zebco Tulsa OK) in an acrylic frame filled up to 4 in with vegetable oil

(Target Brands Inc Minneapolis MN) The system and phantom are shown in Figure

14 Twenty-five projections with an angular range of 44deg were acquired and subsequently

reconstructed to produce a volume with a voxel size of 01times01times10 mm3 The voxels were

reformatted to have an isotropic size of 01 mm The uncorrected ESF LSF and MTF

were calculated as described in the previous section

II3 Results

II3i Reconstruction

The reconstructed volume is shown in Figure 15 Notice the edge enhancement

along the x-direction as indicated by the sharp shadowing artifacts on either side of the

spheres The background was effectively homogenized using the background

subtraction technique This also took account of the curved edges of the breast phantom

With the close spacing of the spheres in the phantom the shadows along the x direction

for the fifteen spheres overlap with each other As the nine centrally located spheres

experience this effect the same way they were used for determining the ESF

A 3D rendering of the ROI containing a sphere shown in Figure 16 indicates the

anisotropic resolution of the reconstruction Note that the sphere is not accurately

reconstructed and has an oblong shape especially along the z axis Cross sectional views

of the ROI also in Figure 16 clearly demonstrate the edge enhancement causing a

shadow artifact in the x direction caused by the incomplete angular sampling of

36

tomosynthesis The sampling also introduces the triangular reconstruction of the sphere

as seen in the x-z plane Note the gradual edge drop-off in the z direction much beyond

the sphere radius

Figure 15 View of the central slice of the breast phantom reconstruction before (top)

and after (bottom) background subtraction The z axis is through the page

37

Figure 16 3D rendering of the ROI volume (left) and cross-sectional views of the most

centrally located sphere with centroid indicated with red circle (right)

II3ii Theoretical MTF

The theoretical MTFs for x y and z directions as determined from the line

profiles of the 3D MTF are shown in Figure 17 The theoretical MTF in the x direction

has a maximum value that is toward higher frequencies Its 10 response occurs at

about 125 cyclesmm which is at 50 of the cutoff frequency The rapid increase from

the zero-frequency intercept to the peak corresponds to the ramp filter used in filtered

backprojection which decreases the weighting of low frequency contributions due to the

incomplete angular sampling of the frequency-space The MTF does not reach a value of

0 at the zero-frequency intercept as it is very difficult to assess the zero-frequency

intercept due to the finite size of the phantom The theoretical MTF in the y direction

peaks at the zero-frequency intercept and reaches 20 proximal to the cutoff frequency

38

The 10 MTF is well beyond the cutoff frequency The theoretical MTF in the z direction

has a rapid drop-off at very low spatial frequencies indicating the lack of resolution in

that dimension

Figure 17 Theoretical 3D MTF results along the three major planes (top) and along x

y and z directions (bottom) Also note that the angular spread seen in the fx-fz plane is

equal to the angular range of 44deg for the acquisition

II3iii Uncorrected MTF

The ESF LSF and MTF using the cone-based method are shown for the x y and

z directions in Figure 18 It was found that a bin size of one-tenth the voxel size (002

mm) and a cone angle of 30deg to establish the ESF were enough to minimize noise and

maximize accuracy in the uncorrected MTFs considering the reasonable comparison of

the shapes of the MTF curves with the theoretical results in Figure 17 The LSFs are

generally noisy because differentiation of the ESF increases the amplitude of the noise

39

The data shown reflect a convolution with a smoothing Gaussian filter which was later

further corrected for in the reported MTF Nevertheless the high frequency components

of the noise are well beyond the MTF cutoff frequency of 25 cyclesmm and do not

impact the MTF results greatly

For the ESF in the x direction the shadow effect evident at the edge of the sphere

is visible as a steep decline followed by an increase Due to the finite distance range

provided by the ROI the ESF beyond the edge did not asymptotically reach the

background value The corresponding LSF demonstrates a low frequency modulation

that is indicated by the shift of 03 cyclesmm in the x direction for the peak of the MTF

The MTF exhibits a zero-frequency intercept that is non-zero unlike the theoretical MTF

and a 10 value at approximately 1 cyclesmm These features may be a direct

consequence of MTF information ldquocontaminationrdquo from y and z directions Furthermore

the ESF in the y direction demonstrates a reasonably shaped curve except for the slight

upward trend within the radius of the sphere which can be attributed to the shadow

artifact overlapping with the sphere volume The associated MTF has a peak shifted by

approximately 01 cyclesmm away from the axis and a 10 MTF occurring at

approximately 15 cyclesmm Both features which are not present in the theoretical

results may also be attributed to contaminant MTF information from x and z directions

The ESF in the z direction has a drop-off that occurs at a small fraction of the cutoff

frequency similar to that demonstrated by the theoretical MTF

40

Uncorrected ESF LSF and MTF

Figure 18 Uncorrected ESF (top) LSF (middle) and MTF (bottom) for x y and z

directions

41

Figure 19 Comparisons of the directional MTFs as calculated by the sphere method

(dashed line) by theoretical line profiles (light-weight line) by theoretical cone

regions (heavy-weight line)

II3iv Comparison of Theoretical and Simulated MTFs

The theoretical MTF results obtained from line profiles through the 3D MTF and

the simulated MTFs using the cone-based technique did not match very well except for

the general shape of the curves It was assumed in the previous section that the cone-

based technique contains information from other planes Figure 19 compares MTFs in

each direction for the two methods described in the methods and an additional method

based on conical regions of the 3D MTF The latter computes the MTF by averaging

contributions of the 3D MTF using the same cone prescription method used to define the

ESFs Comparison of the curves indicate some interesting correlations aside from the

fact that using conical regions with the 3D MTF results produce more noisy MTF results

partly due to the low sampling provided by the theoretical calculations The same

conclusions regarding the z direction MTF can be confirmed regardless of either

theoretical MTF procedures The experimental x direction MTF seems to agree best with

42

the line profile method whereas the y direction MTF agrees better with the cone region

method The fact that the experimental x direction MTF has a drop-off frequency that is

lower than those of either of the theoretical MTFs in Figure 19 suggests that this might

be due to integration of the z-direction in the in-plane slices considering how slices are

essentially averages of z direction information contained within it [33]

II3v Modified MTF for x and y

Modified ESF LSF and MTF curves for x and y directions are shown in Figure

20 The modified ESF and the resulting LSF in the x direction appear symmetric as

expected from the inverse and flip operation of the interior ESF about the detected edge

The modified MTF appears with less variation than the uncorrected MTF and the MTF

peak occurs at the zero-frequency axis The correction yields a 10 MTF at about 15

cyclesmm an improvement from the uncorrected MTF but still distant from the cutoff

frequency The modified ESF in the y direction demonstrates the detrended curve within

the sphere radius after a quadratic polynomial fit The resulting modified MTF still

appears similar to the uncorrected MTF except that the peak now coincides with the

zero-frequency axis For both x and y directions the low response of the modified MTFs

at the higher frequencies suggests that the contamination from other directions is

substantial due to the angular range of the cone

43

Modified ESF LSF and MTF

Figure 20 Modified ESF (top) LSF (middle) and MTF (bottom) for x and y directions

44

II3v Preliminary Experimental Validation

Cross-sections of the reconstructed sphere volume are shown in Figure 21

Relative to the simulation reconstructions the reconstructions of the experimental

phantom images produce lower contrast and higher noise The preliminary results

shown in Figure 22 indicate that our technique can be applied to actual experimental

breast tomosynthesis reconstructions However due to the noise exhibited by the MTF

curves for the x and y directions we did not determine the modified MTFs to separate

resolution and artifact information

Figure 21 Cross sectional views of the experimental sphere image with centroid

indicated with red circle

45

Uncorrected ESF LSF and MTF for Real Image

Figure 22 ESF (top) LSF (middle) and MTF (bottom) of real image for x y

and z directions

46

II4 Discussion

II4i Evaluation of Cone-based Method

The cone-based MTF technique was introduced by Thornton and Flynn [28] for

evaluation of volumetric CT images To utilize this technique as a characterization of a

3D system spatial resolution one must first consider the validity of the assumption of

shift invariance such that the same MTF result may be obtained regardless of the

location of the sphere The study by Zhao et al [23] found that there was no shift

variance for the MTF measurements along the vertical axis but this was only considering

the in-plane resolution along one axis On the other hand this study evaluated the MTF

with images simulated with cascaded systems analysis which includes conditions of

linearity and shift invariance Additionally the MTF was calculated by averaging the

ESF from several spheres in the same volume only after performing a background

subtraction This step was essential to account for the sensitivity of centroid calculations

as well as ensuring symmetric ESFs for opposing axes of the sphere ROIs

The measurement of MTF with the cone-based technique inherently

supersamples the edge of the sphere to increase signal-to-noise-ratio (SNR) of edge

information by averaging the contributions of each voxel to the ESF [713] This method

also takes into account the discrete sampling of the voxels by accounting for various

shifts of the edge in the voxel (also known as the partial volume effect) However using

the curved surface of the sphere phantom to approximate an edge along a given

47

direction naturally leads to contamination of information from other directions aside

from the one of interest Preferably a directional ESF should be created by using a single

radial line but this would limit the available voxels to obtain edge information An ideal

situation theoretically would be to use a larger-sized sphere such that the surface is

nearly flat and perpendicular to the axes of interest This would also permit a reduction

in the angular range of the cone and thus the introduction of out-of-plane information in

the resulting MTF However sphere size is a limitation in breast tomosynthesis and the

use of a large phantom might void the assumption of shift invariance of the spatial

resolution

The choice of a sphere phantom nevertheless may be based on the clinical need

to quickly acquire a single image for MTF evaluation especially for multiple directions

without presenting extra logistical challenges The use of a wire or edge phantom

requires more precise mechanical alignment to achieve the correct set up The edge

phantom [23] would require at least two images to sample all three dimensions In the

case of the three wire phantom [2425] all three dimensions of the frame must be aligned

simultaneously with respect to the axis of rotation A similar situation would be

encountered when considering a cubic phantom with the planes normal to the axis of

interest In contrast to these phantoms the sphere eliminates the need for precise

alignment especially with respect to three spatial dimensions simultaneously A sphere

48

has ideal symmetry in all directions and can be used to evaluate MTF in any arbitrary

direction

This study unlike others [242532] did not explore the effects of physical

parameters such as scatter or contrast on the final MTF result but it demonstrated the

feasibility of using the cone-based method with an actual breast tomosynthesis image of

a sphere phantom as shown in Error Reference source not found and Error Reference

source not found These effects should be addressed in future works A further look

into deriving the principles of comparing the theoretical MTF with the experimental

MTF using the cone-based method is further warranted

II4ii Separation of Artifact and Resolution Information

The focus of this study was to develop a technique for measuring spatial

resolution of tomosynthesis images The intrinsic artifacts from tomosynthesis

reconstructions however lead to uncharacteristic MTFs and possible misinterpretation

of the effective resolution information When considering previous techniques for

calculating the presampled MTF [713152328] the analysis was performed using an

edge or a line to produce the corresponding ESF The resolution information is

essentially contained only along the edge indicated by the need to calculate the LSF In a

way the method of extracting artifact information is to focus the analysis only on the

edge part of the ESF to calculate the modified MTF This will lead to a better

understanding of the limiting size of objects that may be seen in the reconstructed 3D

49

image The presampled MTF without correction should still be analyzed to understand

the entire system response Note that the ESFs attempt to reflect information only at the

detected edge of the sphere

II5 Conclusions

The directional MTF of a simulated breast tomosynthesis reconstruction was

determined by using the cone-based MTF technique demonstrating the feasibility of a

single phantom for MTF evaluation This study further presented methods of analyzing

only the edge information in the ESF to create a modified MTF along in-slice (x and y)

axes It can provide insight into the actual spatial resolution information contained in the

image while separating the resolution information from the information introduced by

artifacts caused by the reconstruction and insufficient volumetric sampling The idea of

separating the resolution and artifacts from the measured ESF are expected to facilitate

the interpretation of MTF measurements in breast tomosynthesis Similar methods may

be applied to characterize the resolution of other 3D imaging modalities

50

References

1 Garmer M Hannigs SP Jaumlger HJ et al ldquoDigital Radiography Versus

Conventional Radiology in Chest Imaging Diagnostic Performance of a Large-

Area Silicon Flat-Panel Detector in a Clinical CT-Controlled Studyrdquo American

Journal of Roentgenology Volume 74 75-80 (2000)

2 Cowen AR Kengyelics SM and Davies AG ldquoSolid-state flat-panel digital

radiography detectors and their physical imaging characteristics rdquoClinical

Radiology Volume 63 487-498 (2008)

3 Chotas HG Dobbins III JT and Ravin CE ldquoPrinciples of Digital

Radiography with Large-Area Electronically Readable Detectors A Review of

the Basicsrdquo Radiology Volume 210 Number 3 595-599 (1999)

4 Flynn MJ and Samei E Experimental comparison of noise and resolution for

2k and 4k storage phosphor radiography systems Medical Physics Volume 26

Number 8 1612-1623 (1999)

5 Rong XJ Shaw CC Liu X Lemacks MR and Thompson SK

ldquoComparison of an amorphous siliconcesium iodide flat-panel digital chest

radiography system with screenfilm and computed radiography systems ndash A

contrast-detail phantom studyrdquo Medical Physics Volume 28 Number 11 2328-

2335 (2001)

6 Ranger NT Samei E Dobbins III JT and Ravin CE Measurement of the

detective quantum efficiency in digital detectors consistent with the IEC 62220-1

standard Practical considerations regarding the choice of filter material

Medical Physics Volume 30 Number 7 2305-2311 (2005)

7 Samei E Buhr E Granfors P Vandenbroucke D and Wang X Comparison

of edge analysis techniques for the determination of the MTF of digital

radiographic systems Physics in Medicine and Biology Volume 50 3613-3625

(2005)

8 Samei E and Flynn MJ An experimental comparison of detector performance

for computed radiography systems Medical Physics Volume 29 Number 4 447-

459 (2002)

51

9 Samei E and Flynn MJ An experimental comparison of detector performance

for direct and indirect digital radiography systems Medical Physics Volume 30

Number 4 608-622 (2003)

10 Samei E Ranger NT MacKenzie A Honey ID Dobbins III JT and Ravin

CE Effective DQE (eDQE) and speed of digital radiographic systems An

experimental methodology Medical Physics Volume 36 Number 8 3806-3817

(2009)

11 Samei E Ranger NT MacKenzie A Honey ID Dobbins III JT and Ravin

CE Detector or System Extending the Concept of Detective Quantum

Efficiency to Characterize the Performance of Digital Radiographic Imaging

Systems Radiology Volume 249 Number 3 926-937 (2008)

12 ldquoIEC 62220-1 Medical Electrical Equipment ndash Characteristics of Digital X-Ray

Imaging Devices ndash Part 1 Determination of the Detective Quantum Efficiencyrdquo

International Electrotechnical Commission Geneva Switzerland (2003)

13 Samei E Ranger NT Dobbins III JT and Chen Y Intercomparison of

methods for image quality characterization I Modulation transfer function

Medical Physics Volume 33 Number 5 1454-1465 (2006)

14 Dobbins III JT Samei E Ranger NT and Chen Y Intercomparison of

methods for image quality characterization II Noise power spectrum Medical

Physics Volume 33 Number 5 1466-1475 (2006)

15 Samei E Flynn MJ and Reimann DA A method for measuring the

presampled MTF of digital radiographic systems using an edge test device

Medical Physics Volume 25 Number 1 102-113 (1998)

16 Nagel HD ldquoAluminum equivalence of materials used in diagnostic radiology

and its dependence on beam qualityrdquo Physics in Medicine and Biology Volume

31 Number 12 1381-1399 (1986)

17 Niklason LT Christian BT Niklason LE et al ldquoDigital Tomosynthesis in

Breast Imagingrdquo Radiology Volume 205 399-406 (1997)

18 Gur D ldquoTomosynthesis Potential Clinical Role in Breast Imagingrdquo American

Journal of Roentgenology Volume 189 614-615 (2007)

52

19 Park JM Franken Jr EA Garg M Fajardo LL and Niklason LT ldquoBreast

Tomosynthesis Present Considerations and Future Applicationsrdquo

RadioGraphics Volume 27 S231-S240 (2007)

20 Good WF Abrams GS Catullo VJ Chough DM Ganott MA Hakim

CM and Gur D ldquoDigital Breast Tomosynthesis A Pilot Observer Studyrdquo

American Journal of Roentgenology Volume 190 865-869 (2008)

21 Hu Y-H Zhao W Mertelmeier T and Ludwig J ldquoImage Artifact in Digital

Breast Tomosynthesis and Its Dependence on System and Reconstruction

Parametersrdquo IWDM 2008 LNCS 5116 628-634 (2008)

22 Chen Y Lo JY Ranger NT Samei E Dobbins III JT ldquoMethodology of

NEQ(f) analysis for optimization and comparison of digital breast tomosynthesis

acquisition techniques and reconstruction algorithmsrdquo Proceedings of SPIE

Volume 6510 65101I (2007)

23 Zhao B Zhou J Hu Y-H Mertelmeier T Ludwig J and Zhao W

ldquoExperimental validation of a three-dimensional linear system model for breast

tomosynthesisrdquo Medical Physics Volume 36 Number 1 240-251 (2009)

24 Madhav P Brzymialkiewicz CN Cutler SJ Bowsher JE and Tornai MP

ldquoCharacterizing the MTF in 3D for a Quantized SPECT Camera Having Arbitrary

Trajectoriesrdquo 2005 IEEE Nuclear Science Symposium Conference Record 1722-

1726 (2005)

25 Madhav P McKinley RL Samei E Bowsher JE and Tornai MP ldquoA Novel

Method to Characterize the MTF in 3D for Computed Mammotomographyrdquo

Proceedings of SPIE Volume 6142 61421Y (2006)

26 Hu Y-H Zhao B and Zhao W ldquoImage artifacts in digital breast

tomosynthesis Investigation of the effects of system geometry and

reconstruction parameters using a linear system approachrdquo Medical Physics

Volume 35 Number 12 5242-5252 (2008)

27 Seifert A and Flynn MJ ldquoResolving power of 3D x-ray microtomography

systemsrdquo Proceedings of SPIE Volume 4682 407-413 (2002)

28 Thornton MM and Flynn MJ Measurement of the spatial resolution of a

clinical volumetric computed tomography scanner using a sphere phantom

Proceedings of SPIE Volume 6142 61421Z (2006)

53

29 Baek J Pelc NJ ldquoUse of sphere phantoms to measure the 3D MTF of FDK

reconstructionsrdquo Proceedings of SPIE Volume 7961 79610D (2011)

30 Richard S and Samei E ldquoQuantitative imaging in breast tomosynthesis and CT

Comparison of detection and estimation task performancerdquo Medical Physics

Volume 37 Number 6 2627-2637 (2010)

31 Chen Y Lo JY and Dobbins III JT ldquoImpulse response analysis for several

digital tomosynthesis mammography reconstruction algorithmsrdquo Proceedings of

SPIE Volume 5745 541-549 (2005)

32 Zhao B and Zhao W ldquoThree-dimensional linear system analysis for breast

tomosynthesisrdquo Medical Physics Volume 35 Number 12 5219-5232 (2008)

33 Wu G Mainprize JG Boone JM and Yaffe MJ ldquoEvaluation of scatter

effects on image quality for breast tomosynthesisrdquo Medical Physics Volume 36

Number 10 4425-4432 (2009)

Page 14: Development and Evaluation of 2D and 3D Image Quality ...

1

I Evaluation of 2D Digital Image Receptors

I1 Introduction

In the past decade many areas of radiological practice have seen a conversion

from screen films to the storage phosphor cassettes of computed radiography (CR) to the

active-matrix flat-panel detectors of digital radiography (DR) Both CR and DR are

digital systems that offer many potential benefits including but not limited to better

image quality wider dynamic range quicker readout lower radiation dose and higher

throughput [1-3] Even with advances in DR technologies such as improved detective

quantum efficiency (DQE) the primary radiographic system of today continues to be CR

A major obstacle to completely accepting DR is the high capital cost of acquiring an

entire system per examination room while also providing capability for portable

applications Recently manufacturers like Carestream Health Fuji and Toshiba have

introduced wireless digital image receptors that can serve as replacements for CR

cassettes As these are new technologies a further investigation to characterize these

detectors is warranted

In the case of radiographic receptors DQE has historically been the metric of

choice [4] because it indicates the ability of the image receptor to convert incident x-ray

photons into useable signal ndash essentially a measure of signal-to-noise ratio (SNR)

efficiency and overall system performance [23] DQE is observed across a range of

spatial frequencies for evaluating how the detector depicts small and large objects [3]

2

DQE metrics have been used in numerous studies to characterize CR phosphor-screens

as well as indirect and direct digital detectors [4-11] The importance of this highly

quantitative metric may be implied by the introduction of a DQE measurement standard

by the International Electrotechnical Commission (IEC) [12]

The standard measurement methodology of the International Electrotechnical

Commission (IEC) pertains to the image quality of 2D digital radiographic detectors

While the IEC formalism is well-developed some of the components that it requires are

not necessarily the most optimal for characterizing DQE This has been explored in

previous studies in terms of filtration material purity beam limitations and region of

interest (ROI) configuration [1314] To reduce the variability in the radiographic output

across various x-ray tubes due to inherent filtration differences the IEC formalism

prescribes specific additional aluminum filtration to attain radiation beam qualities

based on target half value layers (HVL) Achieving and verifying the desired HVL

however requires applying a substantial amount of aluminum at the exit window of the

x-ray tube which is often directed toward the ground This can be a logistical

inconvenience and can increase the risk of damage to the image receptor and

measurement equipment Similar beam qualities on the other hand may be attained

more conveniently using a thinner lighter filtration combination utilizing a higher Z

number material Care is warranted however as a previous study [6] had indicated that

the choice of filtration material could impact the DQE

3

The purpose of this study was two-fold First we aimed to evaluate and compare

two wireless image receptors with a conventional flat-panel detector on the basis of DQE

performance Second we compared DQE results using the IEC-prescribed filtration with

an alternative filtration For the latter an optimum filtration composition was

determined and compared with the IEC filtration on the basis of DQE

I2 Materials and Methods

I2i Detectors

The physical characteristics of the three digital image receptors evaluated in this

study are listed in Table 1 The Pixium 4600 was a conventional digital flat-panel The

DRX-1C and DRX-1 were both wireless digital cassettes that were tethered for the

purposes of this study All detectors were FDA approved and available commercially

Each detector was calibrated according to its manufacturer specifications to correct for

gain offset and bad pixels They were all dedicated for non-clinical laboratory research

purposes and hence could be operated under service settings that permitted acquisition

of raw (ie for processing) images

I2ii Beam Characterization

I2iia X-ray Techniques

All measurements for this study were taken with a well-characterized standard

radiographic system (Super80CP Philips Healthcare Andover MA) The x-ray tube had

an inherent filtration of 27 mm Al Free in-air exposures were measured using

4

Table 1 Physical Characteristics of Digital Image Receptors

Manufacturer Detector

Detector

type

Detector

material

Pixel pitch

(size) Array size

Imaging

area

Trixell

(Moirans France)

Pixium

4600 Indirect

CsITl

(CsI) 0143 mm

3121times3121

4 subpanels 45times45 cm2

Carestream Health Inc

(Rochester NY)

DRX-1C

(wireless) Indirect

CsITl

(CsI) 0139 mm

2560times3072

single panel 35times43 cm2

Carestream Health Inc

(Rochester NY)

DRX-1

(wireless) Indirect

G2O2STb

(GOS) 0139 mm

2560times3072

single panel 35times43 cm2

calibrated radiation meters (Mult-O-Meter Type 407 Unfors Instruments AB Billdal

Sweden) at 183 cm source-to-chamber-distance (SCD) The SCD also corresponded to

same plane as the image receptor surface The x-ray output was made to conform to IEC

beam quality definitions [1215] on the basis of half value layer (HVL) and peak

kilovoltage setting using an aluminum filtration (type-1100 99 purity) and an

alternative filtration consisting of copper (UNS C11000 999 purity) and aluminum

(type-1100 99 purity) The IEC radiation quality numbers (RQA) used in this study are

summarized in Table 2 HVLs were determined by iteratively adding successive

thicknesses of aluminum until reaching reduced exposure levels within a tolerance of

0485-0515 [12] As for the alternative filtration the aluminum was placed downstream

of the copper filter to attenuate characteristic radiation peaks from copper at

approximately 9 keV

I2iib Data Linearization

The system response function was determined for each detector and filtration

combination by acquiring flat-field images at increasing photon fluence until just before

5

Table 2 Beam Qualities and Required Filtrations

IEC Radiation

Quality Number

Peak

kilovoltage

Required

HVL

Required IEC

Filtration

Actual IEC

Filtration

Alternative

Filtration

RQA5 70 kVp 71 mm Al 21 mm Al 21 mm Al 05 mm Cu +

10 mm Al

RQA9 120 kVp 115 mm Al 42 mm Al 40 mm Al 104 mm Cu +

10 mm Al

For reasons of convenience these will be referred to as RQA5A RQA5C RQA9A and RQA9C

saturation levels To avoid the influence of detector backscatter on exposure

measurements a relationship for each filtration was first determined for two radiation

meters A target meter was placed at the central axis and a reference meter was placed at

the edge of the light field (large enough to cover the detectors) The reference meter

served as a surrogate for the target meter to avoid direct exposure measurements in the

plane of the image receptor Exposure relationships were determined before each

measurement set (ie detector and filtration combination) to account for changes in

temperature pressure and humidity The system response function was calculated by

using a regression of ADU (pixel value) versus exposure Images acquired for each

series were then converted to achieve a linear response with zero offset and scaled to

achieve high quantization (adequate dynamic range) Linearization of the detector

responses ensured that zero exposure corresponded to zero pixel value

I2iic Spectral Simulation

The effects of additional filtration on x-ray output spectra were observed with

spectral simulation software (XSPECT V40 Henry Ford Hospital Detroit MI) To more

6

adequately describe the performance of a typical X-ray generator inherent filtration of 3

mm oil 148 mm Pyrex glass and 2 mm aluminum was input into the simulation in

addition to the filters of interest The ideal signal to noise ratio squared or incident

photon fluence per exposure (q) was estimated for each filtration by integrating the

energy-dependent photon counts per unit exposure over all energy bins

I2iii DQE Measurements

The assessment of the linearized images followed the formalism described by

IEC 62220-1 for measuring the DQE [12] For this study the normal exposure level XN

was set at 1 mR to the detector surface as measured at the central axis perpendicular to

the anode-cathode axis

I2iiia Modulation Transfer Function

Spatial resolution was characterized by evaluating the presampled modulation

transfer function (MTF) along directions parallel (vertical) and perpendicular

(horizontal) to the anode-cathode axis using the angled-edge method [6-1013] A radio-

opaque edge test device [7] was placed in the center of the field at a pitch of

approximately 301 (about 2deg) to the axis perpendicular to that being measured as

shown in Figure 1 External lead apertures were not used [6] instead the internal

collimation from the radiographic unit was used to collimate the beam to the detector

area Raw images were acquired of the edge with the normal exposure level XN of 1 mR

at the detector face The procedure of calculating the MTF followed previously described

7

methods [6-1013] The edge spread function (ESF) was determined along lines crossing

the edge of the angled test device The derivative of the ESF was calculated to form the

line spread function (LSF) to which a Hanning filter was applied The MTF was then

calculated as the fast Fourier transform (FFT) of the LSF and normalized at the zero-

frequency axis To conform to IEC guidelines the MTF was resampled into frequency

steps of 005 cyclesmm [12]

Figure 1 MTF images for DRX-1C detector with radio-opaque edge test device with

arrows indicating the horizontal (left) and vertical (right) directions

I2iiib Noise Power Spectrum

Noise amplitude and texture were characterized by determining the normalized

noise power spectrum (NNPS) which was evaluated with flat field exposures at

approximate exposure levels of XN2 XN and 2XN (05 10 and 20 mR) to the image

receptor surface Analysis of the flat-field images followed previously defined methods

[41415] using over 4 million independent pixels with regions of interest (ROIs) of size

8

128x128 The NNPS images were detrended using a quadratic (second order)

background subtraction Small variations in exposure across ROIs were corrected by

normalizing pixel values of each ROI to the mean value in the top left ROI as shown in

Figure 2 The NNPS was then calculated with the 2D FFT including the zero-frequency

axes corresponding to the horizontal and vertical directions The results were then

resampled using 005 frequency bins according to IEC guidelines [12]

Figure 2 NNPS image for DRX-1C detector indicating the top left ROI that served as

the reference for normalizing other ROIs in the image The ROI array was formed

along the directions indicated by the arrows The heel effect visible along the vertical

axis of the detector is an example of small variation in signal across the image

I2iiic DQE Calculation

The DQE was calculated using the following relationship [615]

9

where the frequency-dependent MTF and NNPS were determined as described in

previous sections X was the exposure value in mR corresponding to the NNPS image

and q was the ideal signal to noise ratio squared in units of photonsmiddotmm-2middotmR-1 as

estimated from the spectral simulations

I3 Results

I3i Data Linearization

The detectors in this study provided raw ADU (or pixel) values in a linear scale

The data were converted using the following system conversion function

where Q(ij) is the raw image data m and b are slope and intercept parameters obtained

from linear regression of the system response function and I(ij) is the linearized scaled

data The factor of 1000 was found to scale I(ij) such that the maximum value was a

large 16-bit number Figure 3 shows the original and linearized system responses for the

Pixium 4600 Note that the y-intercepts of the regressions for the linearized responses

are negligible (lt 01) with respect to the slopes a sufficient condition for zero offset

considerations

I3ii Spectral Simulation

The spectral simulations of the IEC filtrations and alternative filtrations indicate

many similarities in their effective energies HVLs and overall shapes of normalized

spectra Results are summarized in Table 3

10

Pixium 4600 Original System

Response

Pixium 4600 Linearized System

Response R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 3 Original (left) and linearized (right) system responses for Pixium 4600 The

linearized system responses were measured from actual images The offsets are small

with respect to the slope sufficient enough for zero-offset conditions

y = 13971x - 13236

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x - 00106Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 13576x + 28292

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

7000

0000 1000 2000 3000 4000 5000

AD

U

Exposure (mR)

y = 99997x - 00067Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0000 1000 2000 3000 4000 5000

AD

U

Exposure (mR)

y = 13644x + 16167Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x + 00044

Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 13845x + 13541

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x - 00177

Rsup2= 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

11

Table 3 Spectral Simulation Results

Beam Quality Filtration

Mean Energy

(kV)

Photon Fluence

(mRmm2)

RQA5A 21 mm Al 5243 259543

RQA5C 05 mm Cu + 10 mm Al 5214 259554

diff 055 0004

RQA9A 40 mm Al 7619 273281

RQA9C 104 mm Cu + 10 mm Al 7579 273964

diff 052 025

Figure 4 Spectral simulations for RQA5 (top) and RQA9 (bottom) conditions Note

the similarities of spectral shapes of the normalized spectra (right) Also note the

significant differences in fluence between filtrations in the simulated spectra (left)

00E+00

50E+04

10E+05

15E+05

20E+05

25E+05

30E+05

35E+05

40E+05

45E+05

0 20 40 60 80

ph

oto

ns

mA

s-1

cm

-2

keV

RQA5 Spectra Comparison

21 mm Al

05 mm Cu + 10 mm Al

00

02

04

06

08

10

12

0 20 40 60 80

keV

RQA5 Normalized Spectra Comparison

21 mm Al

05 mm Cu +

10 mm Al

00E+00

50E+05

10E+06

15E+06

20E+06

25E+06

30E+06

35E+06

40E+06

45E+06

50E+06

0 50 100 150

ph

oto

ns

mA

s-1

cm

-2

keV

RQA9 Spectra Comparison

40 mm Al

104 mm Cu +

10 mm Al

00

02

04

06

08

10

12

0 50 100 150

keV

RQA9 Normalized Spectra Comparison

40 mm Al104 mm Cu + 10 mm Al

12

I3iii Modulation Transfer Function

The limiting spatial resolutions of the systems were indicated by the cutoff

frequencies which were approximately 35 cyclesmm for all three detectors The spatial

resolutions also demonstrated a good degree of isotropy as confirmed by the close

alignment of MTF curves between vertical and horizontal directions differentiated in

Figure 5 by dashed and solid lines respectively The MTF curves for the Pixium 4600

and DRX-1C were nearly equal to each other whereas the DRX-1 MTF curve showed a

more rapid decrease at high frequencies as shown in Figure 6 This difference may be

due to the differences in the inherent optical properties of the scintillating materials

where finer image details are provided by structured CsI more than by granulated GOS

There were no significant differences in MTF curves across beam qualities and filtrations

as shown by the curve comparisons in Figure 6 although the alternative filtration

produced slightly higher MTF curves as seen in Figure 4 Table 4 lists the experimental

specific spatial frequencies for varying levels of MTF

I3iv Noise Power Spectrum

The noise characteristics are indicated by the NNPS curves shown in Figure 7

The noise was similar for both horizontal and vertical directions As exposure increased

the NNPS decreased consistent with the characteristics of Poisson noise describing the

relationship between signal and noise in the presence of increased photon fluence At

13

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 5 MTF results by detector (columns) and beam quality (rows)

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

horizontal

vertical

14

Figure 6 Plots of MTF for RQA5 (top) and RQA9 (bottom) showing the relationships

between detectors (blue red and green) and by filtration (solid and dashed)

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm-1)

MTF

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm-1)

MTF

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

15

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 7 NNPS results by detector (columns) and beam quality (rows)

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

05 mR - horizontal

05 mR - vertical

10 mR - horizontal

10 mR - vertical

20 mR - horizontal

20 mR - vertical

16

Figure 8 Plots of NNPS for RQA5 (top) and RQA9 (bottom) at 1 mR exposure

showing the relationships between detectors (blue red and green) and by filtration

(solid and dashed)

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm-1)

NNPS (1 mR)

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm-1)

NNPS (1 mR)

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

17

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 9 DQE results by detector (columns) and beam quality (rows)

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

05 mR - horizontal

05 mR - vertical

10 mR - horizontal

10 mR - vertical

20 mR - horizontal

20 mR - vertical

18

Figure 10 Plots of DQE for RQA5 (top) and RQA9 (bottom) at 1 mR exposure showing

the relationships between detectors (blue red and green) and by filtration (solid and

dashed)

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm-1)

DQE (1 mR)

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm-1)

DQE

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

19

higher frequencies the NNPS curves of the Pixium 4600 and DRX-1 diverge slightly for

the different directions illustrating increased noise in the readout direction (vertical)

Differences in the noise characteristics were more apparent among detectors as

shown for 1 mR in Figure 8 The NNPS curve for the DRX-1 was higher in magnitude

across the entire frequency range than either the Pixium 4600 or DRX-1C which both

seemed to demonstrate reasonably similar NNPS curves The higher magnitude noise of

the DRX-1 indicates higher relative noise content overall Closer inspection of the NNPS

curves of the Pixium 4600 and DRX-1C detectors in Figure 7 revealed differences in the

spacing between the three exposure levels The gaps between the Pixium 4600 NNPS

curves do not correspond to the factor of two differences between each exposure level

especially at low- to mid- spatial frequencies suggesting a higher level of fixed pattern

noise additional noise with increasing exposure levels due to ineffective gain map

corrections Between filtration schemes the differences in NNPS curves for a given beam

quality were not substantial as shown in Figure 7

I3v Detective Quantum Efficiency

The DQE results are shown in Figure 9 DQE curves across exposure levels were

almost collinear except for Pixium 4600 and in general could be inferred from the

NNPS results Additionally the DQE curves demonstrated a relatively linear response

with spatial frequencies as expected for flat-panel detectors [9] Differences in DQE

among detectors were consistent for the most part with the type of scintillating material

20

As depicted for 1 mR exposure in Figure 10 differences between Pixium 4600 and DRX-

1C DQE curves correspond to the differences in their NNPS curves DRX-1 DQE curves

were consistently lower than either the Pixium 4600 or DRX-1C curves The DQE curves

for the alternative filtration were consistently higher than those for the IEC filtration

and the most noticeable differences were near the zero-frequency axis These effects can

be both attributed to ineffective gain map correction DQE values for 1 mR exposure are

listed in Table 5

I4 Discussion

I4i Comparisons of Detectors

The limiting spatial resolutions of all three detectors were almost exactly the

same considering that their pixel areas were similar in size The decrease in high-

frequency MTF of the DRX-1 compared to the other detectors is probably a result of

increased optical blurring due to the differences in the powdered structure of GOS

versus the needle-like structure of CsI [2] The fact that the DRX-1C and Pixium 4600

have comparable MTFs suggests similar scintillator thicknesses assuming that the

materials were processed alike

The noise of the three detectors demonstrated similar trends with each other The

higher NNPS curves of the DRX-1 detector are probably due also to the scintillating

material and its operation in converting photons into signal The conversion process is

less efficient because of the less favorable stopping power of the GOS compared to CsI

21

especially with higher energy beams The noise of the Pixium 4600 and DRX-1C were

similar except for the spacing between exposures The DRX-1C NNPS curve spacing is

consistent with a factor of two difference in exposure levels but the Pixium 4600 has a

smaller spacing The 05 mR NNPS curve of the Pixium 4600 is closer to that of the 05

mR NNPS curve of the DRX-1C This demonstrates that at higher exposures the Pixium

4600 produces a larger amount of additional noise beyond that explained by simple

stochastic effects It suggests bad performance in the gain map corrections

The DQE results indicate SNR properties of each detector The Pixium 4600 and

DRX-1C are comparable for the most part with the DRX-1C performing slightly better

The DRX-1 as predicted from MTF and NNPS results has a DQE much lower than

either of the previous two This is a reflection of the detection properties as provided by

its scintillator material The DQE of the DRX-1 however is comparable to CR image

receptors [2] The mid-frequency dips in the DQE for Pixium 4600 may be due to the

optical properties of the CsI phosphor layer which can affect the MTF in this manner

Because the DQE is calculated by squaring the MTF this effect at the mid-range

frequencies becomes more apparent The dips may also be further evidence of bad gain

map corrections

I4ii Comparisons of Filtrations

The alternative filtration closely matches for the most part the IEC-based

filtration for MTF NNPS and DQEs at RQA5 but not at RQA9 The filters do not have

22

Table 4 Experimental MTF frequency locations for 1 mR exposure

Detector Filtration

50 MTF

(mm-1)

40 MTF

(mm-1)

30 MTF

(mm-1)

20 MTF

(mm-1)

10 MTF

(mm-1)

Pixium

4600

RQA5A 115 145 185 245 330

RQA5C 125 155 195 250 345

RQA9A 110 175 175 235 330

RQA9C 125 155 195 255 345

DRX-1C

RQA5A 120 150 185 245 350

RQA5C 125 155 195 255 355

RQA9A 120 150 190 250 355

RQA9C 130 160 210 265 360

DRX-1

RQA5A 110 135 160 205 280

RQA5C 110 135 170 210 285

RQA9A 105 125 155 195 270

RQA9C 110 135 165 210 285

Table 5 Estimated DQE values for 1 mR exposure by frequency bins

Detector Filtration DQE(00 mm-1) DQE(10 mm-1) DQE(20 mm-1) DQE(30 mm-1)

Pixium

4600

RQA5A 62 42 32 21

RQA5C 63 45 36 25

RQA9A 41 27 30 13

RQA9C 43 33 27 19

DRX-1C

RQA5A 72 52 35 21

RQA5C 76 55 41 24

RQA9A 49 33 23 15

RQA9C 51 40 31 20

DRX-1

RQA5A 38 24 12 4

RQA5C 38 25 14 5

RQA9A 28 18 9 4

RQA9C 28 19 12 5

DQE values at the zero-frequency axis were estimated by the intercept of a linear fit of low-frequency data

but excluding most proximal to the axis due to large fluctuations Other estimated values are grouped into

frequency bins due to the noisiness of the data

23

considerable differences in the spatial resolutions of the detectors as expected The noise

responses for each filtration were also similar except at the lower frequencies of the

NNPS especially near the zero-frequency axis There observing the NNPS responses at

RQA5 for Pixium 4600 and DRX-1C in Figure 8 the NNPS for the IEC-based filtration

(solid lines) tend to drop faster than the NNPS for the alternative filtration This

subsequently appears as a drop in DQE near the zero-frequency axis shown for those

detectors in Figure 10 Overall as indicated in Table 5 the DQEs of the two filtrations

while similar in trend indicate that the alternative filtration increases the DQE by a

small amount of 3-5 Part of this may be explained by the slightly higher beam

energy which may be more optimal for the energy response of the detectors or may

weigh the pixel responses slightly considering that they are energy-integrating types

The most probable explanation is the gain map correction for the alternative filtration

where fixed pattern noise is more sufficiently reduced

A previous study [6] had discussed the choice of filter material in the analysis of

DQE when achieving the beam conditions defined by IEC It found that visible

nonuniformities were present with the higher purity aluminum filter (type-11999 alloy)

The low frequency mottle in the flat-field images for NPS measurements were also

attributed to structured noise from the grain size in the IEC-based filter with an

attenuating thickness that would reveal nonuniformities The mottle in the current study

was only observable under very narrow windowing as shown in Figure 11 Such low

24

frequency artifacts which are not readily noticeable may also be caused by shading

artifacts inverse square law or even the heel effect A possible method to correct for this

is a subtraction method by taking the average of the flat-field images for an exposure

level and then subtracting that from each of them This would remove nonuniformities

that were not corrected using a suboptimal gain map calibration

Figure 11 DRX1-C NNPS images at 1 mR for RQA5 with IEC filtration (left) and

alternative filtration (right) Images are equally windowed at 45 and leveled at 980

One convenient aspect of the copper and aluminum filtration is that it requires

much less tube current to achieve the same amount of exposure at the detector than the

much thicker aluminum filtration As shown in the non-normalized spectra in Figure 2

the exiting photon fluence exiting the copper and aluminum filtration is substantially

higher than that of the IEC-specified filtration This is due to the smaller total filtration

25

attenuation For extensive DQE analysis multiple sets of exposures may be acquired

before tube overheating becomes a concern

One limitation to the comparison of the two filtrations is that calibration

procedures specified copper and aluminum filtration at 80 kVp (for all detectors 05 mm

Cu and 10 mm Al) This may have influenced the results in favor of the alternative

filtration A further investigation involving the calibration procedures and performing

DQE measurements is encouraged Another factor may be influenced by the fact that the

tests were performed at 70 kVp and 120 kVp different from the recommended

calibration tube potential Clearly there would be differences in the linear attenuation

coefficients of the filters and different energy responses of the detectors themselves This

must be considered when interpreting DQE results The current results support a

previous study decades ago that described filtration of different material types in terms

of an aluminum equivalent [16] The results show that the two filtration schemes are

essentially equivalent when considering beam qualities and spatial resolutions The

NNPS and DQE results can be seen as close enough where their small differences are

insignificant when performing quality assurance tests in a clinical setting Overall our

results indicate that the alternative filtration with copper and aluminum may be more

convenient to use than the current IEC standard filtration

26

I4iii Implications of Wireless DR

This study has shown that wireless image receptors can have the same DQE

performance if not better than conventional flat-panel detectors They operate on the

same basic physical principles the new features offered by the DRX-1C and DRX-1 are

wireless communication with the workstation and electronics packaging technology

The latter feature may pose limitations for these units in terms of possible degradation

in the detectors in routine clinical conditions A consideration for future work would be

to longitudinally track DQE performance of the wireless detectors over time while being

utilized in a clinical environment In the end one must consider risks versus benefits of

choosing portable DR technology over CR one of which includes the cost and fragility

of DR detectors

The DQE performance of one wireless system is just as good as or better than

conventional systems as seen by the DRX-1C performance compared to the Pixium

4600 Wireless systems can also reduce the need for CR readers especially in portable

applications in other regions of the world (eg military hospitals developing countries)

However while DQE performance indicates the physical performance of the detector

system it is still unknown how it relates to observer performance

I5 Conclusions

Two wireless image receptors DRX-1C and DRX-1 were evaluated and

compared with the conventional DR flat-panel Pixium 4600 in terms of DQE

27

performance along with MTF and NNPS performances The detectors have similar

resolution properties although the DRX-1 is inferior at higher spatial frequencies The

NNPS and DQE results both indicate that the DRX-1C is superior to the DRX-1 and

comparable if not better to the Pixium 4600

The results from the filtration comparison indicate no substantial differences

between the IEC-based filtration and the copper-based alternative filtration Only slight

differences were found in the low frequency components of the NNPS and the DQE due

to the inherent nonuniformities of the IEC specified filtration Given the similarity of the

results and low attenuation advantage of the copper and aluminum filter its use is

encouraged

28

II Directional MTF for Breast Tomosynthesis

II1 Introduction

Breast tomosynthesis is an emerging 3D imaging modality that has potential use

for screening and diagnosis of breast cancer Breast tomosynthesis along with other 3D

techniques is preferable to planar imaging methods (eg mammography) because they

reduce anatomical noise by removing overlying structures above and below the plane of

an image slice [17-20] Recent advances in detectors and computer technology have

made digital tomosynthesis feasible

An image quality metric of particular importance in breast tomosynthesis is

spatial resolution Resolution is important to know in order to assess small-detail

structures such as microcalcifications A descriptive metric for characterizing spatial

resolution in the Fourier (or frequency) domain is the modulation transfer function

(MTF) Affected by reconstruction filters [21] the limited angular projections involved in

breast tomosynthesis results in highly anisotropic (or nonuniform) resolution Many

studies have looked only at characterizing the in-plane spatial resolution (ie in an

individual slice) with an elevated angled edge phantom [2223] A few studies have

looked at characterizing a more comprehensive 3D spatial resolution by using a

phantom with angled wires or tubes [24-26] However such studies require precise

mechanical alignment of the phantoms Several studies have explored a method using a

29

sphere phantom for the directional 3D MTF evaluation for microtomography [27] and

multi-slice CT [2829] This method has not yet been extended to breast tomosynthesis

This chapter focuses on breast tomosynthesis because it is highly anisotropic in

spatial resolution and like its predecessor mammography requires high spatial

resolution Additionally breast tomosynthesis acquisitions and reconstructions produce

several types of artifacts The use of a cone-based method using a sphere phantom [28] is

explored to characterize the directional 3D spatial resolution of simulated images from

breast tomosynthesis A technique for removing out-of-plane artifacts of the ESFs for the

in-plane axes is investigated to yield a modified MTF in a method that separates artifact

information from resolution information

II2 Materials and Methods

II2i Image Simulation

Breast tomosynthesis images were simulated by using a virtual imaging system

depicted in Figure 12 A volumetric breast phantom was voxelized as a rectangular mass

of uniform breast equivalent tissue of 4 cm thickness embedded with fifteen evenly

spaced plastic sphere inserts of 12 mm diameter The spheres were placed in a grid

formation within the central plane of the phantom The x-ray fluence was modeled from

a 28 kVp beam incident upon an indirect flat-panel detector with 200 micro m pixel size

Twenty-three projections within an angular range of 44deg were simulated using cascaded

systems analysis to generate characteristic 2D noise and spatial blurring [29] Each

30

projection was simulated to have an exposure of 174 mR with a fluence of 79 times 105

photonsmm-2 A standard filtered backprojection technique based on the Feldkamp

reconstruction algorithm [29] was used to reconstruct the projections and produce a

volumetric dataset with an isotropic voxel size of 200 micro m

Figure 12 Depiction of the virtual image system

II2ii Uncorrected MTF

To enable comparison of multiple spheres the reconstructed volume was

initially homogenized by performing a background subtraction based on a portion of the

volume devoid of spheres The voxel values were rescaled between one and zero to

eliminate negative values

31

The volumetric data were segmented to extract individual regions of interest

(ROIs) each containing a single sphere The ROIs extended along the full range of the z-

axis A thresholded ROI was generated by determining the exterior and interior voxels

relative to the sphere in the ROI The threshold value was set at 45 of the maximum

voxel value prior to thresholding The exterior and interior voxel values were then set to

values of 0 and 1 respectively Using the thresholded volume the center of mass was

calculated to determine the centroid The voxel values from the original ROI were

subsequently tabulated with the associated distances azimuthal angles and polar

angles relative to the centroid

Conical regions were prescribed along the positive and negative directions along

the three major axes extending from the centroid of the sphere as depicted in Figure 13

The axes about which the extent of the cone angle was delineated were defined with

the azimuthal and polar angles

Voxels with centers within the angular range of the cone were considered for

generating the edge spread function (ESF) To improve regularity of the distance

sampling interval the ESF values were rebinned to discrete distances corresponding to a

fraction of the voxel size Only voxels with distances ranging from the voxel size (ie

200 micro m) to the maximum distance were considered The ESFs from multiple spheres

were averaged together for each of the three major axes to produce an averaged ESF

which was further smoothed utilizing a Gaussian filter

32

Figure 13 Example of 30-degree cone prescribed along z axis of the sphere

The resulting ESF was then differentiated using the central difference method to

produce the line spread function (LSF) A Hanning filter with the same length as the LSF

was applied to zero out the tails of the LSF The presampled MTF was subsequently

computed as the amplitude of the Fourier transform of the LSF The MTF was

normalized with respect to the maximum value occurring within the range of the cutoff

frequency Binning size and conical range for the ESF were considered for maximizing

accuracy and minimizing noise of the MTF verified by comparison against the

theoretical MTF as determined in the previous section

II2iii Theoretical Directional MTF

The theoretical 3D MTF was calculated using a priori knowledge of the transfer

function of the virtual imaging system described in the previous section A phantom

was created with a set of point objects in a uniform and noise-free background with the

objects spanning across the volume of the breast [29] Twenty-one realizations were

33

generated from the reconstructed images of the point objects to yield a set of 3D point

spread functions (PSFs) The 3D fast Fourier transform (FFT) was performed for each 3D

PSF and averaged to give an ldquoexpectationrdquo 3D MTF [29] The theoretical directional

MTFs in the three major spatial axes were determined by line profiles along each of the

corresponding spatial frequency axes in the 3D MTF An additional theoretical MTF for

each direction was determined by using the application of conical regions along the axes

in frequency-space to take into account the contributions of MTF information from other

planes

II2iv Modified MTF

The tomosynthesis reconstruction is known to have edge enhancements which

affect the overall MTF by shifting the peaks of the MTF toward the higher frequencies

[23] The presence of this artifact complicates the interpretation of the actual spatial

resolution of the images Several steps were performed to remove the artifact

contribution to the resolution information particularly for the in-plane x and y

directions with the assumption that resolution information was contained immediately

near the edge

For the x-direction averaged ESF only values that were detected to be inside the

edge of the sphere were considered Those values were previously determined via

thresholding for calculating the centroid The ESF information corresponding to these

values was inversed and flipped about the detected edge to produce a symmetric

34

modified ESF The modified MTF was subsequently calculated from this modified ESF

as described in the previous section

For the y-direction averaged ESF an upward trend was found in the initial part

of the ESF This section was detrended with a polynomial fit and subtracted to produce a

flatter curve in that region The resulting detrended ESF was used to calculate the y axis

modified MTF

Figure 14 Photograph of the imaging system with the acrylic sphere phantom

embedded in oil

II2v Preliminary Experimental Validation

A clinical breast tomosynthesis system (Mammomat Inspiration Siemens AG

Munich Germany) was used to perform a preliminary evaluation of the cone-based

MTF technique The phantom for the experiment consisted of a single acrylic ball of 075

in diameter (SmallParts Seattle WA) suspended by a 0029 in diameter plastic filament

35

(Omniflex Zebco Tulsa OK) in an acrylic frame filled up to 4 in with vegetable oil

(Target Brands Inc Minneapolis MN) The system and phantom are shown in Figure

14 Twenty-five projections with an angular range of 44deg were acquired and subsequently

reconstructed to produce a volume with a voxel size of 01times01times10 mm3 The voxels were

reformatted to have an isotropic size of 01 mm The uncorrected ESF LSF and MTF

were calculated as described in the previous section

II3 Results

II3i Reconstruction

The reconstructed volume is shown in Figure 15 Notice the edge enhancement

along the x-direction as indicated by the sharp shadowing artifacts on either side of the

spheres The background was effectively homogenized using the background

subtraction technique This also took account of the curved edges of the breast phantom

With the close spacing of the spheres in the phantom the shadows along the x direction

for the fifteen spheres overlap with each other As the nine centrally located spheres

experience this effect the same way they were used for determining the ESF

A 3D rendering of the ROI containing a sphere shown in Figure 16 indicates the

anisotropic resolution of the reconstruction Note that the sphere is not accurately

reconstructed and has an oblong shape especially along the z axis Cross sectional views

of the ROI also in Figure 16 clearly demonstrate the edge enhancement causing a

shadow artifact in the x direction caused by the incomplete angular sampling of

36

tomosynthesis The sampling also introduces the triangular reconstruction of the sphere

as seen in the x-z plane Note the gradual edge drop-off in the z direction much beyond

the sphere radius

Figure 15 View of the central slice of the breast phantom reconstruction before (top)

and after (bottom) background subtraction The z axis is through the page

37

Figure 16 3D rendering of the ROI volume (left) and cross-sectional views of the most

centrally located sphere with centroid indicated with red circle (right)

II3ii Theoretical MTF

The theoretical MTFs for x y and z directions as determined from the line

profiles of the 3D MTF are shown in Figure 17 The theoretical MTF in the x direction

has a maximum value that is toward higher frequencies Its 10 response occurs at

about 125 cyclesmm which is at 50 of the cutoff frequency The rapid increase from

the zero-frequency intercept to the peak corresponds to the ramp filter used in filtered

backprojection which decreases the weighting of low frequency contributions due to the

incomplete angular sampling of the frequency-space The MTF does not reach a value of

0 at the zero-frequency intercept as it is very difficult to assess the zero-frequency

intercept due to the finite size of the phantom The theoretical MTF in the y direction

peaks at the zero-frequency intercept and reaches 20 proximal to the cutoff frequency

38

The 10 MTF is well beyond the cutoff frequency The theoretical MTF in the z direction

has a rapid drop-off at very low spatial frequencies indicating the lack of resolution in

that dimension

Figure 17 Theoretical 3D MTF results along the three major planes (top) and along x

y and z directions (bottom) Also note that the angular spread seen in the fx-fz plane is

equal to the angular range of 44deg for the acquisition

II3iii Uncorrected MTF

The ESF LSF and MTF using the cone-based method are shown for the x y and

z directions in Figure 18 It was found that a bin size of one-tenth the voxel size (002

mm) and a cone angle of 30deg to establish the ESF were enough to minimize noise and

maximize accuracy in the uncorrected MTFs considering the reasonable comparison of

the shapes of the MTF curves with the theoretical results in Figure 17 The LSFs are

generally noisy because differentiation of the ESF increases the amplitude of the noise

39

The data shown reflect a convolution with a smoothing Gaussian filter which was later

further corrected for in the reported MTF Nevertheless the high frequency components

of the noise are well beyond the MTF cutoff frequency of 25 cyclesmm and do not

impact the MTF results greatly

For the ESF in the x direction the shadow effect evident at the edge of the sphere

is visible as a steep decline followed by an increase Due to the finite distance range

provided by the ROI the ESF beyond the edge did not asymptotically reach the

background value The corresponding LSF demonstrates a low frequency modulation

that is indicated by the shift of 03 cyclesmm in the x direction for the peak of the MTF

The MTF exhibits a zero-frequency intercept that is non-zero unlike the theoretical MTF

and a 10 value at approximately 1 cyclesmm These features may be a direct

consequence of MTF information ldquocontaminationrdquo from y and z directions Furthermore

the ESF in the y direction demonstrates a reasonably shaped curve except for the slight

upward trend within the radius of the sphere which can be attributed to the shadow

artifact overlapping with the sphere volume The associated MTF has a peak shifted by

approximately 01 cyclesmm away from the axis and a 10 MTF occurring at

approximately 15 cyclesmm Both features which are not present in the theoretical

results may also be attributed to contaminant MTF information from x and z directions

The ESF in the z direction has a drop-off that occurs at a small fraction of the cutoff

frequency similar to that demonstrated by the theoretical MTF

40

Uncorrected ESF LSF and MTF

Figure 18 Uncorrected ESF (top) LSF (middle) and MTF (bottom) for x y and z

directions

41

Figure 19 Comparisons of the directional MTFs as calculated by the sphere method

(dashed line) by theoretical line profiles (light-weight line) by theoretical cone

regions (heavy-weight line)

II3iv Comparison of Theoretical and Simulated MTFs

The theoretical MTF results obtained from line profiles through the 3D MTF and

the simulated MTFs using the cone-based technique did not match very well except for

the general shape of the curves It was assumed in the previous section that the cone-

based technique contains information from other planes Figure 19 compares MTFs in

each direction for the two methods described in the methods and an additional method

based on conical regions of the 3D MTF The latter computes the MTF by averaging

contributions of the 3D MTF using the same cone prescription method used to define the

ESFs Comparison of the curves indicate some interesting correlations aside from the

fact that using conical regions with the 3D MTF results produce more noisy MTF results

partly due to the low sampling provided by the theoretical calculations The same

conclusions regarding the z direction MTF can be confirmed regardless of either

theoretical MTF procedures The experimental x direction MTF seems to agree best with

42

the line profile method whereas the y direction MTF agrees better with the cone region

method The fact that the experimental x direction MTF has a drop-off frequency that is

lower than those of either of the theoretical MTFs in Figure 19 suggests that this might

be due to integration of the z-direction in the in-plane slices considering how slices are

essentially averages of z direction information contained within it [33]

II3v Modified MTF for x and y

Modified ESF LSF and MTF curves for x and y directions are shown in Figure

20 The modified ESF and the resulting LSF in the x direction appear symmetric as

expected from the inverse and flip operation of the interior ESF about the detected edge

The modified MTF appears with less variation than the uncorrected MTF and the MTF

peak occurs at the zero-frequency axis The correction yields a 10 MTF at about 15

cyclesmm an improvement from the uncorrected MTF but still distant from the cutoff

frequency The modified ESF in the y direction demonstrates the detrended curve within

the sphere radius after a quadratic polynomial fit The resulting modified MTF still

appears similar to the uncorrected MTF except that the peak now coincides with the

zero-frequency axis For both x and y directions the low response of the modified MTFs

at the higher frequencies suggests that the contamination from other directions is

substantial due to the angular range of the cone

43

Modified ESF LSF and MTF

Figure 20 Modified ESF (top) LSF (middle) and MTF (bottom) for x and y directions

44

II3v Preliminary Experimental Validation

Cross-sections of the reconstructed sphere volume are shown in Figure 21

Relative to the simulation reconstructions the reconstructions of the experimental

phantom images produce lower contrast and higher noise The preliminary results

shown in Figure 22 indicate that our technique can be applied to actual experimental

breast tomosynthesis reconstructions However due to the noise exhibited by the MTF

curves for the x and y directions we did not determine the modified MTFs to separate

resolution and artifact information

Figure 21 Cross sectional views of the experimental sphere image with centroid

indicated with red circle

45

Uncorrected ESF LSF and MTF for Real Image

Figure 22 ESF (top) LSF (middle) and MTF (bottom) of real image for x y

and z directions

46

II4 Discussion

II4i Evaluation of Cone-based Method

The cone-based MTF technique was introduced by Thornton and Flynn [28] for

evaluation of volumetric CT images To utilize this technique as a characterization of a

3D system spatial resolution one must first consider the validity of the assumption of

shift invariance such that the same MTF result may be obtained regardless of the

location of the sphere The study by Zhao et al [23] found that there was no shift

variance for the MTF measurements along the vertical axis but this was only considering

the in-plane resolution along one axis On the other hand this study evaluated the MTF

with images simulated with cascaded systems analysis which includes conditions of

linearity and shift invariance Additionally the MTF was calculated by averaging the

ESF from several spheres in the same volume only after performing a background

subtraction This step was essential to account for the sensitivity of centroid calculations

as well as ensuring symmetric ESFs for opposing axes of the sphere ROIs

The measurement of MTF with the cone-based technique inherently

supersamples the edge of the sphere to increase signal-to-noise-ratio (SNR) of edge

information by averaging the contributions of each voxel to the ESF [713] This method

also takes into account the discrete sampling of the voxels by accounting for various

shifts of the edge in the voxel (also known as the partial volume effect) However using

the curved surface of the sphere phantom to approximate an edge along a given

47

direction naturally leads to contamination of information from other directions aside

from the one of interest Preferably a directional ESF should be created by using a single

radial line but this would limit the available voxels to obtain edge information An ideal

situation theoretically would be to use a larger-sized sphere such that the surface is

nearly flat and perpendicular to the axes of interest This would also permit a reduction

in the angular range of the cone and thus the introduction of out-of-plane information in

the resulting MTF However sphere size is a limitation in breast tomosynthesis and the

use of a large phantom might void the assumption of shift invariance of the spatial

resolution

The choice of a sphere phantom nevertheless may be based on the clinical need

to quickly acquire a single image for MTF evaluation especially for multiple directions

without presenting extra logistical challenges The use of a wire or edge phantom

requires more precise mechanical alignment to achieve the correct set up The edge

phantom [23] would require at least two images to sample all three dimensions In the

case of the three wire phantom [2425] all three dimensions of the frame must be aligned

simultaneously with respect to the axis of rotation A similar situation would be

encountered when considering a cubic phantom with the planes normal to the axis of

interest In contrast to these phantoms the sphere eliminates the need for precise

alignment especially with respect to three spatial dimensions simultaneously A sphere

48

has ideal symmetry in all directions and can be used to evaluate MTF in any arbitrary

direction

This study unlike others [242532] did not explore the effects of physical

parameters such as scatter or contrast on the final MTF result but it demonstrated the

feasibility of using the cone-based method with an actual breast tomosynthesis image of

a sphere phantom as shown in Error Reference source not found and Error Reference

source not found These effects should be addressed in future works A further look

into deriving the principles of comparing the theoretical MTF with the experimental

MTF using the cone-based method is further warranted

II4ii Separation of Artifact and Resolution Information

The focus of this study was to develop a technique for measuring spatial

resolution of tomosynthesis images The intrinsic artifacts from tomosynthesis

reconstructions however lead to uncharacteristic MTFs and possible misinterpretation

of the effective resolution information When considering previous techniques for

calculating the presampled MTF [713152328] the analysis was performed using an

edge or a line to produce the corresponding ESF The resolution information is

essentially contained only along the edge indicated by the need to calculate the LSF In a

way the method of extracting artifact information is to focus the analysis only on the

edge part of the ESF to calculate the modified MTF This will lead to a better

understanding of the limiting size of objects that may be seen in the reconstructed 3D

49

image The presampled MTF without correction should still be analyzed to understand

the entire system response Note that the ESFs attempt to reflect information only at the

detected edge of the sphere

II5 Conclusions

The directional MTF of a simulated breast tomosynthesis reconstruction was

determined by using the cone-based MTF technique demonstrating the feasibility of a

single phantom for MTF evaluation This study further presented methods of analyzing

only the edge information in the ESF to create a modified MTF along in-slice (x and y)

axes It can provide insight into the actual spatial resolution information contained in the

image while separating the resolution information from the information introduced by

artifacts caused by the reconstruction and insufficient volumetric sampling The idea of

separating the resolution and artifacts from the measured ESF are expected to facilitate

the interpretation of MTF measurements in breast tomosynthesis Similar methods may

be applied to characterize the resolution of other 3D imaging modalities

50

References

1 Garmer M Hannigs SP Jaumlger HJ et al ldquoDigital Radiography Versus

Conventional Radiology in Chest Imaging Diagnostic Performance of a Large-

Area Silicon Flat-Panel Detector in a Clinical CT-Controlled Studyrdquo American

Journal of Roentgenology Volume 74 75-80 (2000)

2 Cowen AR Kengyelics SM and Davies AG ldquoSolid-state flat-panel digital

radiography detectors and their physical imaging characteristics rdquoClinical

Radiology Volume 63 487-498 (2008)

3 Chotas HG Dobbins III JT and Ravin CE ldquoPrinciples of Digital

Radiography with Large-Area Electronically Readable Detectors A Review of

the Basicsrdquo Radiology Volume 210 Number 3 595-599 (1999)

4 Flynn MJ and Samei E Experimental comparison of noise and resolution for

2k and 4k storage phosphor radiography systems Medical Physics Volume 26

Number 8 1612-1623 (1999)

5 Rong XJ Shaw CC Liu X Lemacks MR and Thompson SK

ldquoComparison of an amorphous siliconcesium iodide flat-panel digital chest

radiography system with screenfilm and computed radiography systems ndash A

contrast-detail phantom studyrdquo Medical Physics Volume 28 Number 11 2328-

2335 (2001)

6 Ranger NT Samei E Dobbins III JT and Ravin CE Measurement of the

detective quantum efficiency in digital detectors consistent with the IEC 62220-1

standard Practical considerations regarding the choice of filter material

Medical Physics Volume 30 Number 7 2305-2311 (2005)

7 Samei E Buhr E Granfors P Vandenbroucke D and Wang X Comparison

of edge analysis techniques for the determination of the MTF of digital

radiographic systems Physics in Medicine and Biology Volume 50 3613-3625

(2005)

8 Samei E and Flynn MJ An experimental comparison of detector performance

for computed radiography systems Medical Physics Volume 29 Number 4 447-

459 (2002)

51

9 Samei E and Flynn MJ An experimental comparison of detector performance

for direct and indirect digital radiography systems Medical Physics Volume 30

Number 4 608-622 (2003)

10 Samei E Ranger NT MacKenzie A Honey ID Dobbins III JT and Ravin

CE Effective DQE (eDQE) and speed of digital radiographic systems An

experimental methodology Medical Physics Volume 36 Number 8 3806-3817

(2009)

11 Samei E Ranger NT MacKenzie A Honey ID Dobbins III JT and Ravin

CE Detector or System Extending the Concept of Detective Quantum

Efficiency to Characterize the Performance of Digital Radiographic Imaging

Systems Radiology Volume 249 Number 3 926-937 (2008)

12 ldquoIEC 62220-1 Medical Electrical Equipment ndash Characteristics of Digital X-Ray

Imaging Devices ndash Part 1 Determination of the Detective Quantum Efficiencyrdquo

International Electrotechnical Commission Geneva Switzerland (2003)

13 Samei E Ranger NT Dobbins III JT and Chen Y Intercomparison of

methods for image quality characterization I Modulation transfer function

Medical Physics Volume 33 Number 5 1454-1465 (2006)

14 Dobbins III JT Samei E Ranger NT and Chen Y Intercomparison of

methods for image quality characterization II Noise power spectrum Medical

Physics Volume 33 Number 5 1466-1475 (2006)

15 Samei E Flynn MJ and Reimann DA A method for measuring the

presampled MTF of digital radiographic systems using an edge test device

Medical Physics Volume 25 Number 1 102-113 (1998)

16 Nagel HD ldquoAluminum equivalence of materials used in diagnostic radiology

and its dependence on beam qualityrdquo Physics in Medicine and Biology Volume

31 Number 12 1381-1399 (1986)

17 Niklason LT Christian BT Niklason LE et al ldquoDigital Tomosynthesis in

Breast Imagingrdquo Radiology Volume 205 399-406 (1997)

18 Gur D ldquoTomosynthesis Potential Clinical Role in Breast Imagingrdquo American

Journal of Roentgenology Volume 189 614-615 (2007)

52

19 Park JM Franken Jr EA Garg M Fajardo LL and Niklason LT ldquoBreast

Tomosynthesis Present Considerations and Future Applicationsrdquo

RadioGraphics Volume 27 S231-S240 (2007)

20 Good WF Abrams GS Catullo VJ Chough DM Ganott MA Hakim

CM and Gur D ldquoDigital Breast Tomosynthesis A Pilot Observer Studyrdquo

American Journal of Roentgenology Volume 190 865-869 (2008)

21 Hu Y-H Zhao W Mertelmeier T and Ludwig J ldquoImage Artifact in Digital

Breast Tomosynthesis and Its Dependence on System and Reconstruction

Parametersrdquo IWDM 2008 LNCS 5116 628-634 (2008)

22 Chen Y Lo JY Ranger NT Samei E Dobbins III JT ldquoMethodology of

NEQ(f) analysis for optimization and comparison of digital breast tomosynthesis

acquisition techniques and reconstruction algorithmsrdquo Proceedings of SPIE

Volume 6510 65101I (2007)

23 Zhao B Zhou J Hu Y-H Mertelmeier T Ludwig J and Zhao W

ldquoExperimental validation of a three-dimensional linear system model for breast

tomosynthesisrdquo Medical Physics Volume 36 Number 1 240-251 (2009)

24 Madhav P Brzymialkiewicz CN Cutler SJ Bowsher JE and Tornai MP

ldquoCharacterizing the MTF in 3D for a Quantized SPECT Camera Having Arbitrary

Trajectoriesrdquo 2005 IEEE Nuclear Science Symposium Conference Record 1722-

1726 (2005)

25 Madhav P McKinley RL Samei E Bowsher JE and Tornai MP ldquoA Novel

Method to Characterize the MTF in 3D for Computed Mammotomographyrdquo

Proceedings of SPIE Volume 6142 61421Y (2006)

26 Hu Y-H Zhao B and Zhao W ldquoImage artifacts in digital breast

tomosynthesis Investigation of the effects of system geometry and

reconstruction parameters using a linear system approachrdquo Medical Physics

Volume 35 Number 12 5242-5252 (2008)

27 Seifert A and Flynn MJ ldquoResolving power of 3D x-ray microtomography

systemsrdquo Proceedings of SPIE Volume 4682 407-413 (2002)

28 Thornton MM and Flynn MJ Measurement of the spatial resolution of a

clinical volumetric computed tomography scanner using a sphere phantom

Proceedings of SPIE Volume 6142 61421Z (2006)

53

29 Baek J Pelc NJ ldquoUse of sphere phantoms to measure the 3D MTF of FDK

reconstructionsrdquo Proceedings of SPIE Volume 7961 79610D (2011)

30 Richard S and Samei E ldquoQuantitative imaging in breast tomosynthesis and CT

Comparison of detection and estimation task performancerdquo Medical Physics

Volume 37 Number 6 2627-2637 (2010)

31 Chen Y Lo JY and Dobbins III JT ldquoImpulse response analysis for several

digital tomosynthesis mammography reconstruction algorithmsrdquo Proceedings of

SPIE Volume 5745 541-549 (2005)

32 Zhao B and Zhao W ldquoThree-dimensional linear system analysis for breast

tomosynthesisrdquo Medical Physics Volume 35 Number 12 5219-5232 (2008)

33 Wu G Mainprize JG Boone JM and Yaffe MJ ldquoEvaluation of scatter

effects on image quality for breast tomosynthesisrdquo Medical Physics Volume 36

Number 10 4425-4432 (2009)

Page 15: Development and Evaluation of 2D and 3D Image Quality ...

2

DQE metrics have been used in numerous studies to characterize CR phosphor-screens

as well as indirect and direct digital detectors [4-11] The importance of this highly

quantitative metric may be implied by the introduction of a DQE measurement standard

by the International Electrotechnical Commission (IEC) [12]

The standard measurement methodology of the International Electrotechnical

Commission (IEC) pertains to the image quality of 2D digital radiographic detectors

While the IEC formalism is well-developed some of the components that it requires are

not necessarily the most optimal for characterizing DQE This has been explored in

previous studies in terms of filtration material purity beam limitations and region of

interest (ROI) configuration [1314] To reduce the variability in the radiographic output

across various x-ray tubes due to inherent filtration differences the IEC formalism

prescribes specific additional aluminum filtration to attain radiation beam qualities

based on target half value layers (HVL) Achieving and verifying the desired HVL

however requires applying a substantial amount of aluminum at the exit window of the

x-ray tube which is often directed toward the ground This can be a logistical

inconvenience and can increase the risk of damage to the image receptor and

measurement equipment Similar beam qualities on the other hand may be attained

more conveniently using a thinner lighter filtration combination utilizing a higher Z

number material Care is warranted however as a previous study [6] had indicated that

the choice of filtration material could impact the DQE

3

The purpose of this study was two-fold First we aimed to evaluate and compare

two wireless image receptors with a conventional flat-panel detector on the basis of DQE

performance Second we compared DQE results using the IEC-prescribed filtration with

an alternative filtration For the latter an optimum filtration composition was

determined and compared with the IEC filtration on the basis of DQE

I2 Materials and Methods

I2i Detectors

The physical characteristics of the three digital image receptors evaluated in this

study are listed in Table 1 The Pixium 4600 was a conventional digital flat-panel The

DRX-1C and DRX-1 were both wireless digital cassettes that were tethered for the

purposes of this study All detectors were FDA approved and available commercially

Each detector was calibrated according to its manufacturer specifications to correct for

gain offset and bad pixels They were all dedicated for non-clinical laboratory research

purposes and hence could be operated under service settings that permitted acquisition

of raw (ie for processing) images

I2ii Beam Characterization

I2iia X-ray Techniques

All measurements for this study were taken with a well-characterized standard

radiographic system (Super80CP Philips Healthcare Andover MA) The x-ray tube had

an inherent filtration of 27 mm Al Free in-air exposures were measured using

4

Table 1 Physical Characteristics of Digital Image Receptors

Manufacturer Detector

Detector

type

Detector

material

Pixel pitch

(size) Array size

Imaging

area

Trixell

(Moirans France)

Pixium

4600 Indirect

CsITl

(CsI) 0143 mm

3121times3121

4 subpanels 45times45 cm2

Carestream Health Inc

(Rochester NY)

DRX-1C

(wireless) Indirect

CsITl

(CsI) 0139 mm

2560times3072

single panel 35times43 cm2

Carestream Health Inc

(Rochester NY)

DRX-1

(wireless) Indirect

G2O2STb

(GOS) 0139 mm

2560times3072

single panel 35times43 cm2

calibrated radiation meters (Mult-O-Meter Type 407 Unfors Instruments AB Billdal

Sweden) at 183 cm source-to-chamber-distance (SCD) The SCD also corresponded to

same plane as the image receptor surface The x-ray output was made to conform to IEC

beam quality definitions [1215] on the basis of half value layer (HVL) and peak

kilovoltage setting using an aluminum filtration (type-1100 99 purity) and an

alternative filtration consisting of copper (UNS C11000 999 purity) and aluminum

(type-1100 99 purity) The IEC radiation quality numbers (RQA) used in this study are

summarized in Table 2 HVLs were determined by iteratively adding successive

thicknesses of aluminum until reaching reduced exposure levels within a tolerance of

0485-0515 [12] As for the alternative filtration the aluminum was placed downstream

of the copper filter to attenuate characteristic radiation peaks from copper at

approximately 9 keV

I2iib Data Linearization

The system response function was determined for each detector and filtration

combination by acquiring flat-field images at increasing photon fluence until just before

5

Table 2 Beam Qualities and Required Filtrations

IEC Radiation

Quality Number

Peak

kilovoltage

Required

HVL

Required IEC

Filtration

Actual IEC

Filtration

Alternative

Filtration

RQA5 70 kVp 71 mm Al 21 mm Al 21 mm Al 05 mm Cu +

10 mm Al

RQA9 120 kVp 115 mm Al 42 mm Al 40 mm Al 104 mm Cu +

10 mm Al

For reasons of convenience these will be referred to as RQA5A RQA5C RQA9A and RQA9C

saturation levels To avoid the influence of detector backscatter on exposure

measurements a relationship for each filtration was first determined for two radiation

meters A target meter was placed at the central axis and a reference meter was placed at

the edge of the light field (large enough to cover the detectors) The reference meter

served as a surrogate for the target meter to avoid direct exposure measurements in the

plane of the image receptor Exposure relationships were determined before each

measurement set (ie detector and filtration combination) to account for changes in

temperature pressure and humidity The system response function was calculated by

using a regression of ADU (pixel value) versus exposure Images acquired for each

series were then converted to achieve a linear response with zero offset and scaled to

achieve high quantization (adequate dynamic range) Linearization of the detector

responses ensured that zero exposure corresponded to zero pixel value

I2iic Spectral Simulation

The effects of additional filtration on x-ray output spectra were observed with

spectral simulation software (XSPECT V40 Henry Ford Hospital Detroit MI) To more

6

adequately describe the performance of a typical X-ray generator inherent filtration of 3

mm oil 148 mm Pyrex glass and 2 mm aluminum was input into the simulation in

addition to the filters of interest The ideal signal to noise ratio squared or incident

photon fluence per exposure (q) was estimated for each filtration by integrating the

energy-dependent photon counts per unit exposure over all energy bins

I2iii DQE Measurements

The assessment of the linearized images followed the formalism described by

IEC 62220-1 for measuring the DQE [12] For this study the normal exposure level XN

was set at 1 mR to the detector surface as measured at the central axis perpendicular to

the anode-cathode axis

I2iiia Modulation Transfer Function

Spatial resolution was characterized by evaluating the presampled modulation

transfer function (MTF) along directions parallel (vertical) and perpendicular

(horizontal) to the anode-cathode axis using the angled-edge method [6-1013] A radio-

opaque edge test device [7] was placed in the center of the field at a pitch of

approximately 301 (about 2deg) to the axis perpendicular to that being measured as

shown in Figure 1 External lead apertures were not used [6] instead the internal

collimation from the radiographic unit was used to collimate the beam to the detector

area Raw images were acquired of the edge with the normal exposure level XN of 1 mR

at the detector face The procedure of calculating the MTF followed previously described

7

methods [6-1013] The edge spread function (ESF) was determined along lines crossing

the edge of the angled test device The derivative of the ESF was calculated to form the

line spread function (LSF) to which a Hanning filter was applied The MTF was then

calculated as the fast Fourier transform (FFT) of the LSF and normalized at the zero-

frequency axis To conform to IEC guidelines the MTF was resampled into frequency

steps of 005 cyclesmm [12]

Figure 1 MTF images for DRX-1C detector with radio-opaque edge test device with

arrows indicating the horizontal (left) and vertical (right) directions

I2iiib Noise Power Spectrum

Noise amplitude and texture were characterized by determining the normalized

noise power spectrum (NNPS) which was evaluated with flat field exposures at

approximate exposure levels of XN2 XN and 2XN (05 10 and 20 mR) to the image

receptor surface Analysis of the flat-field images followed previously defined methods

[41415] using over 4 million independent pixels with regions of interest (ROIs) of size

8

128x128 The NNPS images were detrended using a quadratic (second order)

background subtraction Small variations in exposure across ROIs were corrected by

normalizing pixel values of each ROI to the mean value in the top left ROI as shown in

Figure 2 The NNPS was then calculated with the 2D FFT including the zero-frequency

axes corresponding to the horizontal and vertical directions The results were then

resampled using 005 frequency bins according to IEC guidelines [12]

Figure 2 NNPS image for DRX-1C detector indicating the top left ROI that served as

the reference for normalizing other ROIs in the image The ROI array was formed

along the directions indicated by the arrows The heel effect visible along the vertical

axis of the detector is an example of small variation in signal across the image

I2iiic DQE Calculation

The DQE was calculated using the following relationship [615]

9

where the frequency-dependent MTF and NNPS were determined as described in

previous sections X was the exposure value in mR corresponding to the NNPS image

and q was the ideal signal to noise ratio squared in units of photonsmiddotmm-2middotmR-1 as

estimated from the spectral simulations

I3 Results

I3i Data Linearization

The detectors in this study provided raw ADU (or pixel) values in a linear scale

The data were converted using the following system conversion function

where Q(ij) is the raw image data m and b are slope and intercept parameters obtained

from linear regression of the system response function and I(ij) is the linearized scaled

data The factor of 1000 was found to scale I(ij) such that the maximum value was a

large 16-bit number Figure 3 shows the original and linearized system responses for the

Pixium 4600 Note that the y-intercepts of the regressions for the linearized responses

are negligible (lt 01) with respect to the slopes a sufficient condition for zero offset

considerations

I3ii Spectral Simulation

The spectral simulations of the IEC filtrations and alternative filtrations indicate

many similarities in their effective energies HVLs and overall shapes of normalized

spectra Results are summarized in Table 3

10

Pixium 4600 Original System

Response

Pixium 4600 Linearized System

Response R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 3 Original (left) and linearized (right) system responses for Pixium 4600 The

linearized system responses were measured from actual images The offsets are small

with respect to the slope sufficient enough for zero-offset conditions

y = 13971x - 13236

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x - 00106Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 13576x + 28292

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

7000

0000 1000 2000 3000 4000 5000

AD

U

Exposure (mR)

y = 99997x - 00067Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0000 1000 2000 3000 4000 5000

AD

U

Exposure (mR)

y = 13644x + 16167Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x + 00044

Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 13845x + 13541

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x - 00177

Rsup2= 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

11

Table 3 Spectral Simulation Results

Beam Quality Filtration

Mean Energy

(kV)

Photon Fluence

(mRmm2)

RQA5A 21 mm Al 5243 259543

RQA5C 05 mm Cu + 10 mm Al 5214 259554

diff 055 0004

RQA9A 40 mm Al 7619 273281

RQA9C 104 mm Cu + 10 mm Al 7579 273964

diff 052 025

Figure 4 Spectral simulations for RQA5 (top) and RQA9 (bottom) conditions Note

the similarities of spectral shapes of the normalized spectra (right) Also note the

significant differences in fluence between filtrations in the simulated spectra (left)

00E+00

50E+04

10E+05

15E+05

20E+05

25E+05

30E+05

35E+05

40E+05

45E+05

0 20 40 60 80

ph

oto

ns

mA

s-1

cm

-2

keV

RQA5 Spectra Comparison

21 mm Al

05 mm Cu + 10 mm Al

00

02

04

06

08

10

12

0 20 40 60 80

keV

RQA5 Normalized Spectra Comparison

21 mm Al

05 mm Cu +

10 mm Al

00E+00

50E+05

10E+06

15E+06

20E+06

25E+06

30E+06

35E+06

40E+06

45E+06

50E+06

0 50 100 150

ph

oto

ns

mA

s-1

cm

-2

keV

RQA9 Spectra Comparison

40 mm Al

104 mm Cu +

10 mm Al

00

02

04

06

08

10

12

0 50 100 150

keV

RQA9 Normalized Spectra Comparison

40 mm Al104 mm Cu + 10 mm Al

12

I3iii Modulation Transfer Function

The limiting spatial resolutions of the systems were indicated by the cutoff

frequencies which were approximately 35 cyclesmm for all three detectors The spatial

resolutions also demonstrated a good degree of isotropy as confirmed by the close

alignment of MTF curves between vertical and horizontal directions differentiated in

Figure 5 by dashed and solid lines respectively The MTF curves for the Pixium 4600

and DRX-1C were nearly equal to each other whereas the DRX-1 MTF curve showed a

more rapid decrease at high frequencies as shown in Figure 6 This difference may be

due to the differences in the inherent optical properties of the scintillating materials

where finer image details are provided by structured CsI more than by granulated GOS

There were no significant differences in MTF curves across beam qualities and filtrations

as shown by the curve comparisons in Figure 6 although the alternative filtration

produced slightly higher MTF curves as seen in Figure 4 Table 4 lists the experimental

specific spatial frequencies for varying levels of MTF

I3iv Noise Power Spectrum

The noise characteristics are indicated by the NNPS curves shown in Figure 7

The noise was similar for both horizontal and vertical directions As exposure increased

the NNPS decreased consistent with the characteristics of Poisson noise describing the

relationship between signal and noise in the presence of increased photon fluence At

13

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 5 MTF results by detector (columns) and beam quality (rows)

00

01

02

03

04

05

06

07

08

09

10

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14

Figure 6 Plots of MTF for RQA5 (top) and RQA9 (bottom) showing the relationships

between detectors (blue red and green) and by filtration (solid and dashed)

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15

Pixium 4600 DRX-1C DRX-1 R

QA

5A

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Figure 7 NNPS results by detector (columns) and beam quality (rows)

1E-7

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16

Figure 8 Plots of NNPS for RQA5 (top) and RQA9 (bottom) at 1 mR exposure

showing the relationships between detectors (blue red and green) and by filtration

(solid and dashed)

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17

Pixium 4600 DRX-1C DRX-1 R

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Figure 9 DQE results by detector (columns) and beam quality (rows)

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18

Figure 10 Plots of DQE for RQA5 (top) and RQA9 (bottom) at 1 mR exposure showing

the relationships between detectors (blue red and green) and by filtration (solid and

dashed)

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19

higher frequencies the NNPS curves of the Pixium 4600 and DRX-1 diverge slightly for

the different directions illustrating increased noise in the readout direction (vertical)

Differences in the noise characteristics were more apparent among detectors as

shown for 1 mR in Figure 8 The NNPS curve for the DRX-1 was higher in magnitude

across the entire frequency range than either the Pixium 4600 or DRX-1C which both

seemed to demonstrate reasonably similar NNPS curves The higher magnitude noise of

the DRX-1 indicates higher relative noise content overall Closer inspection of the NNPS

curves of the Pixium 4600 and DRX-1C detectors in Figure 7 revealed differences in the

spacing between the three exposure levels The gaps between the Pixium 4600 NNPS

curves do not correspond to the factor of two differences between each exposure level

especially at low- to mid- spatial frequencies suggesting a higher level of fixed pattern

noise additional noise with increasing exposure levels due to ineffective gain map

corrections Between filtration schemes the differences in NNPS curves for a given beam

quality were not substantial as shown in Figure 7

I3v Detective Quantum Efficiency

The DQE results are shown in Figure 9 DQE curves across exposure levels were

almost collinear except for Pixium 4600 and in general could be inferred from the

NNPS results Additionally the DQE curves demonstrated a relatively linear response

with spatial frequencies as expected for flat-panel detectors [9] Differences in DQE

among detectors were consistent for the most part with the type of scintillating material

20

As depicted for 1 mR exposure in Figure 10 differences between Pixium 4600 and DRX-

1C DQE curves correspond to the differences in their NNPS curves DRX-1 DQE curves

were consistently lower than either the Pixium 4600 or DRX-1C curves The DQE curves

for the alternative filtration were consistently higher than those for the IEC filtration

and the most noticeable differences were near the zero-frequency axis These effects can

be both attributed to ineffective gain map correction DQE values for 1 mR exposure are

listed in Table 5

I4 Discussion

I4i Comparisons of Detectors

The limiting spatial resolutions of all three detectors were almost exactly the

same considering that their pixel areas were similar in size The decrease in high-

frequency MTF of the DRX-1 compared to the other detectors is probably a result of

increased optical blurring due to the differences in the powdered structure of GOS

versus the needle-like structure of CsI [2] The fact that the DRX-1C and Pixium 4600

have comparable MTFs suggests similar scintillator thicknesses assuming that the

materials were processed alike

The noise of the three detectors demonstrated similar trends with each other The

higher NNPS curves of the DRX-1 detector are probably due also to the scintillating

material and its operation in converting photons into signal The conversion process is

less efficient because of the less favorable stopping power of the GOS compared to CsI

21

especially with higher energy beams The noise of the Pixium 4600 and DRX-1C were

similar except for the spacing between exposures The DRX-1C NNPS curve spacing is

consistent with a factor of two difference in exposure levels but the Pixium 4600 has a

smaller spacing The 05 mR NNPS curve of the Pixium 4600 is closer to that of the 05

mR NNPS curve of the DRX-1C This demonstrates that at higher exposures the Pixium

4600 produces a larger amount of additional noise beyond that explained by simple

stochastic effects It suggests bad performance in the gain map corrections

The DQE results indicate SNR properties of each detector The Pixium 4600 and

DRX-1C are comparable for the most part with the DRX-1C performing slightly better

The DRX-1 as predicted from MTF and NNPS results has a DQE much lower than

either of the previous two This is a reflection of the detection properties as provided by

its scintillator material The DQE of the DRX-1 however is comparable to CR image

receptors [2] The mid-frequency dips in the DQE for Pixium 4600 may be due to the

optical properties of the CsI phosphor layer which can affect the MTF in this manner

Because the DQE is calculated by squaring the MTF this effect at the mid-range

frequencies becomes more apparent The dips may also be further evidence of bad gain

map corrections

I4ii Comparisons of Filtrations

The alternative filtration closely matches for the most part the IEC-based

filtration for MTF NNPS and DQEs at RQA5 but not at RQA9 The filters do not have

22

Table 4 Experimental MTF frequency locations for 1 mR exposure

Detector Filtration

50 MTF

(mm-1)

40 MTF

(mm-1)

30 MTF

(mm-1)

20 MTF

(mm-1)

10 MTF

(mm-1)

Pixium

4600

RQA5A 115 145 185 245 330

RQA5C 125 155 195 250 345

RQA9A 110 175 175 235 330

RQA9C 125 155 195 255 345

DRX-1C

RQA5A 120 150 185 245 350

RQA5C 125 155 195 255 355

RQA9A 120 150 190 250 355

RQA9C 130 160 210 265 360

DRX-1

RQA5A 110 135 160 205 280

RQA5C 110 135 170 210 285

RQA9A 105 125 155 195 270

RQA9C 110 135 165 210 285

Table 5 Estimated DQE values for 1 mR exposure by frequency bins

Detector Filtration DQE(00 mm-1) DQE(10 mm-1) DQE(20 mm-1) DQE(30 mm-1)

Pixium

4600

RQA5A 62 42 32 21

RQA5C 63 45 36 25

RQA9A 41 27 30 13

RQA9C 43 33 27 19

DRX-1C

RQA5A 72 52 35 21

RQA5C 76 55 41 24

RQA9A 49 33 23 15

RQA9C 51 40 31 20

DRX-1

RQA5A 38 24 12 4

RQA5C 38 25 14 5

RQA9A 28 18 9 4

RQA9C 28 19 12 5

DQE values at the zero-frequency axis were estimated by the intercept of a linear fit of low-frequency data

but excluding most proximal to the axis due to large fluctuations Other estimated values are grouped into

frequency bins due to the noisiness of the data

23

considerable differences in the spatial resolutions of the detectors as expected The noise

responses for each filtration were also similar except at the lower frequencies of the

NNPS especially near the zero-frequency axis There observing the NNPS responses at

RQA5 for Pixium 4600 and DRX-1C in Figure 8 the NNPS for the IEC-based filtration

(solid lines) tend to drop faster than the NNPS for the alternative filtration This

subsequently appears as a drop in DQE near the zero-frequency axis shown for those

detectors in Figure 10 Overall as indicated in Table 5 the DQEs of the two filtrations

while similar in trend indicate that the alternative filtration increases the DQE by a

small amount of 3-5 Part of this may be explained by the slightly higher beam

energy which may be more optimal for the energy response of the detectors or may

weigh the pixel responses slightly considering that they are energy-integrating types

The most probable explanation is the gain map correction for the alternative filtration

where fixed pattern noise is more sufficiently reduced

A previous study [6] had discussed the choice of filter material in the analysis of

DQE when achieving the beam conditions defined by IEC It found that visible

nonuniformities were present with the higher purity aluminum filter (type-11999 alloy)

The low frequency mottle in the flat-field images for NPS measurements were also

attributed to structured noise from the grain size in the IEC-based filter with an

attenuating thickness that would reveal nonuniformities The mottle in the current study

was only observable under very narrow windowing as shown in Figure 11 Such low

24

frequency artifacts which are not readily noticeable may also be caused by shading

artifacts inverse square law or even the heel effect A possible method to correct for this

is a subtraction method by taking the average of the flat-field images for an exposure

level and then subtracting that from each of them This would remove nonuniformities

that were not corrected using a suboptimal gain map calibration

Figure 11 DRX1-C NNPS images at 1 mR for RQA5 with IEC filtration (left) and

alternative filtration (right) Images are equally windowed at 45 and leveled at 980

One convenient aspect of the copper and aluminum filtration is that it requires

much less tube current to achieve the same amount of exposure at the detector than the

much thicker aluminum filtration As shown in the non-normalized spectra in Figure 2

the exiting photon fluence exiting the copper and aluminum filtration is substantially

higher than that of the IEC-specified filtration This is due to the smaller total filtration

25

attenuation For extensive DQE analysis multiple sets of exposures may be acquired

before tube overheating becomes a concern

One limitation to the comparison of the two filtrations is that calibration

procedures specified copper and aluminum filtration at 80 kVp (for all detectors 05 mm

Cu and 10 mm Al) This may have influenced the results in favor of the alternative

filtration A further investigation involving the calibration procedures and performing

DQE measurements is encouraged Another factor may be influenced by the fact that the

tests were performed at 70 kVp and 120 kVp different from the recommended

calibration tube potential Clearly there would be differences in the linear attenuation

coefficients of the filters and different energy responses of the detectors themselves This

must be considered when interpreting DQE results The current results support a

previous study decades ago that described filtration of different material types in terms

of an aluminum equivalent [16] The results show that the two filtration schemes are

essentially equivalent when considering beam qualities and spatial resolutions The

NNPS and DQE results can be seen as close enough where their small differences are

insignificant when performing quality assurance tests in a clinical setting Overall our

results indicate that the alternative filtration with copper and aluminum may be more

convenient to use than the current IEC standard filtration

26

I4iii Implications of Wireless DR

This study has shown that wireless image receptors can have the same DQE

performance if not better than conventional flat-panel detectors They operate on the

same basic physical principles the new features offered by the DRX-1C and DRX-1 are

wireless communication with the workstation and electronics packaging technology

The latter feature may pose limitations for these units in terms of possible degradation

in the detectors in routine clinical conditions A consideration for future work would be

to longitudinally track DQE performance of the wireless detectors over time while being

utilized in a clinical environment In the end one must consider risks versus benefits of

choosing portable DR technology over CR one of which includes the cost and fragility

of DR detectors

The DQE performance of one wireless system is just as good as or better than

conventional systems as seen by the DRX-1C performance compared to the Pixium

4600 Wireless systems can also reduce the need for CR readers especially in portable

applications in other regions of the world (eg military hospitals developing countries)

However while DQE performance indicates the physical performance of the detector

system it is still unknown how it relates to observer performance

I5 Conclusions

Two wireless image receptors DRX-1C and DRX-1 were evaluated and

compared with the conventional DR flat-panel Pixium 4600 in terms of DQE

27

performance along with MTF and NNPS performances The detectors have similar

resolution properties although the DRX-1 is inferior at higher spatial frequencies The

NNPS and DQE results both indicate that the DRX-1C is superior to the DRX-1 and

comparable if not better to the Pixium 4600

The results from the filtration comparison indicate no substantial differences

between the IEC-based filtration and the copper-based alternative filtration Only slight

differences were found in the low frequency components of the NNPS and the DQE due

to the inherent nonuniformities of the IEC specified filtration Given the similarity of the

results and low attenuation advantage of the copper and aluminum filter its use is

encouraged

28

II Directional MTF for Breast Tomosynthesis

II1 Introduction

Breast tomosynthesis is an emerging 3D imaging modality that has potential use

for screening and diagnosis of breast cancer Breast tomosynthesis along with other 3D

techniques is preferable to planar imaging methods (eg mammography) because they

reduce anatomical noise by removing overlying structures above and below the plane of

an image slice [17-20] Recent advances in detectors and computer technology have

made digital tomosynthesis feasible

An image quality metric of particular importance in breast tomosynthesis is

spatial resolution Resolution is important to know in order to assess small-detail

structures such as microcalcifications A descriptive metric for characterizing spatial

resolution in the Fourier (or frequency) domain is the modulation transfer function

(MTF) Affected by reconstruction filters [21] the limited angular projections involved in

breast tomosynthesis results in highly anisotropic (or nonuniform) resolution Many

studies have looked only at characterizing the in-plane spatial resolution (ie in an

individual slice) with an elevated angled edge phantom [2223] A few studies have

looked at characterizing a more comprehensive 3D spatial resolution by using a

phantom with angled wires or tubes [24-26] However such studies require precise

mechanical alignment of the phantoms Several studies have explored a method using a

29

sphere phantom for the directional 3D MTF evaluation for microtomography [27] and

multi-slice CT [2829] This method has not yet been extended to breast tomosynthesis

This chapter focuses on breast tomosynthesis because it is highly anisotropic in

spatial resolution and like its predecessor mammography requires high spatial

resolution Additionally breast tomosynthesis acquisitions and reconstructions produce

several types of artifacts The use of a cone-based method using a sphere phantom [28] is

explored to characterize the directional 3D spatial resolution of simulated images from

breast tomosynthesis A technique for removing out-of-plane artifacts of the ESFs for the

in-plane axes is investigated to yield a modified MTF in a method that separates artifact

information from resolution information

II2 Materials and Methods

II2i Image Simulation

Breast tomosynthesis images were simulated by using a virtual imaging system

depicted in Figure 12 A volumetric breast phantom was voxelized as a rectangular mass

of uniform breast equivalent tissue of 4 cm thickness embedded with fifteen evenly

spaced plastic sphere inserts of 12 mm diameter The spheres were placed in a grid

formation within the central plane of the phantom The x-ray fluence was modeled from

a 28 kVp beam incident upon an indirect flat-panel detector with 200 micro m pixel size

Twenty-three projections within an angular range of 44deg were simulated using cascaded

systems analysis to generate characteristic 2D noise and spatial blurring [29] Each

30

projection was simulated to have an exposure of 174 mR with a fluence of 79 times 105

photonsmm-2 A standard filtered backprojection technique based on the Feldkamp

reconstruction algorithm [29] was used to reconstruct the projections and produce a

volumetric dataset with an isotropic voxel size of 200 micro m

Figure 12 Depiction of the virtual image system

II2ii Uncorrected MTF

To enable comparison of multiple spheres the reconstructed volume was

initially homogenized by performing a background subtraction based on a portion of the

volume devoid of spheres The voxel values were rescaled between one and zero to

eliminate negative values

31

The volumetric data were segmented to extract individual regions of interest

(ROIs) each containing a single sphere The ROIs extended along the full range of the z-

axis A thresholded ROI was generated by determining the exterior and interior voxels

relative to the sphere in the ROI The threshold value was set at 45 of the maximum

voxel value prior to thresholding The exterior and interior voxel values were then set to

values of 0 and 1 respectively Using the thresholded volume the center of mass was

calculated to determine the centroid The voxel values from the original ROI were

subsequently tabulated with the associated distances azimuthal angles and polar

angles relative to the centroid

Conical regions were prescribed along the positive and negative directions along

the three major axes extending from the centroid of the sphere as depicted in Figure 13

The axes about which the extent of the cone angle was delineated were defined with

the azimuthal and polar angles

Voxels with centers within the angular range of the cone were considered for

generating the edge spread function (ESF) To improve regularity of the distance

sampling interval the ESF values were rebinned to discrete distances corresponding to a

fraction of the voxel size Only voxels with distances ranging from the voxel size (ie

200 micro m) to the maximum distance were considered The ESFs from multiple spheres

were averaged together for each of the three major axes to produce an averaged ESF

which was further smoothed utilizing a Gaussian filter

32

Figure 13 Example of 30-degree cone prescribed along z axis of the sphere

The resulting ESF was then differentiated using the central difference method to

produce the line spread function (LSF) A Hanning filter with the same length as the LSF

was applied to zero out the tails of the LSF The presampled MTF was subsequently

computed as the amplitude of the Fourier transform of the LSF The MTF was

normalized with respect to the maximum value occurring within the range of the cutoff

frequency Binning size and conical range for the ESF were considered for maximizing

accuracy and minimizing noise of the MTF verified by comparison against the

theoretical MTF as determined in the previous section

II2iii Theoretical Directional MTF

The theoretical 3D MTF was calculated using a priori knowledge of the transfer

function of the virtual imaging system described in the previous section A phantom

was created with a set of point objects in a uniform and noise-free background with the

objects spanning across the volume of the breast [29] Twenty-one realizations were

33

generated from the reconstructed images of the point objects to yield a set of 3D point

spread functions (PSFs) The 3D fast Fourier transform (FFT) was performed for each 3D

PSF and averaged to give an ldquoexpectationrdquo 3D MTF [29] The theoretical directional

MTFs in the three major spatial axes were determined by line profiles along each of the

corresponding spatial frequency axes in the 3D MTF An additional theoretical MTF for

each direction was determined by using the application of conical regions along the axes

in frequency-space to take into account the contributions of MTF information from other

planes

II2iv Modified MTF

The tomosynthesis reconstruction is known to have edge enhancements which

affect the overall MTF by shifting the peaks of the MTF toward the higher frequencies

[23] The presence of this artifact complicates the interpretation of the actual spatial

resolution of the images Several steps were performed to remove the artifact

contribution to the resolution information particularly for the in-plane x and y

directions with the assumption that resolution information was contained immediately

near the edge

For the x-direction averaged ESF only values that were detected to be inside the

edge of the sphere were considered Those values were previously determined via

thresholding for calculating the centroid The ESF information corresponding to these

values was inversed and flipped about the detected edge to produce a symmetric

34

modified ESF The modified MTF was subsequently calculated from this modified ESF

as described in the previous section

For the y-direction averaged ESF an upward trend was found in the initial part

of the ESF This section was detrended with a polynomial fit and subtracted to produce a

flatter curve in that region The resulting detrended ESF was used to calculate the y axis

modified MTF

Figure 14 Photograph of the imaging system with the acrylic sphere phantom

embedded in oil

II2v Preliminary Experimental Validation

A clinical breast tomosynthesis system (Mammomat Inspiration Siemens AG

Munich Germany) was used to perform a preliminary evaluation of the cone-based

MTF technique The phantom for the experiment consisted of a single acrylic ball of 075

in diameter (SmallParts Seattle WA) suspended by a 0029 in diameter plastic filament

35

(Omniflex Zebco Tulsa OK) in an acrylic frame filled up to 4 in with vegetable oil

(Target Brands Inc Minneapolis MN) The system and phantom are shown in Figure

14 Twenty-five projections with an angular range of 44deg were acquired and subsequently

reconstructed to produce a volume with a voxel size of 01times01times10 mm3 The voxels were

reformatted to have an isotropic size of 01 mm The uncorrected ESF LSF and MTF

were calculated as described in the previous section

II3 Results

II3i Reconstruction

The reconstructed volume is shown in Figure 15 Notice the edge enhancement

along the x-direction as indicated by the sharp shadowing artifacts on either side of the

spheres The background was effectively homogenized using the background

subtraction technique This also took account of the curved edges of the breast phantom

With the close spacing of the spheres in the phantom the shadows along the x direction

for the fifteen spheres overlap with each other As the nine centrally located spheres

experience this effect the same way they were used for determining the ESF

A 3D rendering of the ROI containing a sphere shown in Figure 16 indicates the

anisotropic resolution of the reconstruction Note that the sphere is not accurately

reconstructed and has an oblong shape especially along the z axis Cross sectional views

of the ROI also in Figure 16 clearly demonstrate the edge enhancement causing a

shadow artifact in the x direction caused by the incomplete angular sampling of

36

tomosynthesis The sampling also introduces the triangular reconstruction of the sphere

as seen in the x-z plane Note the gradual edge drop-off in the z direction much beyond

the sphere radius

Figure 15 View of the central slice of the breast phantom reconstruction before (top)

and after (bottom) background subtraction The z axis is through the page

37

Figure 16 3D rendering of the ROI volume (left) and cross-sectional views of the most

centrally located sphere with centroid indicated with red circle (right)

II3ii Theoretical MTF

The theoretical MTFs for x y and z directions as determined from the line

profiles of the 3D MTF are shown in Figure 17 The theoretical MTF in the x direction

has a maximum value that is toward higher frequencies Its 10 response occurs at

about 125 cyclesmm which is at 50 of the cutoff frequency The rapid increase from

the zero-frequency intercept to the peak corresponds to the ramp filter used in filtered

backprojection which decreases the weighting of low frequency contributions due to the

incomplete angular sampling of the frequency-space The MTF does not reach a value of

0 at the zero-frequency intercept as it is very difficult to assess the zero-frequency

intercept due to the finite size of the phantom The theoretical MTF in the y direction

peaks at the zero-frequency intercept and reaches 20 proximal to the cutoff frequency

38

The 10 MTF is well beyond the cutoff frequency The theoretical MTF in the z direction

has a rapid drop-off at very low spatial frequencies indicating the lack of resolution in

that dimension

Figure 17 Theoretical 3D MTF results along the three major planes (top) and along x

y and z directions (bottom) Also note that the angular spread seen in the fx-fz plane is

equal to the angular range of 44deg for the acquisition

II3iii Uncorrected MTF

The ESF LSF and MTF using the cone-based method are shown for the x y and

z directions in Figure 18 It was found that a bin size of one-tenth the voxel size (002

mm) and a cone angle of 30deg to establish the ESF were enough to minimize noise and

maximize accuracy in the uncorrected MTFs considering the reasonable comparison of

the shapes of the MTF curves with the theoretical results in Figure 17 The LSFs are

generally noisy because differentiation of the ESF increases the amplitude of the noise

39

The data shown reflect a convolution with a smoothing Gaussian filter which was later

further corrected for in the reported MTF Nevertheless the high frequency components

of the noise are well beyond the MTF cutoff frequency of 25 cyclesmm and do not

impact the MTF results greatly

For the ESF in the x direction the shadow effect evident at the edge of the sphere

is visible as a steep decline followed by an increase Due to the finite distance range

provided by the ROI the ESF beyond the edge did not asymptotically reach the

background value The corresponding LSF demonstrates a low frequency modulation

that is indicated by the shift of 03 cyclesmm in the x direction for the peak of the MTF

The MTF exhibits a zero-frequency intercept that is non-zero unlike the theoretical MTF

and a 10 value at approximately 1 cyclesmm These features may be a direct

consequence of MTF information ldquocontaminationrdquo from y and z directions Furthermore

the ESF in the y direction demonstrates a reasonably shaped curve except for the slight

upward trend within the radius of the sphere which can be attributed to the shadow

artifact overlapping with the sphere volume The associated MTF has a peak shifted by

approximately 01 cyclesmm away from the axis and a 10 MTF occurring at

approximately 15 cyclesmm Both features which are not present in the theoretical

results may also be attributed to contaminant MTF information from x and z directions

The ESF in the z direction has a drop-off that occurs at a small fraction of the cutoff

frequency similar to that demonstrated by the theoretical MTF

40

Uncorrected ESF LSF and MTF

Figure 18 Uncorrected ESF (top) LSF (middle) and MTF (bottom) for x y and z

directions

41

Figure 19 Comparisons of the directional MTFs as calculated by the sphere method

(dashed line) by theoretical line profiles (light-weight line) by theoretical cone

regions (heavy-weight line)

II3iv Comparison of Theoretical and Simulated MTFs

The theoretical MTF results obtained from line profiles through the 3D MTF and

the simulated MTFs using the cone-based technique did not match very well except for

the general shape of the curves It was assumed in the previous section that the cone-

based technique contains information from other planes Figure 19 compares MTFs in

each direction for the two methods described in the methods and an additional method

based on conical regions of the 3D MTF The latter computes the MTF by averaging

contributions of the 3D MTF using the same cone prescription method used to define the

ESFs Comparison of the curves indicate some interesting correlations aside from the

fact that using conical regions with the 3D MTF results produce more noisy MTF results

partly due to the low sampling provided by the theoretical calculations The same

conclusions regarding the z direction MTF can be confirmed regardless of either

theoretical MTF procedures The experimental x direction MTF seems to agree best with

42

the line profile method whereas the y direction MTF agrees better with the cone region

method The fact that the experimental x direction MTF has a drop-off frequency that is

lower than those of either of the theoretical MTFs in Figure 19 suggests that this might

be due to integration of the z-direction in the in-plane slices considering how slices are

essentially averages of z direction information contained within it [33]

II3v Modified MTF for x and y

Modified ESF LSF and MTF curves for x and y directions are shown in Figure

20 The modified ESF and the resulting LSF in the x direction appear symmetric as

expected from the inverse and flip operation of the interior ESF about the detected edge

The modified MTF appears with less variation than the uncorrected MTF and the MTF

peak occurs at the zero-frequency axis The correction yields a 10 MTF at about 15

cyclesmm an improvement from the uncorrected MTF but still distant from the cutoff

frequency The modified ESF in the y direction demonstrates the detrended curve within

the sphere radius after a quadratic polynomial fit The resulting modified MTF still

appears similar to the uncorrected MTF except that the peak now coincides with the

zero-frequency axis For both x and y directions the low response of the modified MTFs

at the higher frequencies suggests that the contamination from other directions is

substantial due to the angular range of the cone

43

Modified ESF LSF and MTF

Figure 20 Modified ESF (top) LSF (middle) and MTF (bottom) for x and y directions

44

II3v Preliminary Experimental Validation

Cross-sections of the reconstructed sphere volume are shown in Figure 21

Relative to the simulation reconstructions the reconstructions of the experimental

phantom images produce lower contrast and higher noise The preliminary results

shown in Figure 22 indicate that our technique can be applied to actual experimental

breast tomosynthesis reconstructions However due to the noise exhibited by the MTF

curves for the x and y directions we did not determine the modified MTFs to separate

resolution and artifact information

Figure 21 Cross sectional views of the experimental sphere image with centroid

indicated with red circle

45

Uncorrected ESF LSF and MTF for Real Image

Figure 22 ESF (top) LSF (middle) and MTF (bottom) of real image for x y

and z directions

46

II4 Discussion

II4i Evaluation of Cone-based Method

The cone-based MTF technique was introduced by Thornton and Flynn [28] for

evaluation of volumetric CT images To utilize this technique as a characterization of a

3D system spatial resolution one must first consider the validity of the assumption of

shift invariance such that the same MTF result may be obtained regardless of the

location of the sphere The study by Zhao et al [23] found that there was no shift

variance for the MTF measurements along the vertical axis but this was only considering

the in-plane resolution along one axis On the other hand this study evaluated the MTF

with images simulated with cascaded systems analysis which includes conditions of

linearity and shift invariance Additionally the MTF was calculated by averaging the

ESF from several spheres in the same volume only after performing a background

subtraction This step was essential to account for the sensitivity of centroid calculations

as well as ensuring symmetric ESFs for opposing axes of the sphere ROIs

The measurement of MTF with the cone-based technique inherently

supersamples the edge of the sphere to increase signal-to-noise-ratio (SNR) of edge

information by averaging the contributions of each voxel to the ESF [713] This method

also takes into account the discrete sampling of the voxels by accounting for various

shifts of the edge in the voxel (also known as the partial volume effect) However using

the curved surface of the sphere phantom to approximate an edge along a given

47

direction naturally leads to contamination of information from other directions aside

from the one of interest Preferably a directional ESF should be created by using a single

radial line but this would limit the available voxels to obtain edge information An ideal

situation theoretically would be to use a larger-sized sphere such that the surface is

nearly flat and perpendicular to the axes of interest This would also permit a reduction

in the angular range of the cone and thus the introduction of out-of-plane information in

the resulting MTF However sphere size is a limitation in breast tomosynthesis and the

use of a large phantom might void the assumption of shift invariance of the spatial

resolution

The choice of a sphere phantom nevertheless may be based on the clinical need

to quickly acquire a single image for MTF evaluation especially for multiple directions

without presenting extra logistical challenges The use of a wire or edge phantom

requires more precise mechanical alignment to achieve the correct set up The edge

phantom [23] would require at least two images to sample all three dimensions In the

case of the three wire phantom [2425] all three dimensions of the frame must be aligned

simultaneously with respect to the axis of rotation A similar situation would be

encountered when considering a cubic phantom with the planes normal to the axis of

interest In contrast to these phantoms the sphere eliminates the need for precise

alignment especially with respect to three spatial dimensions simultaneously A sphere

48

has ideal symmetry in all directions and can be used to evaluate MTF in any arbitrary

direction

This study unlike others [242532] did not explore the effects of physical

parameters such as scatter or contrast on the final MTF result but it demonstrated the

feasibility of using the cone-based method with an actual breast tomosynthesis image of

a sphere phantom as shown in Error Reference source not found and Error Reference

source not found These effects should be addressed in future works A further look

into deriving the principles of comparing the theoretical MTF with the experimental

MTF using the cone-based method is further warranted

II4ii Separation of Artifact and Resolution Information

The focus of this study was to develop a technique for measuring spatial

resolution of tomosynthesis images The intrinsic artifacts from tomosynthesis

reconstructions however lead to uncharacteristic MTFs and possible misinterpretation

of the effective resolution information When considering previous techniques for

calculating the presampled MTF [713152328] the analysis was performed using an

edge or a line to produce the corresponding ESF The resolution information is

essentially contained only along the edge indicated by the need to calculate the LSF In a

way the method of extracting artifact information is to focus the analysis only on the

edge part of the ESF to calculate the modified MTF This will lead to a better

understanding of the limiting size of objects that may be seen in the reconstructed 3D

49

image The presampled MTF without correction should still be analyzed to understand

the entire system response Note that the ESFs attempt to reflect information only at the

detected edge of the sphere

II5 Conclusions

The directional MTF of a simulated breast tomosynthesis reconstruction was

determined by using the cone-based MTF technique demonstrating the feasibility of a

single phantom for MTF evaluation This study further presented methods of analyzing

only the edge information in the ESF to create a modified MTF along in-slice (x and y)

axes It can provide insight into the actual spatial resolution information contained in the

image while separating the resolution information from the information introduced by

artifacts caused by the reconstruction and insufficient volumetric sampling The idea of

separating the resolution and artifacts from the measured ESF are expected to facilitate

the interpretation of MTF measurements in breast tomosynthesis Similar methods may

be applied to characterize the resolution of other 3D imaging modalities

50

References

1 Garmer M Hannigs SP Jaumlger HJ et al ldquoDigital Radiography Versus

Conventional Radiology in Chest Imaging Diagnostic Performance of a Large-

Area Silicon Flat-Panel Detector in a Clinical CT-Controlled Studyrdquo American

Journal of Roentgenology Volume 74 75-80 (2000)

2 Cowen AR Kengyelics SM and Davies AG ldquoSolid-state flat-panel digital

radiography detectors and their physical imaging characteristics rdquoClinical

Radiology Volume 63 487-498 (2008)

3 Chotas HG Dobbins III JT and Ravin CE ldquoPrinciples of Digital

Radiography with Large-Area Electronically Readable Detectors A Review of

the Basicsrdquo Radiology Volume 210 Number 3 595-599 (1999)

4 Flynn MJ and Samei E Experimental comparison of noise and resolution for

2k and 4k storage phosphor radiography systems Medical Physics Volume 26

Number 8 1612-1623 (1999)

5 Rong XJ Shaw CC Liu X Lemacks MR and Thompson SK

ldquoComparison of an amorphous siliconcesium iodide flat-panel digital chest

radiography system with screenfilm and computed radiography systems ndash A

contrast-detail phantom studyrdquo Medical Physics Volume 28 Number 11 2328-

2335 (2001)

6 Ranger NT Samei E Dobbins III JT and Ravin CE Measurement of the

detective quantum efficiency in digital detectors consistent with the IEC 62220-1

standard Practical considerations regarding the choice of filter material

Medical Physics Volume 30 Number 7 2305-2311 (2005)

7 Samei E Buhr E Granfors P Vandenbroucke D and Wang X Comparison

of edge analysis techniques for the determination of the MTF of digital

radiographic systems Physics in Medicine and Biology Volume 50 3613-3625

(2005)

8 Samei E and Flynn MJ An experimental comparison of detector performance

for computed radiography systems Medical Physics Volume 29 Number 4 447-

459 (2002)

51

9 Samei E and Flynn MJ An experimental comparison of detector performance

for direct and indirect digital radiography systems Medical Physics Volume 30

Number 4 608-622 (2003)

10 Samei E Ranger NT MacKenzie A Honey ID Dobbins III JT and Ravin

CE Effective DQE (eDQE) and speed of digital radiographic systems An

experimental methodology Medical Physics Volume 36 Number 8 3806-3817

(2009)

11 Samei E Ranger NT MacKenzie A Honey ID Dobbins III JT and Ravin

CE Detector or System Extending the Concept of Detective Quantum

Efficiency to Characterize the Performance of Digital Radiographic Imaging

Systems Radiology Volume 249 Number 3 926-937 (2008)

12 ldquoIEC 62220-1 Medical Electrical Equipment ndash Characteristics of Digital X-Ray

Imaging Devices ndash Part 1 Determination of the Detective Quantum Efficiencyrdquo

International Electrotechnical Commission Geneva Switzerland (2003)

13 Samei E Ranger NT Dobbins III JT and Chen Y Intercomparison of

methods for image quality characterization I Modulation transfer function

Medical Physics Volume 33 Number 5 1454-1465 (2006)

14 Dobbins III JT Samei E Ranger NT and Chen Y Intercomparison of

methods for image quality characterization II Noise power spectrum Medical

Physics Volume 33 Number 5 1466-1475 (2006)

15 Samei E Flynn MJ and Reimann DA A method for measuring the

presampled MTF of digital radiographic systems using an edge test device

Medical Physics Volume 25 Number 1 102-113 (1998)

16 Nagel HD ldquoAluminum equivalence of materials used in diagnostic radiology

and its dependence on beam qualityrdquo Physics in Medicine and Biology Volume

31 Number 12 1381-1399 (1986)

17 Niklason LT Christian BT Niklason LE et al ldquoDigital Tomosynthesis in

Breast Imagingrdquo Radiology Volume 205 399-406 (1997)

18 Gur D ldquoTomosynthesis Potential Clinical Role in Breast Imagingrdquo American

Journal of Roentgenology Volume 189 614-615 (2007)

52

19 Park JM Franken Jr EA Garg M Fajardo LL and Niklason LT ldquoBreast

Tomosynthesis Present Considerations and Future Applicationsrdquo

RadioGraphics Volume 27 S231-S240 (2007)

20 Good WF Abrams GS Catullo VJ Chough DM Ganott MA Hakim

CM and Gur D ldquoDigital Breast Tomosynthesis A Pilot Observer Studyrdquo

American Journal of Roentgenology Volume 190 865-869 (2008)

21 Hu Y-H Zhao W Mertelmeier T and Ludwig J ldquoImage Artifact in Digital

Breast Tomosynthesis and Its Dependence on System and Reconstruction

Parametersrdquo IWDM 2008 LNCS 5116 628-634 (2008)

22 Chen Y Lo JY Ranger NT Samei E Dobbins III JT ldquoMethodology of

NEQ(f) analysis for optimization and comparison of digital breast tomosynthesis

acquisition techniques and reconstruction algorithmsrdquo Proceedings of SPIE

Volume 6510 65101I (2007)

23 Zhao B Zhou J Hu Y-H Mertelmeier T Ludwig J and Zhao W

ldquoExperimental validation of a three-dimensional linear system model for breast

tomosynthesisrdquo Medical Physics Volume 36 Number 1 240-251 (2009)

24 Madhav P Brzymialkiewicz CN Cutler SJ Bowsher JE and Tornai MP

ldquoCharacterizing the MTF in 3D for a Quantized SPECT Camera Having Arbitrary

Trajectoriesrdquo 2005 IEEE Nuclear Science Symposium Conference Record 1722-

1726 (2005)

25 Madhav P McKinley RL Samei E Bowsher JE and Tornai MP ldquoA Novel

Method to Characterize the MTF in 3D for Computed Mammotomographyrdquo

Proceedings of SPIE Volume 6142 61421Y (2006)

26 Hu Y-H Zhao B and Zhao W ldquoImage artifacts in digital breast

tomosynthesis Investigation of the effects of system geometry and

reconstruction parameters using a linear system approachrdquo Medical Physics

Volume 35 Number 12 5242-5252 (2008)

27 Seifert A and Flynn MJ ldquoResolving power of 3D x-ray microtomography

systemsrdquo Proceedings of SPIE Volume 4682 407-413 (2002)

28 Thornton MM and Flynn MJ Measurement of the spatial resolution of a

clinical volumetric computed tomography scanner using a sphere phantom

Proceedings of SPIE Volume 6142 61421Z (2006)

53

29 Baek J Pelc NJ ldquoUse of sphere phantoms to measure the 3D MTF of FDK

reconstructionsrdquo Proceedings of SPIE Volume 7961 79610D (2011)

30 Richard S and Samei E ldquoQuantitative imaging in breast tomosynthesis and CT

Comparison of detection and estimation task performancerdquo Medical Physics

Volume 37 Number 6 2627-2637 (2010)

31 Chen Y Lo JY and Dobbins III JT ldquoImpulse response analysis for several

digital tomosynthesis mammography reconstruction algorithmsrdquo Proceedings of

SPIE Volume 5745 541-549 (2005)

32 Zhao B and Zhao W ldquoThree-dimensional linear system analysis for breast

tomosynthesisrdquo Medical Physics Volume 35 Number 12 5219-5232 (2008)

33 Wu G Mainprize JG Boone JM and Yaffe MJ ldquoEvaluation of scatter

effects on image quality for breast tomosynthesisrdquo Medical Physics Volume 36

Number 10 4425-4432 (2009)

Page 16: Development and Evaluation of 2D and 3D Image Quality ...

3

The purpose of this study was two-fold First we aimed to evaluate and compare

two wireless image receptors with a conventional flat-panel detector on the basis of DQE

performance Second we compared DQE results using the IEC-prescribed filtration with

an alternative filtration For the latter an optimum filtration composition was

determined and compared with the IEC filtration on the basis of DQE

I2 Materials and Methods

I2i Detectors

The physical characteristics of the three digital image receptors evaluated in this

study are listed in Table 1 The Pixium 4600 was a conventional digital flat-panel The

DRX-1C and DRX-1 were both wireless digital cassettes that were tethered for the

purposes of this study All detectors were FDA approved and available commercially

Each detector was calibrated according to its manufacturer specifications to correct for

gain offset and bad pixels They were all dedicated for non-clinical laboratory research

purposes and hence could be operated under service settings that permitted acquisition

of raw (ie for processing) images

I2ii Beam Characterization

I2iia X-ray Techniques

All measurements for this study were taken with a well-characterized standard

radiographic system (Super80CP Philips Healthcare Andover MA) The x-ray tube had

an inherent filtration of 27 mm Al Free in-air exposures were measured using

4

Table 1 Physical Characteristics of Digital Image Receptors

Manufacturer Detector

Detector

type

Detector

material

Pixel pitch

(size) Array size

Imaging

area

Trixell

(Moirans France)

Pixium

4600 Indirect

CsITl

(CsI) 0143 mm

3121times3121

4 subpanels 45times45 cm2

Carestream Health Inc

(Rochester NY)

DRX-1C

(wireless) Indirect

CsITl

(CsI) 0139 mm

2560times3072

single panel 35times43 cm2

Carestream Health Inc

(Rochester NY)

DRX-1

(wireless) Indirect

G2O2STb

(GOS) 0139 mm

2560times3072

single panel 35times43 cm2

calibrated radiation meters (Mult-O-Meter Type 407 Unfors Instruments AB Billdal

Sweden) at 183 cm source-to-chamber-distance (SCD) The SCD also corresponded to

same plane as the image receptor surface The x-ray output was made to conform to IEC

beam quality definitions [1215] on the basis of half value layer (HVL) and peak

kilovoltage setting using an aluminum filtration (type-1100 99 purity) and an

alternative filtration consisting of copper (UNS C11000 999 purity) and aluminum

(type-1100 99 purity) The IEC radiation quality numbers (RQA) used in this study are

summarized in Table 2 HVLs were determined by iteratively adding successive

thicknesses of aluminum until reaching reduced exposure levels within a tolerance of

0485-0515 [12] As for the alternative filtration the aluminum was placed downstream

of the copper filter to attenuate characteristic radiation peaks from copper at

approximately 9 keV

I2iib Data Linearization

The system response function was determined for each detector and filtration

combination by acquiring flat-field images at increasing photon fluence until just before

5

Table 2 Beam Qualities and Required Filtrations

IEC Radiation

Quality Number

Peak

kilovoltage

Required

HVL

Required IEC

Filtration

Actual IEC

Filtration

Alternative

Filtration

RQA5 70 kVp 71 mm Al 21 mm Al 21 mm Al 05 mm Cu +

10 mm Al

RQA9 120 kVp 115 mm Al 42 mm Al 40 mm Al 104 mm Cu +

10 mm Al

For reasons of convenience these will be referred to as RQA5A RQA5C RQA9A and RQA9C

saturation levels To avoid the influence of detector backscatter on exposure

measurements a relationship for each filtration was first determined for two radiation

meters A target meter was placed at the central axis and a reference meter was placed at

the edge of the light field (large enough to cover the detectors) The reference meter

served as a surrogate for the target meter to avoid direct exposure measurements in the

plane of the image receptor Exposure relationships were determined before each

measurement set (ie detector and filtration combination) to account for changes in

temperature pressure and humidity The system response function was calculated by

using a regression of ADU (pixel value) versus exposure Images acquired for each

series were then converted to achieve a linear response with zero offset and scaled to

achieve high quantization (adequate dynamic range) Linearization of the detector

responses ensured that zero exposure corresponded to zero pixel value

I2iic Spectral Simulation

The effects of additional filtration on x-ray output spectra were observed with

spectral simulation software (XSPECT V40 Henry Ford Hospital Detroit MI) To more

6

adequately describe the performance of a typical X-ray generator inherent filtration of 3

mm oil 148 mm Pyrex glass and 2 mm aluminum was input into the simulation in

addition to the filters of interest The ideal signal to noise ratio squared or incident

photon fluence per exposure (q) was estimated for each filtration by integrating the

energy-dependent photon counts per unit exposure over all energy bins

I2iii DQE Measurements

The assessment of the linearized images followed the formalism described by

IEC 62220-1 for measuring the DQE [12] For this study the normal exposure level XN

was set at 1 mR to the detector surface as measured at the central axis perpendicular to

the anode-cathode axis

I2iiia Modulation Transfer Function

Spatial resolution was characterized by evaluating the presampled modulation

transfer function (MTF) along directions parallel (vertical) and perpendicular

(horizontal) to the anode-cathode axis using the angled-edge method [6-1013] A radio-

opaque edge test device [7] was placed in the center of the field at a pitch of

approximately 301 (about 2deg) to the axis perpendicular to that being measured as

shown in Figure 1 External lead apertures were not used [6] instead the internal

collimation from the radiographic unit was used to collimate the beam to the detector

area Raw images were acquired of the edge with the normal exposure level XN of 1 mR

at the detector face The procedure of calculating the MTF followed previously described

7

methods [6-1013] The edge spread function (ESF) was determined along lines crossing

the edge of the angled test device The derivative of the ESF was calculated to form the

line spread function (LSF) to which a Hanning filter was applied The MTF was then

calculated as the fast Fourier transform (FFT) of the LSF and normalized at the zero-

frequency axis To conform to IEC guidelines the MTF was resampled into frequency

steps of 005 cyclesmm [12]

Figure 1 MTF images for DRX-1C detector with radio-opaque edge test device with

arrows indicating the horizontal (left) and vertical (right) directions

I2iiib Noise Power Spectrum

Noise amplitude and texture were characterized by determining the normalized

noise power spectrum (NNPS) which was evaluated with flat field exposures at

approximate exposure levels of XN2 XN and 2XN (05 10 and 20 mR) to the image

receptor surface Analysis of the flat-field images followed previously defined methods

[41415] using over 4 million independent pixels with regions of interest (ROIs) of size

8

128x128 The NNPS images were detrended using a quadratic (second order)

background subtraction Small variations in exposure across ROIs were corrected by

normalizing pixel values of each ROI to the mean value in the top left ROI as shown in

Figure 2 The NNPS was then calculated with the 2D FFT including the zero-frequency

axes corresponding to the horizontal and vertical directions The results were then

resampled using 005 frequency bins according to IEC guidelines [12]

Figure 2 NNPS image for DRX-1C detector indicating the top left ROI that served as

the reference for normalizing other ROIs in the image The ROI array was formed

along the directions indicated by the arrows The heel effect visible along the vertical

axis of the detector is an example of small variation in signal across the image

I2iiic DQE Calculation

The DQE was calculated using the following relationship [615]

9

where the frequency-dependent MTF and NNPS were determined as described in

previous sections X was the exposure value in mR corresponding to the NNPS image

and q was the ideal signal to noise ratio squared in units of photonsmiddotmm-2middotmR-1 as

estimated from the spectral simulations

I3 Results

I3i Data Linearization

The detectors in this study provided raw ADU (or pixel) values in a linear scale

The data were converted using the following system conversion function

where Q(ij) is the raw image data m and b are slope and intercept parameters obtained

from linear regression of the system response function and I(ij) is the linearized scaled

data The factor of 1000 was found to scale I(ij) such that the maximum value was a

large 16-bit number Figure 3 shows the original and linearized system responses for the

Pixium 4600 Note that the y-intercepts of the regressions for the linearized responses

are negligible (lt 01) with respect to the slopes a sufficient condition for zero offset

considerations

I3ii Spectral Simulation

The spectral simulations of the IEC filtrations and alternative filtrations indicate

many similarities in their effective energies HVLs and overall shapes of normalized

spectra Results are summarized in Table 3

10

Pixium 4600 Original System

Response

Pixium 4600 Linearized System

Response R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 3 Original (left) and linearized (right) system responses for Pixium 4600 The

linearized system responses were measured from actual images The offsets are small

with respect to the slope sufficient enough for zero-offset conditions

y = 13971x - 13236

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x - 00106Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 13576x + 28292

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

7000

0000 1000 2000 3000 4000 5000

AD

U

Exposure (mR)

y = 99997x - 00067Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0000 1000 2000 3000 4000 5000

AD

U

Exposure (mR)

y = 13644x + 16167Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x + 00044

Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 13845x + 13541

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x - 00177

Rsup2= 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

11

Table 3 Spectral Simulation Results

Beam Quality Filtration

Mean Energy

(kV)

Photon Fluence

(mRmm2)

RQA5A 21 mm Al 5243 259543

RQA5C 05 mm Cu + 10 mm Al 5214 259554

diff 055 0004

RQA9A 40 mm Al 7619 273281

RQA9C 104 mm Cu + 10 mm Al 7579 273964

diff 052 025

Figure 4 Spectral simulations for RQA5 (top) and RQA9 (bottom) conditions Note

the similarities of spectral shapes of the normalized spectra (right) Also note the

significant differences in fluence between filtrations in the simulated spectra (left)

00E+00

50E+04

10E+05

15E+05

20E+05

25E+05

30E+05

35E+05

40E+05

45E+05

0 20 40 60 80

ph

oto

ns

mA

s-1

cm

-2

keV

RQA5 Spectra Comparison

21 mm Al

05 mm Cu + 10 mm Al

00

02

04

06

08

10

12

0 20 40 60 80

keV

RQA5 Normalized Spectra Comparison

21 mm Al

05 mm Cu +

10 mm Al

00E+00

50E+05

10E+06

15E+06

20E+06

25E+06

30E+06

35E+06

40E+06

45E+06

50E+06

0 50 100 150

ph

oto

ns

mA

s-1

cm

-2

keV

RQA9 Spectra Comparison

40 mm Al

104 mm Cu +

10 mm Al

00

02

04

06

08

10

12

0 50 100 150

keV

RQA9 Normalized Spectra Comparison

40 mm Al104 mm Cu + 10 mm Al

12

I3iii Modulation Transfer Function

The limiting spatial resolutions of the systems were indicated by the cutoff

frequencies which were approximately 35 cyclesmm for all three detectors The spatial

resolutions also demonstrated a good degree of isotropy as confirmed by the close

alignment of MTF curves between vertical and horizontal directions differentiated in

Figure 5 by dashed and solid lines respectively The MTF curves for the Pixium 4600

and DRX-1C were nearly equal to each other whereas the DRX-1 MTF curve showed a

more rapid decrease at high frequencies as shown in Figure 6 This difference may be

due to the differences in the inherent optical properties of the scintillating materials

where finer image details are provided by structured CsI more than by granulated GOS

There were no significant differences in MTF curves across beam qualities and filtrations

as shown by the curve comparisons in Figure 6 although the alternative filtration

produced slightly higher MTF curves as seen in Figure 4 Table 4 lists the experimental

specific spatial frequencies for varying levels of MTF

I3iv Noise Power Spectrum

The noise characteristics are indicated by the NNPS curves shown in Figure 7

The noise was similar for both horizontal and vertical directions As exposure increased

the NNPS decreased consistent with the characteristics of Poisson noise describing the

relationship between signal and noise in the presence of increased photon fluence At

13

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 5 MTF results by detector (columns) and beam quality (rows)

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

horizontal

vertical

14

Figure 6 Plots of MTF for RQA5 (top) and RQA9 (bottom) showing the relationships

between detectors (blue red and green) and by filtration (solid and dashed)

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm-1)

MTF

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm-1)

MTF

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

15

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 7 NNPS results by detector (columns) and beam quality (rows)

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

05 mR - horizontal

05 mR - vertical

10 mR - horizontal

10 mR - vertical

20 mR - horizontal

20 mR - vertical

16

Figure 8 Plots of NNPS for RQA5 (top) and RQA9 (bottom) at 1 mR exposure

showing the relationships between detectors (blue red and green) and by filtration

(solid and dashed)

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm-1)

NNPS (1 mR)

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm-1)

NNPS (1 mR)

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

17

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 9 DQE results by detector (columns) and beam quality (rows)

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

05 mR - horizontal

05 mR - vertical

10 mR - horizontal

10 mR - vertical

20 mR - horizontal

20 mR - vertical

18

Figure 10 Plots of DQE for RQA5 (top) and RQA9 (bottom) at 1 mR exposure showing

the relationships between detectors (blue red and green) and by filtration (solid and

dashed)

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm-1)

DQE (1 mR)

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm-1)

DQE

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

19

higher frequencies the NNPS curves of the Pixium 4600 and DRX-1 diverge slightly for

the different directions illustrating increased noise in the readout direction (vertical)

Differences in the noise characteristics were more apparent among detectors as

shown for 1 mR in Figure 8 The NNPS curve for the DRX-1 was higher in magnitude

across the entire frequency range than either the Pixium 4600 or DRX-1C which both

seemed to demonstrate reasonably similar NNPS curves The higher magnitude noise of

the DRX-1 indicates higher relative noise content overall Closer inspection of the NNPS

curves of the Pixium 4600 and DRX-1C detectors in Figure 7 revealed differences in the

spacing between the three exposure levels The gaps between the Pixium 4600 NNPS

curves do not correspond to the factor of two differences between each exposure level

especially at low- to mid- spatial frequencies suggesting a higher level of fixed pattern

noise additional noise with increasing exposure levels due to ineffective gain map

corrections Between filtration schemes the differences in NNPS curves for a given beam

quality were not substantial as shown in Figure 7

I3v Detective Quantum Efficiency

The DQE results are shown in Figure 9 DQE curves across exposure levels were

almost collinear except for Pixium 4600 and in general could be inferred from the

NNPS results Additionally the DQE curves demonstrated a relatively linear response

with spatial frequencies as expected for flat-panel detectors [9] Differences in DQE

among detectors were consistent for the most part with the type of scintillating material

20

As depicted for 1 mR exposure in Figure 10 differences between Pixium 4600 and DRX-

1C DQE curves correspond to the differences in their NNPS curves DRX-1 DQE curves

were consistently lower than either the Pixium 4600 or DRX-1C curves The DQE curves

for the alternative filtration were consistently higher than those for the IEC filtration

and the most noticeable differences were near the zero-frequency axis These effects can

be both attributed to ineffective gain map correction DQE values for 1 mR exposure are

listed in Table 5

I4 Discussion

I4i Comparisons of Detectors

The limiting spatial resolutions of all three detectors were almost exactly the

same considering that their pixel areas were similar in size The decrease in high-

frequency MTF of the DRX-1 compared to the other detectors is probably a result of

increased optical blurring due to the differences in the powdered structure of GOS

versus the needle-like structure of CsI [2] The fact that the DRX-1C and Pixium 4600

have comparable MTFs suggests similar scintillator thicknesses assuming that the

materials were processed alike

The noise of the three detectors demonstrated similar trends with each other The

higher NNPS curves of the DRX-1 detector are probably due also to the scintillating

material and its operation in converting photons into signal The conversion process is

less efficient because of the less favorable stopping power of the GOS compared to CsI

21

especially with higher energy beams The noise of the Pixium 4600 and DRX-1C were

similar except for the spacing between exposures The DRX-1C NNPS curve spacing is

consistent with a factor of two difference in exposure levels but the Pixium 4600 has a

smaller spacing The 05 mR NNPS curve of the Pixium 4600 is closer to that of the 05

mR NNPS curve of the DRX-1C This demonstrates that at higher exposures the Pixium

4600 produces a larger amount of additional noise beyond that explained by simple

stochastic effects It suggests bad performance in the gain map corrections

The DQE results indicate SNR properties of each detector The Pixium 4600 and

DRX-1C are comparable for the most part with the DRX-1C performing slightly better

The DRX-1 as predicted from MTF and NNPS results has a DQE much lower than

either of the previous two This is a reflection of the detection properties as provided by

its scintillator material The DQE of the DRX-1 however is comparable to CR image

receptors [2] The mid-frequency dips in the DQE for Pixium 4600 may be due to the

optical properties of the CsI phosphor layer which can affect the MTF in this manner

Because the DQE is calculated by squaring the MTF this effect at the mid-range

frequencies becomes more apparent The dips may also be further evidence of bad gain

map corrections

I4ii Comparisons of Filtrations

The alternative filtration closely matches for the most part the IEC-based

filtration for MTF NNPS and DQEs at RQA5 but not at RQA9 The filters do not have

22

Table 4 Experimental MTF frequency locations for 1 mR exposure

Detector Filtration

50 MTF

(mm-1)

40 MTF

(mm-1)

30 MTF

(mm-1)

20 MTF

(mm-1)

10 MTF

(mm-1)

Pixium

4600

RQA5A 115 145 185 245 330

RQA5C 125 155 195 250 345

RQA9A 110 175 175 235 330

RQA9C 125 155 195 255 345

DRX-1C

RQA5A 120 150 185 245 350

RQA5C 125 155 195 255 355

RQA9A 120 150 190 250 355

RQA9C 130 160 210 265 360

DRX-1

RQA5A 110 135 160 205 280

RQA5C 110 135 170 210 285

RQA9A 105 125 155 195 270

RQA9C 110 135 165 210 285

Table 5 Estimated DQE values for 1 mR exposure by frequency bins

Detector Filtration DQE(00 mm-1) DQE(10 mm-1) DQE(20 mm-1) DQE(30 mm-1)

Pixium

4600

RQA5A 62 42 32 21

RQA5C 63 45 36 25

RQA9A 41 27 30 13

RQA9C 43 33 27 19

DRX-1C

RQA5A 72 52 35 21

RQA5C 76 55 41 24

RQA9A 49 33 23 15

RQA9C 51 40 31 20

DRX-1

RQA5A 38 24 12 4

RQA5C 38 25 14 5

RQA9A 28 18 9 4

RQA9C 28 19 12 5

DQE values at the zero-frequency axis were estimated by the intercept of a linear fit of low-frequency data

but excluding most proximal to the axis due to large fluctuations Other estimated values are grouped into

frequency bins due to the noisiness of the data

23

considerable differences in the spatial resolutions of the detectors as expected The noise

responses for each filtration were also similar except at the lower frequencies of the

NNPS especially near the zero-frequency axis There observing the NNPS responses at

RQA5 for Pixium 4600 and DRX-1C in Figure 8 the NNPS for the IEC-based filtration

(solid lines) tend to drop faster than the NNPS for the alternative filtration This

subsequently appears as a drop in DQE near the zero-frequency axis shown for those

detectors in Figure 10 Overall as indicated in Table 5 the DQEs of the two filtrations

while similar in trend indicate that the alternative filtration increases the DQE by a

small amount of 3-5 Part of this may be explained by the slightly higher beam

energy which may be more optimal for the energy response of the detectors or may

weigh the pixel responses slightly considering that they are energy-integrating types

The most probable explanation is the gain map correction for the alternative filtration

where fixed pattern noise is more sufficiently reduced

A previous study [6] had discussed the choice of filter material in the analysis of

DQE when achieving the beam conditions defined by IEC It found that visible

nonuniformities were present with the higher purity aluminum filter (type-11999 alloy)

The low frequency mottle in the flat-field images for NPS measurements were also

attributed to structured noise from the grain size in the IEC-based filter with an

attenuating thickness that would reveal nonuniformities The mottle in the current study

was only observable under very narrow windowing as shown in Figure 11 Such low

24

frequency artifacts which are not readily noticeable may also be caused by shading

artifacts inverse square law or even the heel effect A possible method to correct for this

is a subtraction method by taking the average of the flat-field images for an exposure

level and then subtracting that from each of them This would remove nonuniformities

that were not corrected using a suboptimal gain map calibration

Figure 11 DRX1-C NNPS images at 1 mR for RQA5 with IEC filtration (left) and

alternative filtration (right) Images are equally windowed at 45 and leveled at 980

One convenient aspect of the copper and aluminum filtration is that it requires

much less tube current to achieve the same amount of exposure at the detector than the

much thicker aluminum filtration As shown in the non-normalized spectra in Figure 2

the exiting photon fluence exiting the copper and aluminum filtration is substantially

higher than that of the IEC-specified filtration This is due to the smaller total filtration

25

attenuation For extensive DQE analysis multiple sets of exposures may be acquired

before tube overheating becomes a concern

One limitation to the comparison of the two filtrations is that calibration

procedures specified copper and aluminum filtration at 80 kVp (for all detectors 05 mm

Cu and 10 mm Al) This may have influenced the results in favor of the alternative

filtration A further investigation involving the calibration procedures and performing

DQE measurements is encouraged Another factor may be influenced by the fact that the

tests were performed at 70 kVp and 120 kVp different from the recommended

calibration tube potential Clearly there would be differences in the linear attenuation

coefficients of the filters and different energy responses of the detectors themselves This

must be considered when interpreting DQE results The current results support a

previous study decades ago that described filtration of different material types in terms

of an aluminum equivalent [16] The results show that the two filtration schemes are

essentially equivalent when considering beam qualities and spatial resolutions The

NNPS and DQE results can be seen as close enough where their small differences are

insignificant when performing quality assurance tests in a clinical setting Overall our

results indicate that the alternative filtration with copper and aluminum may be more

convenient to use than the current IEC standard filtration

26

I4iii Implications of Wireless DR

This study has shown that wireless image receptors can have the same DQE

performance if not better than conventional flat-panel detectors They operate on the

same basic physical principles the new features offered by the DRX-1C and DRX-1 are

wireless communication with the workstation and electronics packaging technology

The latter feature may pose limitations for these units in terms of possible degradation

in the detectors in routine clinical conditions A consideration for future work would be

to longitudinally track DQE performance of the wireless detectors over time while being

utilized in a clinical environment In the end one must consider risks versus benefits of

choosing portable DR technology over CR one of which includes the cost and fragility

of DR detectors

The DQE performance of one wireless system is just as good as or better than

conventional systems as seen by the DRX-1C performance compared to the Pixium

4600 Wireless systems can also reduce the need for CR readers especially in portable

applications in other regions of the world (eg military hospitals developing countries)

However while DQE performance indicates the physical performance of the detector

system it is still unknown how it relates to observer performance

I5 Conclusions

Two wireless image receptors DRX-1C and DRX-1 were evaluated and

compared with the conventional DR flat-panel Pixium 4600 in terms of DQE

27

performance along with MTF and NNPS performances The detectors have similar

resolution properties although the DRX-1 is inferior at higher spatial frequencies The

NNPS and DQE results both indicate that the DRX-1C is superior to the DRX-1 and

comparable if not better to the Pixium 4600

The results from the filtration comparison indicate no substantial differences

between the IEC-based filtration and the copper-based alternative filtration Only slight

differences were found in the low frequency components of the NNPS and the DQE due

to the inherent nonuniformities of the IEC specified filtration Given the similarity of the

results and low attenuation advantage of the copper and aluminum filter its use is

encouraged

28

II Directional MTF for Breast Tomosynthesis

II1 Introduction

Breast tomosynthesis is an emerging 3D imaging modality that has potential use

for screening and diagnosis of breast cancer Breast tomosynthesis along with other 3D

techniques is preferable to planar imaging methods (eg mammography) because they

reduce anatomical noise by removing overlying structures above and below the plane of

an image slice [17-20] Recent advances in detectors and computer technology have

made digital tomosynthesis feasible

An image quality metric of particular importance in breast tomosynthesis is

spatial resolution Resolution is important to know in order to assess small-detail

structures such as microcalcifications A descriptive metric for characterizing spatial

resolution in the Fourier (or frequency) domain is the modulation transfer function

(MTF) Affected by reconstruction filters [21] the limited angular projections involved in

breast tomosynthesis results in highly anisotropic (or nonuniform) resolution Many

studies have looked only at characterizing the in-plane spatial resolution (ie in an

individual slice) with an elevated angled edge phantom [2223] A few studies have

looked at characterizing a more comprehensive 3D spatial resolution by using a

phantom with angled wires or tubes [24-26] However such studies require precise

mechanical alignment of the phantoms Several studies have explored a method using a

29

sphere phantom for the directional 3D MTF evaluation for microtomography [27] and

multi-slice CT [2829] This method has not yet been extended to breast tomosynthesis

This chapter focuses on breast tomosynthesis because it is highly anisotropic in

spatial resolution and like its predecessor mammography requires high spatial

resolution Additionally breast tomosynthesis acquisitions and reconstructions produce

several types of artifacts The use of a cone-based method using a sphere phantom [28] is

explored to characterize the directional 3D spatial resolution of simulated images from

breast tomosynthesis A technique for removing out-of-plane artifacts of the ESFs for the

in-plane axes is investigated to yield a modified MTF in a method that separates artifact

information from resolution information

II2 Materials and Methods

II2i Image Simulation

Breast tomosynthesis images were simulated by using a virtual imaging system

depicted in Figure 12 A volumetric breast phantom was voxelized as a rectangular mass

of uniform breast equivalent tissue of 4 cm thickness embedded with fifteen evenly

spaced plastic sphere inserts of 12 mm diameter The spheres were placed in a grid

formation within the central plane of the phantom The x-ray fluence was modeled from

a 28 kVp beam incident upon an indirect flat-panel detector with 200 micro m pixel size

Twenty-three projections within an angular range of 44deg were simulated using cascaded

systems analysis to generate characteristic 2D noise and spatial blurring [29] Each

30

projection was simulated to have an exposure of 174 mR with a fluence of 79 times 105

photonsmm-2 A standard filtered backprojection technique based on the Feldkamp

reconstruction algorithm [29] was used to reconstruct the projections and produce a

volumetric dataset with an isotropic voxel size of 200 micro m

Figure 12 Depiction of the virtual image system

II2ii Uncorrected MTF

To enable comparison of multiple spheres the reconstructed volume was

initially homogenized by performing a background subtraction based on a portion of the

volume devoid of spheres The voxel values were rescaled between one and zero to

eliminate negative values

31

The volumetric data were segmented to extract individual regions of interest

(ROIs) each containing a single sphere The ROIs extended along the full range of the z-

axis A thresholded ROI was generated by determining the exterior and interior voxels

relative to the sphere in the ROI The threshold value was set at 45 of the maximum

voxel value prior to thresholding The exterior and interior voxel values were then set to

values of 0 and 1 respectively Using the thresholded volume the center of mass was

calculated to determine the centroid The voxel values from the original ROI were

subsequently tabulated with the associated distances azimuthal angles and polar

angles relative to the centroid

Conical regions were prescribed along the positive and negative directions along

the three major axes extending from the centroid of the sphere as depicted in Figure 13

The axes about which the extent of the cone angle was delineated were defined with

the azimuthal and polar angles

Voxels with centers within the angular range of the cone were considered for

generating the edge spread function (ESF) To improve regularity of the distance

sampling interval the ESF values were rebinned to discrete distances corresponding to a

fraction of the voxel size Only voxels with distances ranging from the voxel size (ie

200 micro m) to the maximum distance were considered The ESFs from multiple spheres

were averaged together for each of the three major axes to produce an averaged ESF

which was further smoothed utilizing a Gaussian filter

32

Figure 13 Example of 30-degree cone prescribed along z axis of the sphere

The resulting ESF was then differentiated using the central difference method to

produce the line spread function (LSF) A Hanning filter with the same length as the LSF

was applied to zero out the tails of the LSF The presampled MTF was subsequently

computed as the amplitude of the Fourier transform of the LSF The MTF was

normalized with respect to the maximum value occurring within the range of the cutoff

frequency Binning size and conical range for the ESF were considered for maximizing

accuracy and minimizing noise of the MTF verified by comparison against the

theoretical MTF as determined in the previous section

II2iii Theoretical Directional MTF

The theoretical 3D MTF was calculated using a priori knowledge of the transfer

function of the virtual imaging system described in the previous section A phantom

was created with a set of point objects in a uniform and noise-free background with the

objects spanning across the volume of the breast [29] Twenty-one realizations were

33

generated from the reconstructed images of the point objects to yield a set of 3D point

spread functions (PSFs) The 3D fast Fourier transform (FFT) was performed for each 3D

PSF and averaged to give an ldquoexpectationrdquo 3D MTF [29] The theoretical directional

MTFs in the three major spatial axes were determined by line profiles along each of the

corresponding spatial frequency axes in the 3D MTF An additional theoretical MTF for

each direction was determined by using the application of conical regions along the axes

in frequency-space to take into account the contributions of MTF information from other

planes

II2iv Modified MTF

The tomosynthesis reconstruction is known to have edge enhancements which

affect the overall MTF by shifting the peaks of the MTF toward the higher frequencies

[23] The presence of this artifact complicates the interpretation of the actual spatial

resolution of the images Several steps were performed to remove the artifact

contribution to the resolution information particularly for the in-plane x and y

directions with the assumption that resolution information was contained immediately

near the edge

For the x-direction averaged ESF only values that were detected to be inside the

edge of the sphere were considered Those values were previously determined via

thresholding for calculating the centroid The ESF information corresponding to these

values was inversed and flipped about the detected edge to produce a symmetric

34

modified ESF The modified MTF was subsequently calculated from this modified ESF

as described in the previous section

For the y-direction averaged ESF an upward trend was found in the initial part

of the ESF This section was detrended with a polynomial fit and subtracted to produce a

flatter curve in that region The resulting detrended ESF was used to calculate the y axis

modified MTF

Figure 14 Photograph of the imaging system with the acrylic sphere phantom

embedded in oil

II2v Preliminary Experimental Validation

A clinical breast tomosynthesis system (Mammomat Inspiration Siemens AG

Munich Germany) was used to perform a preliminary evaluation of the cone-based

MTF technique The phantom for the experiment consisted of a single acrylic ball of 075

in diameter (SmallParts Seattle WA) suspended by a 0029 in diameter plastic filament

35

(Omniflex Zebco Tulsa OK) in an acrylic frame filled up to 4 in with vegetable oil

(Target Brands Inc Minneapolis MN) The system and phantom are shown in Figure

14 Twenty-five projections with an angular range of 44deg were acquired and subsequently

reconstructed to produce a volume with a voxel size of 01times01times10 mm3 The voxels were

reformatted to have an isotropic size of 01 mm The uncorrected ESF LSF and MTF

were calculated as described in the previous section

II3 Results

II3i Reconstruction

The reconstructed volume is shown in Figure 15 Notice the edge enhancement

along the x-direction as indicated by the sharp shadowing artifacts on either side of the

spheres The background was effectively homogenized using the background

subtraction technique This also took account of the curved edges of the breast phantom

With the close spacing of the spheres in the phantom the shadows along the x direction

for the fifteen spheres overlap with each other As the nine centrally located spheres

experience this effect the same way they were used for determining the ESF

A 3D rendering of the ROI containing a sphere shown in Figure 16 indicates the

anisotropic resolution of the reconstruction Note that the sphere is not accurately

reconstructed and has an oblong shape especially along the z axis Cross sectional views

of the ROI also in Figure 16 clearly demonstrate the edge enhancement causing a

shadow artifact in the x direction caused by the incomplete angular sampling of

36

tomosynthesis The sampling also introduces the triangular reconstruction of the sphere

as seen in the x-z plane Note the gradual edge drop-off in the z direction much beyond

the sphere radius

Figure 15 View of the central slice of the breast phantom reconstruction before (top)

and after (bottom) background subtraction The z axis is through the page

37

Figure 16 3D rendering of the ROI volume (left) and cross-sectional views of the most

centrally located sphere with centroid indicated with red circle (right)

II3ii Theoretical MTF

The theoretical MTFs for x y and z directions as determined from the line

profiles of the 3D MTF are shown in Figure 17 The theoretical MTF in the x direction

has a maximum value that is toward higher frequencies Its 10 response occurs at

about 125 cyclesmm which is at 50 of the cutoff frequency The rapid increase from

the zero-frequency intercept to the peak corresponds to the ramp filter used in filtered

backprojection which decreases the weighting of low frequency contributions due to the

incomplete angular sampling of the frequency-space The MTF does not reach a value of

0 at the zero-frequency intercept as it is very difficult to assess the zero-frequency

intercept due to the finite size of the phantom The theoretical MTF in the y direction

peaks at the zero-frequency intercept and reaches 20 proximal to the cutoff frequency

38

The 10 MTF is well beyond the cutoff frequency The theoretical MTF in the z direction

has a rapid drop-off at very low spatial frequencies indicating the lack of resolution in

that dimension

Figure 17 Theoretical 3D MTF results along the three major planes (top) and along x

y and z directions (bottom) Also note that the angular spread seen in the fx-fz plane is

equal to the angular range of 44deg for the acquisition

II3iii Uncorrected MTF

The ESF LSF and MTF using the cone-based method are shown for the x y and

z directions in Figure 18 It was found that a bin size of one-tenth the voxel size (002

mm) and a cone angle of 30deg to establish the ESF were enough to minimize noise and

maximize accuracy in the uncorrected MTFs considering the reasonable comparison of

the shapes of the MTF curves with the theoretical results in Figure 17 The LSFs are

generally noisy because differentiation of the ESF increases the amplitude of the noise

39

The data shown reflect a convolution with a smoothing Gaussian filter which was later

further corrected for in the reported MTF Nevertheless the high frequency components

of the noise are well beyond the MTF cutoff frequency of 25 cyclesmm and do not

impact the MTF results greatly

For the ESF in the x direction the shadow effect evident at the edge of the sphere

is visible as a steep decline followed by an increase Due to the finite distance range

provided by the ROI the ESF beyond the edge did not asymptotically reach the

background value The corresponding LSF demonstrates a low frequency modulation

that is indicated by the shift of 03 cyclesmm in the x direction for the peak of the MTF

The MTF exhibits a zero-frequency intercept that is non-zero unlike the theoretical MTF

and a 10 value at approximately 1 cyclesmm These features may be a direct

consequence of MTF information ldquocontaminationrdquo from y and z directions Furthermore

the ESF in the y direction demonstrates a reasonably shaped curve except for the slight

upward trend within the radius of the sphere which can be attributed to the shadow

artifact overlapping with the sphere volume The associated MTF has a peak shifted by

approximately 01 cyclesmm away from the axis and a 10 MTF occurring at

approximately 15 cyclesmm Both features which are not present in the theoretical

results may also be attributed to contaminant MTF information from x and z directions

The ESF in the z direction has a drop-off that occurs at a small fraction of the cutoff

frequency similar to that demonstrated by the theoretical MTF

40

Uncorrected ESF LSF and MTF

Figure 18 Uncorrected ESF (top) LSF (middle) and MTF (bottom) for x y and z

directions

41

Figure 19 Comparisons of the directional MTFs as calculated by the sphere method

(dashed line) by theoretical line profiles (light-weight line) by theoretical cone

regions (heavy-weight line)

II3iv Comparison of Theoretical and Simulated MTFs

The theoretical MTF results obtained from line profiles through the 3D MTF and

the simulated MTFs using the cone-based technique did not match very well except for

the general shape of the curves It was assumed in the previous section that the cone-

based technique contains information from other planes Figure 19 compares MTFs in

each direction for the two methods described in the methods and an additional method

based on conical regions of the 3D MTF The latter computes the MTF by averaging

contributions of the 3D MTF using the same cone prescription method used to define the

ESFs Comparison of the curves indicate some interesting correlations aside from the

fact that using conical regions with the 3D MTF results produce more noisy MTF results

partly due to the low sampling provided by the theoretical calculations The same

conclusions regarding the z direction MTF can be confirmed regardless of either

theoretical MTF procedures The experimental x direction MTF seems to agree best with

42

the line profile method whereas the y direction MTF agrees better with the cone region

method The fact that the experimental x direction MTF has a drop-off frequency that is

lower than those of either of the theoretical MTFs in Figure 19 suggests that this might

be due to integration of the z-direction in the in-plane slices considering how slices are

essentially averages of z direction information contained within it [33]

II3v Modified MTF for x and y

Modified ESF LSF and MTF curves for x and y directions are shown in Figure

20 The modified ESF and the resulting LSF in the x direction appear symmetric as

expected from the inverse and flip operation of the interior ESF about the detected edge

The modified MTF appears with less variation than the uncorrected MTF and the MTF

peak occurs at the zero-frequency axis The correction yields a 10 MTF at about 15

cyclesmm an improvement from the uncorrected MTF but still distant from the cutoff

frequency The modified ESF in the y direction demonstrates the detrended curve within

the sphere radius after a quadratic polynomial fit The resulting modified MTF still

appears similar to the uncorrected MTF except that the peak now coincides with the

zero-frequency axis For both x and y directions the low response of the modified MTFs

at the higher frequencies suggests that the contamination from other directions is

substantial due to the angular range of the cone

43

Modified ESF LSF and MTF

Figure 20 Modified ESF (top) LSF (middle) and MTF (bottom) for x and y directions

44

II3v Preliminary Experimental Validation

Cross-sections of the reconstructed sphere volume are shown in Figure 21

Relative to the simulation reconstructions the reconstructions of the experimental

phantom images produce lower contrast and higher noise The preliminary results

shown in Figure 22 indicate that our technique can be applied to actual experimental

breast tomosynthesis reconstructions However due to the noise exhibited by the MTF

curves for the x and y directions we did not determine the modified MTFs to separate

resolution and artifact information

Figure 21 Cross sectional views of the experimental sphere image with centroid

indicated with red circle

45

Uncorrected ESF LSF and MTF for Real Image

Figure 22 ESF (top) LSF (middle) and MTF (bottom) of real image for x y

and z directions

46

II4 Discussion

II4i Evaluation of Cone-based Method

The cone-based MTF technique was introduced by Thornton and Flynn [28] for

evaluation of volumetric CT images To utilize this technique as a characterization of a

3D system spatial resolution one must first consider the validity of the assumption of

shift invariance such that the same MTF result may be obtained regardless of the

location of the sphere The study by Zhao et al [23] found that there was no shift

variance for the MTF measurements along the vertical axis but this was only considering

the in-plane resolution along one axis On the other hand this study evaluated the MTF

with images simulated with cascaded systems analysis which includes conditions of

linearity and shift invariance Additionally the MTF was calculated by averaging the

ESF from several spheres in the same volume only after performing a background

subtraction This step was essential to account for the sensitivity of centroid calculations

as well as ensuring symmetric ESFs for opposing axes of the sphere ROIs

The measurement of MTF with the cone-based technique inherently

supersamples the edge of the sphere to increase signal-to-noise-ratio (SNR) of edge

information by averaging the contributions of each voxel to the ESF [713] This method

also takes into account the discrete sampling of the voxels by accounting for various

shifts of the edge in the voxel (also known as the partial volume effect) However using

the curved surface of the sphere phantom to approximate an edge along a given

47

direction naturally leads to contamination of information from other directions aside

from the one of interest Preferably a directional ESF should be created by using a single

radial line but this would limit the available voxels to obtain edge information An ideal

situation theoretically would be to use a larger-sized sphere such that the surface is

nearly flat and perpendicular to the axes of interest This would also permit a reduction

in the angular range of the cone and thus the introduction of out-of-plane information in

the resulting MTF However sphere size is a limitation in breast tomosynthesis and the

use of a large phantom might void the assumption of shift invariance of the spatial

resolution

The choice of a sphere phantom nevertheless may be based on the clinical need

to quickly acquire a single image for MTF evaluation especially for multiple directions

without presenting extra logistical challenges The use of a wire or edge phantom

requires more precise mechanical alignment to achieve the correct set up The edge

phantom [23] would require at least two images to sample all three dimensions In the

case of the three wire phantom [2425] all three dimensions of the frame must be aligned

simultaneously with respect to the axis of rotation A similar situation would be

encountered when considering a cubic phantom with the planes normal to the axis of

interest In contrast to these phantoms the sphere eliminates the need for precise

alignment especially with respect to three spatial dimensions simultaneously A sphere

48

has ideal symmetry in all directions and can be used to evaluate MTF in any arbitrary

direction

This study unlike others [242532] did not explore the effects of physical

parameters such as scatter or contrast on the final MTF result but it demonstrated the

feasibility of using the cone-based method with an actual breast tomosynthesis image of

a sphere phantom as shown in Error Reference source not found and Error Reference

source not found These effects should be addressed in future works A further look

into deriving the principles of comparing the theoretical MTF with the experimental

MTF using the cone-based method is further warranted

II4ii Separation of Artifact and Resolution Information

The focus of this study was to develop a technique for measuring spatial

resolution of tomosynthesis images The intrinsic artifacts from tomosynthesis

reconstructions however lead to uncharacteristic MTFs and possible misinterpretation

of the effective resolution information When considering previous techniques for

calculating the presampled MTF [713152328] the analysis was performed using an

edge or a line to produce the corresponding ESF The resolution information is

essentially contained only along the edge indicated by the need to calculate the LSF In a

way the method of extracting artifact information is to focus the analysis only on the

edge part of the ESF to calculate the modified MTF This will lead to a better

understanding of the limiting size of objects that may be seen in the reconstructed 3D

49

image The presampled MTF without correction should still be analyzed to understand

the entire system response Note that the ESFs attempt to reflect information only at the

detected edge of the sphere

II5 Conclusions

The directional MTF of a simulated breast tomosynthesis reconstruction was

determined by using the cone-based MTF technique demonstrating the feasibility of a

single phantom for MTF evaluation This study further presented methods of analyzing

only the edge information in the ESF to create a modified MTF along in-slice (x and y)

axes It can provide insight into the actual spatial resolution information contained in the

image while separating the resolution information from the information introduced by

artifacts caused by the reconstruction and insufficient volumetric sampling The idea of

separating the resolution and artifacts from the measured ESF are expected to facilitate

the interpretation of MTF measurements in breast tomosynthesis Similar methods may

be applied to characterize the resolution of other 3D imaging modalities

50

References

1 Garmer M Hannigs SP Jaumlger HJ et al ldquoDigital Radiography Versus

Conventional Radiology in Chest Imaging Diagnostic Performance of a Large-

Area Silicon Flat-Panel Detector in a Clinical CT-Controlled Studyrdquo American

Journal of Roentgenology Volume 74 75-80 (2000)

2 Cowen AR Kengyelics SM and Davies AG ldquoSolid-state flat-panel digital

radiography detectors and their physical imaging characteristics rdquoClinical

Radiology Volume 63 487-498 (2008)

3 Chotas HG Dobbins III JT and Ravin CE ldquoPrinciples of Digital

Radiography with Large-Area Electronically Readable Detectors A Review of

the Basicsrdquo Radiology Volume 210 Number 3 595-599 (1999)

4 Flynn MJ and Samei E Experimental comparison of noise and resolution for

2k and 4k storage phosphor radiography systems Medical Physics Volume 26

Number 8 1612-1623 (1999)

5 Rong XJ Shaw CC Liu X Lemacks MR and Thompson SK

ldquoComparison of an amorphous siliconcesium iodide flat-panel digital chest

radiography system with screenfilm and computed radiography systems ndash A

contrast-detail phantom studyrdquo Medical Physics Volume 28 Number 11 2328-

2335 (2001)

6 Ranger NT Samei E Dobbins III JT and Ravin CE Measurement of the

detective quantum efficiency in digital detectors consistent with the IEC 62220-1

standard Practical considerations regarding the choice of filter material

Medical Physics Volume 30 Number 7 2305-2311 (2005)

7 Samei E Buhr E Granfors P Vandenbroucke D and Wang X Comparison

of edge analysis techniques for the determination of the MTF of digital

radiographic systems Physics in Medicine and Biology Volume 50 3613-3625

(2005)

8 Samei E and Flynn MJ An experimental comparison of detector performance

for computed radiography systems Medical Physics Volume 29 Number 4 447-

459 (2002)

51

9 Samei E and Flynn MJ An experimental comparison of detector performance

for direct and indirect digital radiography systems Medical Physics Volume 30

Number 4 608-622 (2003)

10 Samei E Ranger NT MacKenzie A Honey ID Dobbins III JT and Ravin

CE Effective DQE (eDQE) and speed of digital radiographic systems An

experimental methodology Medical Physics Volume 36 Number 8 3806-3817

(2009)

11 Samei E Ranger NT MacKenzie A Honey ID Dobbins III JT and Ravin

CE Detector or System Extending the Concept of Detective Quantum

Efficiency to Characterize the Performance of Digital Radiographic Imaging

Systems Radiology Volume 249 Number 3 926-937 (2008)

12 ldquoIEC 62220-1 Medical Electrical Equipment ndash Characteristics of Digital X-Ray

Imaging Devices ndash Part 1 Determination of the Detective Quantum Efficiencyrdquo

International Electrotechnical Commission Geneva Switzerland (2003)

13 Samei E Ranger NT Dobbins III JT and Chen Y Intercomparison of

methods for image quality characterization I Modulation transfer function

Medical Physics Volume 33 Number 5 1454-1465 (2006)

14 Dobbins III JT Samei E Ranger NT and Chen Y Intercomparison of

methods for image quality characterization II Noise power spectrum Medical

Physics Volume 33 Number 5 1466-1475 (2006)

15 Samei E Flynn MJ and Reimann DA A method for measuring the

presampled MTF of digital radiographic systems using an edge test device

Medical Physics Volume 25 Number 1 102-113 (1998)

16 Nagel HD ldquoAluminum equivalence of materials used in diagnostic radiology

and its dependence on beam qualityrdquo Physics in Medicine and Biology Volume

31 Number 12 1381-1399 (1986)

17 Niklason LT Christian BT Niklason LE et al ldquoDigital Tomosynthesis in

Breast Imagingrdquo Radiology Volume 205 399-406 (1997)

18 Gur D ldquoTomosynthesis Potential Clinical Role in Breast Imagingrdquo American

Journal of Roentgenology Volume 189 614-615 (2007)

52

19 Park JM Franken Jr EA Garg M Fajardo LL and Niklason LT ldquoBreast

Tomosynthesis Present Considerations and Future Applicationsrdquo

RadioGraphics Volume 27 S231-S240 (2007)

20 Good WF Abrams GS Catullo VJ Chough DM Ganott MA Hakim

CM and Gur D ldquoDigital Breast Tomosynthesis A Pilot Observer Studyrdquo

American Journal of Roentgenology Volume 190 865-869 (2008)

21 Hu Y-H Zhao W Mertelmeier T and Ludwig J ldquoImage Artifact in Digital

Breast Tomosynthesis and Its Dependence on System and Reconstruction

Parametersrdquo IWDM 2008 LNCS 5116 628-634 (2008)

22 Chen Y Lo JY Ranger NT Samei E Dobbins III JT ldquoMethodology of

NEQ(f) analysis for optimization and comparison of digital breast tomosynthesis

acquisition techniques and reconstruction algorithmsrdquo Proceedings of SPIE

Volume 6510 65101I (2007)

23 Zhao B Zhou J Hu Y-H Mertelmeier T Ludwig J and Zhao W

ldquoExperimental validation of a three-dimensional linear system model for breast

tomosynthesisrdquo Medical Physics Volume 36 Number 1 240-251 (2009)

24 Madhav P Brzymialkiewicz CN Cutler SJ Bowsher JE and Tornai MP

ldquoCharacterizing the MTF in 3D for a Quantized SPECT Camera Having Arbitrary

Trajectoriesrdquo 2005 IEEE Nuclear Science Symposium Conference Record 1722-

1726 (2005)

25 Madhav P McKinley RL Samei E Bowsher JE and Tornai MP ldquoA Novel

Method to Characterize the MTF in 3D for Computed Mammotomographyrdquo

Proceedings of SPIE Volume 6142 61421Y (2006)

26 Hu Y-H Zhao B and Zhao W ldquoImage artifacts in digital breast

tomosynthesis Investigation of the effects of system geometry and

reconstruction parameters using a linear system approachrdquo Medical Physics

Volume 35 Number 12 5242-5252 (2008)

27 Seifert A and Flynn MJ ldquoResolving power of 3D x-ray microtomography

systemsrdquo Proceedings of SPIE Volume 4682 407-413 (2002)

28 Thornton MM and Flynn MJ Measurement of the spatial resolution of a

clinical volumetric computed tomography scanner using a sphere phantom

Proceedings of SPIE Volume 6142 61421Z (2006)

53

29 Baek J Pelc NJ ldquoUse of sphere phantoms to measure the 3D MTF of FDK

reconstructionsrdquo Proceedings of SPIE Volume 7961 79610D (2011)

30 Richard S and Samei E ldquoQuantitative imaging in breast tomosynthesis and CT

Comparison of detection and estimation task performancerdquo Medical Physics

Volume 37 Number 6 2627-2637 (2010)

31 Chen Y Lo JY and Dobbins III JT ldquoImpulse response analysis for several

digital tomosynthesis mammography reconstruction algorithmsrdquo Proceedings of

SPIE Volume 5745 541-549 (2005)

32 Zhao B and Zhao W ldquoThree-dimensional linear system analysis for breast

tomosynthesisrdquo Medical Physics Volume 35 Number 12 5219-5232 (2008)

33 Wu G Mainprize JG Boone JM and Yaffe MJ ldquoEvaluation of scatter

effects on image quality for breast tomosynthesisrdquo Medical Physics Volume 36

Number 10 4425-4432 (2009)

Page 17: Development and Evaluation of 2D and 3D Image Quality ...

4

Table 1 Physical Characteristics of Digital Image Receptors

Manufacturer Detector

Detector

type

Detector

material

Pixel pitch

(size) Array size

Imaging

area

Trixell

(Moirans France)

Pixium

4600 Indirect

CsITl

(CsI) 0143 mm

3121times3121

4 subpanels 45times45 cm2

Carestream Health Inc

(Rochester NY)

DRX-1C

(wireless) Indirect

CsITl

(CsI) 0139 mm

2560times3072

single panel 35times43 cm2

Carestream Health Inc

(Rochester NY)

DRX-1

(wireless) Indirect

G2O2STb

(GOS) 0139 mm

2560times3072

single panel 35times43 cm2

calibrated radiation meters (Mult-O-Meter Type 407 Unfors Instruments AB Billdal

Sweden) at 183 cm source-to-chamber-distance (SCD) The SCD also corresponded to

same plane as the image receptor surface The x-ray output was made to conform to IEC

beam quality definitions [1215] on the basis of half value layer (HVL) and peak

kilovoltage setting using an aluminum filtration (type-1100 99 purity) and an

alternative filtration consisting of copper (UNS C11000 999 purity) and aluminum

(type-1100 99 purity) The IEC radiation quality numbers (RQA) used in this study are

summarized in Table 2 HVLs were determined by iteratively adding successive

thicknesses of aluminum until reaching reduced exposure levels within a tolerance of

0485-0515 [12] As for the alternative filtration the aluminum was placed downstream

of the copper filter to attenuate characteristic radiation peaks from copper at

approximately 9 keV

I2iib Data Linearization

The system response function was determined for each detector and filtration

combination by acquiring flat-field images at increasing photon fluence until just before

5

Table 2 Beam Qualities and Required Filtrations

IEC Radiation

Quality Number

Peak

kilovoltage

Required

HVL

Required IEC

Filtration

Actual IEC

Filtration

Alternative

Filtration

RQA5 70 kVp 71 mm Al 21 mm Al 21 mm Al 05 mm Cu +

10 mm Al

RQA9 120 kVp 115 mm Al 42 mm Al 40 mm Al 104 mm Cu +

10 mm Al

For reasons of convenience these will be referred to as RQA5A RQA5C RQA9A and RQA9C

saturation levels To avoid the influence of detector backscatter on exposure

measurements a relationship for each filtration was first determined for two radiation

meters A target meter was placed at the central axis and a reference meter was placed at

the edge of the light field (large enough to cover the detectors) The reference meter

served as a surrogate for the target meter to avoid direct exposure measurements in the

plane of the image receptor Exposure relationships were determined before each

measurement set (ie detector and filtration combination) to account for changes in

temperature pressure and humidity The system response function was calculated by

using a regression of ADU (pixel value) versus exposure Images acquired for each

series were then converted to achieve a linear response with zero offset and scaled to

achieve high quantization (adequate dynamic range) Linearization of the detector

responses ensured that zero exposure corresponded to zero pixel value

I2iic Spectral Simulation

The effects of additional filtration on x-ray output spectra were observed with

spectral simulation software (XSPECT V40 Henry Ford Hospital Detroit MI) To more

6

adequately describe the performance of a typical X-ray generator inherent filtration of 3

mm oil 148 mm Pyrex glass and 2 mm aluminum was input into the simulation in

addition to the filters of interest The ideal signal to noise ratio squared or incident

photon fluence per exposure (q) was estimated for each filtration by integrating the

energy-dependent photon counts per unit exposure over all energy bins

I2iii DQE Measurements

The assessment of the linearized images followed the formalism described by

IEC 62220-1 for measuring the DQE [12] For this study the normal exposure level XN

was set at 1 mR to the detector surface as measured at the central axis perpendicular to

the anode-cathode axis

I2iiia Modulation Transfer Function

Spatial resolution was characterized by evaluating the presampled modulation

transfer function (MTF) along directions parallel (vertical) and perpendicular

(horizontal) to the anode-cathode axis using the angled-edge method [6-1013] A radio-

opaque edge test device [7] was placed in the center of the field at a pitch of

approximately 301 (about 2deg) to the axis perpendicular to that being measured as

shown in Figure 1 External lead apertures were not used [6] instead the internal

collimation from the radiographic unit was used to collimate the beam to the detector

area Raw images were acquired of the edge with the normal exposure level XN of 1 mR

at the detector face The procedure of calculating the MTF followed previously described

7

methods [6-1013] The edge spread function (ESF) was determined along lines crossing

the edge of the angled test device The derivative of the ESF was calculated to form the

line spread function (LSF) to which a Hanning filter was applied The MTF was then

calculated as the fast Fourier transform (FFT) of the LSF and normalized at the zero-

frequency axis To conform to IEC guidelines the MTF was resampled into frequency

steps of 005 cyclesmm [12]

Figure 1 MTF images for DRX-1C detector with radio-opaque edge test device with

arrows indicating the horizontal (left) and vertical (right) directions

I2iiib Noise Power Spectrum

Noise amplitude and texture were characterized by determining the normalized

noise power spectrum (NNPS) which was evaluated with flat field exposures at

approximate exposure levels of XN2 XN and 2XN (05 10 and 20 mR) to the image

receptor surface Analysis of the flat-field images followed previously defined methods

[41415] using over 4 million independent pixels with regions of interest (ROIs) of size

8

128x128 The NNPS images were detrended using a quadratic (second order)

background subtraction Small variations in exposure across ROIs were corrected by

normalizing pixel values of each ROI to the mean value in the top left ROI as shown in

Figure 2 The NNPS was then calculated with the 2D FFT including the zero-frequency

axes corresponding to the horizontal and vertical directions The results were then

resampled using 005 frequency bins according to IEC guidelines [12]

Figure 2 NNPS image for DRX-1C detector indicating the top left ROI that served as

the reference for normalizing other ROIs in the image The ROI array was formed

along the directions indicated by the arrows The heel effect visible along the vertical

axis of the detector is an example of small variation in signal across the image

I2iiic DQE Calculation

The DQE was calculated using the following relationship [615]

9

where the frequency-dependent MTF and NNPS were determined as described in

previous sections X was the exposure value in mR corresponding to the NNPS image

and q was the ideal signal to noise ratio squared in units of photonsmiddotmm-2middotmR-1 as

estimated from the spectral simulations

I3 Results

I3i Data Linearization

The detectors in this study provided raw ADU (or pixel) values in a linear scale

The data were converted using the following system conversion function

where Q(ij) is the raw image data m and b are slope and intercept parameters obtained

from linear regression of the system response function and I(ij) is the linearized scaled

data The factor of 1000 was found to scale I(ij) such that the maximum value was a

large 16-bit number Figure 3 shows the original and linearized system responses for the

Pixium 4600 Note that the y-intercepts of the regressions for the linearized responses

are negligible (lt 01) with respect to the slopes a sufficient condition for zero offset

considerations

I3ii Spectral Simulation

The spectral simulations of the IEC filtrations and alternative filtrations indicate

many similarities in their effective energies HVLs and overall shapes of normalized

spectra Results are summarized in Table 3

10

Pixium 4600 Original System

Response

Pixium 4600 Linearized System

Response R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 3 Original (left) and linearized (right) system responses for Pixium 4600 The

linearized system responses were measured from actual images The offsets are small

with respect to the slope sufficient enough for zero-offset conditions

y = 13971x - 13236

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x - 00106Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 13576x + 28292

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

7000

0000 1000 2000 3000 4000 5000

AD

U

Exposure (mR)

y = 99997x - 00067Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0000 1000 2000 3000 4000 5000

AD

U

Exposure (mR)

y = 13644x + 16167Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x + 00044

Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 13845x + 13541

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x - 00177

Rsup2= 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

11

Table 3 Spectral Simulation Results

Beam Quality Filtration

Mean Energy

(kV)

Photon Fluence

(mRmm2)

RQA5A 21 mm Al 5243 259543

RQA5C 05 mm Cu + 10 mm Al 5214 259554

diff 055 0004

RQA9A 40 mm Al 7619 273281

RQA9C 104 mm Cu + 10 mm Al 7579 273964

diff 052 025

Figure 4 Spectral simulations for RQA5 (top) and RQA9 (bottom) conditions Note

the similarities of spectral shapes of the normalized spectra (right) Also note the

significant differences in fluence between filtrations in the simulated spectra (left)

00E+00

50E+04

10E+05

15E+05

20E+05

25E+05

30E+05

35E+05

40E+05

45E+05

0 20 40 60 80

ph

oto

ns

mA

s-1

cm

-2

keV

RQA5 Spectra Comparison

21 mm Al

05 mm Cu + 10 mm Al

00

02

04

06

08

10

12

0 20 40 60 80

keV

RQA5 Normalized Spectra Comparison

21 mm Al

05 mm Cu +

10 mm Al

00E+00

50E+05

10E+06

15E+06

20E+06

25E+06

30E+06

35E+06

40E+06

45E+06

50E+06

0 50 100 150

ph

oto

ns

mA

s-1

cm

-2

keV

RQA9 Spectra Comparison

40 mm Al

104 mm Cu +

10 mm Al

00

02

04

06

08

10

12

0 50 100 150

keV

RQA9 Normalized Spectra Comparison

40 mm Al104 mm Cu + 10 mm Al

12

I3iii Modulation Transfer Function

The limiting spatial resolutions of the systems were indicated by the cutoff

frequencies which were approximately 35 cyclesmm for all three detectors The spatial

resolutions also demonstrated a good degree of isotropy as confirmed by the close

alignment of MTF curves between vertical and horizontal directions differentiated in

Figure 5 by dashed and solid lines respectively The MTF curves for the Pixium 4600

and DRX-1C were nearly equal to each other whereas the DRX-1 MTF curve showed a

more rapid decrease at high frequencies as shown in Figure 6 This difference may be

due to the differences in the inherent optical properties of the scintillating materials

where finer image details are provided by structured CsI more than by granulated GOS

There were no significant differences in MTF curves across beam qualities and filtrations

as shown by the curve comparisons in Figure 6 although the alternative filtration

produced slightly higher MTF curves as seen in Figure 4 Table 4 lists the experimental

specific spatial frequencies for varying levels of MTF

I3iv Noise Power Spectrum

The noise characteristics are indicated by the NNPS curves shown in Figure 7

The noise was similar for both horizontal and vertical directions As exposure increased

the NNPS decreased consistent with the characteristics of Poisson noise describing the

relationship between signal and noise in the presence of increased photon fluence At

13

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 5 MTF results by detector (columns) and beam quality (rows)

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

horizontal

vertical

14

Figure 6 Plots of MTF for RQA5 (top) and RQA9 (bottom) showing the relationships

between detectors (blue red and green) and by filtration (solid and dashed)

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm-1)

MTF

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm-1)

MTF

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

15

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 7 NNPS results by detector (columns) and beam quality (rows)

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

05 mR - horizontal

05 mR - vertical

10 mR - horizontal

10 mR - vertical

20 mR - horizontal

20 mR - vertical

16

Figure 8 Plots of NNPS for RQA5 (top) and RQA9 (bottom) at 1 mR exposure

showing the relationships between detectors (blue red and green) and by filtration

(solid and dashed)

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm-1)

NNPS (1 mR)

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm-1)

NNPS (1 mR)

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

17

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 9 DQE results by detector (columns) and beam quality (rows)

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

05 mR - horizontal

05 mR - vertical

10 mR - horizontal

10 mR - vertical

20 mR - horizontal

20 mR - vertical

18

Figure 10 Plots of DQE for RQA5 (top) and RQA9 (bottom) at 1 mR exposure showing

the relationships between detectors (blue red and green) and by filtration (solid and

dashed)

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm-1)

DQE (1 mR)

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm-1)

DQE

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

19

higher frequencies the NNPS curves of the Pixium 4600 and DRX-1 diverge slightly for

the different directions illustrating increased noise in the readout direction (vertical)

Differences in the noise characteristics were more apparent among detectors as

shown for 1 mR in Figure 8 The NNPS curve for the DRX-1 was higher in magnitude

across the entire frequency range than either the Pixium 4600 or DRX-1C which both

seemed to demonstrate reasonably similar NNPS curves The higher magnitude noise of

the DRX-1 indicates higher relative noise content overall Closer inspection of the NNPS

curves of the Pixium 4600 and DRX-1C detectors in Figure 7 revealed differences in the

spacing between the three exposure levels The gaps between the Pixium 4600 NNPS

curves do not correspond to the factor of two differences between each exposure level

especially at low- to mid- spatial frequencies suggesting a higher level of fixed pattern

noise additional noise with increasing exposure levels due to ineffective gain map

corrections Between filtration schemes the differences in NNPS curves for a given beam

quality were not substantial as shown in Figure 7

I3v Detective Quantum Efficiency

The DQE results are shown in Figure 9 DQE curves across exposure levels were

almost collinear except for Pixium 4600 and in general could be inferred from the

NNPS results Additionally the DQE curves demonstrated a relatively linear response

with spatial frequencies as expected for flat-panel detectors [9] Differences in DQE

among detectors were consistent for the most part with the type of scintillating material

20

As depicted for 1 mR exposure in Figure 10 differences between Pixium 4600 and DRX-

1C DQE curves correspond to the differences in their NNPS curves DRX-1 DQE curves

were consistently lower than either the Pixium 4600 or DRX-1C curves The DQE curves

for the alternative filtration were consistently higher than those for the IEC filtration

and the most noticeable differences were near the zero-frequency axis These effects can

be both attributed to ineffective gain map correction DQE values for 1 mR exposure are

listed in Table 5

I4 Discussion

I4i Comparisons of Detectors

The limiting spatial resolutions of all three detectors were almost exactly the

same considering that their pixel areas were similar in size The decrease in high-

frequency MTF of the DRX-1 compared to the other detectors is probably a result of

increased optical blurring due to the differences in the powdered structure of GOS

versus the needle-like structure of CsI [2] The fact that the DRX-1C and Pixium 4600

have comparable MTFs suggests similar scintillator thicknesses assuming that the

materials were processed alike

The noise of the three detectors demonstrated similar trends with each other The

higher NNPS curves of the DRX-1 detector are probably due also to the scintillating

material and its operation in converting photons into signal The conversion process is

less efficient because of the less favorable stopping power of the GOS compared to CsI

21

especially with higher energy beams The noise of the Pixium 4600 and DRX-1C were

similar except for the spacing between exposures The DRX-1C NNPS curve spacing is

consistent with a factor of two difference in exposure levels but the Pixium 4600 has a

smaller spacing The 05 mR NNPS curve of the Pixium 4600 is closer to that of the 05

mR NNPS curve of the DRX-1C This demonstrates that at higher exposures the Pixium

4600 produces a larger amount of additional noise beyond that explained by simple

stochastic effects It suggests bad performance in the gain map corrections

The DQE results indicate SNR properties of each detector The Pixium 4600 and

DRX-1C are comparable for the most part with the DRX-1C performing slightly better

The DRX-1 as predicted from MTF and NNPS results has a DQE much lower than

either of the previous two This is a reflection of the detection properties as provided by

its scintillator material The DQE of the DRX-1 however is comparable to CR image

receptors [2] The mid-frequency dips in the DQE for Pixium 4600 may be due to the

optical properties of the CsI phosphor layer which can affect the MTF in this manner

Because the DQE is calculated by squaring the MTF this effect at the mid-range

frequencies becomes more apparent The dips may also be further evidence of bad gain

map corrections

I4ii Comparisons of Filtrations

The alternative filtration closely matches for the most part the IEC-based

filtration for MTF NNPS and DQEs at RQA5 but not at RQA9 The filters do not have

22

Table 4 Experimental MTF frequency locations for 1 mR exposure

Detector Filtration

50 MTF

(mm-1)

40 MTF

(mm-1)

30 MTF

(mm-1)

20 MTF

(mm-1)

10 MTF

(mm-1)

Pixium

4600

RQA5A 115 145 185 245 330

RQA5C 125 155 195 250 345

RQA9A 110 175 175 235 330

RQA9C 125 155 195 255 345

DRX-1C

RQA5A 120 150 185 245 350

RQA5C 125 155 195 255 355

RQA9A 120 150 190 250 355

RQA9C 130 160 210 265 360

DRX-1

RQA5A 110 135 160 205 280

RQA5C 110 135 170 210 285

RQA9A 105 125 155 195 270

RQA9C 110 135 165 210 285

Table 5 Estimated DQE values for 1 mR exposure by frequency bins

Detector Filtration DQE(00 mm-1) DQE(10 mm-1) DQE(20 mm-1) DQE(30 mm-1)

Pixium

4600

RQA5A 62 42 32 21

RQA5C 63 45 36 25

RQA9A 41 27 30 13

RQA9C 43 33 27 19

DRX-1C

RQA5A 72 52 35 21

RQA5C 76 55 41 24

RQA9A 49 33 23 15

RQA9C 51 40 31 20

DRX-1

RQA5A 38 24 12 4

RQA5C 38 25 14 5

RQA9A 28 18 9 4

RQA9C 28 19 12 5

DQE values at the zero-frequency axis were estimated by the intercept of a linear fit of low-frequency data

but excluding most proximal to the axis due to large fluctuations Other estimated values are grouped into

frequency bins due to the noisiness of the data

23

considerable differences in the spatial resolutions of the detectors as expected The noise

responses for each filtration were also similar except at the lower frequencies of the

NNPS especially near the zero-frequency axis There observing the NNPS responses at

RQA5 for Pixium 4600 and DRX-1C in Figure 8 the NNPS for the IEC-based filtration

(solid lines) tend to drop faster than the NNPS for the alternative filtration This

subsequently appears as a drop in DQE near the zero-frequency axis shown for those

detectors in Figure 10 Overall as indicated in Table 5 the DQEs of the two filtrations

while similar in trend indicate that the alternative filtration increases the DQE by a

small amount of 3-5 Part of this may be explained by the slightly higher beam

energy which may be more optimal for the energy response of the detectors or may

weigh the pixel responses slightly considering that they are energy-integrating types

The most probable explanation is the gain map correction for the alternative filtration

where fixed pattern noise is more sufficiently reduced

A previous study [6] had discussed the choice of filter material in the analysis of

DQE when achieving the beam conditions defined by IEC It found that visible

nonuniformities were present with the higher purity aluminum filter (type-11999 alloy)

The low frequency mottle in the flat-field images for NPS measurements were also

attributed to structured noise from the grain size in the IEC-based filter with an

attenuating thickness that would reveal nonuniformities The mottle in the current study

was only observable under very narrow windowing as shown in Figure 11 Such low

24

frequency artifacts which are not readily noticeable may also be caused by shading

artifacts inverse square law or even the heel effect A possible method to correct for this

is a subtraction method by taking the average of the flat-field images for an exposure

level and then subtracting that from each of them This would remove nonuniformities

that were not corrected using a suboptimal gain map calibration

Figure 11 DRX1-C NNPS images at 1 mR for RQA5 with IEC filtration (left) and

alternative filtration (right) Images are equally windowed at 45 and leveled at 980

One convenient aspect of the copper and aluminum filtration is that it requires

much less tube current to achieve the same amount of exposure at the detector than the

much thicker aluminum filtration As shown in the non-normalized spectra in Figure 2

the exiting photon fluence exiting the copper and aluminum filtration is substantially

higher than that of the IEC-specified filtration This is due to the smaller total filtration

25

attenuation For extensive DQE analysis multiple sets of exposures may be acquired

before tube overheating becomes a concern

One limitation to the comparison of the two filtrations is that calibration

procedures specified copper and aluminum filtration at 80 kVp (for all detectors 05 mm

Cu and 10 mm Al) This may have influenced the results in favor of the alternative

filtration A further investigation involving the calibration procedures and performing

DQE measurements is encouraged Another factor may be influenced by the fact that the

tests were performed at 70 kVp and 120 kVp different from the recommended

calibration tube potential Clearly there would be differences in the linear attenuation

coefficients of the filters and different energy responses of the detectors themselves This

must be considered when interpreting DQE results The current results support a

previous study decades ago that described filtration of different material types in terms

of an aluminum equivalent [16] The results show that the two filtration schemes are

essentially equivalent when considering beam qualities and spatial resolutions The

NNPS and DQE results can be seen as close enough where their small differences are

insignificant when performing quality assurance tests in a clinical setting Overall our

results indicate that the alternative filtration with copper and aluminum may be more

convenient to use than the current IEC standard filtration

26

I4iii Implications of Wireless DR

This study has shown that wireless image receptors can have the same DQE

performance if not better than conventional flat-panel detectors They operate on the

same basic physical principles the new features offered by the DRX-1C and DRX-1 are

wireless communication with the workstation and electronics packaging technology

The latter feature may pose limitations for these units in terms of possible degradation

in the detectors in routine clinical conditions A consideration for future work would be

to longitudinally track DQE performance of the wireless detectors over time while being

utilized in a clinical environment In the end one must consider risks versus benefits of

choosing portable DR technology over CR one of which includes the cost and fragility

of DR detectors

The DQE performance of one wireless system is just as good as or better than

conventional systems as seen by the DRX-1C performance compared to the Pixium

4600 Wireless systems can also reduce the need for CR readers especially in portable

applications in other regions of the world (eg military hospitals developing countries)

However while DQE performance indicates the physical performance of the detector

system it is still unknown how it relates to observer performance

I5 Conclusions

Two wireless image receptors DRX-1C and DRX-1 were evaluated and

compared with the conventional DR flat-panel Pixium 4600 in terms of DQE

27

performance along with MTF and NNPS performances The detectors have similar

resolution properties although the DRX-1 is inferior at higher spatial frequencies The

NNPS and DQE results both indicate that the DRX-1C is superior to the DRX-1 and

comparable if not better to the Pixium 4600

The results from the filtration comparison indicate no substantial differences

between the IEC-based filtration and the copper-based alternative filtration Only slight

differences were found in the low frequency components of the NNPS and the DQE due

to the inherent nonuniformities of the IEC specified filtration Given the similarity of the

results and low attenuation advantage of the copper and aluminum filter its use is

encouraged

28

II Directional MTF for Breast Tomosynthesis

II1 Introduction

Breast tomosynthesis is an emerging 3D imaging modality that has potential use

for screening and diagnosis of breast cancer Breast tomosynthesis along with other 3D

techniques is preferable to planar imaging methods (eg mammography) because they

reduce anatomical noise by removing overlying structures above and below the plane of

an image slice [17-20] Recent advances in detectors and computer technology have

made digital tomosynthesis feasible

An image quality metric of particular importance in breast tomosynthesis is

spatial resolution Resolution is important to know in order to assess small-detail

structures such as microcalcifications A descriptive metric for characterizing spatial

resolution in the Fourier (or frequency) domain is the modulation transfer function

(MTF) Affected by reconstruction filters [21] the limited angular projections involved in

breast tomosynthesis results in highly anisotropic (or nonuniform) resolution Many

studies have looked only at characterizing the in-plane spatial resolution (ie in an

individual slice) with an elevated angled edge phantom [2223] A few studies have

looked at characterizing a more comprehensive 3D spatial resolution by using a

phantom with angled wires or tubes [24-26] However such studies require precise

mechanical alignment of the phantoms Several studies have explored a method using a

29

sphere phantom for the directional 3D MTF evaluation for microtomography [27] and

multi-slice CT [2829] This method has not yet been extended to breast tomosynthesis

This chapter focuses on breast tomosynthesis because it is highly anisotropic in

spatial resolution and like its predecessor mammography requires high spatial

resolution Additionally breast tomosynthesis acquisitions and reconstructions produce

several types of artifacts The use of a cone-based method using a sphere phantom [28] is

explored to characterize the directional 3D spatial resolution of simulated images from

breast tomosynthesis A technique for removing out-of-plane artifacts of the ESFs for the

in-plane axes is investigated to yield a modified MTF in a method that separates artifact

information from resolution information

II2 Materials and Methods

II2i Image Simulation

Breast tomosynthesis images were simulated by using a virtual imaging system

depicted in Figure 12 A volumetric breast phantom was voxelized as a rectangular mass

of uniform breast equivalent tissue of 4 cm thickness embedded with fifteen evenly

spaced plastic sphere inserts of 12 mm diameter The spheres were placed in a grid

formation within the central plane of the phantom The x-ray fluence was modeled from

a 28 kVp beam incident upon an indirect flat-panel detector with 200 micro m pixel size

Twenty-three projections within an angular range of 44deg were simulated using cascaded

systems analysis to generate characteristic 2D noise and spatial blurring [29] Each

30

projection was simulated to have an exposure of 174 mR with a fluence of 79 times 105

photonsmm-2 A standard filtered backprojection technique based on the Feldkamp

reconstruction algorithm [29] was used to reconstruct the projections and produce a

volumetric dataset with an isotropic voxel size of 200 micro m

Figure 12 Depiction of the virtual image system

II2ii Uncorrected MTF

To enable comparison of multiple spheres the reconstructed volume was

initially homogenized by performing a background subtraction based on a portion of the

volume devoid of spheres The voxel values were rescaled between one and zero to

eliminate negative values

31

The volumetric data were segmented to extract individual regions of interest

(ROIs) each containing a single sphere The ROIs extended along the full range of the z-

axis A thresholded ROI was generated by determining the exterior and interior voxels

relative to the sphere in the ROI The threshold value was set at 45 of the maximum

voxel value prior to thresholding The exterior and interior voxel values were then set to

values of 0 and 1 respectively Using the thresholded volume the center of mass was

calculated to determine the centroid The voxel values from the original ROI were

subsequently tabulated with the associated distances azimuthal angles and polar

angles relative to the centroid

Conical regions were prescribed along the positive and negative directions along

the three major axes extending from the centroid of the sphere as depicted in Figure 13

The axes about which the extent of the cone angle was delineated were defined with

the azimuthal and polar angles

Voxels with centers within the angular range of the cone were considered for

generating the edge spread function (ESF) To improve regularity of the distance

sampling interval the ESF values were rebinned to discrete distances corresponding to a

fraction of the voxel size Only voxels with distances ranging from the voxel size (ie

200 micro m) to the maximum distance were considered The ESFs from multiple spheres

were averaged together for each of the three major axes to produce an averaged ESF

which was further smoothed utilizing a Gaussian filter

32

Figure 13 Example of 30-degree cone prescribed along z axis of the sphere

The resulting ESF was then differentiated using the central difference method to

produce the line spread function (LSF) A Hanning filter with the same length as the LSF

was applied to zero out the tails of the LSF The presampled MTF was subsequently

computed as the amplitude of the Fourier transform of the LSF The MTF was

normalized with respect to the maximum value occurring within the range of the cutoff

frequency Binning size and conical range for the ESF were considered for maximizing

accuracy and minimizing noise of the MTF verified by comparison against the

theoretical MTF as determined in the previous section

II2iii Theoretical Directional MTF

The theoretical 3D MTF was calculated using a priori knowledge of the transfer

function of the virtual imaging system described in the previous section A phantom

was created with a set of point objects in a uniform and noise-free background with the

objects spanning across the volume of the breast [29] Twenty-one realizations were

33

generated from the reconstructed images of the point objects to yield a set of 3D point

spread functions (PSFs) The 3D fast Fourier transform (FFT) was performed for each 3D

PSF and averaged to give an ldquoexpectationrdquo 3D MTF [29] The theoretical directional

MTFs in the three major spatial axes were determined by line profiles along each of the

corresponding spatial frequency axes in the 3D MTF An additional theoretical MTF for

each direction was determined by using the application of conical regions along the axes

in frequency-space to take into account the contributions of MTF information from other

planes

II2iv Modified MTF

The tomosynthesis reconstruction is known to have edge enhancements which

affect the overall MTF by shifting the peaks of the MTF toward the higher frequencies

[23] The presence of this artifact complicates the interpretation of the actual spatial

resolution of the images Several steps were performed to remove the artifact

contribution to the resolution information particularly for the in-plane x and y

directions with the assumption that resolution information was contained immediately

near the edge

For the x-direction averaged ESF only values that were detected to be inside the

edge of the sphere were considered Those values were previously determined via

thresholding for calculating the centroid The ESF information corresponding to these

values was inversed and flipped about the detected edge to produce a symmetric

34

modified ESF The modified MTF was subsequently calculated from this modified ESF

as described in the previous section

For the y-direction averaged ESF an upward trend was found in the initial part

of the ESF This section was detrended with a polynomial fit and subtracted to produce a

flatter curve in that region The resulting detrended ESF was used to calculate the y axis

modified MTF

Figure 14 Photograph of the imaging system with the acrylic sphere phantom

embedded in oil

II2v Preliminary Experimental Validation

A clinical breast tomosynthesis system (Mammomat Inspiration Siemens AG

Munich Germany) was used to perform a preliminary evaluation of the cone-based

MTF technique The phantom for the experiment consisted of a single acrylic ball of 075

in diameter (SmallParts Seattle WA) suspended by a 0029 in diameter plastic filament

35

(Omniflex Zebco Tulsa OK) in an acrylic frame filled up to 4 in with vegetable oil

(Target Brands Inc Minneapolis MN) The system and phantom are shown in Figure

14 Twenty-five projections with an angular range of 44deg were acquired and subsequently

reconstructed to produce a volume with a voxel size of 01times01times10 mm3 The voxels were

reformatted to have an isotropic size of 01 mm The uncorrected ESF LSF and MTF

were calculated as described in the previous section

II3 Results

II3i Reconstruction

The reconstructed volume is shown in Figure 15 Notice the edge enhancement

along the x-direction as indicated by the sharp shadowing artifacts on either side of the

spheres The background was effectively homogenized using the background

subtraction technique This also took account of the curved edges of the breast phantom

With the close spacing of the spheres in the phantom the shadows along the x direction

for the fifteen spheres overlap with each other As the nine centrally located spheres

experience this effect the same way they were used for determining the ESF

A 3D rendering of the ROI containing a sphere shown in Figure 16 indicates the

anisotropic resolution of the reconstruction Note that the sphere is not accurately

reconstructed and has an oblong shape especially along the z axis Cross sectional views

of the ROI also in Figure 16 clearly demonstrate the edge enhancement causing a

shadow artifact in the x direction caused by the incomplete angular sampling of

36

tomosynthesis The sampling also introduces the triangular reconstruction of the sphere

as seen in the x-z plane Note the gradual edge drop-off in the z direction much beyond

the sphere radius

Figure 15 View of the central slice of the breast phantom reconstruction before (top)

and after (bottom) background subtraction The z axis is through the page

37

Figure 16 3D rendering of the ROI volume (left) and cross-sectional views of the most

centrally located sphere with centroid indicated with red circle (right)

II3ii Theoretical MTF

The theoretical MTFs for x y and z directions as determined from the line

profiles of the 3D MTF are shown in Figure 17 The theoretical MTF in the x direction

has a maximum value that is toward higher frequencies Its 10 response occurs at

about 125 cyclesmm which is at 50 of the cutoff frequency The rapid increase from

the zero-frequency intercept to the peak corresponds to the ramp filter used in filtered

backprojection which decreases the weighting of low frequency contributions due to the

incomplete angular sampling of the frequency-space The MTF does not reach a value of

0 at the zero-frequency intercept as it is very difficult to assess the zero-frequency

intercept due to the finite size of the phantom The theoretical MTF in the y direction

peaks at the zero-frequency intercept and reaches 20 proximal to the cutoff frequency

38

The 10 MTF is well beyond the cutoff frequency The theoretical MTF in the z direction

has a rapid drop-off at very low spatial frequencies indicating the lack of resolution in

that dimension

Figure 17 Theoretical 3D MTF results along the three major planes (top) and along x

y and z directions (bottom) Also note that the angular spread seen in the fx-fz plane is

equal to the angular range of 44deg for the acquisition

II3iii Uncorrected MTF

The ESF LSF and MTF using the cone-based method are shown for the x y and

z directions in Figure 18 It was found that a bin size of one-tenth the voxel size (002

mm) and a cone angle of 30deg to establish the ESF were enough to minimize noise and

maximize accuracy in the uncorrected MTFs considering the reasonable comparison of

the shapes of the MTF curves with the theoretical results in Figure 17 The LSFs are

generally noisy because differentiation of the ESF increases the amplitude of the noise

39

The data shown reflect a convolution with a smoothing Gaussian filter which was later

further corrected for in the reported MTF Nevertheless the high frequency components

of the noise are well beyond the MTF cutoff frequency of 25 cyclesmm and do not

impact the MTF results greatly

For the ESF in the x direction the shadow effect evident at the edge of the sphere

is visible as a steep decline followed by an increase Due to the finite distance range

provided by the ROI the ESF beyond the edge did not asymptotically reach the

background value The corresponding LSF demonstrates a low frequency modulation

that is indicated by the shift of 03 cyclesmm in the x direction for the peak of the MTF

The MTF exhibits a zero-frequency intercept that is non-zero unlike the theoretical MTF

and a 10 value at approximately 1 cyclesmm These features may be a direct

consequence of MTF information ldquocontaminationrdquo from y and z directions Furthermore

the ESF in the y direction demonstrates a reasonably shaped curve except for the slight

upward trend within the radius of the sphere which can be attributed to the shadow

artifact overlapping with the sphere volume The associated MTF has a peak shifted by

approximately 01 cyclesmm away from the axis and a 10 MTF occurring at

approximately 15 cyclesmm Both features which are not present in the theoretical

results may also be attributed to contaminant MTF information from x and z directions

The ESF in the z direction has a drop-off that occurs at a small fraction of the cutoff

frequency similar to that demonstrated by the theoretical MTF

40

Uncorrected ESF LSF and MTF

Figure 18 Uncorrected ESF (top) LSF (middle) and MTF (bottom) for x y and z

directions

41

Figure 19 Comparisons of the directional MTFs as calculated by the sphere method

(dashed line) by theoretical line profiles (light-weight line) by theoretical cone

regions (heavy-weight line)

II3iv Comparison of Theoretical and Simulated MTFs

The theoretical MTF results obtained from line profiles through the 3D MTF and

the simulated MTFs using the cone-based technique did not match very well except for

the general shape of the curves It was assumed in the previous section that the cone-

based technique contains information from other planes Figure 19 compares MTFs in

each direction for the two methods described in the methods and an additional method

based on conical regions of the 3D MTF The latter computes the MTF by averaging

contributions of the 3D MTF using the same cone prescription method used to define the

ESFs Comparison of the curves indicate some interesting correlations aside from the

fact that using conical regions with the 3D MTF results produce more noisy MTF results

partly due to the low sampling provided by the theoretical calculations The same

conclusions regarding the z direction MTF can be confirmed regardless of either

theoretical MTF procedures The experimental x direction MTF seems to agree best with

42

the line profile method whereas the y direction MTF agrees better with the cone region

method The fact that the experimental x direction MTF has a drop-off frequency that is

lower than those of either of the theoretical MTFs in Figure 19 suggests that this might

be due to integration of the z-direction in the in-plane slices considering how slices are

essentially averages of z direction information contained within it [33]

II3v Modified MTF for x and y

Modified ESF LSF and MTF curves for x and y directions are shown in Figure

20 The modified ESF and the resulting LSF in the x direction appear symmetric as

expected from the inverse and flip operation of the interior ESF about the detected edge

The modified MTF appears with less variation than the uncorrected MTF and the MTF

peak occurs at the zero-frequency axis The correction yields a 10 MTF at about 15

cyclesmm an improvement from the uncorrected MTF but still distant from the cutoff

frequency The modified ESF in the y direction demonstrates the detrended curve within

the sphere radius after a quadratic polynomial fit The resulting modified MTF still

appears similar to the uncorrected MTF except that the peak now coincides with the

zero-frequency axis For both x and y directions the low response of the modified MTFs

at the higher frequencies suggests that the contamination from other directions is

substantial due to the angular range of the cone

43

Modified ESF LSF and MTF

Figure 20 Modified ESF (top) LSF (middle) and MTF (bottom) for x and y directions

44

II3v Preliminary Experimental Validation

Cross-sections of the reconstructed sphere volume are shown in Figure 21

Relative to the simulation reconstructions the reconstructions of the experimental

phantom images produce lower contrast and higher noise The preliminary results

shown in Figure 22 indicate that our technique can be applied to actual experimental

breast tomosynthesis reconstructions However due to the noise exhibited by the MTF

curves for the x and y directions we did not determine the modified MTFs to separate

resolution and artifact information

Figure 21 Cross sectional views of the experimental sphere image with centroid

indicated with red circle

45

Uncorrected ESF LSF and MTF for Real Image

Figure 22 ESF (top) LSF (middle) and MTF (bottom) of real image for x y

and z directions

46

II4 Discussion

II4i Evaluation of Cone-based Method

The cone-based MTF technique was introduced by Thornton and Flynn [28] for

evaluation of volumetric CT images To utilize this technique as a characterization of a

3D system spatial resolution one must first consider the validity of the assumption of

shift invariance such that the same MTF result may be obtained regardless of the

location of the sphere The study by Zhao et al [23] found that there was no shift

variance for the MTF measurements along the vertical axis but this was only considering

the in-plane resolution along one axis On the other hand this study evaluated the MTF

with images simulated with cascaded systems analysis which includes conditions of

linearity and shift invariance Additionally the MTF was calculated by averaging the

ESF from several spheres in the same volume only after performing a background

subtraction This step was essential to account for the sensitivity of centroid calculations

as well as ensuring symmetric ESFs for opposing axes of the sphere ROIs

The measurement of MTF with the cone-based technique inherently

supersamples the edge of the sphere to increase signal-to-noise-ratio (SNR) of edge

information by averaging the contributions of each voxel to the ESF [713] This method

also takes into account the discrete sampling of the voxels by accounting for various

shifts of the edge in the voxel (also known as the partial volume effect) However using

the curved surface of the sphere phantom to approximate an edge along a given

47

direction naturally leads to contamination of information from other directions aside

from the one of interest Preferably a directional ESF should be created by using a single

radial line but this would limit the available voxels to obtain edge information An ideal

situation theoretically would be to use a larger-sized sphere such that the surface is

nearly flat and perpendicular to the axes of interest This would also permit a reduction

in the angular range of the cone and thus the introduction of out-of-plane information in

the resulting MTF However sphere size is a limitation in breast tomosynthesis and the

use of a large phantom might void the assumption of shift invariance of the spatial

resolution

The choice of a sphere phantom nevertheless may be based on the clinical need

to quickly acquire a single image for MTF evaluation especially for multiple directions

without presenting extra logistical challenges The use of a wire or edge phantom

requires more precise mechanical alignment to achieve the correct set up The edge

phantom [23] would require at least two images to sample all three dimensions In the

case of the three wire phantom [2425] all three dimensions of the frame must be aligned

simultaneously with respect to the axis of rotation A similar situation would be

encountered when considering a cubic phantom with the planes normal to the axis of

interest In contrast to these phantoms the sphere eliminates the need for precise

alignment especially with respect to three spatial dimensions simultaneously A sphere

48

has ideal symmetry in all directions and can be used to evaluate MTF in any arbitrary

direction

This study unlike others [242532] did not explore the effects of physical

parameters such as scatter or contrast on the final MTF result but it demonstrated the

feasibility of using the cone-based method with an actual breast tomosynthesis image of

a sphere phantom as shown in Error Reference source not found and Error Reference

source not found These effects should be addressed in future works A further look

into deriving the principles of comparing the theoretical MTF with the experimental

MTF using the cone-based method is further warranted

II4ii Separation of Artifact and Resolution Information

The focus of this study was to develop a technique for measuring spatial

resolution of tomosynthesis images The intrinsic artifacts from tomosynthesis

reconstructions however lead to uncharacteristic MTFs and possible misinterpretation

of the effective resolution information When considering previous techniques for

calculating the presampled MTF [713152328] the analysis was performed using an

edge or a line to produce the corresponding ESF The resolution information is

essentially contained only along the edge indicated by the need to calculate the LSF In a

way the method of extracting artifact information is to focus the analysis only on the

edge part of the ESF to calculate the modified MTF This will lead to a better

understanding of the limiting size of objects that may be seen in the reconstructed 3D

49

image The presampled MTF without correction should still be analyzed to understand

the entire system response Note that the ESFs attempt to reflect information only at the

detected edge of the sphere

II5 Conclusions

The directional MTF of a simulated breast tomosynthesis reconstruction was

determined by using the cone-based MTF technique demonstrating the feasibility of a

single phantom for MTF evaluation This study further presented methods of analyzing

only the edge information in the ESF to create a modified MTF along in-slice (x and y)

axes It can provide insight into the actual spatial resolution information contained in the

image while separating the resolution information from the information introduced by

artifacts caused by the reconstruction and insufficient volumetric sampling The idea of

separating the resolution and artifacts from the measured ESF are expected to facilitate

the interpretation of MTF measurements in breast tomosynthesis Similar methods may

be applied to characterize the resolution of other 3D imaging modalities

50

References

1 Garmer M Hannigs SP Jaumlger HJ et al ldquoDigital Radiography Versus

Conventional Radiology in Chest Imaging Diagnostic Performance of a Large-

Area Silicon Flat-Panel Detector in a Clinical CT-Controlled Studyrdquo American

Journal of Roentgenology Volume 74 75-80 (2000)

2 Cowen AR Kengyelics SM and Davies AG ldquoSolid-state flat-panel digital

radiography detectors and their physical imaging characteristics rdquoClinical

Radiology Volume 63 487-498 (2008)

3 Chotas HG Dobbins III JT and Ravin CE ldquoPrinciples of Digital

Radiography with Large-Area Electronically Readable Detectors A Review of

the Basicsrdquo Radiology Volume 210 Number 3 595-599 (1999)

4 Flynn MJ and Samei E Experimental comparison of noise and resolution for

2k and 4k storage phosphor radiography systems Medical Physics Volume 26

Number 8 1612-1623 (1999)

5 Rong XJ Shaw CC Liu X Lemacks MR and Thompson SK

ldquoComparison of an amorphous siliconcesium iodide flat-panel digital chest

radiography system with screenfilm and computed radiography systems ndash A

contrast-detail phantom studyrdquo Medical Physics Volume 28 Number 11 2328-

2335 (2001)

6 Ranger NT Samei E Dobbins III JT and Ravin CE Measurement of the

detective quantum efficiency in digital detectors consistent with the IEC 62220-1

standard Practical considerations regarding the choice of filter material

Medical Physics Volume 30 Number 7 2305-2311 (2005)

7 Samei E Buhr E Granfors P Vandenbroucke D and Wang X Comparison

of edge analysis techniques for the determination of the MTF of digital

radiographic systems Physics in Medicine and Biology Volume 50 3613-3625

(2005)

8 Samei E and Flynn MJ An experimental comparison of detector performance

for computed radiography systems Medical Physics Volume 29 Number 4 447-

459 (2002)

51

9 Samei E and Flynn MJ An experimental comparison of detector performance

for direct and indirect digital radiography systems Medical Physics Volume 30

Number 4 608-622 (2003)

10 Samei E Ranger NT MacKenzie A Honey ID Dobbins III JT and Ravin

CE Effective DQE (eDQE) and speed of digital radiographic systems An

experimental methodology Medical Physics Volume 36 Number 8 3806-3817

(2009)

11 Samei E Ranger NT MacKenzie A Honey ID Dobbins III JT and Ravin

CE Detector or System Extending the Concept of Detective Quantum

Efficiency to Characterize the Performance of Digital Radiographic Imaging

Systems Radiology Volume 249 Number 3 926-937 (2008)

12 ldquoIEC 62220-1 Medical Electrical Equipment ndash Characteristics of Digital X-Ray

Imaging Devices ndash Part 1 Determination of the Detective Quantum Efficiencyrdquo

International Electrotechnical Commission Geneva Switzerland (2003)

13 Samei E Ranger NT Dobbins III JT and Chen Y Intercomparison of

methods for image quality characterization I Modulation transfer function

Medical Physics Volume 33 Number 5 1454-1465 (2006)

14 Dobbins III JT Samei E Ranger NT and Chen Y Intercomparison of

methods for image quality characterization II Noise power spectrum Medical

Physics Volume 33 Number 5 1466-1475 (2006)

15 Samei E Flynn MJ and Reimann DA A method for measuring the

presampled MTF of digital radiographic systems using an edge test device

Medical Physics Volume 25 Number 1 102-113 (1998)

16 Nagel HD ldquoAluminum equivalence of materials used in diagnostic radiology

and its dependence on beam qualityrdquo Physics in Medicine and Biology Volume

31 Number 12 1381-1399 (1986)

17 Niklason LT Christian BT Niklason LE et al ldquoDigital Tomosynthesis in

Breast Imagingrdquo Radiology Volume 205 399-406 (1997)

18 Gur D ldquoTomosynthesis Potential Clinical Role in Breast Imagingrdquo American

Journal of Roentgenology Volume 189 614-615 (2007)

52

19 Park JM Franken Jr EA Garg M Fajardo LL and Niklason LT ldquoBreast

Tomosynthesis Present Considerations and Future Applicationsrdquo

RadioGraphics Volume 27 S231-S240 (2007)

20 Good WF Abrams GS Catullo VJ Chough DM Ganott MA Hakim

CM and Gur D ldquoDigital Breast Tomosynthesis A Pilot Observer Studyrdquo

American Journal of Roentgenology Volume 190 865-869 (2008)

21 Hu Y-H Zhao W Mertelmeier T and Ludwig J ldquoImage Artifact in Digital

Breast Tomosynthesis and Its Dependence on System and Reconstruction

Parametersrdquo IWDM 2008 LNCS 5116 628-634 (2008)

22 Chen Y Lo JY Ranger NT Samei E Dobbins III JT ldquoMethodology of

NEQ(f) analysis for optimization and comparison of digital breast tomosynthesis

acquisition techniques and reconstruction algorithmsrdquo Proceedings of SPIE

Volume 6510 65101I (2007)

23 Zhao B Zhou J Hu Y-H Mertelmeier T Ludwig J and Zhao W

ldquoExperimental validation of a three-dimensional linear system model for breast

tomosynthesisrdquo Medical Physics Volume 36 Number 1 240-251 (2009)

24 Madhav P Brzymialkiewicz CN Cutler SJ Bowsher JE and Tornai MP

ldquoCharacterizing the MTF in 3D for a Quantized SPECT Camera Having Arbitrary

Trajectoriesrdquo 2005 IEEE Nuclear Science Symposium Conference Record 1722-

1726 (2005)

25 Madhav P McKinley RL Samei E Bowsher JE and Tornai MP ldquoA Novel

Method to Characterize the MTF in 3D for Computed Mammotomographyrdquo

Proceedings of SPIE Volume 6142 61421Y (2006)

26 Hu Y-H Zhao B and Zhao W ldquoImage artifacts in digital breast

tomosynthesis Investigation of the effects of system geometry and

reconstruction parameters using a linear system approachrdquo Medical Physics

Volume 35 Number 12 5242-5252 (2008)

27 Seifert A and Flynn MJ ldquoResolving power of 3D x-ray microtomography

systemsrdquo Proceedings of SPIE Volume 4682 407-413 (2002)

28 Thornton MM and Flynn MJ Measurement of the spatial resolution of a

clinical volumetric computed tomography scanner using a sphere phantom

Proceedings of SPIE Volume 6142 61421Z (2006)

53

29 Baek J Pelc NJ ldquoUse of sphere phantoms to measure the 3D MTF of FDK

reconstructionsrdquo Proceedings of SPIE Volume 7961 79610D (2011)

30 Richard S and Samei E ldquoQuantitative imaging in breast tomosynthesis and CT

Comparison of detection and estimation task performancerdquo Medical Physics

Volume 37 Number 6 2627-2637 (2010)

31 Chen Y Lo JY and Dobbins III JT ldquoImpulse response analysis for several

digital tomosynthesis mammography reconstruction algorithmsrdquo Proceedings of

SPIE Volume 5745 541-549 (2005)

32 Zhao B and Zhao W ldquoThree-dimensional linear system analysis for breast

tomosynthesisrdquo Medical Physics Volume 35 Number 12 5219-5232 (2008)

33 Wu G Mainprize JG Boone JM and Yaffe MJ ldquoEvaluation of scatter

effects on image quality for breast tomosynthesisrdquo Medical Physics Volume 36

Number 10 4425-4432 (2009)

Page 18: Development and Evaluation of 2D and 3D Image Quality ...

5

Table 2 Beam Qualities and Required Filtrations

IEC Radiation

Quality Number

Peak

kilovoltage

Required

HVL

Required IEC

Filtration

Actual IEC

Filtration

Alternative

Filtration

RQA5 70 kVp 71 mm Al 21 mm Al 21 mm Al 05 mm Cu +

10 mm Al

RQA9 120 kVp 115 mm Al 42 mm Al 40 mm Al 104 mm Cu +

10 mm Al

For reasons of convenience these will be referred to as RQA5A RQA5C RQA9A and RQA9C

saturation levels To avoid the influence of detector backscatter on exposure

measurements a relationship for each filtration was first determined for two radiation

meters A target meter was placed at the central axis and a reference meter was placed at

the edge of the light field (large enough to cover the detectors) The reference meter

served as a surrogate for the target meter to avoid direct exposure measurements in the

plane of the image receptor Exposure relationships were determined before each

measurement set (ie detector and filtration combination) to account for changes in

temperature pressure and humidity The system response function was calculated by

using a regression of ADU (pixel value) versus exposure Images acquired for each

series were then converted to achieve a linear response with zero offset and scaled to

achieve high quantization (adequate dynamic range) Linearization of the detector

responses ensured that zero exposure corresponded to zero pixel value

I2iic Spectral Simulation

The effects of additional filtration on x-ray output spectra were observed with

spectral simulation software (XSPECT V40 Henry Ford Hospital Detroit MI) To more

6

adequately describe the performance of a typical X-ray generator inherent filtration of 3

mm oil 148 mm Pyrex glass and 2 mm aluminum was input into the simulation in

addition to the filters of interest The ideal signal to noise ratio squared or incident

photon fluence per exposure (q) was estimated for each filtration by integrating the

energy-dependent photon counts per unit exposure over all energy bins

I2iii DQE Measurements

The assessment of the linearized images followed the formalism described by

IEC 62220-1 for measuring the DQE [12] For this study the normal exposure level XN

was set at 1 mR to the detector surface as measured at the central axis perpendicular to

the anode-cathode axis

I2iiia Modulation Transfer Function

Spatial resolution was characterized by evaluating the presampled modulation

transfer function (MTF) along directions parallel (vertical) and perpendicular

(horizontal) to the anode-cathode axis using the angled-edge method [6-1013] A radio-

opaque edge test device [7] was placed in the center of the field at a pitch of

approximately 301 (about 2deg) to the axis perpendicular to that being measured as

shown in Figure 1 External lead apertures were not used [6] instead the internal

collimation from the radiographic unit was used to collimate the beam to the detector

area Raw images were acquired of the edge with the normal exposure level XN of 1 mR

at the detector face The procedure of calculating the MTF followed previously described

7

methods [6-1013] The edge spread function (ESF) was determined along lines crossing

the edge of the angled test device The derivative of the ESF was calculated to form the

line spread function (LSF) to which a Hanning filter was applied The MTF was then

calculated as the fast Fourier transform (FFT) of the LSF and normalized at the zero-

frequency axis To conform to IEC guidelines the MTF was resampled into frequency

steps of 005 cyclesmm [12]

Figure 1 MTF images for DRX-1C detector with radio-opaque edge test device with

arrows indicating the horizontal (left) and vertical (right) directions

I2iiib Noise Power Spectrum

Noise amplitude and texture were characterized by determining the normalized

noise power spectrum (NNPS) which was evaluated with flat field exposures at

approximate exposure levels of XN2 XN and 2XN (05 10 and 20 mR) to the image

receptor surface Analysis of the flat-field images followed previously defined methods

[41415] using over 4 million independent pixels with regions of interest (ROIs) of size

8

128x128 The NNPS images were detrended using a quadratic (second order)

background subtraction Small variations in exposure across ROIs were corrected by

normalizing pixel values of each ROI to the mean value in the top left ROI as shown in

Figure 2 The NNPS was then calculated with the 2D FFT including the zero-frequency

axes corresponding to the horizontal and vertical directions The results were then

resampled using 005 frequency bins according to IEC guidelines [12]

Figure 2 NNPS image for DRX-1C detector indicating the top left ROI that served as

the reference for normalizing other ROIs in the image The ROI array was formed

along the directions indicated by the arrows The heel effect visible along the vertical

axis of the detector is an example of small variation in signal across the image

I2iiic DQE Calculation

The DQE was calculated using the following relationship [615]

9

where the frequency-dependent MTF and NNPS were determined as described in

previous sections X was the exposure value in mR corresponding to the NNPS image

and q was the ideal signal to noise ratio squared in units of photonsmiddotmm-2middotmR-1 as

estimated from the spectral simulations

I3 Results

I3i Data Linearization

The detectors in this study provided raw ADU (or pixel) values in a linear scale

The data were converted using the following system conversion function

where Q(ij) is the raw image data m and b are slope and intercept parameters obtained

from linear regression of the system response function and I(ij) is the linearized scaled

data The factor of 1000 was found to scale I(ij) such that the maximum value was a

large 16-bit number Figure 3 shows the original and linearized system responses for the

Pixium 4600 Note that the y-intercepts of the regressions for the linearized responses

are negligible (lt 01) with respect to the slopes a sufficient condition for zero offset

considerations

I3ii Spectral Simulation

The spectral simulations of the IEC filtrations and alternative filtrations indicate

many similarities in their effective energies HVLs and overall shapes of normalized

spectra Results are summarized in Table 3

10

Pixium 4600 Original System

Response

Pixium 4600 Linearized System

Response R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 3 Original (left) and linearized (right) system responses for Pixium 4600 The

linearized system responses were measured from actual images The offsets are small

with respect to the slope sufficient enough for zero-offset conditions

y = 13971x - 13236

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x - 00106Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 13576x + 28292

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

7000

0000 1000 2000 3000 4000 5000

AD

U

Exposure (mR)

y = 99997x - 00067Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0000 1000 2000 3000 4000 5000

AD

U

Exposure (mR)

y = 13644x + 16167Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x + 00044

Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 13845x + 13541

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x - 00177

Rsup2= 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

11

Table 3 Spectral Simulation Results

Beam Quality Filtration

Mean Energy

(kV)

Photon Fluence

(mRmm2)

RQA5A 21 mm Al 5243 259543

RQA5C 05 mm Cu + 10 mm Al 5214 259554

diff 055 0004

RQA9A 40 mm Al 7619 273281

RQA9C 104 mm Cu + 10 mm Al 7579 273964

diff 052 025

Figure 4 Spectral simulations for RQA5 (top) and RQA9 (bottom) conditions Note

the similarities of spectral shapes of the normalized spectra (right) Also note the

significant differences in fluence between filtrations in the simulated spectra (left)

00E+00

50E+04

10E+05

15E+05

20E+05

25E+05

30E+05

35E+05

40E+05

45E+05

0 20 40 60 80

ph

oto

ns

mA

s-1

cm

-2

keV

RQA5 Spectra Comparison

21 mm Al

05 mm Cu + 10 mm Al

00

02

04

06

08

10

12

0 20 40 60 80

keV

RQA5 Normalized Spectra Comparison

21 mm Al

05 mm Cu +

10 mm Al

00E+00

50E+05

10E+06

15E+06

20E+06

25E+06

30E+06

35E+06

40E+06

45E+06

50E+06

0 50 100 150

ph

oto

ns

mA

s-1

cm

-2

keV

RQA9 Spectra Comparison

40 mm Al

104 mm Cu +

10 mm Al

00

02

04

06

08

10

12

0 50 100 150

keV

RQA9 Normalized Spectra Comparison

40 mm Al104 mm Cu + 10 mm Al

12

I3iii Modulation Transfer Function

The limiting spatial resolutions of the systems were indicated by the cutoff

frequencies which were approximately 35 cyclesmm for all three detectors The spatial

resolutions also demonstrated a good degree of isotropy as confirmed by the close

alignment of MTF curves between vertical and horizontal directions differentiated in

Figure 5 by dashed and solid lines respectively The MTF curves for the Pixium 4600

and DRX-1C were nearly equal to each other whereas the DRX-1 MTF curve showed a

more rapid decrease at high frequencies as shown in Figure 6 This difference may be

due to the differences in the inherent optical properties of the scintillating materials

where finer image details are provided by structured CsI more than by granulated GOS

There were no significant differences in MTF curves across beam qualities and filtrations

as shown by the curve comparisons in Figure 6 although the alternative filtration

produced slightly higher MTF curves as seen in Figure 4 Table 4 lists the experimental

specific spatial frequencies for varying levels of MTF

I3iv Noise Power Spectrum

The noise characteristics are indicated by the NNPS curves shown in Figure 7

The noise was similar for both horizontal and vertical directions As exposure increased

the NNPS decreased consistent with the characteristics of Poisson noise describing the

relationship between signal and noise in the presence of increased photon fluence At

13

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 5 MTF results by detector (columns) and beam quality (rows)

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

horizontal

vertical

14

Figure 6 Plots of MTF for RQA5 (top) and RQA9 (bottom) showing the relationships

between detectors (blue red and green) and by filtration (solid and dashed)

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm-1)

MTF

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm-1)

MTF

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

15

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 7 NNPS results by detector (columns) and beam quality (rows)

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

05 mR - horizontal

05 mR - vertical

10 mR - horizontal

10 mR - vertical

20 mR - horizontal

20 mR - vertical

16

Figure 8 Plots of NNPS for RQA5 (top) and RQA9 (bottom) at 1 mR exposure

showing the relationships between detectors (blue red and green) and by filtration

(solid and dashed)

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm-1)

NNPS (1 mR)

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm-1)

NNPS (1 mR)

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

17

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 9 DQE results by detector (columns) and beam quality (rows)

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

05 mR - horizontal

05 mR - vertical

10 mR - horizontal

10 mR - vertical

20 mR - horizontal

20 mR - vertical

18

Figure 10 Plots of DQE for RQA5 (top) and RQA9 (bottom) at 1 mR exposure showing

the relationships between detectors (blue red and green) and by filtration (solid and

dashed)

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm-1)

DQE (1 mR)

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm-1)

DQE

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

19

higher frequencies the NNPS curves of the Pixium 4600 and DRX-1 diverge slightly for

the different directions illustrating increased noise in the readout direction (vertical)

Differences in the noise characteristics were more apparent among detectors as

shown for 1 mR in Figure 8 The NNPS curve for the DRX-1 was higher in magnitude

across the entire frequency range than either the Pixium 4600 or DRX-1C which both

seemed to demonstrate reasonably similar NNPS curves The higher magnitude noise of

the DRX-1 indicates higher relative noise content overall Closer inspection of the NNPS

curves of the Pixium 4600 and DRX-1C detectors in Figure 7 revealed differences in the

spacing between the three exposure levels The gaps between the Pixium 4600 NNPS

curves do not correspond to the factor of two differences between each exposure level

especially at low- to mid- spatial frequencies suggesting a higher level of fixed pattern

noise additional noise with increasing exposure levels due to ineffective gain map

corrections Between filtration schemes the differences in NNPS curves for a given beam

quality were not substantial as shown in Figure 7

I3v Detective Quantum Efficiency

The DQE results are shown in Figure 9 DQE curves across exposure levels were

almost collinear except for Pixium 4600 and in general could be inferred from the

NNPS results Additionally the DQE curves demonstrated a relatively linear response

with spatial frequencies as expected for flat-panel detectors [9] Differences in DQE

among detectors were consistent for the most part with the type of scintillating material

20

As depicted for 1 mR exposure in Figure 10 differences between Pixium 4600 and DRX-

1C DQE curves correspond to the differences in their NNPS curves DRX-1 DQE curves

were consistently lower than either the Pixium 4600 or DRX-1C curves The DQE curves

for the alternative filtration were consistently higher than those for the IEC filtration

and the most noticeable differences were near the zero-frequency axis These effects can

be both attributed to ineffective gain map correction DQE values for 1 mR exposure are

listed in Table 5

I4 Discussion

I4i Comparisons of Detectors

The limiting spatial resolutions of all three detectors were almost exactly the

same considering that their pixel areas were similar in size The decrease in high-

frequency MTF of the DRX-1 compared to the other detectors is probably a result of

increased optical blurring due to the differences in the powdered structure of GOS

versus the needle-like structure of CsI [2] The fact that the DRX-1C and Pixium 4600

have comparable MTFs suggests similar scintillator thicknesses assuming that the

materials were processed alike

The noise of the three detectors demonstrated similar trends with each other The

higher NNPS curves of the DRX-1 detector are probably due also to the scintillating

material and its operation in converting photons into signal The conversion process is

less efficient because of the less favorable stopping power of the GOS compared to CsI

21

especially with higher energy beams The noise of the Pixium 4600 and DRX-1C were

similar except for the spacing between exposures The DRX-1C NNPS curve spacing is

consistent with a factor of two difference in exposure levels but the Pixium 4600 has a

smaller spacing The 05 mR NNPS curve of the Pixium 4600 is closer to that of the 05

mR NNPS curve of the DRX-1C This demonstrates that at higher exposures the Pixium

4600 produces a larger amount of additional noise beyond that explained by simple

stochastic effects It suggests bad performance in the gain map corrections

The DQE results indicate SNR properties of each detector The Pixium 4600 and

DRX-1C are comparable for the most part with the DRX-1C performing slightly better

The DRX-1 as predicted from MTF and NNPS results has a DQE much lower than

either of the previous two This is a reflection of the detection properties as provided by

its scintillator material The DQE of the DRX-1 however is comparable to CR image

receptors [2] The mid-frequency dips in the DQE for Pixium 4600 may be due to the

optical properties of the CsI phosphor layer which can affect the MTF in this manner

Because the DQE is calculated by squaring the MTF this effect at the mid-range

frequencies becomes more apparent The dips may also be further evidence of bad gain

map corrections

I4ii Comparisons of Filtrations

The alternative filtration closely matches for the most part the IEC-based

filtration for MTF NNPS and DQEs at RQA5 but not at RQA9 The filters do not have

22

Table 4 Experimental MTF frequency locations for 1 mR exposure

Detector Filtration

50 MTF

(mm-1)

40 MTF

(mm-1)

30 MTF

(mm-1)

20 MTF

(mm-1)

10 MTF

(mm-1)

Pixium

4600

RQA5A 115 145 185 245 330

RQA5C 125 155 195 250 345

RQA9A 110 175 175 235 330

RQA9C 125 155 195 255 345

DRX-1C

RQA5A 120 150 185 245 350

RQA5C 125 155 195 255 355

RQA9A 120 150 190 250 355

RQA9C 130 160 210 265 360

DRX-1

RQA5A 110 135 160 205 280

RQA5C 110 135 170 210 285

RQA9A 105 125 155 195 270

RQA9C 110 135 165 210 285

Table 5 Estimated DQE values for 1 mR exposure by frequency bins

Detector Filtration DQE(00 mm-1) DQE(10 mm-1) DQE(20 mm-1) DQE(30 mm-1)

Pixium

4600

RQA5A 62 42 32 21

RQA5C 63 45 36 25

RQA9A 41 27 30 13

RQA9C 43 33 27 19

DRX-1C

RQA5A 72 52 35 21

RQA5C 76 55 41 24

RQA9A 49 33 23 15

RQA9C 51 40 31 20

DRX-1

RQA5A 38 24 12 4

RQA5C 38 25 14 5

RQA9A 28 18 9 4

RQA9C 28 19 12 5

DQE values at the zero-frequency axis were estimated by the intercept of a linear fit of low-frequency data

but excluding most proximal to the axis due to large fluctuations Other estimated values are grouped into

frequency bins due to the noisiness of the data

23

considerable differences in the spatial resolutions of the detectors as expected The noise

responses for each filtration were also similar except at the lower frequencies of the

NNPS especially near the zero-frequency axis There observing the NNPS responses at

RQA5 for Pixium 4600 and DRX-1C in Figure 8 the NNPS for the IEC-based filtration

(solid lines) tend to drop faster than the NNPS for the alternative filtration This

subsequently appears as a drop in DQE near the zero-frequency axis shown for those

detectors in Figure 10 Overall as indicated in Table 5 the DQEs of the two filtrations

while similar in trend indicate that the alternative filtration increases the DQE by a

small amount of 3-5 Part of this may be explained by the slightly higher beam

energy which may be more optimal for the energy response of the detectors or may

weigh the pixel responses slightly considering that they are energy-integrating types

The most probable explanation is the gain map correction for the alternative filtration

where fixed pattern noise is more sufficiently reduced

A previous study [6] had discussed the choice of filter material in the analysis of

DQE when achieving the beam conditions defined by IEC It found that visible

nonuniformities were present with the higher purity aluminum filter (type-11999 alloy)

The low frequency mottle in the flat-field images for NPS measurements were also

attributed to structured noise from the grain size in the IEC-based filter with an

attenuating thickness that would reveal nonuniformities The mottle in the current study

was only observable under very narrow windowing as shown in Figure 11 Such low

24

frequency artifacts which are not readily noticeable may also be caused by shading

artifacts inverse square law or even the heel effect A possible method to correct for this

is a subtraction method by taking the average of the flat-field images for an exposure

level and then subtracting that from each of them This would remove nonuniformities

that were not corrected using a suboptimal gain map calibration

Figure 11 DRX1-C NNPS images at 1 mR for RQA5 with IEC filtration (left) and

alternative filtration (right) Images are equally windowed at 45 and leveled at 980

One convenient aspect of the copper and aluminum filtration is that it requires

much less tube current to achieve the same amount of exposure at the detector than the

much thicker aluminum filtration As shown in the non-normalized spectra in Figure 2

the exiting photon fluence exiting the copper and aluminum filtration is substantially

higher than that of the IEC-specified filtration This is due to the smaller total filtration

25

attenuation For extensive DQE analysis multiple sets of exposures may be acquired

before tube overheating becomes a concern

One limitation to the comparison of the two filtrations is that calibration

procedures specified copper and aluminum filtration at 80 kVp (for all detectors 05 mm

Cu and 10 mm Al) This may have influenced the results in favor of the alternative

filtration A further investigation involving the calibration procedures and performing

DQE measurements is encouraged Another factor may be influenced by the fact that the

tests were performed at 70 kVp and 120 kVp different from the recommended

calibration tube potential Clearly there would be differences in the linear attenuation

coefficients of the filters and different energy responses of the detectors themselves This

must be considered when interpreting DQE results The current results support a

previous study decades ago that described filtration of different material types in terms

of an aluminum equivalent [16] The results show that the two filtration schemes are

essentially equivalent when considering beam qualities and spatial resolutions The

NNPS and DQE results can be seen as close enough where their small differences are

insignificant when performing quality assurance tests in a clinical setting Overall our

results indicate that the alternative filtration with copper and aluminum may be more

convenient to use than the current IEC standard filtration

26

I4iii Implications of Wireless DR

This study has shown that wireless image receptors can have the same DQE

performance if not better than conventional flat-panel detectors They operate on the

same basic physical principles the new features offered by the DRX-1C and DRX-1 are

wireless communication with the workstation and electronics packaging technology

The latter feature may pose limitations for these units in terms of possible degradation

in the detectors in routine clinical conditions A consideration for future work would be

to longitudinally track DQE performance of the wireless detectors over time while being

utilized in a clinical environment In the end one must consider risks versus benefits of

choosing portable DR technology over CR one of which includes the cost and fragility

of DR detectors

The DQE performance of one wireless system is just as good as or better than

conventional systems as seen by the DRX-1C performance compared to the Pixium

4600 Wireless systems can also reduce the need for CR readers especially in portable

applications in other regions of the world (eg military hospitals developing countries)

However while DQE performance indicates the physical performance of the detector

system it is still unknown how it relates to observer performance

I5 Conclusions

Two wireless image receptors DRX-1C and DRX-1 were evaluated and

compared with the conventional DR flat-panel Pixium 4600 in terms of DQE

27

performance along with MTF and NNPS performances The detectors have similar

resolution properties although the DRX-1 is inferior at higher spatial frequencies The

NNPS and DQE results both indicate that the DRX-1C is superior to the DRX-1 and

comparable if not better to the Pixium 4600

The results from the filtration comparison indicate no substantial differences

between the IEC-based filtration and the copper-based alternative filtration Only slight

differences were found in the low frequency components of the NNPS and the DQE due

to the inherent nonuniformities of the IEC specified filtration Given the similarity of the

results and low attenuation advantage of the copper and aluminum filter its use is

encouraged

28

II Directional MTF for Breast Tomosynthesis

II1 Introduction

Breast tomosynthesis is an emerging 3D imaging modality that has potential use

for screening and diagnosis of breast cancer Breast tomosynthesis along with other 3D

techniques is preferable to planar imaging methods (eg mammography) because they

reduce anatomical noise by removing overlying structures above and below the plane of

an image slice [17-20] Recent advances in detectors and computer technology have

made digital tomosynthesis feasible

An image quality metric of particular importance in breast tomosynthesis is

spatial resolution Resolution is important to know in order to assess small-detail

structures such as microcalcifications A descriptive metric for characterizing spatial

resolution in the Fourier (or frequency) domain is the modulation transfer function

(MTF) Affected by reconstruction filters [21] the limited angular projections involved in

breast tomosynthesis results in highly anisotropic (or nonuniform) resolution Many

studies have looked only at characterizing the in-plane spatial resolution (ie in an

individual slice) with an elevated angled edge phantom [2223] A few studies have

looked at characterizing a more comprehensive 3D spatial resolution by using a

phantom with angled wires or tubes [24-26] However such studies require precise

mechanical alignment of the phantoms Several studies have explored a method using a

29

sphere phantom for the directional 3D MTF evaluation for microtomography [27] and

multi-slice CT [2829] This method has not yet been extended to breast tomosynthesis

This chapter focuses on breast tomosynthesis because it is highly anisotropic in

spatial resolution and like its predecessor mammography requires high spatial

resolution Additionally breast tomosynthesis acquisitions and reconstructions produce

several types of artifacts The use of a cone-based method using a sphere phantom [28] is

explored to characterize the directional 3D spatial resolution of simulated images from

breast tomosynthesis A technique for removing out-of-plane artifacts of the ESFs for the

in-plane axes is investigated to yield a modified MTF in a method that separates artifact

information from resolution information

II2 Materials and Methods

II2i Image Simulation

Breast tomosynthesis images were simulated by using a virtual imaging system

depicted in Figure 12 A volumetric breast phantom was voxelized as a rectangular mass

of uniform breast equivalent tissue of 4 cm thickness embedded with fifteen evenly

spaced plastic sphere inserts of 12 mm diameter The spheres were placed in a grid

formation within the central plane of the phantom The x-ray fluence was modeled from

a 28 kVp beam incident upon an indirect flat-panel detector with 200 micro m pixel size

Twenty-three projections within an angular range of 44deg were simulated using cascaded

systems analysis to generate characteristic 2D noise and spatial blurring [29] Each

30

projection was simulated to have an exposure of 174 mR with a fluence of 79 times 105

photonsmm-2 A standard filtered backprojection technique based on the Feldkamp

reconstruction algorithm [29] was used to reconstruct the projections and produce a

volumetric dataset with an isotropic voxel size of 200 micro m

Figure 12 Depiction of the virtual image system

II2ii Uncorrected MTF

To enable comparison of multiple spheres the reconstructed volume was

initially homogenized by performing a background subtraction based on a portion of the

volume devoid of spheres The voxel values were rescaled between one and zero to

eliminate negative values

31

The volumetric data were segmented to extract individual regions of interest

(ROIs) each containing a single sphere The ROIs extended along the full range of the z-

axis A thresholded ROI was generated by determining the exterior and interior voxels

relative to the sphere in the ROI The threshold value was set at 45 of the maximum

voxel value prior to thresholding The exterior and interior voxel values were then set to

values of 0 and 1 respectively Using the thresholded volume the center of mass was

calculated to determine the centroid The voxel values from the original ROI were

subsequently tabulated with the associated distances azimuthal angles and polar

angles relative to the centroid

Conical regions were prescribed along the positive and negative directions along

the three major axes extending from the centroid of the sphere as depicted in Figure 13

The axes about which the extent of the cone angle was delineated were defined with

the azimuthal and polar angles

Voxels with centers within the angular range of the cone were considered for

generating the edge spread function (ESF) To improve regularity of the distance

sampling interval the ESF values were rebinned to discrete distances corresponding to a

fraction of the voxel size Only voxels with distances ranging from the voxel size (ie

200 micro m) to the maximum distance were considered The ESFs from multiple spheres

were averaged together for each of the three major axes to produce an averaged ESF

which was further smoothed utilizing a Gaussian filter

32

Figure 13 Example of 30-degree cone prescribed along z axis of the sphere

The resulting ESF was then differentiated using the central difference method to

produce the line spread function (LSF) A Hanning filter with the same length as the LSF

was applied to zero out the tails of the LSF The presampled MTF was subsequently

computed as the amplitude of the Fourier transform of the LSF The MTF was

normalized with respect to the maximum value occurring within the range of the cutoff

frequency Binning size and conical range for the ESF were considered for maximizing

accuracy and minimizing noise of the MTF verified by comparison against the

theoretical MTF as determined in the previous section

II2iii Theoretical Directional MTF

The theoretical 3D MTF was calculated using a priori knowledge of the transfer

function of the virtual imaging system described in the previous section A phantom

was created with a set of point objects in a uniform and noise-free background with the

objects spanning across the volume of the breast [29] Twenty-one realizations were

33

generated from the reconstructed images of the point objects to yield a set of 3D point

spread functions (PSFs) The 3D fast Fourier transform (FFT) was performed for each 3D

PSF and averaged to give an ldquoexpectationrdquo 3D MTF [29] The theoretical directional

MTFs in the three major spatial axes were determined by line profiles along each of the

corresponding spatial frequency axes in the 3D MTF An additional theoretical MTF for

each direction was determined by using the application of conical regions along the axes

in frequency-space to take into account the contributions of MTF information from other

planes

II2iv Modified MTF

The tomosynthesis reconstruction is known to have edge enhancements which

affect the overall MTF by shifting the peaks of the MTF toward the higher frequencies

[23] The presence of this artifact complicates the interpretation of the actual spatial

resolution of the images Several steps were performed to remove the artifact

contribution to the resolution information particularly for the in-plane x and y

directions with the assumption that resolution information was contained immediately

near the edge

For the x-direction averaged ESF only values that were detected to be inside the

edge of the sphere were considered Those values were previously determined via

thresholding for calculating the centroid The ESF information corresponding to these

values was inversed and flipped about the detected edge to produce a symmetric

34

modified ESF The modified MTF was subsequently calculated from this modified ESF

as described in the previous section

For the y-direction averaged ESF an upward trend was found in the initial part

of the ESF This section was detrended with a polynomial fit and subtracted to produce a

flatter curve in that region The resulting detrended ESF was used to calculate the y axis

modified MTF

Figure 14 Photograph of the imaging system with the acrylic sphere phantom

embedded in oil

II2v Preliminary Experimental Validation

A clinical breast tomosynthesis system (Mammomat Inspiration Siemens AG

Munich Germany) was used to perform a preliminary evaluation of the cone-based

MTF technique The phantom for the experiment consisted of a single acrylic ball of 075

in diameter (SmallParts Seattle WA) suspended by a 0029 in diameter plastic filament

35

(Omniflex Zebco Tulsa OK) in an acrylic frame filled up to 4 in with vegetable oil

(Target Brands Inc Minneapolis MN) The system and phantom are shown in Figure

14 Twenty-five projections with an angular range of 44deg were acquired and subsequently

reconstructed to produce a volume with a voxel size of 01times01times10 mm3 The voxels were

reformatted to have an isotropic size of 01 mm The uncorrected ESF LSF and MTF

were calculated as described in the previous section

II3 Results

II3i Reconstruction

The reconstructed volume is shown in Figure 15 Notice the edge enhancement

along the x-direction as indicated by the sharp shadowing artifacts on either side of the

spheres The background was effectively homogenized using the background

subtraction technique This also took account of the curved edges of the breast phantom

With the close spacing of the spheres in the phantom the shadows along the x direction

for the fifteen spheres overlap with each other As the nine centrally located spheres

experience this effect the same way they were used for determining the ESF

A 3D rendering of the ROI containing a sphere shown in Figure 16 indicates the

anisotropic resolution of the reconstruction Note that the sphere is not accurately

reconstructed and has an oblong shape especially along the z axis Cross sectional views

of the ROI also in Figure 16 clearly demonstrate the edge enhancement causing a

shadow artifact in the x direction caused by the incomplete angular sampling of

36

tomosynthesis The sampling also introduces the triangular reconstruction of the sphere

as seen in the x-z plane Note the gradual edge drop-off in the z direction much beyond

the sphere radius

Figure 15 View of the central slice of the breast phantom reconstruction before (top)

and after (bottom) background subtraction The z axis is through the page

37

Figure 16 3D rendering of the ROI volume (left) and cross-sectional views of the most

centrally located sphere with centroid indicated with red circle (right)

II3ii Theoretical MTF

The theoretical MTFs for x y and z directions as determined from the line

profiles of the 3D MTF are shown in Figure 17 The theoretical MTF in the x direction

has a maximum value that is toward higher frequencies Its 10 response occurs at

about 125 cyclesmm which is at 50 of the cutoff frequency The rapid increase from

the zero-frequency intercept to the peak corresponds to the ramp filter used in filtered

backprojection which decreases the weighting of low frequency contributions due to the

incomplete angular sampling of the frequency-space The MTF does not reach a value of

0 at the zero-frequency intercept as it is very difficult to assess the zero-frequency

intercept due to the finite size of the phantom The theoretical MTF in the y direction

peaks at the zero-frequency intercept and reaches 20 proximal to the cutoff frequency

38

The 10 MTF is well beyond the cutoff frequency The theoretical MTF in the z direction

has a rapid drop-off at very low spatial frequencies indicating the lack of resolution in

that dimension

Figure 17 Theoretical 3D MTF results along the three major planes (top) and along x

y and z directions (bottom) Also note that the angular spread seen in the fx-fz plane is

equal to the angular range of 44deg for the acquisition

II3iii Uncorrected MTF

The ESF LSF and MTF using the cone-based method are shown for the x y and

z directions in Figure 18 It was found that a bin size of one-tenth the voxel size (002

mm) and a cone angle of 30deg to establish the ESF were enough to minimize noise and

maximize accuracy in the uncorrected MTFs considering the reasonable comparison of

the shapes of the MTF curves with the theoretical results in Figure 17 The LSFs are

generally noisy because differentiation of the ESF increases the amplitude of the noise

39

The data shown reflect a convolution with a smoothing Gaussian filter which was later

further corrected for in the reported MTF Nevertheless the high frequency components

of the noise are well beyond the MTF cutoff frequency of 25 cyclesmm and do not

impact the MTF results greatly

For the ESF in the x direction the shadow effect evident at the edge of the sphere

is visible as a steep decline followed by an increase Due to the finite distance range

provided by the ROI the ESF beyond the edge did not asymptotically reach the

background value The corresponding LSF demonstrates a low frequency modulation

that is indicated by the shift of 03 cyclesmm in the x direction for the peak of the MTF

The MTF exhibits a zero-frequency intercept that is non-zero unlike the theoretical MTF

and a 10 value at approximately 1 cyclesmm These features may be a direct

consequence of MTF information ldquocontaminationrdquo from y and z directions Furthermore

the ESF in the y direction demonstrates a reasonably shaped curve except for the slight

upward trend within the radius of the sphere which can be attributed to the shadow

artifact overlapping with the sphere volume The associated MTF has a peak shifted by

approximately 01 cyclesmm away from the axis and a 10 MTF occurring at

approximately 15 cyclesmm Both features which are not present in the theoretical

results may also be attributed to contaminant MTF information from x and z directions

The ESF in the z direction has a drop-off that occurs at a small fraction of the cutoff

frequency similar to that demonstrated by the theoretical MTF

40

Uncorrected ESF LSF and MTF

Figure 18 Uncorrected ESF (top) LSF (middle) and MTF (bottom) for x y and z

directions

41

Figure 19 Comparisons of the directional MTFs as calculated by the sphere method

(dashed line) by theoretical line profiles (light-weight line) by theoretical cone

regions (heavy-weight line)

II3iv Comparison of Theoretical and Simulated MTFs

The theoretical MTF results obtained from line profiles through the 3D MTF and

the simulated MTFs using the cone-based technique did not match very well except for

the general shape of the curves It was assumed in the previous section that the cone-

based technique contains information from other planes Figure 19 compares MTFs in

each direction for the two methods described in the methods and an additional method

based on conical regions of the 3D MTF The latter computes the MTF by averaging

contributions of the 3D MTF using the same cone prescription method used to define the

ESFs Comparison of the curves indicate some interesting correlations aside from the

fact that using conical regions with the 3D MTF results produce more noisy MTF results

partly due to the low sampling provided by the theoretical calculations The same

conclusions regarding the z direction MTF can be confirmed regardless of either

theoretical MTF procedures The experimental x direction MTF seems to agree best with

42

the line profile method whereas the y direction MTF agrees better with the cone region

method The fact that the experimental x direction MTF has a drop-off frequency that is

lower than those of either of the theoretical MTFs in Figure 19 suggests that this might

be due to integration of the z-direction in the in-plane slices considering how slices are

essentially averages of z direction information contained within it [33]

II3v Modified MTF for x and y

Modified ESF LSF and MTF curves for x and y directions are shown in Figure

20 The modified ESF and the resulting LSF in the x direction appear symmetric as

expected from the inverse and flip operation of the interior ESF about the detected edge

The modified MTF appears with less variation than the uncorrected MTF and the MTF

peak occurs at the zero-frequency axis The correction yields a 10 MTF at about 15

cyclesmm an improvement from the uncorrected MTF but still distant from the cutoff

frequency The modified ESF in the y direction demonstrates the detrended curve within

the sphere radius after a quadratic polynomial fit The resulting modified MTF still

appears similar to the uncorrected MTF except that the peak now coincides with the

zero-frequency axis For both x and y directions the low response of the modified MTFs

at the higher frequencies suggests that the contamination from other directions is

substantial due to the angular range of the cone

43

Modified ESF LSF and MTF

Figure 20 Modified ESF (top) LSF (middle) and MTF (bottom) for x and y directions

44

II3v Preliminary Experimental Validation

Cross-sections of the reconstructed sphere volume are shown in Figure 21

Relative to the simulation reconstructions the reconstructions of the experimental

phantom images produce lower contrast and higher noise The preliminary results

shown in Figure 22 indicate that our technique can be applied to actual experimental

breast tomosynthesis reconstructions However due to the noise exhibited by the MTF

curves for the x and y directions we did not determine the modified MTFs to separate

resolution and artifact information

Figure 21 Cross sectional views of the experimental sphere image with centroid

indicated with red circle

45

Uncorrected ESF LSF and MTF for Real Image

Figure 22 ESF (top) LSF (middle) and MTF (bottom) of real image for x y

and z directions

46

II4 Discussion

II4i Evaluation of Cone-based Method

The cone-based MTF technique was introduced by Thornton and Flynn [28] for

evaluation of volumetric CT images To utilize this technique as a characterization of a

3D system spatial resolution one must first consider the validity of the assumption of

shift invariance such that the same MTF result may be obtained regardless of the

location of the sphere The study by Zhao et al [23] found that there was no shift

variance for the MTF measurements along the vertical axis but this was only considering

the in-plane resolution along one axis On the other hand this study evaluated the MTF

with images simulated with cascaded systems analysis which includes conditions of

linearity and shift invariance Additionally the MTF was calculated by averaging the

ESF from several spheres in the same volume only after performing a background

subtraction This step was essential to account for the sensitivity of centroid calculations

as well as ensuring symmetric ESFs for opposing axes of the sphere ROIs

The measurement of MTF with the cone-based technique inherently

supersamples the edge of the sphere to increase signal-to-noise-ratio (SNR) of edge

information by averaging the contributions of each voxel to the ESF [713] This method

also takes into account the discrete sampling of the voxels by accounting for various

shifts of the edge in the voxel (also known as the partial volume effect) However using

the curved surface of the sphere phantom to approximate an edge along a given

47

direction naturally leads to contamination of information from other directions aside

from the one of interest Preferably a directional ESF should be created by using a single

radial line but this would limit the available voxels to obtain edge information An ideal

situation theoretically would be to use a larger-sized sphere such that the surface is

nearly flat and perpendicular to the axes of interest This would also permit a reduction

in the angular range of the cone and thus the introduction of out-of-plane information in

the resulting MTF However sphere size is a limitation in breast tomosynthesis and the

use of a large phantom might void the assumption of shift invariance of the spatial

resolution

The choice of a sphere phantom nevertheless may be based on the clinical need

to quickly acquire a single image for MTF evaluation especially for multiple directions

without presenting extra logistical challenges The use of a wire or edge phantom

requires more precise mechanical alignment to achieve the correct set up The edge

phantom [23] would require at least two images to sample all three dimensions In the

case of the three wire phantom [2425] all three dimensions of the frame must be aligned

simultaneously with respect to the axis of rotation A similar situation would be

encountered when considering a cubic phantom with the planes normal to the axis of

interest In contrast to these phantoms the sphere eliminates the need for precise

alignment especially with respect to three spatial dimensions simultaneously A sphere

48

has ideal symmetry in all directions and can be used to evaluate MTF in any arbitrary

direction

This study unlike others [242532] did not explore the effects of physical

parameters such as scatter or contrast on the final MTF result but it demonstrated the

feasibility of using the cone-based method with an actual breast tomosynthesis image of

a sphere phantom as shown in Error Reference source not found and Error Reference

source not found These effects should be addressed in future works A further look

into deriving the principles of comparing the theoretical MTF with the experimental

MTF using the cone-based method is further warranted

II4ii Separation of Artifact and Resolution Information

The focus of this study was to develop a technique for measuring spatial

resolution of tomosynthesis images The intrinsic artifacts from tomosynthesis

reconstructions however lead to uncharacteristic MTFs and possible misinterpretation

of the effective resolution information When considering previous techniques for

calculating the presampled MTF [713152328] the analysis was performed using an

edge or a line to produce the corresponding ESF The resolution information is

essentially contained only along the edge indicated by the need to calculate the LSF In a

way the method of extracting artifact information is to focus the analysis only on the

edge part of the ESF to calculate the modified MTF This will lead to a better

understanding of the limiting size of objects that may be seen in the reconstructed 3D

49

image The presampled MTF without correction should still be analyzed to understand

the entire system response Note that the ESFs attempt to reflect information only at the

detected edge of the sphere

II5 Conclusions

The directional MTF of a simulated breast tomosynthesis reconstruction was

determined by using the cone-based MTF technique demonstrating the feasibility of a

single phantom for MTF evaluation This study further presented methods of analyzing

only the edge information in the ESF to create a modified MTF along in-slice (x and y)

axes It can provide insight into the actual spatial resolution information contained in the

image while separating the resolution information from the information introduced by

artifacts caused by the reconstruction and insufficient volumetric sampling The idea of

separating the resolution and artifacts from the measured ESF are expected to facilitate

the interpretation of MTF measurements in breast tomosynthesis Similar methods may

be applied to characterize the resolution of other 3D imaging modalities

50

References

1 Garmer M Hannigs SP Jaumlger HJ et al ldquoDigital Radiography Versus

Conventional Radiology in Chest Imaging Diagnostic Performance of a Large-

Area Silicon Flat-Panel Detector in a Clinical CT-Controlled Studyrdquo American

Journal of Roentgenology Volume 74 75-80 (2000)

2 Cowen AR Kengyelics SM and Davies AG ldquoSolid-state flat-panel digital

radiography detectors and their physical imaging characteristics rdquoClinical

Radiology Volume 63 487-498 (2008)

3 Chotas HG Dobbins III JT and Ravin CE ldquoPrinciples of Digital

Radiography with Large-Area Electronically Readable Detectors A Review of

the Basicsrdquo Radiology Volume 210 Number 3 595-599 (1999)

4 Flynn MJ and Samei E Experimental comparison of noise and resolution for

2k and 4k storage phosphor radiography systems Medical Physics Volume 26

Number 8 1612-1623 (1999)

5 Rong XJ Shaw CC Liu X Lemacks MR and Thompson SK

ldquoComparison of an amorphous siliconcesium iodide flat-panel digital chest

radiography system with screenfilm and computed radiography systems ndash A

contrast-detail phantom studyrdquo Medical Physics Volume 28 Number 11 2328-

2335 (2001)

6 Ranger NT Samei E Dobbins III JT and Ravin CE Measurement of the

detective quantum efficiency in digital detectors consistent with the IEC 62220-1

standard Practical considerations regarding the choice of filter material

Medical Physics Volume 30 Number 7 2305-2311 (2005)

7 Samei E Buhr E Granfors P Vandenbroucke D and Wang X Comparison

of edge analysis techniques for the determination of the MTF of digital

radiographic systems Physics in Medicine and Biology Volume 50 3613-3625

(2005)

8 Samei E and Flynn MJ An experimental comparison of detector performance

for computed radiography systems Medical Physics Volume 29 Number 4 447-

459 (2002)

51

9 Samei E and Flynn MJ An experimental comparison of detector performance

for direct and indirect digital radiography systems Medical Physics Volume 30

Number 4 608-622 (2003)

10 Samei E Ranger NT MacKenzie A Honey ID Dobbins III JT and Ravin

CE Effective DQE (eDQE) and speed of digital radiographic systems An

experimental methodology Medical Physics Volume 36 Number 8 3806-3817

(2009)

11 Samei E Ranger NT MacKenzie A Honey ID Dobbins III JT and Ravin

CE Detector or System Extending the Concept of Detective Quantum

Efficiency to Characterize the Performance of Digital Radiographic Imaging

Systems Radiology Volume 249 Number 3 926-937 (2008)

12 ldquoIEC 62220-1 Medical Electrical Equipment ndash Characteristics of Digital X-Ray

Imaging Devices ndash Part 1 Determination of the Detective Quantum Efficiencyrdquo

International Electrotechnical Commission Geneva Switzerland (2003)

13 Samei E Ranger NT Dobbins III JT and Chen Y Intercomparison of

methods for image quality characterization I Modulation transfer function

Medical Physics Volume 33 Number 5 1454-1465 (2006)

14 Dobbins III JT Samei E Ranger NT and Chen Y Intercomparison of

methods for image quality characterization II Noise power spectrum Medical

Physics Volume 33 Number 5 1466-1475 (2006)

15 Samei E Flynn MJ and Reimann DA A method for measuring the

presampled MTF of digital radiographic systems using an edge test device

Medical Physics Volume 25 Number 1 102-113 (1998)

16 Nagel HD ldquoAluminum equivalence of materials used in diagnostic radiology

and its dependence on beam qualityrdquo Physics in Medicine and Biology Volume

31 Number 12 1381-1399 (1986)

17 Niklason LT Christian BT Niklason LE et al ldquoDigital Tomosynthesis in

Breast Imagingrdquo Radiology Volume 205 399-406 (1997)

18 Gur D ldquoTomosynthesis Potential Clinical Role in Breast Imagingrdquo American

Journal of Roentgenology Volume 189 614-615 (2007)

52

19 Park JM Franken Jr EA Garg M Fajardo LL and Niklason LT ldquoBreast

Tomosynthesis Present Considerations and Future Applicationsrdquo

RadioGraphics Volume 27 S231-S240 (2007)

20 Good WF Abrams GS Catullo VJ Chough DM Ganott MA Hakim

CM and Gur D ldquoDigital Breast Tomosynthesis A Pilot Observer Studyrdquo

American Journal of Roentgenology Volume 190 865-869 (2008)

21 Hu Y-H Zhao W Mertelmeier T and Ludwig J ldquoImage Artifact in Digital

Breast Tomosynthesis and Its Dependence on System and Reconstruction

Parametersrdquo IWDM 2008 LNCS 5116 628-634 (2008)

22 Chen Y Lo JY Ranger NT Samei E Dobbins III JT ldquoMethodology of

NEQ(f) analysis for optimization and comparison of digital breast tomosynthesis

acquisition techniques and reconstruction algorithmsrdquo Proceedings of SPIE

Volume 6510 65101I (2007)

23 Zhao B Zhou J Hu Y-H Mertelmeier T Ludwig J and Zhao W

ldquoExperimental validation of a three-dimensional linear system model for breast

tomosynthesisrdquo Medical Physics Volume 36 Number 1 240-251 (2009)

24 Madhav P Brzymialkiewicz CN Cutler SJ Bowsher JE and Tornai MP

ldquoCharacterizing the MTF in 3D for a Quantized SPECT Camera Having Arbitrary

Trajectoriesrdquo 2005 IEEE Nuclear Science Symposium Conference Record 1722-

1726 (2005)

25 Madhav P McKinley RL Samei E Bowsher JE and Tornai MP ldquoA Novel

Method to Characterize the MTF in 3D for Computed Mammotomographyrdquo

Proceedings of SPIE Volume 6142 61421Y (2006)

26 Hu Y-H Zhao B and Zhao W ldquoImage artifacts in digital breast

tomosynthesis Investigation of the effects of system geometry and

reconstruction parameters using a linear system approachrdquo Medical Physics

Volume 35 Number 12 5242-5252 (2008)

27 Seifert A and Flynn MJ ldquoResolving power of 3D x-ray microtomography

systemsrdquo Proceedings of SPIE Volume 4682 407-413 (2002)

28 Thornton MM and Flynn MJ Measurement of the spatial resolution of a

clinical volumetric computed tomography scanner using a sphere phantom

Proceedings of SPIE Volume 6142 61421Z (2006)

53

29 Baek J Pelc NJ ldquoUse of sphere phantoms to measure the 3D MTF of FDK

reconstructionsrdquo Proceedings of SPIE Volume 7961 79610D (2011)

30 Richard S and Samei E ldquoQuantitative imaging in breast tomosynthesis and CT

Comparison of detection and estimation task performancerdquo Medical Physics

Volume 37 Number 6 2627-2637 (2010)

31 Chen Y Lo JY and Dobbins III JT ldquoImpulse response analysis for several

digital tomosynthesis mammography reconstruction algorithmsrdquo Proceedings of

SPIE Volume 5745 541-549 (2005)

32 Zhao B and Zhao W ldquoThree-dimensional linear system analysis for breast

tomosynthesisrdquo Medical Physics Volume 35 Number 12 5219-5232 (2008)

33 Wu G Mainprize JG Boone JM and Yaffe MJ ldquoEvaluation of scatter

effects on image quality for breast tomosynthesisrdquo Medical Physics Volume 36

Number 10 4425-4432 (2009)

Page 19: Development and Evaluation of 2D and 3D Image Quality ...

6

adequately describe the performance of a typical X-ray generator inherent filtration of 3

mm oil 148 mm Pyrex glass and 2 mm aluminum was input into the simulation in

addition to the filters of interest The ideal signal to noise ratio squared or incident

photon fluence per exposure (q) was estimated for each filtration by integrating the

energy-dependent photon counts per unit exposure over all energy bins

I2iii DQE Measurements

The assessment of the linearized images followed the formalism described by

IEC 62220-1 for measuring the DQE [12] For this study the normal exposure level XN

was set at 1 mR to the detector surface as measured at the central axis perpendicular to

the anode-cathode axis

I2iiia Modulation Transfer Function

Spatial resolution was characterized by evaluating the presampled modulation

transfer function (MTF) along directions parallel (vertical) and perpendicular

(horizontal) to the anode-cathode axis using the angled-edge method [6-1013] A radio-

opaque edge test device [7] was placed in the center of the field at a pitch of

approximately 301 (about 2deg) to the axis perpendicular to that being measured as

shown in Figure 1 External lead apertures were not used [6] instead the internal

collimation from the radiographic unit was used to collimate the beam to the detector

area Raw images were acquired of the edge with the normal exposure level XN of 1 mR

at the detector face The procedure of calculating the MTF followed previously described

7

methods [6-1013] The edge spread function (ESF) was determined along lines crossing

the edge of the angled test device The derivative of the ESF was calculated to form the

line spread function (LSF) to which a Hanning filter was applied The MTF was then

calculated as the fast Fourier transform (FFT) of the LSF and normalized at the zero-

frequency axis To conform to IEC guidelines the MTF was resampled into frequency

steps of 005 cyclesmm [12]

Figure 1 MTF images for DRX-1C detector with radio-opaque edge test device with

arrows indicating the horizontal (left) and vertical (right) directions

I2iiib Noise Power Spectrum

Noise amplitude and texture were characterized by determining the normalized

noise power spectrum (NNPS) which was evaluated with flat field exposures at

approximate exposure levels of XN2 XN and 2XN (05 10 and 20 mR) to the image

receptor surface Analysis of the flat-field images followed previously defined methods

[41415] using over 4 million independent pixels with regions of interest (ROIs) of size

8

128x128 The NNPS images were detrended using a quadratic (second order)

background subtraction Small variations in exposure across ROIs were corrected by

normalizing pixel values of each ROI to the mean value in the top left ROI as shown in

Figure 2 The NNPS was then calculated with the 2D FFT including the zero-frequency

axes corresponding to the horizontal and vertical directions The results were then

resampled using 005 frequency bins according to IEC guidelines [12]

Figure 2 NNPS image for DRX-1C detector indicating the top left ROI that served as

the reference for normalizing other ROIs in the image The ROI array was formed

along the directions indicated by the arrows The heel effect visible along the vertical

axis of the detector is an example of small variation in signal across the image

I2iiic DQE Calculation

The DQE was calculated using the following relationship [615]

9

where the frequency-dependent MTF and NNPS were determined as described in

previous sections X was the exposure value in mR corresponding to the NNPS image

and q was the ideal signal to noise ratio squared in units of photonsmiddotmm-2middotmR-1 as

estimated from the spectral simulations

I3 Results

I3i Data Linearization

The detectors in this study provided raw ADU (or pixel) values in a linear scale

The data were converted using the following system conversion function

where Q(ij) is the raw image data m and b are slope and intercept parameters obtained

from linear regression of the system response function and I(ij) is the linearized scaled

data The factor of 1000 was found to scale I(ij) such that the maximum value was a

large 16-bit number Figure 3 shows the original and linearized system responses for the

Pixium 4600 Note that the y-intercepts of the regressions for the linearized responses

are negligible (lt 01) with respect to the slopes a sufficient condition for zero offset

considerations

I3ii Spectral Simulation

The spectral simulations of the IEC filtrations and alternative filtrations indicate

many similarities in their effective energies HVLs and overall shapes of normalized

spectra Results are summarized in Table 3

10

Pixium 4600 Original System

Response

Pixium 4600 Linearized System

Response R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 3 Original (left) and linearized (right) system responses for Pixium 4600 The

linearized system responses were measured from actual images The offsets are small

with respect to the slope sufficient enough for zero-offset conditions

y = 13971x - 13236

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x - 00106Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 13576x + 28292

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

7000

0000 1000 2000 3000 4000 5000

AD

U

Exposure (mR)

y = 99997x - 00067Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0000 1000 2000 3000 4000 5000

AD

U

Exposure (mR)

y = 13644x + 16167Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x + 00044

Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 13845x + 13541

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x - 00177

Rsup2= 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

11

Table 3 Spectral Simulation Results

Beam Quality Filtration

Mean Energy

(kV)

Photon Fluence

(mRmm2)

RQA5A 21 mm Al 5243 259543

RQA5C 05 mm Cu + 10 mm Al 5214 259554

diff 055 0004

RQA9A 40 mm Al 7619 273281

RQA9C 104 mm Cu + 10 mm Al 7579 273964

diff 052 025

Figure 4 Spectral simulations for RQA5 (top) and RQA9 (bottom) conditions Note

the similarities of spectral shapes of the normalized spectra (right) Also note the

significant differences in fluence between filtrations in the simulated spectra (left)

00E+00

50E+04

10E+05

15E+05

20E+05

25E+05

30E+05

35E+05

40E+05

45E+05

0 20 40 60 80

ph

oto

ns

mA

s-1

cm

-2

keV

RQA5 Spectra Comparison

21 mm Al

05 mm Cu + 10 mm Al

00

02

04

06

08

10

12

0 20 40 60 80

keV

RQA5 Normalized Spectra Comparison

21 mm Al

05 mm Cu +

10 mm Al

00E+00

50E+05

10E+06

15E+06

20E+06

25E+06

30E+06

35E+06

40E+06

45E+06

50E+06

0 50 100 150

ph

oto

ns

mA

s-1

cm

-2

keV

RQA9 Spectra Comparison

40 mm Al

104 mm Cu +

10 mm Al

00

02

04

06

08

10

12

0 50 100 150

keV

RQA9 Normalized Spectra Comparison

40 mm Al104 mm Cu + 10 mm Al

12

I3iii Modulation Transfer Function

The limiting spatial resolutions of the systems were indicated by the cutoff

frequencies which were approximately 35 cyclesmm for all three detectors The spatial

resolutions also demonstrated a good degree of isotropy as confirmed by the close

alignment of MTF curves between vertical and horizontal directions differentiated in

Figure 5 by dashed and solid lines respectively The MTF curves for the Pixium 4600

and DRX-1C were nearly equal to each other whereas the DRX-1 MTF curve showed a

more rapid decrease at high frequencies as shown in Figure 6 This difference may be

due to the differences in the inherent optical properties of the scintillating materials

where finer image details are provided by structured CsI more than by granulated GOS

There were no significant differences in MTF curves across beam qualities and filtrations

as shown by the curve comparisons in Figure 6 although the alternative filtration

produced slightly higher MTF curves as seen in Figure 4 Table 4 lists the experimental

specific spatial frequencies for varying levels of MTF

I3iv Noise Power Spectrum

The noise characteristics are indicated by the NNPS curves shown in Figure 7

The noise was similar for both horizontal and vertical directions As exposure increased

the NNPS decreased consistent with the characteristics of Poisson noise describing the

relationship between signal and noise in the presence of increased photon fluence At

13

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 5 MTF results by detector (columns) and beam quality (rows)

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

horizontal

vertical

14

Figure 6 Plots of MTF for RQA5 (top) and RQA9 (bottom) showing the relationships

between detectors (blue red and green) and by filtration (solid and dashed)

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm-1)

MTF

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm-1)

MTF

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

15

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 7 NNPS results by detector (columns) and beam quality (rows)

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

05 mR - horizontal

05 mR - vertical

10 mR - horizontal

10 mR - vertical

20 mR - horizontal

20 mR - vertical

16

Figure 8 Plots of NNPS for RQA5 (top) and RQA9 (bottom) at 1 mR exposure

showing the relationships between detectors (blue red and green) and by filtration

(solid and dashed)

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm-1)

NNPS (1 mR)

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm-1)

NNPS (1 mR)

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

17

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 9 DQE results by detector (columns) and beam quality (rows)

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

05 mR - horizontal

05 mR - vertical

10 mR - horizontal

10 mR - vertical

20 mR - horizontal

20 mR - vertical

18

Figure 10 Plots of DQE for RQA5 (top) and RQA9 (bottom) at 1 mR exposure showing

the relationships between detectors (blue red and green) and by filtration (solid and

dashed)

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm-1)

DQE (1 mR)

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm-1)

DQE

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

19

higher frequencies the NNPS curves of the Pixium 4600 and DRX-1 diverge slightly for

the different directions illustrating increased noise in the readout direction (vertical)

Differences in the noise characteristics were more apparent among detectors as

shown for 1 mR in Figure 8 The NNPS curve for the DRX-1 was higher in magnitude

across the entire frequency range than either the Pixium 4600 or DRX-1C which both

seemed to demonstrate reasonably similar NNPS curves The higher magnitude noise of

the DRX-1 indicates higher relative noise content overall Closer inspection of the NNPS

curves of the Pixium 4600 and DRX-1C detectors in Figure 7 revealed differences in the

spacing between the three exposure levels The gaps between the Pixium 4600 NNPS

curves do not correspond to the factor of two differences between each exposure level

especially at low- to mid- spatial frequencies suggesting a higher level of fixed pattern

noise additional noise with increasing exposure levels due to ineffective gain map

corrections Between filtration schemes the differences in NNPS curves for a given beam

quality were not substantial as shown in Figure 7

I3v Detective Quantum Efficiency

The DQE results are shown in Figure 9 DQE curves across exposure levels were

almost collinear except for Pixium 4600 and in general could be inferred from the

NNPS results Additionally the DQE curves demonstrated a relatively linear response

with spatial frequencies as expected for flat-panel detectors [9] Differences in DQE

among detectors were consistent for the most part with the type of scintillating material

20

As depicted for 1 mR exposure in Figure 10 differences between Pixium 4600 and DRX-

1C DQE curves correspond to the differences in their NNPS curves DRX-1 DQE curves

were consistently lower than either the Pixium 4600 or DRX-1C curves The DQE curves

for the alternative filtration were consistently higher than those for the IEC filtration

and the most noticeable differences were near the zero-frequency axis These effects can

be both attributed to ineffective gain map correction DQE values for 1 mR exposure are

listed in Table 5

I4 Discussion

I4i Comparisons of Detectors

The limiting spatial resolutions of all three detectors were almost exactly the

same considering that their pixel areas were similar in size The decrease in high-

frequency MTF of the DRX-1 compared to the other detectors is probably a result of

increased optical blurring due to the differences in the powdered structure of GOS

versus the needle-like structure of CsI [2] The fact that the DRX-1C and Pixium 4600

have comparable MTFs suggests similar scintillator thicknesses assuming that the

materials were processed alike

The noise of the three detectors demonstrated similar trends with each other The

higher NNPS curves of the DRX-1 detector are probably due also to the scintillating

material and its operation in converting photons into signal The conversion process is

less efficient because of the less favorable stopping power of the GOS compared to CsI

21

especially with higher energy beams The noise of the Pixium 4600 and DRX-1C were

similar except for the spacing between exposures The DRX-1C NNPS curve spacing is

consistent with a factor of two difference in exposure levels but the Pixium 4600 has a

smaller spacing The 05 mR NNPS curve of the Pixium 4600 is closer to that of the 05

mR NNPS curve of the DRX-1C This demonstrates that at higher exposures the Pixium

4600 produces a larger amount of additional noise beyond that explained by simple

stochastic effects It suggests bad performance in the gain map corrections

The DQE results indicate SNR properties of each detector The Pixium 4600 and

DRX-1C are comparable for the most part with the DRX-1C performing slightly better

The DRX-1 as predicted from MTF and NNPS results has a DQE much lower than

either of the previous two This is a reflection of the detection properties as provided by

its scintillator material The DQE of the DRX-1 however is comparable to CR image

receptors [2] The mid-frequency dips in the DQE for Pixium 4600 may be due to the

optical properties of the CsI phosphor layer which can affect the MTF in this manner

Because the DQE is calculated by squaring the MTF this effect at the mid-range

frequencies becomes more apparent The dips may also be further evidence of bad gain

map corrections

I4ii Comparisons of Filtrations

The alternative filtration closely matches for the most part the IEC-based

filtration for MTF NNPS and DQEs at RQA5 but not at RQA9 The filters do not have

22

Table 4 Experimental MTF frequency locations for 1 mR exposure

Detector Filtration

50 MTF

(mm-1)

40 MTF

(mm-1)

30 MTF

(mm-1)

20 MTF

(mm-1)

10 MTF

(mm-1)

Pixium

4600

RQA5A 115 145 185 245 330

RQA5C 125 155 195 250 345

RQA9A 110 175 175 235 330

RQA9C 125 155 195 255 345

DRX-1C

RQA5A 120 150 185 245 350

RQA5C 125 155 195 255 355

RQA9A 120 150 190 250 355

RQA9C 130 160 210 265 360

DRX-1

RQA5A 110 135 160 205 280

RQA5C 110 135 170 210 285

RQA9A 105 125 155 195 270

RQA9C 110 135 165 210 285

Table 5 Estimated DQE values for 1 mR exposure by frequency bins

Detector Filtration DQE(00 mm-1) DQE(10 mm-1) DQE(20 mm-1) DQE(30 mm-1)

Pixium

4600

RQA5A 62 42 32 21

RQA5C 63 45 36 25

RQA9A 41 27 30 13

RQA9C 43 33 27 19

DRX-1C

RQA5A 72 52 35 21

RQA5C 76 55 41 24

RQA9A 49 33 23 15

RQA9C 51 40 31 20

DRX-1

RQA5A 38 24 12 4

RQA5C 38 25 14 5

RQA9A 28 18 9 4

RQA9C 28 19 12 5

DQE values at the zero-frequency axis were estimated by the intercept of a linear fit of low-frequency data

but excluding most proximal to the axis due to large fluctuations Other estimated values are grouped into

frequency bins due to the noisiness of the data

23

considerable differences in the spatial resolutions of the detectors as expected The noise

responses for each filtration were also similar except at the lower frequencies of the

NNPS especially near the zero-frequency axis There observing the NNPS responses at

RQA5 for Pixium 4600 and DRX-1C in Figure 8 the NNPS for the IEC-based filtration

(solid lines) tend to drop faster than the NNPS for the alternative filtration This

subsequently appears as a drop in DQE near the zero-frequency axis shown for those

detectors in Figure 10 Overall as indicated in Table 5 the DQEs of the two filtrations

while similar in trend indicate that the alternative filtration increases the DQE by a

small amount of 3-5 Part of this may be explained by the slightly higher beam

energy which may be more optimal for the energy response of the detectors or may

weigh the pixel responses slightly considering that they are energy-integrating types

The most probable explanation is the gain map correction for the alternative filtration

where fixed pattern noise is more sufficiently reduced

A previous study [6] had discussed the choice of filter material in the analysis of

DQE when achieving the beam conditions defined by IEC It found that visible

nonuniformities were present with the higher purity aluminum filter (type-11999 alloy)

The low frequency mottle in the flat-field images for NPS measurements were also

attributed to structured noise from the grain size in the IEC-based filter with an

attenuating thickness that would reveal nonuniformities The mottle in the current study

was only observable under very narrow windowing as shown in Figure 11 Such low

24

frequency artifacts which are not readily noticeable may also be caused by shading

artifacts inverse square law or even the heel effect A possible method to correct for this

is a subtraction method by taking the average of the flat-field images for an exposure

level and then subtracting that from each of them This would remove nonuniformities

that were not corrected using a suboptimal gain map calibration

Figure 11 DRX1-C NNPS images at 1 mR for RQA5 with IEC filtration (left) and

alternative filtration (right) Images are equally windowed at 45 and leveled at 980

One convenient aspect of the copper and aluminum filtration is that it requires

much less tube current to achieve the same amount of exposure at the detector than the

much thicker aluminum filtration As shown in the non-normalized spectra in Figure 2

the exiting photon fluence exiting the copper and aluminum filtration is substantially

higher than that of the IEC-specified filtration This is due to the smaller total filtration

25

attenuation For extensive DQE analysis multiple sets of exposures may be acquired

before tube overheating becomes a concern

One limitation to the comparison of the two filtrations is that calibration

procedures specified copper and aluminum filtration at 80 kVp (for all detectors 05 mm

Cu and 10 mm Al) This may have influenced the results in favor of the alternative

filtration A further investigation involving the calibration procedures and performing

DQE measurements is encouraged Another factor may be influenced by the fact that the

tests were performed at 70 kVp and 120 kVp different from the recommended

calibration tube potential Clearly there would be differences in the linear attenuation

coefficients of the filters and different energy responses of the detectors themselves This

must be considered when interpreting DQE results The current results support a

previous study decades ago that described filtration of different material types in terms

of an aluminum equivalent [16] The results show that the two filtration schemes are

essentially equivalent when considering beam qualities and spatial resolutions The

NNPS and DQE results can be seen as close enough where their small differences are

insignificant when performing quality assurance tests in a clinical setting Overall our

results indicate that the alternative filtration with copper and aluminum may be more

convenient to use than the current IEC standard filtration

26

I4iii Implications of Wireless DR

This study has shown that wireless image receptors can have the same DQE

performance if not better than conventional flat-panel detectors They operate on the

same basic physical principles the new features offered by the DRX-1C and DRX-1 are

wireless communication with the workstation and electronics packaging technology

The latter feature may pose limitations for these units in terms of possible degradation

in the detectors in routine clinical conditions A consideration for future work would be

to longitudinally track DQE performance of the wireless detectors over time while being

utilized in a clinical environment In the end one must consider risks versus benefits of

choosing portable DR technology over CR one of which includes the cost and fragility

of DR detectors

The DQE performance of one wireless system is just as good as or better than

conventional systems as seen by the DRX-1C performance compared to the Pixium

4600 Wireless systems can also reduce the need for CR readers especially in portable

applications in other regions of the world (eg military hospitals developing countries)

However while DQE performance indicates the physical performance of the detector

system it is still unknown how it relates to observer performance

I5 Conclusions

Two wireless image receptors DRX-1C and DRX-1 were evaluated and

compared with the conventional DR flat-panel Pixium 4600 in terms of DQE

27

performance along with MTF and NNPS performances The detectors have similar

resolution properties although the DRX-1 is inferior at higher spatial frequencies The

NNPS and DQE results both indicate that the DRX-1C is superior to the DRX-1 and

comparable if not better to the Pixium 4600

The results from the filtration comparison indicate no substantial differences

between the IEC-based filtration and the copper-based alternative filtration Only slight

differences were found in the low frequency components of the NNPS and the DQE due

to the inherent nonuniformities of the IEC specified filtration Given the similarity of the

results and low attenuation advantage of the copper and aluminum filter its use is

encouraged

28

II Directional MTF for Breast Tomosynthesis

II1 Introduction

Breast tomosynthesis is an emerging 3D imaging modality that has potential use

for screening and diagnosis of breast cancer Breast tomosynthesis along with other 3D

techniques is preferable to planar imaging methods (eg mammography) because they

reduce anatomical noise by removing overlying structures above and below the plane of

an image slice [17-20] Recent advances in detectors and computer technology have

made digital tomosynthesis feasible

An image quality metric of particular importance in breast tomosynthesis is

spatial resolution Resolution is important to know in order to assess small-detail

structures such as microcalcifications A descriptive metric for characterizing spatial

resolution in the Fourier (or frequency) domain is the modulation transfer function

(MTF) Affected by reconstruction filters [21] the limited angular projections involved in

breast tomosynthesis results in highly anisotropic (or nonuniform) resolution Many

studies have looked only at characterizing the in-plane spatial resolution (ie in an

individual slice) with an elevated angled edge phantom [2223] A few studies have

looked at characterizing a more comprehensive 3D spatial resolution by using a

phantom with angled wires or tubes [24-26] However such studies require precise

mechanical alignment of the phantoms Several studies have explored a method using a

29

sphere phantom for the directional 3D MTF evaluation for microtomography [27] and

multi-slice CT [2829] This method has not yet been extended to breast tomosynthesis

This chapter focuses on breast tomosynthesis because it is highly anisotropic in

spatial resolution and like its predecessor mammography requires high spatial

resolution Additionally breast tomosynthesis acquisitions and reconstructions produce

several types of artifacts The use of a cone-based method using a sphere phantom [28] is

explored to characterize the directional 3D spatial resolution of simulated images from

breast tomosynthesis A technique for removing out-of-plane artifacts of the ESFs for the

in-plane axes is investigated to yield a modified MTF in a method that separates artifact

information from resolution information

II2 Materials and Methods

II2i Image Simulation

Breast tomosynthesis images were simulated by using a virtual imaging system

depicted in Figure 12 A volumetric breast phantom was voxelized as a rectangular mass

of uniform breast equivalent tissue of 4 cm thickness embedded with fifteen evenly

spaced plastic sphere inserts of 12 mm diameter The spheres were placed in a grid

formation within the central plane of the phantom The x-ray fluence was modeled from

a 28 kVp beam incident upon an indirect flat-panel detector with 200 micro m pixel size

Twenty-three projections within an angular range of 44deg were simulated using cascaded

systems analysis to generate characteristic 2D noise and spatial blurring [29] Each

30

projection was simulated to have an exposure of 174 mR with a fluence of 79 times 105

photonsmm-2 A standard filtered backprojection technique based on the Feldkamp

reconstruction algorithm [29] was used to reconstruct the projections and produce a

volumetric dataset with an isotropic voxel size of 200 micro m

Figure 12 Depiction of the virtual image system

II2ii Uncorrected MTF

To enable comparison of multiple spheres the reconstructed volume was

initially homogenized by performing a background subtraction based on a portion of the

volume devoid of spheres The voxel values were rescaled between one and zero to

eliminate negative values

31

The volumetric data were segmented to extract individual regions of interest

(ROIs) each containing a single sphere The ROIs extended along the full range of the z-

axis A thresholded ROI was generated by determining the exterior and interior voxels

relative to the sphere in the ROI The threshold value was set at 45 of the maximum

voxel value prior to thresholding The exterior and interior voxel values were then set to

values of 0 and 1 respectively Using the thresholded volume the center of mass was

calculated to determine the centroid The voxel values from the original ROI were

subsequently tabulated with the associated distances azimuthal angles and polar

angles relative to the centroid

Conical regions were prescribed along the positive and negative directions along

the three major axes extending from the centroid of the sphere as depicted in Figure 13

The axes about which the extent of the cone angle was delineated were defined with

the azimuthal and polar angles

Voxels with centers within the angular range of the cone were considered for

generating the edge spread function (ESF) To improve regularity of the distance

sampling interval the ESF values were rebinned to discrete distances corresponding to a

fraction of the voxel size Only voxels with distances ranging from the voxel size (ie

200 micro m) to the maximum distance were considered The ESFs from multiple spheres

were averaged together for each of the three major axes to produce an averaged ESF

which was further smoothed utilizing a Gaussian filter

32

Figure 13 Example of 30-degree cone prescribed along z axis of the sphere

The resulting ESF was then differentiated using the central difference method to

produce the line spread function (LSF) A Hanning filter with the same length as the LSF

was applied to zero out the tails of the LSF The presampled MTF was subsequently

computed as the amplitude of the Fourier transform of the LSF The MTF was

normalized with respect to the maximum value occurring within the range of the cutoff

frequency Binning size and conical range for the ESF were considered for maximizing

accuracy and minimizing noise of the MTF verified by comparison against the

theoretical MTF as determined in the previous section

II2iii Theoretical Directional MTF

The theoretical 3D MTF was calculated using a priori knowledge of the transfer

function of the virtual imaging system described in the previous section A phantom

was created with a set of point objects in a uniform and noise-free background with the

objects spanning across the volume of the breast [29] Twenty-one realizations were

33

generated from the reconstructed images of the point objects to yield a set of 3D point

spread functions (PSFs) The 3D fast Fourier transform (FFT) was performed for each 3D

PSF and averaged to give an ldquoexpectationrdquo 3D MTF [29] The theoretical directional

MTFs in the three major spatial axes were determined by line profiles along each of the

corresponding spatial frequency axes in the 3D MTF An additional theoretical MTF for

each direction was determined by using the application of conical regions along the axes

in frequency-space to take into account the contributions of MTF information from other

planes

II2iv Modified MTF

The tomosynthesis reconstruction is known to have edge enhancements which

affect the overall MTF by shifting the peaks of the MTF toward the higher frequencies

[23] The presence of this artifact complicates the interpretation of the actual spatial

resolution of the images Several steps were performed to remove the artifact

contribution to the resolution information particularly for the in-plane x and y

directions with the assumption that resolution information was contained immediately

near the edge

For the x-direction averaged ESF only values that were detected to be inside the

edge of the sphere were considered Those values were previously determined via

thresholding for calculating the centroid The ESF information corresponding to these

values was inversed and flipped about the detected edge to produce a symmetric

34

modified ESF The modified MTF was subsequently calculated from this modified ESF

as described in the previous section

For the y-direction averaged ESF an upward trend was found in the initial part

of the ESF This section was detrended with a polynomial fit and subtracted to produce a

flatter curve in that region The resulting detrended ESF was used to calculate the y axis

modified MTF

Figure 14 Photograph of the imaging system with the acrylic sphere phantom

embedded in oil

II2v Preliminary Experimental Validation

A clinical breast tomosynthesis system (Mammomat Inspiration Siemens AG

Munich Germany) was used to perform a preliminary evaluation of the cone-based

MTF technique The phantom for the experiment consisted of a single acrylic ball of 075

in diameter (SmallParts Seattle WA) suspended by a 0029 in diameter plastic filament

35

(Omniflex Zebco Tulsa OK) in an acrylic frame filled up to 4 in with vegetable oil

(Target Brands Inc Minneapolis MN) The system and phantom are shown in Figure

14 Twenty-five projections with an angular range of 44deg were acquired and subsequently

reconstructed to produce a volume with a voxel size of 01times01times10 mm3 The voxels were

reformatted to have an isotropic size of 01 mm The uncorrected ESF LSF and MTF

were calculated as described in the previous section

II3 Results

II3i Reconstruction

The reconstructed volume is shown in Figure 15 Notice the edge enhancement

along the x-direction as indicated by the sharp shadowing artifacts on either side of the

spheres The background was effectively homogenized using the background

subtraction technique This also took account of the curved edges of the breast phantom

With the close spacing of the spheres in the phantom the shadows along the x direction

for the fifteen spheres overlap with each other As the nine centrally located spheres

experience this effect the same way they were used for determining the ESF

A 3D rendering of the ROI containing a sphere shown in Figure 16 indicates the

anisotropic resolution of the reconstruction Note that the sphere is not accurately

reconstructed and has an oblong shape especially along the z axis Cross sectional views

of the ROI also in Figure 16 clearly demonstrate the edge enhancement causing a

shadow artifact in the x direction caused by the incomplete angular sampling of

36

tomosynthesis The sampling also introduces the triangular reconstruction of the sphere

as seen in the x-z plane Note the gradual edge drop-off in the z direction much beyond

the sphere radius

Figure 15 View of the central slice of the breast phantom reconstruction before (top)

and after (bottom) background subtraction The z axis is through the page

37

Figure 16 3D rendering of the ROI volume (left) and cross-sectional views of the most

centrally located sphere with centroid indicated with red circle (right)

II3ii Theoretical MTF

The theoretical MTFs for x y and z directions as determined from the line

profiles of the 3D MTF are shown in Figure 17 The theoretical MTF in the x direction

has a maximum value that is toward higher frequencies Its 10 response occurs at

about 125 cyclesmm which is at 50 of the cutoff frequency The rapid increase from

the zero-frequency intercept to the peak corresponds to the ramp filter used in filtered

backprojection which decreases the weighting of low frequency contributions due to the

incomplete angular sampling of the frequency-space The MTF does not reach a value of

0 at the zero-frequency intercept as it is very difficult to assess the zero-frequency

intercept due to the finite size of the phantom The theoretical MTF in the y direction

peaks at the zero-frequency intercept and reaches 20 proximal to the cutoff frequency

38

The 10 MTF is well beyond the cutoff frequency The theoretical MTF in the z direction

has a rapid drop-off at very low spatial frequencies indicating the lack of resolution in

that dimension

Figure 17 Theoretical 3D MTF results along the three major planes (top) and along x

y and z directions (bottom) Also note that the angular spread seen in the fx-fz plane is

equal to the angular range of 44deg for the acquisition

II3iii Uncorrected MTF

The ESF LSF and MTF using the cone-based method are shown for the x y and

z directions in Figure 18 It was found that a bin size of one-tenth the voxel size (002

mm) and a cone angle of 30deg to establish the ESF were enough to minimize noise and

maximize accuracy in the uncorrected MTFs considering the reasonable comparison of

the shapes of the MTF curves with the theoretical results in Figure 17 The LSFs are

generally noisy because differentiation of the ESF increases the amplitude of the noise

39

The data shown reflect a convolution with a smoothing Gaussian filter which was later

further corrected for in the reported MTF Nevertheless the high frequency components

of the noise are well beyond the MTF cutoff frequency of 25 cyclesmm and do not

impact the MTF results greatly

For the ESF in the x direction the shadow effect evident at the edge of the sphere

is visible as a steep decline followed by an increase Due to the finite distance range

provided by the ROI the ESF beyond the edge did not asymptotically reach the

background value The corresponding LSF demonstrates a low frequency modulation

that is indicated by the shift of 03 cyclesmm in the x direction for the peak of the MTF

The MTF exhibits a zero-frequency intercept that is non-zero unlike the theoretical MTF

and a 10 value at approximately 1 cyclesmm These features may be a direct

consequence of MTF information ldquocontaminationrdquo from y and z directions Furthermore

the ESF in the y direction demonstrates a reasonably shaped curve except for the slight

upward trend within the radius of the sphere which can be attributed to the shadow

artifact overlapping with the sphere volume The associated MTF has a peak shifted by

approximately 01 cyclesmm away from the axis and a 10 MTF occurring at

approximately 15 cyclesmm Both features which are not present in the theoretical

results may also be attributed to contaminant MTF information from x and z directions

The ESF in the z direction has a drop-off that occurs at a small fraction of the cutoff

frequency similar to that demonstrated by the theoretical MTF

40

Uncorrected ESF LSF and MTF

Figure 18 Uncorrected ESF (top) LSF (middle) and MTF (bottom) for x y and z

directions

41

Figure 19 Comparisons of the directional MTFs as calculated by the sphere method

(dashed line) by theoretical line profiles (light-weight line) by theoretical cone

regions (heavy-weight line)

II3iv Comparison of Theoretical and Simulated MTFs

The theoretical MTF results obtained from line profiles through the 3D MTF and

the simulated MTFs using the cone-based technique did not match very well except for

the general shape of the curves It was assumed in the previous section that the cone-

based technique contains information from other planes Figure 19 compares MTFs in

each direction for the two methods described in the methods and an additional method

based on conical regions of the 3D MTF The latter computes the MTF by averaging

contributions of the 3D MTF using the same cone prescription method used to define the

ESFs Comparison of the curves indicate some interesting correlations aside from the

fact that using conical regions with the 3D MTF results produce more noisy MTF results

partly due to the low sampling provided by the theoretical calculations The same

conclusions regarding the z direction MTF can be confirmed regardless of either

theoretical MTF procedures The experimental x direction MTF seems to agree best with

42

the line profile method whereas the y direction MTF agrees better with the cone region

method The fact that the experimental x direction MTF has a drop-off frequency that is

lower than those of either of the theoretical MTFs in Figure 19 suggests that this might

be due to integration of the z-direction in the in-plane slices considering how slices are

essentially averages of z direction information contained within it [33]

II3v Modified MTF for x and y

Modified ESF LSF and MTF curves for x and y directions are shown in Figure

20 The modified ESF and the resulting LSF in the x direction appear symmetric as

expected from the inverse and flip operation of the interior ESF about the detected edge

The modified MTF appears with less variation than the uncorrected MTF and the MTF

peak occurs at the zero-frequency axis The correction yields a 10 MTF at about 15

cyclesmm an improvement from the uncorrected MTF but still distant from the cutoff

frequency The modified ESF in the y direction demonstrates the detrended curve within

the sphere radius after a quadratic polynomial fit The resulting modified MTF still

appears similar to the uncorrected MTF except that the peak now coincides with the

zero-frequency axis For both x and y directions the low response of the modified MTFs

at the higher frequencies suggests that the contamination from other directions is

substantial due to the angular range of the cone

43

Modified ESF LSF and MTF

Figure 20 Modified ESF (top) LSF (middle) and MTF (bottom) for x and y directions

44

II3v Preliminary Experimental Validation

Cross-sections of the reconstructed sphere volume are shown in Figure 21

Relative to the simulation reconstructions the reconstructions of the experimental

phantom images produce lower contrast and higher noise The preliminary results

shown in Figure 22 indicate that our technique can be applied to actual experimental

breast tomosynthesis reconstructions However due to the noise exhibited by the MTF

curves for the x and y directions we did not determine the modified MTFs to separate

resolution and artifact information

Figure 21 Cross sectional views of the experimental sphere image with centroid

indicated with red circle

45

Uncorrected ESF LSF and MTF for Real Image

Figure 22 ESF (top) LSF (middle) and MTF (bottom) of real image for x y

and z directions

46

II4 Discussion

II4i Evaluation of Cone-based Method

The cone-based MTF technique was introduced by Thornton and Flynn [28] for

evaluation of volumetric CT images To utilize this technique as a characterization of a

3D system spatial resolution one must first consider the validity of the assumption of

shift invariance such that the same MTF result may be obtained regardless of the

location of the sphere The study by Zhao et al [23] found that there was no shift

variance for the MTF measurements along the vertical axis but this was only considering

the in-plane resolution along one axis On the other hand this study evaluated the MTF

with images simulated with cascaded systems analysis which includes conditions of

linearity and shift invariance Additionally the MTF was calculated by averaging the

ESF from several spheres in the same volume only after performing a background

subtraction This step was essential to account for the sensitivity of centroid calculations

as well as ensuring symmetric ESFs for opposing axes of the sphere ROIs

The measurement of MTF with the cone-based technique inherently

supersamples the edge of the sphere to increase signal-to-noise-ratio (SNR) of edge

information by averaging the contributions of each voxel to the ESF [713] This method

also takes into account the discrete sampling of the voxels by accounting for various

shifts of the edge in the voxel (also known as the partial volume effect) However using

the curved surface of the sphere phantom to approximate an edge along a given

47

direction naturally leads to contamination of information from other directions aside

from the one of interest Preferably a directional ESF should be created by using a single

radial line but this would limit the available voxels to obtain edge information An ideal

situation theoretically would be to use a larger-sized sphere such that the surface is

nearly flat and perpendicular to the axes of interest This would also permit a reduction

in the angular range of the cone and thus the introduction of out-of-plane information in

the resulting MTF However sphere size is a limitation in breast tomosynthesis and the

use of a large phantom might void the assumption of shift invariance of the spatial

resolution

The choice of a sphere phantom nevertheless may be based on the clinical need

to quickly acquire a single image for MTF evaluation especially for multiple directions

without presenting extra logistical challenges The use of a wire or edge phantom

requires more precise mechanical alignment to achieve the correct set up The edge

phantom [23] would require at least two images to sample all three dimensions In the

case of the three wire phantom [2425] all three dimensions of the frame must be aligned

simultaneously with respect to the axis of rotation A similar situation would be

encountered when considering a cubic phantom with the planes normal to the axis of

interest In contrast to these phantoms the sphere eliminates the need for precise

alignment especially with respect to three spatial dimensions simultaneously A sphere

48

has ideal symmetry in all directions and can be used to evaluate MTF in any arbitrary

direction

This study unlike others [242532] did not explore the effects of physical

parameters such as scatter or contrast on the final MTF result but it demonstrated the

feasibility of using the cone-based method with an actual breast tomosynthesis image of

a sphere phantom as shown in Error Reference source not found and Error Reference

source not found These effects should be addressed in future works A further look

into deriving the principles of comparing the theoretical MTF with the experimental

MTF using the cone-based method is further warranted

II4ii Separation of Artifact and Resolution Information

The focus of this study was to develop a technique for measuring spatial

resolution of tomosynthesis images The intrinsic artifacts from tomosynthesis

reconstructions however lead to uncharacteristic MTFs and possible misinterpretation

of the effective resolution information When considering previous techniques for

calculating the presampled MTF [713152328] the analysis was performed using an

edge or a line to produce the corresponding ESF The resolution information is

essentially contained only along the edge indicated by the need to calculate the LSF In a

way the method of extracting artifact information is to focus the analysis only on the

edge part of the ESF to calculate the modified MTF This will lead to a better

understanding of the limiting size of objects that may be seen in the reconstructed 3D

49

image The presampled MTF without correction should still be analyzed to understand

the entire system response Note that the ESFs attempt to reflect information only at the

detected edge of the sphere

II5 Conclusions

The directional MTF of a simulated breast tomosynthesis reconstruction was

determined by using the cone-based MTF technique demonstrating the feasibility of a

single phantom for MTF evaluation This study further presented methods of analyzing

only the edge information in the ESF to create a modified MTF along in-slice (x and y)

axes It can provide insight into the actual spatial resolution information contained in the

image while separating the resolution information from the information introduced by

artifacts caused by the reconstruction and insufficient volumetric sampling The idea of

separating the resolution and artifacts from the measured ESF are expected to facilitate

the interpretation of MTF measurements in breast tomosynthesis Similar methods may

be applied to characterize the resolution of other 3D imaging modalities

50

References

1 Garmer M Hannigs SP Jaumlger HJ et al ldquoDigital Radiography Versus

Conventional Radiology in Chest Imaging Diagnostic Performance of a Large-

Area Silicon Flat-Panel Detector in a Clinical CT-Controlled Studyrdquo American

Journal of Roentgenology Volume 74 75-80 (2000)

2 Cowen AR Kengyelics SM and Davies AG ldquoSolid-state flat-panel digital

radiography detectors and their physical imaging characteristics rdquoClinical

Radiology Volume 63 487-498 (2008)

3 Chotas HG Dobbins III JT and Ravin CE ldquoPrinciples of Digital

Radiography with Large-Area Electronically Readable Detectors A Review of

the Basicsrdquo Radiology Volume 210 Number 3 595-599 (1999)

4 Flynn MJ and Samei E Experimental comparison of noise and resolution for

2k and 4k storage phosphor radiography systems Medical Physics Volume 26

Number 8 1612-1623 (1999)

5 Rong XJ Shaw CC Liu X Lemacks MR and Thompson SK

ldquoComparison of an amorphous siliconcesium iodide flat-panel digital chest

radiography system with screenfilm and computed radiography systems ndash A

contrast-detail phantom studyrdquo Medical Physics Volume 28 Number 11 2328-

2335 (2001)

6 Ranger NT Samei E Dobbins III JT and Ravin CE Measurement of the

detective quantum efficiency in digital detectors consistent with the IEC 62220-1

standard Practical considerations regarding the choice of filter material

Medical Physics Volume 30 Number 7 2305-2311 (2005)

7 Samei E Buhr E Granfors P Vandenbroucke D and Wang X Comparison

of edge analysis techniques for the determination of the MTF of digital

radiographic systems Physics in Medicine and Biology Volume 50 3613-3625

(2005)

8 Samei E and Flynn MJ An experimental comparison of detector performance

for computed radiography systems Medical Physics Volume 29 Number 4 447-

459 (2002)

51

9 Samei E and Flynn MJ An experimental comparison of detector performance

for direct and indirect digital radiography systems Medical Physics Volume 30

Number 4 608-622 (2003)

10 Samei E Ranger NT MacKenzie A Honey ID Dobbins III JT and Ravin

CE Effective DQE (eDQE) and speed of digital radiographic systems An

experimental methodology Medical Physics Volume 36 Number 8 3806-3817

(2009)

11 Samei E Ranger NT MacKenzie A Honey ID Dobbins III JT and Ravin

CE Detector or System Extending the Concept of Detective Quantum

Efficiency to Characterize the Performance of Digital Radiographic Imaging

Systems Radiology Volume 249 Number 3 926-937 (2008)

12 ldquoIEC 62220-1 Medical Electrical Equipment ndash Characteristics of Digital X-Ray

Imaging Devices ndash Part 1 Determination of the Detective Quantum Efficiencyrdquo

International Electrotechnical Commission Geneva Switzerland (2003)

13 Samei E Ranger NT Dobbins III JT and Chen Y Intercomparison of

methods for image quality characterization I Modulation transfer function

Medical Physics Volume 33 Number 5 1454-1465 (2006)

14 Dobbins III JT Samei E Ranger NT and Chen Y Intercomparison of

methods for image quality characterization II Noise power spectrum Medical

Physics Volume 33 Number 5 1466-1475 (2006)

15 Samei E Flynn MJ and Reimann DA A method for measuring the

presampled MTF of digital radiographic systems using an edge test device

Medical Physics Volume 25 Number 1 102-113 (1998)

16 Nagel HD ldquoAluminum equivalence of materials used in diagnostic radiology

and its dependence on beam qualityrdquo Physics in Medicine and Biology Volume

31 Number 12 1381-1399 (1986)

17 Niklason LT Christian BT Niklason LE et al ldquoDigital Tomosynthesis in

Breast Imagingrdquo Radiology Volume 205 399-406 (1997)

18 Gur D ldquoTomosynthesis Potential Clinical Role in Breast Imagingrdquo American

Journal of Roentgenology Volume 189 614-615 (2007)

52

19 Park JM Franken Jr EA Garg M Fajardo LL and Niklason LT ldquoBreast

Tomosynthesis Present Considerations and Future Applicationsrdquo

RadioGraphics Volume 27 S231-S240 (2007)

20 Good WF Abrams GS Catullo VJ Chough DM Ganott MA Hakim

CM and Gur D ldquoDigital Breast Tomosynthesis A Pilot Observer Studyrdquo

American Journal of Roentgenology Volume 190 865-869 (2008)

21 Hu Y-H Zhao W Mertelmeier T and Ludwig J ldquoImage Artifact in Digital

Breast Tomosynthesis and Its Dependence on System and Reconstruction

Parametersrdquo IWDM 2008 LNCS 5116 628-634 (2008)

22 Chen Y Lo JY Ranger NT Samei E Dobbins III JT ldquoMethodology of

NEQ(f) analysis for optimization and comparison of digital breast tomosynthesis

acquisition techniques and reconstruction algorithmsrdquo Proceedings of SPIE

Volume 6510 65101I (2007)

23 Zhao B Zhou J Hu Y-H Mertelmeier T Ludwig J and Zhao W

ldquoExperimental validation of a three-dimensional linear system model for breast

tomosynthesisrdquo Medical Physics Volume 36 Number 1 240-251 (2009)

24 Madhav P Brzymialkiewicz CN Cutler SJ Bowsher JE and Tornai MP

ldquoCharacterizing the MTF in 3D for a Quantized SPECT Camera Having Arbitrary

Trajectoriesrdquo 2005 IEEE Nuclear Science Symposium Conference Record 1722-

1726 (2005)

25 Madhav P McKinley RL Samei E Bowsher JE and Tornai MP ldquoA Novel

Method to Characterize the MTF in 3D for Computed Mammotomographyrdquo

Proceedings of SPIE Volume 6142 61421Y (2006)

26 Hu Y-H Zhao B and Zhao W ldquoImage artifacts in digital breast

tomosynthesis Investigation of the effects of system geometry and

reconstruction parameters using a linear system approachrdquo Medical Physics

Volume 35 Number 12 5242-5252 (2008)

27 Seifert A and Flynn MJ ldquoResolving power of 3D x-ray microtomography

systemsrdquo Proceedings of SPIE Volume 4682 407-413 (2002)

28 Thornton MM and Flynn MJ Measurement of the spatial resolution of a

clinical volumetric computed tomography scanner using a sphere phantom

Proceedings of SPIE Volume 6142 61421Z (2006)

53

29 Baek J Pelc NJ ldquoUse of sphere phantoms to measure the 3D MTF of FDK

reconstructionsrdquo Proceedings of SPIE Volume 7961 79610D (2011)

30 Richard S and Samei E ldquoQuantitative imaging in breast tomosynthesis and CT

Comparison of detection and estimation task performancerdquo Medical Physics

Volume 37 Number 6 2627-2637 (2010)

31 Chen Y Lo JY and Dobbins III JT ldquoImpulse response analysis for several

digital tomosynthesis mammography reconstruction algorithmsrdquo Proceedings of

SPIE Volume 5745 541-549 (2005)

32 Zhao B and Zhao W ldquoThree-dimensional linear system analysis for breast

tomosynthesisrdquo Medical Physics Volume 35 Number 12 5219-5232 (2008)

33 Wu G Mainprize JG Boone JM and Yaffe MJ ldquoEvaluation of scatter

effects on image quality for breast tomosynthesisrdquo Medical Physics Volume 36

Number 10 4425-4432 (2009)

Page 20: Development and Evaluation of 2D and 3D Image Quality ...

7

methods [6-1013] The edge spread function (ESF) was determined along lines crossing

the edge of the angled test device The derivative of the ESF was calculated to form the

line spread function (LSF) to which a Hanning filter was applied The MTF was then

calculated as the fast Fourier transform (FFT) of the LSF and normalized at the zero-

frequency axis To conform to IEC guidelines the MTF was resampled into frequency

steps of 005 cyclesmm [12]

Figure 1 MTF images for DRX-1C detector with radio-opaque edge test device with

arrows indicating the horizontal (left) and vertical (right) directions

I2iiib Noise Power Spectrum

Noise amplitude and texture were characterized by determining the normalized

noise power spectrum (NNPS) which was evaluated with flat field exposures at

approximate exposure levels of XN2 XN and 2XN (05 10 and 20 mR) to the image

receptor surface Analysis of the flat-field images followed previously defined methods

[41415] using over 4 million independent pixels with regions of interest (ROIs) of size

8

128x128 The NNPS images were detrended using a quadratic (second order)

background subtraction Small variations in exposure across ROIs were corrected by

normalizing pixel values of each ROI to the mean value in the top left ROI as shown in

Figure 2 The NNPS was then calculated with the 2D FFT including the zero-frequency

axes corresponding to the horizontal and vertical directions The results were then

resampled using 005 frequency bins according to IEC guidelines [12]

Figure 2 NNPS image for DRX-1C detector indicating the top left ROI that served as

the reference for normalizing other ROIs in the image The ROI array was formed

along the directions indicated by the arrows The heel effect visible along the vertical

axis of the detector is an example of small variation in signal across the image

I2iiic DQE Calculation

The DQE was calculated using the following relationship [615]

9

where the frequency-dependent MTF and NNPS were determined as described in

previous sections X was the exposure value in mR corresponding to the NNPS image

and q was the ideal signal to noise ratio squared in units of photonsmiddotmm-2middotmR-1 as

estimated from the spectral simulations

I3 Results

I3i Data Linearization

The detectors in this study provided raw ADU (or pixel) values in a linear scale

The data were converted using the following system conversion function

where Q(ij) is the raw image data m and b are slope and intercept parameters obtained

from linear regression of the system response function and I(ij) is the linearized scaled

data The factor of 1000 was found to scale I(ij) such that the maximum value was a

large 16-bit number Figure 3 shows the original and linearized system responses for the

Pixium 4600 Note that the y-intercepts of the regressions for the linearized responses

are negligible (lt 01) with respect to the slopes a sufficient condition for zero offset

considerations

I3ii Spectral Simulation

The spectral simulations of the IEC filtrations and alternative filtrations indicate

many similarities in their effective energies HVLs and overall shapes of normalized

spectra Results are summarized in Table 3

10

Pixium 4600 Original System

Response

Pixium 4600 Linearized System

Response R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 3 Original (left) and linearized (right) system responses for Pixium 4600 The

linearized system responses were measured from actual images The offsets are small

with respect to the slope sufficient enough for zero-offset conditions

y = 13971x - 13236

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x - 00106Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 13576x + 28292

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

7000

0000 1000 2000 3000 4000 5000

AD

U

Exposure (mR)

y = 99997x - 00067Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0000 1000 2000 3000 4000 5000

AD

U

Exposure (mR)

y = 13644x + 16167Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x + 00044

Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 13845x + 13541

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x - 00177

Rsup2= 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

11

Table 3 Spectral Simulation Results

Beam Quality Filtration

Mean Energy

(kV)

Photon Fluence

(mRmm2)

RQA5A 21 mm Al 5243 259543

RQA5C 05 mm Cu + 10 mm Al 5214 259554

diff 055 0004

RQA9A 40 mm Al 7619 273281

RQA9C 104 mm Cu + 10 mm Al 7579 273964

diff 052 025

Figure 4 Spectral simulations for RQA5 (top) and RQA9 (bottom) conditions Note

the similarities of spectral shapes of the normalized spectra (right) Also note the

significant differences in fluence between filtrations in the simulated spectra (left)

00E+00

50E+04

10E+05

15E+05

20E+05

25E+05

30E+05

35E+05

40E+05

45E+05

0 20 40 60 80

ph

oto

ns

mA

s-1

cm

-2

keV

RQA5 Spectra Comparison

21 mm Al

05 mm Cu + 10 mm Al

00

02

04

06

08

10

12

0 20 40 60 80

keV

RQA5 Normalized Spectra Comparison

21 mm Al

05 mm Cu +

10 mm Al

00E+00

50E+05

10E+06

15E+06

20E+06

25E+06

30E+06

35E+06

40E+06

45E+06

50E+06

0 50 100 150

ph

oto

ns

mA

s-1

cm

-2

keV

RQA9 Spectra Comparison

40 mm Al

104 mm Cu +

10 mm Al

00

02

04

06

08

10

12

0 50 100 150

keV

RQA9 Normalized Spectra Comparison

40 mm Al104 mm Cu + 10 mm Al

12

I3iii Modulation Transfer Function

The limiting spatial resolutions of the systems were indicated by the cutoff

frequencies which were approximately 35 cyclesmm for all three detectors The spatial

resolutions also demonstrated a good degree of isotropy as confirmed by the close

alignment of MTF curves between vertical and horizontal directions differentiated in

Figure 5 by dashed and solid lines respectively The MTF curves for the Pixium 4600

and DRX-1C were nearly equal to each other whereas the DRX-1 MTF curve showed a

more rapid decrease at high frequencies as shown in Figure 6 This difference may be

due to the differences in the inherent optical properties of the scintillating materials

where finer image details are provided by structured CsI more than by granulated GOS

There were no significant differences in MTF curves across beam qualities and filtrations

as shown by the curve comparisons in Figure 6 although the alternative filtration

produced slightly higher MTF curves as seen in Figure 4 Table 4 lists the experimental

specific spatial frequencies for varying levels of MTF

I3iv Noise Power Spectrum

The noise characteristics are indicated by the NNPS curves shown in Figure 7

The noise was similar for both horizontal and vertical directions As exposure increased

the NNPS decreased consistent with the characteristics of Poisson noise describing the

relationship between signal and noise in the presence of increased photon fluence At

13

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 5 MTF results by detector (columns) and beam quality (rows)

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

horizontal

vertical

14

Figure 6 Plots of MTF for RQA5 (top) and RQA9 (bottom) showing the relationships

between detectors (blue red and green) and by filtration (solid and dashed)

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm-1)

MTF

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm-1)

MTF

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

15

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 7 NNPS results by detector (columns) and beam quality (rows)

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

05 mR - horizontal

05 mR - vertical

10 mR - horizontal

10 mR - vertical

20 mR - horizontal

20 mR - vertical

16

Figure 8 Plots of NNPS for RQA5 (top) and RQA9 (bottom) at 1 mR exposure

showing the relationships between detectors (blue red and green) and by filtration

(solid and dashed)

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm-1)

NNPS (1 mR)

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm-1)

NNPS (1 mR)

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

17

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 9 DQE results by detector (columns) and beam quality (rows)

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

05 mR - horizontal

05 mR - vertical

10 mR - horizontal

10 mR - vertical

20 mR - horizontal

20 mR - vertical

18

Figure 10 Plots of DQE for RQA5 (top) and RQA9 (bottom) at 1 mR exposure showing

the relationships between detectors (blue red and green) and by filtration (solid and

dashed)

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm-1)

DQE (1 mR)

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm-1)

DQE

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

19

higher frequencies the NNPS curves of the Pixium 4600 and DRX-1 diverge slightly for

the different directions illustrating increased noise in the readout direction (vertical)

Differences in the noise characteristics were more apparent among detectors as

shown for 1 mR in Figure 8 The NNPS curve for the DRX-1 was higher in magnitude

across the entire frequency range than either the Pixium 4600 or DRX-1C which both

seemed to demonstrate reasonably similar NNPS curves The higher magnitude noise of

the DRX-1 indicates higher relative noise content overall Closer inspection of the NNPS

curves of the Pixium 4600 and DRX-1C detectors in Figure 7 revealed differences in the

spacing between the three exposure levels The gaps between the Pixium 4600 NNPS

curves do not correspond to the factor of two differences between each exposure level

especially at low- to mid- spatial frequencies suggesting a higher level of fixed pattern

noise additional noise with increasing exposure levels due to ineffective gain map

corrections Between filtration schemes the differences in NNPS curves for a given beam

quality were not substantial as shown in Figure 7

I3v Detective Quantum Efficiency

The DQE results are shown in Figure 9 DQE curves across exposure levels were

almost collinear except for Pixium 4600 and in general could be inferred from the

NNPS results Additionally the DQE curves demonstrated a relatively linear response

with spatial frequencies as expected for flat-panel detectors [9] Differences in DQE

among detectors were consistent for the most part with the type of scintillating material

20

As depicted for 1 mR exposure in Figure 10 differences between Pixium 4600 and DRX-

1C DQE curves correspond to the differences in their NNPS curves DRX-1 DQE curves

were consistently lower than either the Pixium 4600 or DRX-1C curves The DQE curves

for the alternative filtration were consistently higher than those for the IEC filtration

and the most noticeable differences were near the zero-frequency axis These effects can

be both attributed to ineffective gain map correction DQE values for 1 mR exposure are

listed in Table 5

I4 Discussion

I4i Comparisons of Detectors

The limiting spatial resolutions of all three detectors were almost exactly the

same considering that their pixel areas were similar in size The decrease in high-

frequency MTF of the DRX-1 compared to the other detectors is probably a result of

increased optical blurring due to the differences in the powdered structure of GOS

versus the needle-like structure of CsI [2] The fact that the DRX-1C and Pixium 4600

have comparable MTFs suggests similar scintillator thicknesses assuming that the

materials were processed alike

The noise of the three detectors demonstrated similar trends with each other The

higher NNPS curves of the DRX-1 detector are probably due also to the scintillating

material and its operation in converting photons into signal The conversion process is

less efficient because of the less favorable stopping power of the GOS compared to CsI

21

especially with higher energy beams The noise of the Pixium 4600 and DRX-1C were

similar except for the spacing between exposures The DRX-1C NNPS curve spacing is

consistent with a factor of two difference in exposure levels but the Pixium 4600 has a

smaller spacing The 05 mR NNPS curve of the Pixium 4600 is closer to that of the 05

mR NNPS curve of the DRX-1C This demonstrates that at higher exposures the Pixium

4600 produces a larger amount of additional noise beyond that explained by simple

stochastic effects It suggests bad performance in the gain map corrections

The DQE results indicate SNR properties of each detector The Pixium 4600 and

DRX-1C are comparable for the most part with the DRX-1C performing slightly better

The DRX-1 as predicted from MTF and NNPS results has a DQE much lower than

either of the previous two This is a reflection of the detection properties as provided by

its scintillator material The DQE of the DRX-1 however is comparable to CR image

receptors [2] The mid-frequency dips in the DQE for Pixium 4600 may be due to the

optical properties of the CsI phosphor layer which can affect the MTF in this manner

Because the DQE is calculated by squaring the MTF this effect at the mid-range

frequencies becomes more apparent The dips may also be further evidence of bad gain

map corrections

I4ii Comparisons of Filtrations

The alternative filtration closely matches for the most part the IEC-based

filtration for MTF NNPS and DQEs at RQA5 but not at RQA9 The filters do not have

22

Table 4 Experimental MTF frequency locations for 1 mR exposure

Detector Filtration

50 MTF

(mm-1)

40 MTF

(mm-1)

30 MTF

(mm-1)

20 MTF

(mm-1)

10 MTF

(mm-1)

Pixium

4600

RQA5A 115 145 185 245 330

RQA5C 125 155 195 250 345

RQA9A 110 175 175 235 330

RQA9C 125 155 195 255 345

DRX-1C

RQA5A 120 150 185 245 350

RQA5C 125 155 195 255 355

RQA9A 120 150 190 250 355

RQA9C 130 160 210 265 360

DRX-1

RQA5A 110 135 160 205 280

RQA5C 110 135 170 210 285

RQA9A 105 125 155 195 270

RQA9C 110 135 165 210 285

Table 5 Estimated DQE values for 1 mR exposure by frequency bins

Detector Filtration DQE(00 mm-1) DQE(10 mm-1) DQE(20 mm-1) DQE(30 mm-1)

Pixium

4600

RQA5A 62 42 32 21

RQA5C 63 45 36 25

RQA9A 41 27 30 13

RQA9C 43 33 27 19

DRX-1C

RQA5A 72 52 35 21

RQA5C 76 55 41 24

RQA9A 49 33 23 15

RQA9C 51 40 31 20

DRX-1

RQA5A 38 24 12 4

RQA5C 38 25 14 5

RQA9A 28 18 9 4

RQA9C 28 19 12 5

DQE values at the zero-frequency axis were estimated by the intercept of a linear fit of low-frequency data

but excluding most proximal to the axis due to large fluctuations Other estimated values are grouped into

frequency bins due to the noisiness of the data

23

considerable differences in the spatial resolutions of the detectors as expected The noise

responses for each filtration were also similar except at the lower frequencies of the

NNPS especially near the zero-frequency axis There observing the NNPS responses at

RQA5 for Pixium 4600 and DRX-1C in Figure 8 the NNPS for the IEC-based filtration

(solid lines) tend to drop faster than the NNPS for the alternative filtration This

subsequently appears as a drop in DQE near the zero-frequency axis shown for those

detectors in Figure 10 Overall as indicated in Table 5 the DQEs of the two filtrations

while similar in trend indicate that the alternative filtration increases the DQE by a

small amount of 3-5 Part of this may be explained by the slightly higher beam

energy which may be more optimal for the energy response of the detectors or may

weigh the pixel responses slightly considering that they are energy-integrating types

The most probable explanation is the gain map correction for the alternative filtration

where fixed pattern noise is more sufficiently reduced

A previous study [6] had discussed the choice of filter material in the analysis of

DQE when achieving the beam conditions defined by IEC It found that visible

nonuniformities were present with the higher purity aluminum filter (type-11999 alloy)

The low frequency mottle in the flat-field images for NPS measurements were also

attributed to structured noise from the grain size in the IEC-based filter with an

attenuating thickness that would reveal nonuniformities The mottle in the current study

was only observable under very narrow windowing as shown in Figure 11 Such low

24

frequency artifacts which are not readily noticeable may also be caused by shading

artifacts inverse square law or even the heel effect A possible method to correct for this

is a subtraction method by taking the average of the flat-field images for an exposure

level and then subtracting that from each of them This would remove nonuniformities

that were not corrected using a suboptimal gain map calibration

Figure 11 DRX1-C NNPS images at 1 mR for RQA5 with IEC filtration (left) and

alternative filtration (right) Images are equally windowed at 45 and leveled at 980

One convenient aspect of the copper and aluminum filtration is that it requires

much less tube current to achieve the same amount of exposure at the detector than the

much thicker aluminum filtration As shown in the non-normalized spectra in Figure 2

the exiting photon fluence exiting the copper and aluminum filtration is substantially

higher than that of the IEC-specified filtration This is due to the smaller total filtration

25

attenuation For extensive DQE analysis multiple sets of exposures may be acquired

before tube overheating becomes a concern

One limitation to the comparison of the two filtrations is that calibration

procedures specified copper and aluminum filtration at 80 kVp (for all detectors 05 mm

Cu and 10 mm Al) This may have influenced the results in favor of the alternative

filtration A further investigation involving the calibration procedures and performing

DQE measurements is encouraged Another factor may be influenced by the fact that the

tests were performed at 70 kVp and 120 kVp different from the recommended

calibration tube potential Clearly there would be differences in the linear attenuation

coefficients of the filters and different energy responses of the detectors themselves This

must be considered when interpreting DQE results The current results support a

previous study decades ago that described filtration of different material types in terms

of an aluminum equivalent [16] The results show that the two filtration schemes are

essentially equivalent when considering beam qualities and spatial resolutions The

NNPS and DQE results can be seen as close enough where their small differences are

insignificant when performing quality assurance tests in a clinical setting Overall our

results indicate that the alternative filtration with copper and aluminum may be more

convenient to use than the current IEC standard filtration

26

I4iii Implications of Wireless DR

This study has shown that wireless image receptors can have the same DQE

performance if not better than conventional flat-panel detectors They operate on the

same basic physical principles the new features offered by the DRX-1C and DRX-1 are

wireless communication with the workstation and electronics packaging technology

The latter feature may pose limitations for these units in terms of possible degradation

in the detectors in routine clinical conditions A consideration for future work would be

to longitudinally track DQE performance of the wireless detectors over time while being

utilized in a clinical environment In the end one must consider risks versus benefits of

choosing portable DR technology over CR one of which includes the cost and fragility

of DR detectors

The DQE performance of one wireless system is just as good as or better than

conventional systems as seen by the DRX-1C performance compared to the Pixium

4600 Wireless systems can also reduce the need for CR readers especially in portable

applications in other regions of the world (eg military hospitals developing countries)

However while DQE performance indicates the physical performance of the detector

system it is still unknown how it relates to observer performance

I5 Conclusions

Two wireless image receptors DRX-1C and DRX-1 were evaluated and

compared with the conventional DR flat-panel Pixium 4600 in terms of DQE

27

performance along with MTF and NNPS performances The detectors have similar

resolution properties although the DRX-1 is inferior at higher spatial frequencies The

NNPS and DQE results both indicate that the DRX-1C is superior to the DRX-1 and

comparable if not better to the Pixium 4600

The results from the filtration comparison indicate no substantial differences

between the IEC-based filtration and the copper-based alternative filtration Only slight

differences were found in the low frequency components of the NNPS and the DQE due

to the inherent nonuniformities of the IEC specified filtration Given the similarity of the

results and low attenuation advantage of the copper and aluminum filter its use is

encouraged

28

II Directional MTF for Breast Tomosynthesis

II1 Introduction

Breast tomosynthesis is an emerging 3D imaging modality that has potential use

for screening and diagnosis of breast cancer Breast tomosynthesis along with other 3D

techniques is preferable to planar imaging methods (eg mammography) because they

reduce anatomical noise by removing overlying structures above and below the plane of

an image slice [17-20] Recent advances in detectors and computer technology have

made digital tomosynthesis feasible

An image quality metric of particular importance in breast tomosynthesis is

spatial resolution Resolution is important to know in order to assess small-detail

structures such as microcalcifications A descriptive metric for characterizing spatial

resolution in the Fourier (or frequency) domain is the modulation transfer function

(MTF) Affected by reconstruction filters [21] the limited angular projections involved in

breast tomosynthesis results in highly anisotropic (or nonuniform) resolution Many

studies have looked only at characterizing the in-plane spatial resolution (ie in an

individual slice) with an elevated angled edge phantom [2223] A few studies have

looked at characterizing a more comprehensive 3D spatial resolution by using a

phantom with angled wires or tubes [24-26] However such studies require precise

mechanical alignment of the phantoms Several studies have explored a method using a

29

sphere phantom for the directional 3D MTF evaluation for microtomography [27] and

multi-slice CT [2829] This method has not yet been extended to breast tomosynthesis

This chapter focuses on breast tomosynthesis because it is highly anisotropic in

spatial resolution and like its predecessor mammography requires high spatial

resolution Additionally breast tomosynthesis acquisitions and reconstructions produce

several types of artifacts The use of a cone-based method using a sphere phantom [28] is

explored to characterize the directional 3D spatial resolution of simulated images from

breast tomosynthesis A technique for removing out-of-plane artifacts of the ESFs for the

in-plane axes is investigated to yield a modified MTF in a method that separates artifact

information from resolution information

II2 Materials and Methods

II2i Image Simulation

Breast tomosynthesis images were simulated by using a virtual imaging system

depicted in Figure 12 A volumetric breast phantom was voxelized as a rectangular mass

of uniform breast equivalent tissue of 4 cm thickness embedded with fifteen evenly

spaced plastic sphere inserts of 12 mm diameter The spheres were placed in a grid

formation within the central plane of the phantom The x-ray fluence was modeled from

a 28 kVp beam incident upon an indirect flat-panel detector with 200 micro m pixel size

Twenty-three projections within an angular range of 44deg were simulated using cascaded

systems analysis to generate characteristic 2D noise and spatial blurring [29] Each

30

projection was simulated to have an exposure of 174 mR with a fluence of 79 times 105

photonsmm-2 A standard filtered backprojection technique based on the Feldkamp

reconstruction algorithm [29] was used to reconstruct the projections and produce a

volumetric dataset with an isotropic voxel size of 200 micro m

Figure 12 Depiction of the virtual image system

II2ii Uncorrected MTF

To enable comparison of multiple spheres the reconstructed volume was

initially homogenized by performing a background subtraction based on a portion of the

volume devoid of spheres The voxel values were rescaled between one and zero to

eliminate negative values

31

The volumetric data were segmented to extract individual regions of interest

(ROIs) each containing a single sphere The ROIs extended along the full range of the z-

axis A thresholded ROI was generated by determining the exterior and interior voxels

relative to the sphere in the ROI The threshold value was set at 45 of the maximum

voxel value prior to thresholding The exterior and interior voxel values were then set to

values of 0 and 1 respectively Using the thresholded volume the center of mass was

calculated to determine the centroid The voxel values from the original ROI were

subsequently tabulated with the associated distances azimuthal angles and polar

angles relative to the centroid

Conical regions were prescribed along the positive and negative directions along

the three major axes extending from the centroid of the sphere as depicted in Figure 13

The axes about which the extent of the cone angle was delineated were defined with

the azimuthal and polar angles

Voxels with centers within the angular range of the cone were considered for

generating the edge spread function (ESF) To improve regularity of the distance

sampling interval the ESF values were rebinned to discrete distances corresponding to a

fraction of the voxel size Only voxels with distances ranging from the voxel size (ie

200 micro m) to the maximum distance were considered The ESFs from multiple spheres

were averaged together for each of the three major axes to produce an averaged ESF

which was further smoothed utilizing a Gaussian filter

32

Figure 13 Example of 30-degree cone prescribed along z axis of the sphere

The resulting ESF was then differentiated using the central difference method to

produce the line spread function (LSF) A Hanning filter with the same length as the LSF

was applied to zero out the tails of the LSF The presampled MTF was subsequently

computed as the amplitude of the Fourier transform of the LSF The MTF was

normalized with respect to the maximum value occurring within the range of the cutoff

frequency Binning size and conical range for the ESF were considered for maximizing

accuracy and minimizing noise of the MTF verified by comparison against the

theoretical MTF as determined in the previous section

II2iii Theoretical Directional MTF

The theoretical 3D MTF was calculated using a priori knowledge of the transfer

function of the virtual imaging system described in the previous section A phantom

was created with a set of point objects in a uniform and noise-free background with the

objects spanning across the volume of the breast [29] Twenty-one realizations were

33

generated from the reconstructed images of the point objects to yield a set of 3D point

spread functions (PSFs) The 3D fast Fourier transform (FFT) was performed for each 3D

PSF and averaged to give an ldquoexpectationrdquo 3D MTF [29] The theoretical directional

MTFs in the three major spatial axes were determined by line profiles along each of the

corresponding spatial frequency axes in the 3D MTF An additional theoretical MTF for

each direction was determined by using the application of conical regions along the axes

in frequency-space to take into account the contributions of MTF information from other

planes

II2iv Modified MTF

The tomosynthesis reconstruction is known to have edge enhancements which

affect the overall MTF by shifting the peaks of the MTF toward the higher frequencies

[23] The presence of this artifact complicates the interpretation of the actual spatial

resolution of the images Several steps were performed to remove the artifact

contribution to the resolution information particularly for the in-plane x and y

directions with the assumption that resolution information was contained immediately

near the edge

For the x-direction averaged ESF only values that were detected to be inside the

edge of the sphere were considered Those values were previously determined via

thresholding for calculating the centroid The ESF information corresponding to these

values was inversed and flipped about the detected edge to produce a symmetric

34

modified ESF The modified MTF was subsequently calculated from this modified ESF

as described in the previous section

For the y-direction averaged ESF an upward trend was found in the initial part

of the ESF This section was detrended with a polynomial fit and subtracted to produce a

flatter curve in that region The resulting detrended ESF was used to calculate the y axis

modified MTF

Figure 14 Photograph of the imaging system with the acrylic sphere phantom

embedded in oil

II2v Preliminary Experimental Validation

A clinical breast tomosynthesis system (Mammomat Inspiration Siemens AG

Munich Germany) was used to perform a preliminary evaluation of the cone-based

MTF technique The phantom for the experiment consisted of a single acrylic ball of 075

in diameter (SmallParts Seattle WA) suspended by a 0029 in diameter plastic filament

35

(Omniflex Zebco Tulsa OK) in an acrylic frame filled up to 4 in with vegetable oil

(Target Brands Inc Minneapolis MN) The system and phantom are shown in Figure

14 Twenty-five projections with an angular range of 44deg were acquired and subsequently

reconstructed to produce a volume with a voxel size of 01times01times10 mm3 The voxels were

reformatted to have an isotropic size of 01 mm The uncorrected ESF LSF and MTF

were calculated as described in the previous section

II3 Results

II3i Reconstruction

The reconstructed volume is shown in Figure 15 Notice the edge enhancement

along the x-direction as indicated by the sharp shadowing artifacts on either side of the

spheres The background was effectively homogenized using the background

subtraction technique This also took account of the curved edges of the breast phantom

With the close spacing of the spheres in the phantom the shadows along the x direction

for the fifteen spheres overlap with each other As the nine centrally located spheres

experience this effect the same way they were used for determining the ESF

A 3D rendering of the ROI containing a sphere shown in Figure 16 indicates the

anisotropic resolution of the reconstruction Note that the sphere is not accurately

reconstructed and has an oblong shape especially along the z axis Cross sectional views

of the ROI also in Figure 16 clearly demonstrate the edge enhancement causing a

shadow artifact in the x direction caused by the incomplete angular sampling of

36

tomosynthesis The sampling also introduces the triangular reconstruction of the sphere

as seen in the x-z plane Note the gradual edge drop-off in the z direction much beyond

the sphere radius

Figure 15 View of the central slice of the breast phantom reconstruction before (top)

and after (bottom) background subtraction The z axis is through the page

37

Figure 16 3D rendering of the ROI volume (left) and cross-sectional views of the most

centrally located sphere with centroid indicated with red circle (right)

II3ii Theoretical MTF

The theoretical MTFs for x y and z directions as determined from the line

profiles of the 3D MTF are shown in Figure 17 The theoretical MTF in the x direction

has a maximum value that is toward higher frequencies Its 10 response occurs at

about 125 cyclesmm which is at 50 of the cutoff frequency The rapid increase from

the zero-frequency intercept to the peak corresponds to the ramp filter used in filtered

backprojection which decreases the weighting of low frequency contributions due to the

incomplete angular sampling of the frequency-space The MTF does not reach a value of

0 at the zero-frequency intercept as it is very difficult to assess the zero-frequency

intercept due to the finite size of the phantom The theoretical MTF in the y direction

peaks at the zero-frequency intercept and reaches 20 proximal to the cutoff frequency

38

The 10 MTF is well beyond the cutoff frequency The theoretical MTF in the z direction

has a rapid drop-off at very low spatial frequencies indicating the lack of resolution in

that dimension

Figure 17 Theoretical 3D MTF results along the three major planes (top) and along x

y and z directions (bottom) Also note that the angular spread seen in the fx-fz plane is

equal to the angular range of 44deg for the acquisition

II3iii Uncorrected MTF

The ESF LSF and MTF using the cone-based method are shown for the x y and

z directions in Figure 18 It was found that a bin size of one-tenth the voxel size (002

mm) and a cone angle of 30deg to establish the ESF were enough to minimize noise and

maximize accuracy in the uncorrected MTFs considering the reasonable comparison of

the shapes of the MTF curves with the theoretical results in Figure 17 The LSFs are

generally noisy because differentiation of the ESF increases the amplitude of the noise

39

The data shown reflect a convolution with a smoothing Gaussian filter which was later

further corrected for in the reported MTF Nevertheless the high frequency components

of the noise are well beyond the MTF cutoff frequency of 25 cyclesmm and do not

impact the MTF results greatly

For the ESF in the x direction the shadow effect evident at the edge of the sphere

is visible as a steep decline followed by an increase Due to the finite distance range

provided by the ROI the ESF beyond the edge did not asymptotically reach the

background value The corresponding LSF demonstrates a low frequency modulation

that is indicated by the shift of 03 cyclesmm in the x direction for the peak of the MTF

The MTF exhibits a zero-frequency intercept that is non-zero unlike the theoretical MTF

and a 10 value at approximately 1 cyclesmm These features may be a direct

consequence of MTF information ldquocontaminationrdquo from y and z directions Furthermore

the ESF in the y direction demonstrates a reasonably shaped curve except for the slight

upward trend within the radius of the sphere which can be attributed to the shadow

artifact overlapping with the sphere volume The associated MTF has a peak shifted by

approximately 01 cyclesmm away from the axis and a 10 MTF occurring at

approximately 15 cyclesmm Both features which are not present in the theoretical

results may also be attributed to contaminant MTF information from x and z directions

The ESF in the z direction has a drop-off that occurs at a small fraction of the cutoff

frequency similar to that demonstrated by the theoretical MTF

40

Uncorrected ESF LSF and MTF

Figure 18 Uncorrected ESF (top) LSF (middle) and MTF (bottom) for x y and z

directions

41

Figure 19 Comparisons of the directional MTFs as calculated by the sphere method

(dashed line) by theoretical line profiles (light-weight line) by theoretical cone

regions (heavy-weight line)

II3iv Comparison of Theoretical and Simulated MTFs

The theoretical MTF results obtained from line profiles through the 3D MTF and

the simulated MTFs using the cone-based technique did not match very well except for

the general shape of the curves It was assumed in the previous section that the cone-

based technique contains information from other planes Figure 19 compares MTFs in

each direction for the two methods described in the methods and an additional method

based on conical regions of the 3D MTF The latter computes the MTF by averaging

contributions of the 3D MTF using the same cone prescription method used to define the

ESFs Comparison of the curves indicate some interesting correlations aside from the

fact that using conical regions with the 3D MTF results produce more noisy MTF results

partly due to the low sampling provided by the theoretical calculations The same

conclusions regarding the z direction MTF can be confirmed regardless of either

theoretical MTF procedures The experimental x direction MTF seems to agree best with

42

the line profile method whereas the y direction MTF agrees better with the cone region

method The fact that the experimental x direction MTF has a drop-off frequency that is

lower than those of either of the theoretical MTFs in Figure 19 suggests that this might

be due to integration of the z-direction in the in-plane slices considering how slices are

essentially averages of z direction information contained within it [33]

II3v Modified MTF for x and y

Modified ESF LSF and MTF curves for x and y directions are shown in Figure

20 The modified ESF and the resulting LSF in the x direction appear symmetric as

expected from the inverse and flip operation of the interior ESF about the detected edge

The modified MTF appears with less variation than the uncorrected MTF and the MTF

peak occurs at the zero-frequency axis The correction yields a 10 MTF at about 15

cyclesmm an improvement from the uncorrected MTF but still distant from the cutoff

frequency The modified ESF in the y direction demonstrates the detrended curve within

the sphere radius after a quadratic polynomial fit The resulting modified MTF still

appears similar to the uncorrected MTF except that the peak now coincides with the

zero-frequency axis For both x and y directions the low response of the modified MTFs

at the higher frequencies suggests that the contamination from other directions is

substantial due to the angular range of the cone

43

Modified ESF LSF and MTF

Figure 20 Modified ESF (top) LSF (middle) and MTF (bottom) for x and y directions

44

II3v Preliminary Experimental Validation

Cross-sections of the reconstructed sphere volume are shown in Figure 21

Relative to the simulation reconstructions the reconstructions of the experimental

phantom images produce lower contrast and higher noise The preliminary results

shown in Figure 22 indicate that our technique can be applied to actual experimental

breast tomosynthesis reconstructions However due to the noise exhibited by the MTF

curves for the x and y directions we did not determine the modified MTFs to separate

resolution and artifact information

Figure 21 Cross sectional views of the experimental sphere image with centroid

indicated with red circle

45

Uncorrected ESF LSF and MTF for Real Image

Figure 22 ESF (top) LSF (middle) and MTF (bottom) of real image for x y

and z directions

46

II4 Discussion

II4i Evaluation of Cone-based Method

The cone-based MTF technique was introduced by Thornton and Flynn [28] for

evaluation of volumetric CT images To utilize this technique as a characterization of a

3D system spatial resolution one must first consider the validity of the assumption of

shift invariance such that the same MTF result may be obtained regardless of the

location of the sphere The study by Zhao et al [23] found that there was no shift

variance for the MTF measurements along the vertical axis but this was only considering

the in-plane resolution along one axis On the other hand this study evaluated the MTF

with images simulated with cascaded systems analysis which includes conditions of

linearity and shift invariance Additionally the MTF was calculated by averaging the

ESF from several spheres in the same volume only after performing a background

subtraction This step was essential to account for the sensitivity of centroid calculations

as well as ensuring symmetric ESFs for opposing axes of the sphere ROIs

The measurement of MTF with the cone-based technique inherently

supersamples the edge of the sphere to increase signal-to-noise-ratio (SNR) of edge

information by averaging the contributions of each voxel to the ESF [713] This method

also takes into account the discrete sampling of the voxels by accounting for various

shifts of the edge in the voxel (also known as the partial volume effect) However using

the curved surface of the sphere phantom to approximate an edge along a given

47

direction naturally leads to contamination of information from other directions aside

from the one of interest Preferably a directional ESF should be created by using a single

radial line but this would limit the available voxels to obtain edge information An ideal

situation theoretically would be to use a larger-sized sphere such that the surface is

nearly flat and perpendicular to the axes of interest This would also permit a reduction

in the angular range of the cone and thus the introduction of out-of-plane information in

the resulting MTF However sphere size is a limitation in breast tomosynthesis and the

use of a large phantom might void the assumption of shift invariance of the spatial

resolution

The choice of a sphere phantom nevertheless may be based on the clinical need

to quickly acquire a single image for MTF evaluation especially for multiple directions

without presenting extra logistical challenges The use of a wire or edge phantom

requires more precise mechanical alignment to achieve the correct set up The edge

phantom [23] would require at least two images to sample all three dimensions In the

case of the three wire phantom [2425] all three dimensions of the frame must be aligned

simultaneously with respect to the axis of rotation A similar situation would be

encountered when considering a cubic phantom with the planes normal to the axis of

interest In contrast to these phantoms the sphere eliminates the need for precise

alignment especially with respect to three spatial dimensions simultaneously A sphere

48

has ideal symmetry in all directions and can be used to evaluate MTF in any arbitrary

direction

This study unlike others [242532] did not explore the effects of physical

parameters such as scatter or contrast on the final MTF result but it demonstrated the

feasibility of using the cone-based method with an actual breast tomosynthesis image of

a sphere phantom as shown in Error Reference source not found and Error Reference

source not found These effects should be addressed in future works A further look

into deriving the principles of comparing the theoretical MTF with the experimental

MTF using the cone-based method is further warranted

II4ii Separation of Artifact and Resolution Information

The focus of this study was to develop a technique for measuring spatial

resolution of tomosynthesis images The intrinsic artifacts from tomosynthesis

reconstructions however lead to uncharacteristic MTFs and possible misinterpretation

of the effective resolution information When considering previous techniques for

calculating the presampled MTF [713152328] the analysis was performed using an

edge or a line to produce the corresponding ESF The resolution information is

essentially contained only along the edge indicated by the need to calculate the LSF In a

way the method of extracting artifact information is to focus the analysis only on the

edge part of the ESF to calculate the modified MTF This will lead to a better

understanding of the limiting size of objects that may be seen in the reconstructed 3D

49

image The presampled MTF without correction should still be analyzed to understand

the entire system response Note that the ESFs attempt to reflect information only at the

detected edge of the sphere

II5 Conclusions

The directional MTF of a simulated breast tomosynthesis reconstruction was

determined by using the cone-based MTF technique demonstrating the feasibility of a

single phantom for MTF evaluation This study further presented methods of analyzing

only the edge information in the ESF to create a modified MTF along in-slice (x and y)

axes It can provide insight into the actual spatial resolution information contained in the

image while separating the resolution information from the information introduced by

artifacts caused by the reconstruction and insufficient volumetric sampling The idea of

separating the resolution and artifacts from the measured ESF are expected to facilitate

the interpretation of MTF measurements in breast tomosynthesis Similar methods may

be applied to characterize the resolution of other 3D imaging modalities

50

References

1 Garmer M Hannigs SP Jaumlger HJ et al ldquoDigital Radiography Versus

Conventional Radiology in Chest Imaging Diagnostic Performance of a Large-

Area Silicon Flat-Panel Detector in a Clinical CT-Controlled Studyrdquo American

Journal of Roentgenology Volume 74 75-80 (2000)

2 Cowen AR Kengyelics SM and Davies AG ldquoSolid-state flat-panel digital

radiography detectors and their physical imaging characteristics rdquoClinical

Radiology Volume 63 487-498 (2008)

3 Chotas HG Dobbins III JT and Ravin CE ldquoPrinciples of Digital

Radiography with Large-Area Electronically Readable Detectors A Review of

the Basicsrdquo Radiology Volume 210 Number 3 595-599 (1999)

4 Flynn MJ and Samei E Experimental comparison of noise and resolution for

2k and 4k storage phosphor radiography systems Medical Physics Volume 26

Number 8 1612-1623 (1999)

5 Rong XJ Shaw CC Liu X Lemacks MR and Thompson SK

ldquoComparison of an amorphous siliconcesium iodide flat-panel digital chest

radiography system with screenfilm and computed radiography systems ndash A

contrast-detail phantom studyrdquo Medical Physics Volume 28 Number 11 2328-

2335 (2001)

6 Ranger NT Samei E Dobbins III JT and Ravin CE Measurement of the

detective quantum efficiency in digital detectors consistent with the IEC 62220-1

standard Practical considerations regarding the choice of filter material

Medical Physics Volume 30 Number 7 2305-2311 (2005)

7 Samei E Buhr E Granfors P Vandenbroucke D and Wang X Comparison

of edge analysis techniques for the determination of the MTF of digital

radiographic systems Physics in Medicine and Biology Volume 50 3613-3625

(2005)

8 Samei E and Flynn MJ An experimental comparison of detector performance

for computed radiography systems Medical Physics Volume 29 Number 4 447-

459 (2002)

51

9 Samei E and Flynn MJ An experimental comparison of detector performance

for direct and indirect digital radiography systems Medical Physics Volume 30

Number 4 608-622 (2003)

10 Samei E Ranger NT MacKenzie A Honey ID Dobbins III JT and Ravin

CE Effective DQE (eDQE) and speed of digital radiographic systems An

experimental methodology Medical Physics Volume 36 Number 8 3806-3817

(2009)

11 Samei E Ranger NT MacKenzie A Honey ID Dobbins III JT and Ravin

CE Detector or System Extending the Concept of Detective Quantum

Efficiency to Characterize the Performance of Digital Radiographic Imaging

Systems Radiology Volume 249 Number 3 926-937 (2008)

12 ldquoIEC 62220-1 Medical Electrical Equipment ndash Characteristics of Digital X-Ray

Imaging Devices ndash Part 1 Determination of the Detective Quantum Efficiencyrdquo

International Electrotechnical Commission Geneva Switzerland (2003)

13 Samei E Ranger NT Dobbins III JT and Chen Y Intercomparison of

methods for image quality characterization I Modulation transfer function

Medical Physics Volume 33 Number 5 1454-1465 (2006)

14 Dobbins III JT Samei E Ranger NT and Chen Y Intercomparison of

methods for image quality characterization II Noise power spectrum Medical

Physics Volume 33 Number 5 1466-1475 (2006)

15 Samei E Flynn MJ and Reimann DA A method for measuring the

presampled MTF of digital radiographic systems using an edge test device

Medical Physics Volume 25 Number 1 102-113 (1998)

16 Nagel HD ldquoAluminum equivalence of materials used in diagnostic radiology

and its dependence on beam qualityrdquo Physics in Medicine and Biology Volume

31 Number 12 1381-1399 (1986)

17 Niklason LT Christian BT Niklason LE et al ldquoDigital Tomosynthesis in

Breast Imagingrdquo Radiology Volume 205 399-406 (1997)

18 Gur D ldquoTomosynthesis Potential Clinical Role in Breast Imagingrdquo American

Journal of Roentgenology Volume 189 614-615 (2007)

52

19 Park JM Franken Jr EA Garg M Fajardo LL and Niklason LT ldquoBreast

Tomosynthesis Present Considerations and Future Applicationsrdquo

RadioGraphics Volume 27 S231-S240 (2007)

20 Good WF Abrams GS Catullo VJ Chough DM Ganott MA Hakim

CM and Gur D ldquoDigital Breast Tomosynthesis A Pilot Observer Studyrdquo

American Journal of Roentgenology Volume 190 865-869 (2008)

21 Hu Y-H Zhao W Mertelmeier T and Ludwig J ldquoImage Artifact in Digital

Breast Tomosynthesis and Its Dependence on System and Reconstruction

Parametersrdquo IWDM 2008 LNCS 5116 628-634 (2008)

22 Chen Y Lo JY Ranger NT Samei E Dobbins III JT ldquoMethodology of

NEQ(f) analysis for optimization and comparison of digital breast tomosynthesis

acquisition techniques and reconstruction algorithmsrdquo Proceedings of SPIE

Volume 6510 65101I (2007)

23 Zhao B Zhou J Hu Y-H Mertelmeier T Ludwig J and Zhao W

ldquoExperimental validation of a three-dimensional linear system model for breast

tomosynthesisrdquo Medical Physics Volume 36 Number 1 240-251 (2009)

24 Madhav P Brzymialkiewicz CN Cutler SJ Bowsher JE and Tornai MP

ldquoCharacterizing the MTF in 3D for a Quantized SPECT Camera Having Arbitrary

Trajectoriesrdquo 2005 IEEE Nuclear Science Symposium Conference Record 1722-

1726 (2005)

25 Madhav P McKinley RL Samei E Bowsher JE and Tornai MP ldquoA Novel

Method to Characterize the MTF in 3D for Computed Mammotomographyrdquo

Proceedings of SPIE Volume 6142 61421Y (2006)

26 Hu Y-H Zhao B and Zhao W ldquoImage artifacts in digital breast

tomosynthesis Investigation of the effects of system geometry and

reconstruction parameters using a linear system approachrdquo Medical Physics

Volume 35 Number 12 5242-5252 (2008)

27 Seifert A and Flynn MJ ldquoResolving power of 3D x-ray microtomography

systemsrdquo Proceedings of SPIE Volume 4682 407-413 (2002)

28 Thornton MM and Flynn MJ Measurement of the spatial resolution of a

clinical volumetric computed tomography scanner using a sphere phantom

Proceedings of SPIE Volume 6142 61421Z (2006)

53

29 Baek J Pelc NJ ldquoUse of sphere phantoms to measure the 3D MTF of FDK

reconstructionsrdquo Proceedings of SPIE Volume 7961 79610D (2011)

30 Richard S and Samei E ldquoQuantitative imaging in breast tomosynthesis and CT

Comparison of detection and estimation task performancerdquo Medical Physics

Volume 37 Number 6 2627-2637 (2010)

31 Chen Y Lo JY and Dobbins III JT ldquoImpulse response analysis for several

digital tomosynthesis mammography reconstruction algorithmsrdquo Proceedings of

SPIE Volume 5745 541-549 (2005)

32 Zhao B and Zhao W ldquoThree-dimensional linear system analysis for breast

tomosynthesisrdquo Medical Physics Volume 35 Number 12 5219-5232 (2008)

33 Wu G Mainprize JG Boone JM and Yaffe MJ ldquoEvaluation of scatter

effects on image quality for breast tomosynthesisrdquo Medical Physics Volume 36

Number 10 4425-4432 (2009)

Page 21: Development and Evaluation of 2D and 3D Image Quality ...

8

128x128 The NNPS images were detrended using a quadratic (second order)

background subtraction Small variations in exposure across ROIs were corrected by

normalizing pixel values of each ROI to the mean value in the top left ROI as shown in

Figure 2 The NNPS was then calculated with the 2D FFT including the zero-frequency

axes corresponding to the horizontal and vertical directions The results were then

resampled using 005 frequency bins according to IEC guidelines [12]

Figure 2 NNPS image for DRX-1C detector indicating the top left ROI that served as

the reference for normalizing other ROIs in the image The ROI array was formed

along the directions indicated by the arrows The heel effect visible along the vertical

axis of the detector is an example of small variation in signal across the image

I2iiic DQE Calculation

The DQE was calculated using the following relationship [615]

9

where the frequency-dependent MTF and NNPS were determined as described in

previous sections X was the exposure value in mR corresponding to the NNPS image

and q was the ideal signal to noise ratio squared in units of photonsmiddotmm-2middotmR-1 as

estimated from the spectral simulations

I3 Results

I3i Data Linearization

The detectors in this study provided raw ADU (or pixel) values in a linear scale

The data were converted using the following system conversion function

where Q(ij) is the raw image data m and b are slope and intercept parameters obtained

from linear regression of the system response function and I(ij) is the linearized scaled

data The factor of 1000 was found to scale I(ij) such that the maximum value was a

large 16-bit number Figure 3 shows the original and linearized system responses for the

Pixium 4600 Note that the y-intercepts of the regressions for the linearized responses

are negligible (lt 01) with respect to the slopes a sufficient condition for zero offset

considerations

I3ii Spectral Simulation

The spectral simulations of the IEC filtrations and alternative filtrations indicate

many similarities in their effective energies HVLs and overall shapes of normalized

spectra Results are summarized in Table 3

10

Pixium 4600 Original System

Response

Pixium 4600 Linearized System

Response R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 3 Original (left) and linearized (right) system responses for Pixium 4600 The

linearized system responses were measured from actual images The offsets are small

with respect to the slope sufficient enough for zero-offset conditions

y = 13971x - 13236

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x - 00106Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 13576x + 28292

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

7000

0000 1000 2000 3000 4000 5000

AD

U

Exposure (mR)

y = 99997x - 00067Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0000 1000 2000 3000 4000 5000

AD

U

Exposure (mR)

y = 13644x + 16167Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x + 00044

Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 13845x + 13541

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x - 00177

Rsup2= 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

11

Table 3 Spectral Simulation Results

Beam Quality Filtration

Mean Energy

(kV)

Photon Fluence

(mRmm2)

RQA5A 21 mm Al 5243 259543

RQA5C 05 mm Cu + 10 mm Al 5214 259554

diff 055 0004

RQA9A 40 mm Al 7619 273281

RQA9C 104 mm Cu + 10 mm Al 7579 273964

diff 052 025

Figure 4 Spectral simulations for RQA5 (top) and RQA9 (bottom) conditions Note

the similarities of spectral shapes of the normalized spectra (right) Also note the

significant differences in fluence between filtrations in the simulated spectra (left)

00E+00

50E+04

10E+05

15E+05

20E+05

25E+05

30E+05

35E+05

40E+05

45E+05

0 20 40 60 80

ph

oto

ns

mA

s-1

cm

-2

keV

RQA5 Spectra Comparison

21 mm Al

05 mm Cu + 10 mm Al

00

02

04

06

08

10

12

0 20 40 60 80

keV

RQA5 Normalized Spectra Comparison

21 mm Al

05 mm Cu +

10 mm Al

00E+00

50E+05

10E+06

15E+06

20E+06

25E+06

30E+06

35E+06

40E+06

45E+06

50E+06

0 50 100 150

ph

oto

ns

mA

s-1

cm

-2

keV

RQA9 Spectra Comparison

40 mm Al

104 mm Cu +

10 mm Al

00

02

04

06

08

10

12

0 50 100 150

keV

RQA9 Normalized Spectra Comparison

40 mm Al104 mm Cu + 10 mm Al

12

I3iii Modulation Transfer Function

The limiting spatial resolutions of the systems were indicated by the cutoff

frequencies which were approximately 35 cyclesmm for all three detectors The spatial

resolutions also demonstrated a good degree of isotropy as confirmed by the close

alignment of MTF curves between vertical and horizontal directions differentiated in

Figure 5 by dashed and solid lines respectively The MTF curves for the Pixium 4600

and DRX-1C were nearly equal to each other whereas the DRX-1 MTF curve showed a

more rapid decrease at high frequencies as shown in Figure 6 This difference may be

due to the differences in the inherent optical properties of the scintillating materials

where finer image details are provided by structured CsI more than by granulated GOS

There were no significant differences in MTF curves across beam qualities and filtrations

as shown by the curve comparisons in Figure 6 although the alternative filtration

produced slightly higher MTF curves as seen in Figure 4 Table 4 lists the experimental

specific spatial frequencies for varying levels of MTF

I3iv Noise Power Spectrum

The noise characteristics are indicated by the NNPS curves shown in Figure 7

The noise was similar for both horizontal and vertical directions As exposure increased

the NNPS decreased consistent with the characteristics of Poisson noise describing the

relationship between signal and noise in the presence of increased photon fluence At

13

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 5 MTF results by detector (columns) and beam quality (rows)

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

horizontal

vertical

14

Figure 6 Plots of MTF for RQA5 (top) and RQA9 (bottom) showing the relationships

between detectors (blue red and green) and by filtration (solid and dashed)

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm-1)

MTF

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm-1)

MTF

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

15

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 7 NNPS results by detector (columns) and beam quality (rows)

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

05 mR - horizontal

05 mR - vertical

10 mR - horizontal

10 mR - vertical

20 mR - horizontal

20 mR - vertical

16

Figure 8 Plots of NNPS for RQA5 (top) and RQA9 (bottom) at 1 mR exposure

showing the relationships between detectors (blue red and green) and by filtration

(solid and dashed)

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm-1)

NNPS (1 mR)

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm-1)

NNPS (1 mR)

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

17

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 9 DQE results by detector (columns) and beam quality (rows)

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

05 mR - horizontal

05 mR - vertical

10 mR - horizontal

10 mR - vertical

20 mR - horizontal

20 mR - vertical

18

Figure 10 Plots of DQE for RQA5 (top) and RQA9 (bottom) at 1 mR exposure showing

the relationships between detectors (blue red and green) and by filtration (solid and

dashed)

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm-1)

DQE (1 mR)

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm-1)

DQE

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

19

higher frequencies the NNPS curves of the Pixium 4600 and DRX-1 diverge slightly for

the different directions illustrating increased noise in the readout direction (vertical)

Differences in the noise characteristics were more apparent among detectors as

shown for 1 mR in Figure 8 The NNPS curve for the DRX-1 was higher in magnitude

across the entire frequency range than either the Pixium 4600 or DRX-1C which both

seemed to demonstrate reasonably similar NNPS curves The higher magnitude noise of

the DRX-1 indicates higher relative noise content overall Closer inspection of the NNPS

curves of the Pixium 4600 and DRX-1C detectors in Figure 7 revealed differences in the

spacing between the three exposure levels The gaps between the Pixium 4600 NNPS

curves do not correspond to the factor of two differences between each exposure level

especially at low- to mid- spatial frequencies suggesting a higher level of fixed pattern

noise additional noise with increasing exposure levels due to ineffective gain map

corrections Between filtration schemes the differences in NNPS curves for a given beam

quality were not substantial as shown in Figure 7

I3v Detective Quantum Efficiency

The DQE results are shown in Figure 9 DQE curves across exposure levels were

almost collinear except for Pixium 4600 and in general could be inferred from the

NNPS results Additionally the DQE curves demonstrated a relatively linear response

with spatial frequencies as expected for flat-panel detectors [9] Differences in DQE

among detectors were consistent for the most part with the type of scintillating material

20

As depicted for 1 mR exposure in Figure 10 differences between Pixium 4600 and DRX-

1C DQE curves correspond to the differences in their NNPS curves DRX-1 DQE curves

were consistently lower than either the Pixium 4600 or DRX-1C curves The DQE curves

for the alternative filtration were consistently higher than those for the IEC filtration

and the most noticeable differences were near the zero-frequency axis These effects can

be both attributed to ineffective gain map correction DQE values for 1 mR exposure are

listed in Table 5

I4 Discussion

I4i Comparisons of Detectors

The limiting spatial resolutions of all three detectors were almost exactly the

same considering that their pixel areas were similar in size The decrease in high-

frequency MTF of the DRX-1 compared to the other detectors is probably a result of

increased optical blurring due to the differences in the powdered structure of GOS

versus the needle-like structure of CsI [2] The fact that the DRX-1C and Pixium 4600

have comparable MTFs suggests similar scintillator thicknesses assuming that the

materials were processed alike

The noise of the three detectors demonstrated similar trends with each other The

higher NNPS curves of the DRX-1 detector are probably due also to the scintillating

material and its operation in converting photons into signal The conversion process is

less efficient because of the less favorable stopping power of the GOS compared to CsI

21

especially with higher energy beams The noise of the Pixium 4600 and DRX-1C were

similar except for the spacing between exposures The DRX-1C NNPS curve spacing is

consistent with a factor of two difference in exposure levels but the Pixium 4600 has a

smaller spacing The 05 mR NNPS curve of the Pixium 4600 is closer to that of the 05

mR NNPS curve of the DRX-1C This demonstrates that at higher exposures the Pixium

4600 produces a larger amount of additional noise beyond that explained by simple

stochastic effects It suggests bad performance in the gain map corrections

The DQE results indicate SNR properties of each detector The Pixium 4600 and

DRX-1C are comparable for the most part with the DRX-1C performing slightly better

The DRX-1 as predicted from MTF and NNPS results has a DQE much lower than

either of the previous two This is a reflection of the detection properties as provided by

its scintillator material The DQE of the DRX-1 however is comparable to CR image

receptors [2] The mid-frequency dips in the DQE for Pixium 4600 may be due to the

optical properties of the CsI phosphor layer which can affect the MTF in this manner

Because the DQE is calculated by squaring the MTF this effect at the mid-range

frequencies becomes more apparent The dips may also be further evidence of bad gain

map corrections

I4ii Comparisons of Filtrations

The alternative filtration closely matches for the most part the IEC-based

filtration for MTF NNPS and DQEs at RQA5 but not at RQA9 The filters do not have

22

Table 4 Experimental MTF frequency locations for 1 mR exposure

Detector Filtration

50 MTF

(mm-1)

40 MTF

(mm-1)

30 MTF

(mm-1)

20 MTF

(mm-1)

10 MTF

(mm-1)

Pixium

4600

RQA5A 115 145 185 245 330

RQA5C 125 155 195 250 345

RQA9A 110 175 175 235 330

RQA9C 125 155 195 255 345

DRX-1C

RQA5A 120 150 185 245 350

RQA5C 125 155 195 255 355

RQA9A 120 150 190 250 355

RQA9C 130 160 210 265 360

DRX-1

RQA5A 110 135 160 205 280

RQA5C 110 135 170 210 285

RQA9A 105 125 155 195 270

RQA9C 110 135 165 210 285

Table 5 Estimated DQE values for 1 mR exposure by frequency bins

Detector Filtration DQE(00 mm-1) DQE(10 mm-1) DQE(20 mm-1) DQE(30 mm-1)

Pixium

4600

RQA5A 62 42 32 21

RQA5C 63 45 36 25

RQA9A 41 27 30 13

RQA9C 43 33 27 19

DRX-1C

RQA5A 72 52 35 21

RQA5C 76 55 41 24

RQA9A 49 33 23 15

RQA9C 51 40 31 20

DRX-1

RQA5A 38 24 12 4

RQA5C 38 25 14 5

RQA9A 28 18 9 4

RQA9C 28 19 12 5

DQE values at the zero-frequency axis were estimated by the intercept of a linear fit of low-frequency data

but excluding most proximal to the axis due to large fluctuations Other estimated values are grouped into

frequency bins due to the noisiness of the data

23

considerable differences in the spatial resolutions of the detectors as expected The noise

responses for each filtration were also similar except at the lower frequencies of the

NNPS especially near the zero-frequency axis There observing the NNPS responses at

RQA5 for Pixium 4600 and DRX-1C in Figure 8 the NNPS for the IEC-based filtration

(solid lines) tend to drop faster than the NNPS for the alternative filtration This

subsequently appears as a drop in DQE near the zero-frequency axis shown for those

detectors in Figure 10 Overall as indicated in Table 5 the DQEs of the two filtrations

while similar in trend indicate that the alternative filtration increases the DQE by a

small amount of 3-5 Part of this may be explained by the slightly higher beam

energy which may be more optimal for the energy response of the detectors or may

weigh the pixel responses slightly considering that they are energy-integrating types

The most probable explanation is the gain map correction for the alternative filtration

where fixed pattern noise is more sufficiently reduced

A previous study [6] had discussed the choice of filter material in the analysis of

DQE when achieving the beam conditions defined by IEC It found that visible

nonuniformities were present with the higher purity aluminum filter (type-11999 alloy)

The low frequency mottle in the flat-field images for NPS measurements were also

attributed to structured noise from the grain size in the IEC-based filter with an

attenuating thickness that would reveal nonuniformities The mottle in the current study

was only observable under very narrow windowing as shown in Figure 11 Such low

24

frequency artifacts which are not readily noticeable may also be caused by shading

artifacts inverse square law or even the heel effect A possible method to correct for this

is a subtraction method by taking the average of the flat-field images for an exposure

level and then subtracting that from each of them This would remove nonuniformities

that were not corrected using a suboptimal gain map calibration

Figure 11 DRX1-C NNPS images at 1 mR for RQA5 with IEC filtration (left) and

alternative filtration (right) Images are equally windowed at 45 and leveled at 980

One convenient aspect of the copper and aluminum filtration is that it requires

much less tube current to achieve the same amount of exposure at the detector than the

much thicker aluminum filtration As shown in the non-normalized spectra in Figure 2

the exiting photon fluence exiting the copper and aluminum filtration is substantially

higher than that of the IEC-specified filtration This is due to the smaller total filtration

25

attenuation For extensive DQE analysis multiple sets of exposures may be acquired

before tube overheating becomes a concern

One limitation to the comparison of the two filtrations is that calibration

procedures specified copper and aluminum filtration at 80 kVp (for all detectors 05 mm

Cu and 10 mm Al) This may have influenced the results in favor of the alternative

filtration A further investigation involving the calibration procedures and performing

DQE measurements is encouraged Another factor may be influenced by the fact that the

tests were performed at 70 kVp and 120 kVp different from the recommended

calibration tube potential Clearly there would be differences in the linear attenuation

coefficients of the filters and different energy responses of the detectors themselves This

must be considered when interpreting DQE results The current results support a

previous study decades ago that described filtration of different material types in terms

of an aluminum equivalent [16] The results show that the two filtration schemes are

essentially equivalent when considering beam qualities and spatial resolutions The

NNPS and DQE results can be seen as close enough where their small differences are

insignificant when performing quality assurance tests in a clinical setting Overall our

results indicate that the alternative filtration with copper and aluminum may be more

convenient to use than the current IEC standard filtration

26

I4iii Implications of Wireless DR

This study has shown that wireless image receptors can have the same DQE

performance if not better than conventional flat-panel detectors They operate on the

same basic physical principles the new features offered by the DRX-1C and DRX-1 are

wireless communication with the workstation and electronics packaging technology

The latter feature may pose limitations for these units in terms of possible degradation

in the detectors in routine clinical conditions A consideration for future work would be

to longitudinally track DQE performance of the wireless detectors over time while being

utilized in a clinical environment In the end one must consider risks versus benefits of

choosing portable DR technology over CR one of which includes the cost and fragility

of DR detectors

The DQE performance of one wireless system is just as good as or better than

conventional systems as seen by the DRX-1C performance compared to the Pixium

4600 Wireless systems can also reduce the need for CR readers especially in portable

applications in other regions of the world (eg military hospitals developing countries)

However while DQE performance indicates the physical performance of the detector

system it is still unknown how it relates to observer performance

I5 Conclusions

Two wireless image receptors DRX-1C and DRX-1 were evaluated and

compared with the conventional DR flat-panel Pixium 4600 in terms of DQE

27

performance along with MTF and NNPS performances The detectors have similar

resolution properties although the DRX-1 is inferior at higher spatial frequencies The

NNPS and DQE results both indicate that the DRX-1C is superior to the DRX-1 and

comparable if not better to the Pixium 4600

The results from the filtration comparison indicate no substantial differences

between the IEC-based filtration and the copper-based alternative filtration Only slight

differences were found in the low frequency components of the NNPS and the DQE due

to the inherent nonuniformities of the IEC specified filtration Given the similarity of the

results and low attenuation advantage of the copper and aluminum filter its use is

encouraged

28

II Directional MTF for Breast Tomosynthesis

II1 Introduction

Breast tomosynthesis is an emerging 3D imaging modality that has potential use

for screening and diagnosis of breast cancer Breast tomosynthesis along with other 3D

techniques is preferable to planar imaging methods (eg mammography) because they

reduce anatomical noise by removing overlying structures above and below the plane of

an image slice [17-20] Recent advances in detectors and computer technology have

made digital tomosynthesis feasible

An image quality metric of particular importance in breast tomosynthesis is

spatial resolution Resolution is important to know in order to assess small-detail

structures such as microcalcifications A descriptive metric for characterizing spatial

resolution in the Fourier (or frequency) domain is the modulation transfer function

(MTF) Affected by reconstruction filters [21] the limited angular projections involved in

breast tomosynthesis results in highly anisotropic (or nonuniform) resolution Many

studies have looked only at characterizing the in-plane spatial resolution (ie in an

individual slice) with an elevated angled edge phantom [2223] A few studies have

looked at characterizing a more comprehensive 3D spatial resolution by using a

phantom with angled wires or tubes [24-26] However such studies require precise

mechanical alignment of the phantoms Several studies have explored a method using a

29

sphere phantom for the directional 3D MTF evaluation for microtomography [27] and

multi-slice CT [2829] This method has not yet been extended to breast tomosynthesis

This chapter focuses on breast tomosynthesis because it is highly anisotropic in

spatial resolution and like its predecessor mammography requires high spatial

resolution Additionally breast tomosynthesis acquisitions and reconstructions produce

several types of artifacts The use of a cone-based method using a sphere phantom [28] is

explored to characterize the directional 3D spatial resolution of simulated images from

breast tomosynthesis A technique for removing out-of-plane artifacts of the ESFs for the

in-plane axes is investigated to yield a modified MTF in a method that separates artifact

information from resolution information

II2 Materials and Methods

II2i Image Simulation

Breast tomosynthesis images were simulated by using a virtual imaging system

depicted in Figure 12 A volumetric breast phantom was voxelized as a rectangular mass

of uniform breast equivalent tissue of 4 cm thickness embedded with fifteen evenly

spaced plastic sphere inserts of 12 mm diameter The spheres were placed in a grid

formation within the central plane of the phantom The x-ray fluence was modeled from

a 28 kVp beam incident upon an indirect flat-panel detector with 200 micro m pixel size

Twenty-three projections within an angular range of 44deg were simulated using cascaded

systems analysis to generate characteristic 2D noise and spatial blurring [29] Each

30

projection was simulated to have an exposure of 174 mR with a fluence of 79 times 105

photonsmm-2 A standard filtered backprojection technique based on the Feldkamp

reconstruction algorithm [29] was used to reconstruct the projections and produce a

volumetric dataset with an isotropic voxel size of 200 micro m

Figure 12 Depiction of the virtual image system

II2ii Uncorrected MTF

To enable comparison of multiple spheres the reconstructed volume was

initially homogenized by performing a background subtraction based on a portion of the

volume devoid of spheres The voxel values were rescaled between one and zero to

eliminate negative values

31

The volumetric data were segmented to extract individual regions of interest

(ROIs) each containing a single sphere The ROIs extended along the full range of the z-

axis A thresholded ROI was generated by determining the exterior and interior voxels

relative to the sphere in the ROI The threshold value was set at 45 of the maximum

voxel value prior to thresholding The exterior and interior voxel values were then set to

values of 0 and 1 respectively Using the thresholded volume the center of mass was

calculated to determine the centroid The voxel values from the original ROI were

subsequently tabulated with the associated distances azimuthal angles and polar

angles relative to the centroid

Conical regions were prescribed along the positive and negative directions along

the three major axes extending from the centroid of the sphere as depicted in Figure 13

The axes about which the extent of the cone angle was delineated were defined with

the azimuthal and polar angles

Voxels with centers within the angular range of the cone were considered for

generating the edge spread function (ESF) To improve regularity of the distance

sampling interval the ESF values were rebinned to discrete distances corresponding to a

fraction of the voxel size Only voxels with distances ranging from the voxel size (ie

200 micro m) to the maximum distance were considered The ESFs from multiple spheres

were averaged together for each of the three major axes to produce an averaged ESF

which was further smoothed utilizing a Gaussian filter

32

Figure 13 Example of 30-degree cone prescribed along z axis of the sphere

The resulting ESF was then differentiated using the central difference method to

produce the line spread function (LSF) A Hanning filter with the same length as the LSF

was applied to zero out the tails of the LSF The presampled MTF was subsequently

computed as the amplitude of the Fourier transform of the LSF The MTF was

normalized with respect to the maximum value occurring within the range of the cutoff

frequency Binning size and conical range for the ESF were considered for maximizing

accuracy and minimizing noise of the MTF verified by comparison against the

theoretical MTF as determined in the previous section

II2iii Theoretical Directional MTF

The theoretical 3D MTF was calculated using a priori knowledge of the transfer

function of the virtual imaging system described in the previous section A phantom

was created with a set of point objects in a uniform and noise-free background with the

objects spanning across the volume of the breast [29] Twenty-one realizations were

33

generated from the reconstructed images of the point objects to yield a set of 3D point

spread functions (PSFs) The 3D fast Fourier transform (FFT) was performed for each 3D

PSF and averaged to give an ldquoexpectationrdquo 3D MTF [29] The theoretical directional

MTFs in the three major spatial axes were determined by line profiles along each of the

corresponding spatial frequency axes in the 3D MTF An additional theoretical MTF for

each direction was determined by using the application of conical regions along the axes

in frequency-space to take into account the contributions of MTF information from other

planes

II2iv Modified MTF

The tomosynthesis reconstruction is known to have edge enhancements which

affect the overall MTF by shifting the peaks of the MTF toward the higher frequencies

[23] The presence of this artifact complicates the interpretation of the actual spatial

resolution of the images Several steps were performed to remove the artifact

contribution to the resolution information particularly for the in-plane x and y

directions with the assumption that resolution information was contained immediately

near the edge

For the x-direction averaged ESF only values that were detected to be inside the

edge of the sphere were considered Those values were previously determined via

thresholding for calculating the centroid The ESF information corresponding to these

values was inversed and flipped about the detected edge to produce a symmetric

34

modified ESF The modified MTF was subsequently calculated from this modified ESF

as described in the previous section

For the y-direction averaged ESF an upward trend was found in the initial part

of the ESF This section was detrended with a polynomial fit and subtracted to produce a

flatter curve in that region The resulting detrended ESF was used to calculate the y axis

modified MTF

Figure 14 Photograph of the imaging system with the acrylic sphere phantom

embedded in oil

II2v Preliminary Experimental Validation

A clinical breast tomosynthesis system (Mammomat Inspiration Siemens AG

Munich Germany) was used to perform a preliminary evaluation of the cone-based

MTF technique The phantom for the experiment consisted of a single acrylic ball of 075

in diameter (SmallParts Seattle WA) suspended by a 0029 in diameter plastic filament

35

(Omniflex Zebco Tulsa OK) in an acrylic frame filled up to 4 in with vegetable oil

(Target Brands Inc Minneapolis MN) The system and phantom are shown in Figure

14 Twenty-five projections with an angular range of 44deg were acquired and subsequently

reconstructed to produce a volume with a voxel size of 01times01times10 mm3 The voxels were

reformatted to have an isotropic size of 01 mm The uncorrected ESF LSF and MTF

were calculated as described in the previous section

II3 Results

II3i Reconstruction

The reconstructed volume is shown in Figure 15 Notice the edge enhancement

along the x-direction as indicated by the sharp shadowing artifacts on either side of the

spheres The background was effectively homogenized using the background

subtraction technique This also took account of the curved edges of the breast phantom

With the close spacing of the spheres in the phantom the shadows along the x direction

for the fifteen spheres overlap with each other As the nine centrally located spheres

experience this effect the same way they were used for determining the ESF

A 3D rendering of the ROI containing a sphere shown in Figure 16 indicates the

anisotropic resolution of the reconstruction Note that the sphere is not accurately

reconstructed and has an oblong shape especially along the z axis Cross sectional views

of the ROI also in Figure 16 clearly demonstrate the edge enhancement causing a

shadow artifact in the x direction caused by the incomplete angular sampling of

36

tomosynthesis The sampling also introduces the triangular reconstruction of the sphere

as seen in the x-z plane Note the gradual edge drop-off in the z direction much beyond

the sphere radius

Figure 15 View of the central slice of the breast phantom reconstruction before (top)

and after (bottom) background subtraction The z axis is through the page

37

Figure 16 3D rendering of the ROI volume (left) and cross-sectional views of the most

centrally located sphere with centroid indicated with red circle (right)

II3ii Theoretical MTF

The theoretical MTFs for x y and z directions as determined from the line

profiles of the 3D MTF are shown in Figure 17 The theoretical MTF in the x direction

has a maximum value that is toward higher frequencies Its 10 response occurs at

about 125 cyclesmm which is at 50 of the cutoff frequency The rapid increase from

the zero-frequency intercept to the peak corresponds to the ramp filter used in filtered

backprojection which decreases the weighting of low frequency contributions due to the

incomplete angular sampling of the frequency-space The MTF does not reach a value of

0 at the zero-frequency intercept as it is very difficult to assess the zero-frequency

intercept due to the finite size of the phantom The theoretical MTF in the y direction

peaks at the zero-frequency intercept and reaches 20 proximal to the cutoff frequency

38

The 10 MTF is well beyond the cutoff frequency The theoretical MTF in the z direction

has a rapid drop-off at very low spatial frequencies indicating the lack of resolution in

that dimension

Figure 17 Theoretical 3D MTF results along the three major planes (top) and along x

y and z directions (bottom) Also note that the angular spread seen in the fx-fz plane is

equal to the angular range of 44deg for the acquisition

II3iii Uncorrected MTF

The ESF LSF and MTF using the cone-based method are shown for the x y and

z directions in Figure 18 It was found that a bin size of one-tenth the voxel size (002

mm) and a cone angle of 30deg to establish the ESF were enough to minimize noise and

maximize accuracy in the uncorrected MTFs considering the reasonable comparison of

the shapes of the MTF curves with the theoretical results in Figure 17 The LSFs are

generally noisy because differentiation of the ESF increases the amplitude of the noise

39

The data shown reflect a convolution with a smoothing Gaussian filter which was later

further corrected for in the reported MTF Nevertheless the high frequency components

of the noise are well beyond the MTF cutoff frequency of 25 cyclesmm and do not

impact the MTF results greatly

For the ESF in the x direction the shadow effect evident at the edge of the sphere

is visible as a steep decline followed by an increase Due to the finite distance range

provided by the ROI the ESF beyond the edge did not asymptotically reach the

background value The corresponding LSF demonstrates a low frequency modulation

that is indicated by the shift of 03 cyclesmm in the x direction for the peak of the MTF

The MTF exhibits a zero-frequency intercept that is non-zero unlike the theoretical MTF

and a 10 value at approximately 1 cyclesmm These features may be a direct

consequence of MTF information ldquocontaminationrdquo from y and z directions Furthermore

the ESF in the y direction demonstrates a reasonably shaped curve except for the slight

upward trend within the radius of the sphere which can be attributed to the shadow

artifact overlapping with the sphere volume The associated MTF has a peak shifted by

approximately 01 cyclesmm away from the axis and a 10 MTF occurring at

approximately 15 cyclesmm Both features which are not present in the theoretical

results may also be attributed to contaminant MTF information from x and z directions

The ESF in the z direction has a drop-off that occurs at a small fraction of the cutoff

frequency similar to that demonstrated by the theoretical MTF

40

Uncorrected ESF LSF and MTF

Figure 18 Uncorrected ESF (top) LSF (middle) and MTF (bottom) for x y and z

directions

41

Figure 19 Comparisons of the directional MTFs as calculated by the sphere method

(dashed line) by theoretical line profiles (light-weight line) by theoretical cone

regions (heavy-weight line)

II3iv Comparison of Theoretical and Simulated MTFs

The theoretical MTF results obtained from line profiles through the 3D MTF and

the simulated MTFs using the cone-based technique did not match very well except for

the general shape of the curves It was assumed in the previous section that the cone-

based technique contains information from other planes Figure 19 compares MTFs in

each direction for the two methods described in the methods and an additional method

based on conical regions of the 3D MTF The latter computes the MTF by averaging

contributions of the 3D MTF using the same cone prescription method used to define the

ESFs Comparison of the curves indicate some interesting correlations aside from the

fact that using conical regions with the 3D MTF results produce more noisy MTF results

partly due to the low sampling provided by the theoretical calculations The same

conclusions regarding the z direction MTF can be confirmed regardless of either

theoretical MTF procedures The experimental x direction MTF seems to agree best with

42

the line profile method whereas the y direction MTF agrees better with the cone region

method The fact that the experimental x direction MTF has a drop-off frequency that is

lower than those of either of the theoretical MTFs in Figure 19 suggests that this might

be due to integration of the z-direction in the in-plane slices considering how slices are

essentially averages of z direction information contained within it [33]

II3v Modified MTF for x and y

Modified ESF LSF and MTF curves for x and y directions are shown in Figure

20 The modified ESF and the resulting LSF in the x direction appear symmetric as

expected from the inverse and flip operation of the interior ESF about the detected edge

The modified MTF appears with less variation than the uncorrected MTF and the MTF

peak occurs at the zero-frequency axis The correction yields a 10 MTF at about 15

cyclesmm an improvement from the uncorrected MTF but still distant from the cutoff

frequency The modified ESF in the y direction demonstrates the detrended curve within

the sphere radius after a quadratic polynomial fit The resulting modified MTF still

appears similar to the uncorrected MTF except that the peak now coincides with the

zero-frequency axis For both x and y directions the low response of the modified MTFs

at the higher frequencies suggests that the contamination from other directions is

substantial due to the angular range of the cone

43

Modified ESF LSF and MTF

Figure 20 Modified ESF (top) LSF (middle) and MTF (bottom) for x and y directions

44

II3v Preliminary Experimental Validation

Cross-sections of the reconstructed sphere volume are shown in Figure 21

Relative to the simulation reconstructions the reconstructions of the experimental

phantom images produce lower contrast and higher noise The preliminary results

shown in Figure 22 indicate that our technique can be applied to actual experimental

breast tomosynthesis reconstructions However due to the noise exhibited by the MTF

curves for the x and y directions we did not determine the modified MTFs to separate

resolution and artifact information

Figure 21 Cross sectional views of the experimental sphere image with centroid

indicated with red circle

45

Uncorrected ESF LSF and MTF for Real Image

Figure 22 ESF (top) LSF (middle) and MTF (bottom) of real image for x y

and z directions

46

II4 Discussion

II4i Evaluation of Cone-based Method

The cone-based MTF technique was introduced by Thornton and Flynn [28] for

evaluation of volumetric CT images To utilize this technique as a characterization of a

3D system spatial resolution one must first consider the validity of the assumption of

shift invariance such that the same MTF result may be obtained regardless of the

location of the sphere The study by Zhao et al [23] found that there was no shift

variance for the MTF measurements along the vertical axis but this was only considering

the in-plane resolution along one axis On the other hand this study evaluated the MTF

with images simulated with cascaded systems analysis which includes conditions of

linearity and shift invariance Additionally the MTF was calculated by averaging the

ESF from several spheres in the same volume only after performing a background

subtraction This step was essential to account for the sensitivity of centroid calculations

as well as ensuring symmetric ESFs for opposing axes of the sphere ROIs

The measurement of MTF with the cone-based technique inherently

supersamples the edge of the sphere to increase signal-to-noise-ratio (SNR) of edge

information by averaging the contributions of each voxel to the ESF [713] This method

also takes into account the discrete sampling of the voxels by accounting for various

shifts of the edge in the voxel (also known as the partial volume effect) However using

the curved surface of the sphere phantom to approximate an edge along a given

47

direction naturally leads to contamination of information from other directions aside

from the one of interest Preferably a directional ESF should be created by using a single

radial line but this would limit the available voxels to obtain edge information An ideal

situation theoretically would be to use a larger-sized sphere such that the surface is

nearly flat and perpendicular to the axes of interest This would also permit a reduction

in the angular range of the cone and thus the introduction of out-of-plane information in

the resulting MTF However sphere size is a limitation in breast tomosynthesis and the

use of a large phantom might void the assumption of shift invariance of the spatial

resolution

The choice of a sphere phantom nevertheless may be based on the clinical need

to quickly acquire a single image for MTF evaluation especially for multiple directions

without presenting extra logistical challenges The use of a wire or edge phantom

requires more precise mechanical alignment to achieve the correct set up The edge

phantom [23] would require at least two images to sample all three dimensions In the

case of the three wire phantom [2425] all three dimensions of the frame must be aligned

simultaneously with respect to the axis of rotation A similar situation would be

encountered when considering a cubic phantom with the planes normal to the axis of

interest In contrast to these phantoms the sphere eliminates the need for precise

alignment especially with respect to three spatial dimensions simultaneously A sphere

48

has ideal symmetry in all directions and can be used to evaluate MTF in any arbitrary

direction

This study unlike others [242532] did not explore the effects of physical

parameters such as scatter or contrast on the final MTF result but it demonstrated the

feasibility of using the cone-based method with an actual breast tomosynthesis image of

a sphere phantom as shown in Error Reference source not found and Error Reference

source not found These effects should be addressed in future works A further look

into deriving the principles of comparing the theoretical MTF with the experimental

MTF using the cone-based method is further warranted

II4ii Separation of Artifact and Resolution Information

The focus of this study was to develop a technique for measuring spatial

resolution of tomosynthesis images The intrinsic artifacts from tomosynthesis

reconstructions however lead to uncharacteristic MTFs and possible misinterpretation

of the effective resolution information When considering previous techniques for

calculating the presampled MTF [713152328] the analysis was performed using an

edge or a line to produce the corresponding ESF The resolution information is

essentially contained only along the edge indicated by the need to calculate the LSF In a

way the method of extracting artifact information is to focus the analysis only on the

edge part of the ESF to calculate the modified MTF This will lead to a better

understanding of the limiting size of objects that may be seen in the reconstructed 3D

49

image The presampled MTF without correction should still be analyzed to understand

the entire system response Note that the ESFs attempt to reflect information only at the

detected edge of the sphere

II5 Conclusions

The directional MTF of a simulated breast tomosynthesis reconstruction was

determined by using the cone-based MTF technique demonstrating the feasibility of a

single phantom for MTF evaluation This study further presented methods of analyzing

only the edge information in the ESF to create a modified MTF along in-slice (x and y)

axes It can provide insight into the actual spatial resolution information contained in the

image while separating the resolution information from the information introduced by

artifacts caused by the reconstruction and insufficient volumetric sampling The idea of

separating the resolution and artifacts from the measured ESF are expected to facilitate

the interpretation of MTF measurements in breast tomosynthesis Similar methods may

be applied to characterize the resolution of other 3D imaging modalities

50

References

1 Garmer M Hannigs SP Jaumlger HJ et al ldquoDigital Radiography Versus

Conventional Radiology in Chest Imaging Diagnostic Performance of a Large-

Area Silicon Flat-Panel Detector in a Clinical CT-Controlled Studyrdquo American

Journal of Roentgenology Volume 74 75-80 (2000)

2 Cowen AR Kengyelics SM and Davies AG ldquoSolid-state flat-panel digital

radiography detectors and their physical imaging characteristics rdquoClinical

Radiology Volume 63 487-498 (2008)

3 Chotas HG Dobbins III JT and Ravin CE ldquoPrinciples of Digital

Radiography with Large-Area Electronically Readable Detectors A Review of

the Basicsrdquo Radiology Volume 210 Number 3 595-599 (1999)

4 Flynn MJ and Samei E Experimental comparison of noise and resolution for

2k and 4k storage phosphor radiography systems Medical Physics Volume 26

Number 8 1612-1623 (1999)

5 Rong XJ Shaw CC Liu X Lemacks MR and Thompson SK

ldquoComparison of an amorphous siliconcesium iodide flat-panel digital chest

radiography system with screenfilm and computed radiography systems ndash A

contrast-detail phantom studyrdquo Medical Physics Volume 28 Number 11 2328-

2335 (2001)

6 Ranger NT Samei E Dobbins III JT and Ravin CE Measurement of the

detective quantum efficiency in digital detectors consistent with the IEC 62220-1

standard Practical considerations regarding the choice of filter material

Medical Physics Volume 30 Number 7 2305-2311 (2005)

7 Samei E Buhr E Granfors P Vandenbroucke D and Wang X Comparison

of edge analysis techniques for the determination of the MTF of digital

radiographic systems Physics in Medicine and Biology Volume 50 3613-3625

(2005)

8 Samei E and Flynn MJ An experimental comparison of detector performance

for computed radiography systems Medical Physics Volume 29 Number 4 447-

459 (2002)

51

9 Samei E and Flynn MJ An experimental comparison of detector performance

for direct and indirect digital radiography systems Medical Physics Volume 30

Number 4 608-622 (2003)

10 Samei E Ranger NT MacKenzie A Honey ID Dobbins III JT and Ravin

CE Effective DQE (eDQE) and speed of digital radiographic systems An

experimental methodology Medical Physics Volume 36 Number 8 3806-3817

(2009)

11 Samei E Ranger NT MacKenzie A Honey ID Dobbins III JT and Ravin

CE Detector or System Extending the Concept of Detective Quantum

Efficiency to Characterize the Performance of Digital Radiographic Imaging

Systems Radiology Volume 249 Number 3 926-937 (2008)

12 ldquoIEC 62220-1 Medical Electrical Equipment ndash Characteristics of Digital X-Ray

Imaging Devices ndash Part 1 Determination of the Detective Quantum Efficiencyrdquo

International Electrotechnical Commission Geneva Switzerland (2003)

13 Samei E Ranger NT Dobbins III JT and Chen Y Intercomparison of

methods for image quality characterization I Modulation transfer function

Medical Physics Volume 33 Number 5 1454-1465 (2006)

14 Dobbins III JT Samei E Ranger NT and Chen Y Intercomparison of

methods for image quality characterization II Noise power spectrum Medical

Physics Volume 33 Number 5 1466-1475 (2006)

15 Samei E Flynn MJ and Reimann DA A method for measuring the

presampled MTF of digital radiographic systems using an edge test device

Medical Physics Volume 25 Number 1 102-113 (1998)

16 Nagel HD ldquoAluminum equivalence of materials used in diagnostic radiology

and its dependence on beam qualityrdquo Physics in Medicine and Biology Volume

31 Number 12 1381-1399 (1986)

17 Niklason LT Christian BT Niklason LE et al ldquoDigital Tomosynthesis in

Breast Imagingrdquo Radiology Volume 205 399-406 (1997)

18 Gur D ldquoTomosynthesis Potential Clinical Role in Breast Imagingrdquo American

Journal of Roentgenology Volume 189 614-615 (2007)

52

19 Park JM Franken Jr EA Garg M Fajardo LL and Niklason LT ldquoBreast

Tomosynthesis Present Considerations and Future Applicationsrdquo

RadioGraphics Volume 27 S231-S240 (2007)

20 Good WF Abrams GS Catullo VJ Chough DM Ganott MA Hakim

CM and Gur D ldquoDigital Breast Tomosynthesis A Pilot Observer Studyrdquo

American Journal of Roentgenology Volume 190 865-869 (2008)

21 Hu Y-H Zhao W Mertelmeier T and Ludwig J ldquoImage Artifact in Digital

Breast Tomosynthesis and Its Dependence on System and Reconstruction

Parametersrdquo IWDM 2008 LNCS 5116 628-634 (2008)

22 Chen Y Lo JY Ranger NT Samei E Dobbins III JT ldquoMethodology of

NEQ(f) analysis for optimization and comparison of digital breast tomosynthesis

acquisition techniques and reconstruction algorithmsrdquo Proceedings of SPIE

Volume 6510 65101I (2007)

23 Zhao B Zhou J Hu Y-H Mertelmeier T Ludwig J and Zhao W

ldquoExperimental validation of a three-dimensional linear system model for breast

tomosynthesisrdquo Medical Physics Volume 36 Number 1 240-251 (2009)

24 Madhav P Brzymialkiewicz CN Cutler SJ Bowsher JE and Tornai MP

ldquoCharacterizing the MTF in 3D for a Quantized SPECT Camera Having Arbitrary

Trajectoriesrdquo 2005 IEEE Nuclear Science Symposium Conference Record 1722-

1726 (2005)

25 Madhav P McKinley RL Samei E Bowsher JE and Tornai MP ldquoA Novel

Method to Characterize the MTF in 3D for Computed Mammotomographyrdquo

Proceedings of SPIE Volume 6142 61421Y (2006)

26 Hu Y-H Zhao B and Zhao W ldquoImage artifacts in digital breast

tomosynthesis Investigation of the effects of system geometry and

reconstruction parameters using a linear system approachrdquo Medical Physics

Volume 35 Number 12 5242-5252 (2008)

27 Seifert A and Flynn MJ ldquoResolving power of 3D x-ray microtomography

systemsrdquo Proceedings of SPIE Volume 4682 407-413 (2002)

28 Thornton MM and Flynn MJ Measurement of the spatial resolution of a

clinical volumetric computed tomography scanner using a sphere phantom

Proceedings of SPIE Volume 6142 61421Z (2006)

53

29 Baek J Pelc NJ ldquoUse of sphere phantoms to measure the 3D MTF of FDK

reconstructionsrdquo Proceedings of SPIE Volume 7961 79610D (2011)

30 Richard S and Samei E ldquoQuantitative imaging in breast tomosynthesis and CT

Comparison of detection and estimation task performancerdquo Medical Physics

Volume 37 Number 6 2627-2637 (2010)

31 Chen Y Lo JY and Dobbins III JT ldquoImpulse response analysis for several

digital tomosynthesis mammography reconstruction algorithmsrdquo Proceedings of

SPIE Volume 5745 541-549 (2005)

32 Zhao B and Zhao W ldquoThree-dimensional linear system analysis for breast

tomosynthesisrdquo Medical Physics Volume 35 Number 12 5219-5232 (2008)

33 Wu G Mainprize JG Boone JM and Yaffe MJ ldquoEvaluation of scatter

effects on image quality for breast tomosynthesisrdquo Medical Physics Volume 36

Number 10 4425-4432 (2009)

Page 22: Development and Evaluation of 2D and 3D Image Quality ...

9

where the frequency-dependent MTF and NNPS were determined as described in

previous sections X was the exposure value in mR corresponding to the NNPS image

and q was the ideal signal to noise ratio squared in units of photonsmiddotmm-2middotmR-1 as

estimated from the spectral simulations

I3 Results

I3i Data Linearization

The detectors in this study provided raw ADU (or pixel) values in a linear scale

The data were converted using the following system conversion function

where Q(ij) is the raw image data m and b are slope and intercept parameters obtained

from linear regression of the system response function and I(ij) is the linearized scaled

data The factor of 1000 was found to scale I(ij) such that the maximum value was a

large 16-bit number Figure 3 shows the original and linearized system responses for the

Pixium 4600 Note that the y-intercepts of the regressions for the linearized responses

are negligible (lt 01) with respect to the slopes a sufficient condition for zero offset

considerations

I3ii Spectral Simulation

The spectral simulations of the IEC filtrations and alternative filtrations indicate

many similarities in their effective energies HVLs and overall shapes of normalized

spectra Results are summarized in Table 3

10

Pixium 4600 Original System

Response

Pixium 4600 Linearized System

Response R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 3 Original (left) and linearized (right) system responses for Pixium 4600 The

linearized system responses were measured from actual images The offsets are small

with respect to the slope sufficient enough for zero-offset conditions

y = 13971x - 13236

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x - 00106Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 13576x + 28292

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

7000

0000 1000 2000 3000 4000 5000

AD

U

Exposure (mR)

y = 99997x - 00067Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0000 1000 2000 3000 4000 5000

AD

U

Exposure (mR)

y = 13644x + 16167Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x + 00044

Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 13845x + 13541

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x - 00177

Rsup2= 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

11

Table 3 Spectral Simulation Results

Beam Quality Filtration

Mean Energy

(kV)

Photon Fluence

(mRmm2)

RQA5A 21 mm Al 5243 259543

RQA5C 05 mm Cu + 10 mm Al 5214 259554

diff 055 0004

RQA9A 40 mm Al 7619 273281

RQA9C 104 mm Cu + 10 mm Al 7579 273964

diff 052 025

Figure 4 Spectral simulations for RQA5 (top) and RQA9 (bottom) conditions Note

the similarities of spectral shapes of the normalized spectra (right) Also note the

significant differences in fluence between filtrations in the simulated spectra (left)

00E+00

50E+04

10E+05

15E+05

20E+05

25E+05

30E+05

35E+05

40E+05

45E+05

0 20 40 60 80

ph

oto

ns

mA

s-1

cm

-2

keV

RQA5 Spectra Comparison

21 mm Al

05 mm Cu + 10 mm Al

00

02

04

06

08

10

12

0 20 40 60 80

keV

RQA5 Normalized Spectra Comparison

21 mm Al

05 mm Cu +

10 mm Al

00E+00

50E+05

10E+06

15E+06

20E+06

25E+06

30E+06

35E+06

40E+06

45E+06

50E+06

0 50 100 150

ph

oto

ns

mA

s-1

cm

-2

keV

RQA9 Spectra Comparison

40 mm Al

104 mm Cu +

10 mm Al

00

02

04

06

08

10

12

0 50 100 150

keV

RQA9 Normalized Spectra Comparison

40 mm Al104 mm Cu + 10 mm Al

12

I3iii Modulation Transfer Function

The limiting spatial resolutions of the systems were indicated by the cutoff

frequencies which were approximately 35 cyclesmm for all three detectors The spatial

resolutions also demonstrated a good degree of isotropy as confirmed by the close

alignment of MTF curves between vertical and horizontal directions differentiated in

Figure 5 by dashed and solid lines respectively The MTF curves for the Pixium 4600

and DRX-1C were nearly equal to each other whereas the DRX-1 MTF curve showed a

more rapid decrease at high frequencies as shown in Figure 6 This difference may be

due to the differences in the inherent optical properties of the scintillating materials

where finer image details are provided by structured CsI more than by granulated GOS

There were no significant differences in MTF curves across beam qualities and filtrations

as shown by the curve comparisons in Figure 6 although the alternative filtration

produced slightly higher MTF curves as seen in Figure 4 Table 4 lists the experimental

specific spatial frequencies for varying levels of MTF

I3iv Noise Power Spectrum

The noise characteristics are indicated by the NNPS curves shown in Figure 7

The noise was similar for both horizontal and vertical directions As exposure increased

the NNPS decreased consistent with the characteristics of Poisson noise describing the

relationship between signal and noise in the presence of increased photon fluence At

13

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 5 MTF results by detector (columns) and beam quality (rows)

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

horizontal

vertical

14

Figure 6 Plots of MTF for RQA5 (top) and RQA9 (bottom) showing the relationships

between detectors (blue red and green) and by filtration (solid and dashed)

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm-1)

MTF

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm-1)

MTF

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

15

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 7 NNPS results by detector (columns) and beam quality (rows)

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

05 mR - horizontal

05 mR - vertical

10 mR - horizontal

10 mR - vertical

20 mR - horizontal

20 mR - vertical

16

Figure 8 Plots of NNPS for RQA5 (top) and RQA9 (bottom) at 1 mR exposure

showing the relationships between detectors (blue red and green) and by filtration

(solid and dashed)

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm-1)

NNPS (1 mR)

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm-1)

NNPS (1 mR)

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

17

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 9 DQE results by detector (columns) and beam quality (rows)

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

05 mR - horizontal

05 mR - vertical

10 mR - horizontal

10 mR - vertical

20 mR - horizontal

20 mR - vertical

18

Figure 10 Plots of DQE for RQA5 (top) and RQA9 (bottom) at 1 mR exposure showing

the relationships between detectors (blue red and green) and by filtration (solid and

dashed)

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm-1)

DQE (1 mR)

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm-1)

DQE

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

19

higher frequencies the NNPS curves of the Pixium 4600 and DRX-1 diverge slightly for

the different directions illustrating increased noise in the readout direction (vertical)

Differences in the noise characteristics were more apparent among detectors as

shown for 1 mR in Figure 8 The NNPS curve for the DRX-1 was higher in magnitude

across the entire frequency range than either the Pixium 4600 or DRX-1C which both

seemed to demonstrate reasonably similar NNPS curves The higher magnitude noise of

the DRX-1 indicates higher relative noise content overall Closer inspection of the NNPS

curves of the Pixium 4600 and DRX-1C detectors in Figure 7 revealed differences in the

spacing between the three exposure levels The gaps between the Pixium 4600 NNPS

curves do not correspond to the factor of two differences between each exposure level

especially at low- to mid- spatial frequencies suggesting a higher level of fixed pattern

noise additional noise with increasing exposure levels due to ineffective gain map

corrections Between filtration schemes the differences in NNPS curves for a given beam

quality were not substantial as shown in Figure 7

I3v Detective Quantum Efficiency

The DQE results are shown in Figure 9 DQE curves across exposure levels were

almost collinear except for Pixium 4600 and in general could be inferred from the

NNPS results Additionally the DQE curves demonstrated a relatively linear response

with spatial frequencies as expected for flat-panel detectors [9] Differences in DQE

among detectors were consistent for the most part with the type of scintillating material

20

As depicted for 1 mR exposure in Figure 10 differences between Pixium 4600 and DRX-

1C DQE curves correspond to the differences in their NNPS curves DRX-1 DQE curves

were consistently lower than either the Pixium 4600 or DRX-1C curves The DQE curves

for the alternative filtration were consistently higher than those for the IEC filtration

and the most noticeable differences were near the zero-frequency axis These effects can

be both attributed to ineffective gain map correction DQE values for 1 mR exposure are

listed in Table 5

I4 Discussion

I4i Comparisons of Detectors

The limiting spatial resolutions of all three detectors were almost exactly the

same considering that their pixel areas were similar in size The decrease in high-

frequency MTF of the DRX-1 compared to the other detectors is probably a result of

increased optical blurring due to the differences in the powdered structure of GOS

versus the needle-like structure of CsI [2] The fact that the DRX-1C and Pixium 4600

have comparable MTFs suggests similar scintillator thicknesses assuming that the

materials were processed alike

The noise of the three detectors demonstrated similar trends with each other The

higher NNPS curves of the DRX-1 detector are probably due also to the scintillating

material and its operation in converting photons into signal The conversion process is

less efficient because of the less favorable stopping power of the GOS compared to CsI

21

especially with higher energy beams The noise of the Pixium 4600 and DRX-1C were

similar except for the spacing between exposures The DRX-1C NNPS curve spacing is

consistent with a factor of two difference in exposure levels but the Pixium 4600 has a

smaller spacing The 05 mR NNPS curve of the Pixium 4600 is closer to that of the 05

mR NNPS curve of the DRX-1C This demonstrates that at higher exposures the Pixium

4600 produces a larger amount of additional noise beyond that explained by simple

stochastic effects It suggests bad performance in the gain map corrections

The DQE results indicate SNR properties of each detector The Pixium 4600 and

DRX-1C are comparable for the most part with the DRX-1C performing slightly better

The DRX-1 as predicted from MTF and NNPS results has a DQE much lower than

either of the previous two This is a reflection of the detection properties as provided by

its scintillator material The DQE of the DRX-1 however is comparable to CR image

receptors [2] The mid-frequency dips in the DQE for Pixium 4600 may be due to the

optical properties of the CsI phosphor layer which can affect the MTF in this manner

Because the DQE is calculated by squaring the MTF this effect at the mid-range

frequencies becomes more apparent The dips may also be further evidence of bad gain

map corrections

I4ii Comparisons of Filtrations

The alternative filtration closely matches for the most part the IEC-based

filtration for MTF NNPS and DQEs at RQA5 but not at RQA9 The filters do not have

22

Table 4 Experimental MTF frequency locations for 1 mR exposure

Detector Filtration

50 MTF

(mm-1)

40 MTF

(mm-1)

30 MTF

(mm-1)

20 MTF

(mm-1)

10 MTF

(mm-1)

Pixium

4600

RQA5A 115 145 185 245 330

RQA5C 125 155 195 250 345

RQA9A 110 175 175 235 330

RQA9C 125 155 195 255 345

DRX-1C

RQA5A 120 150 185 245 350

RQA5C 125 155 195 255 355

RQA9A 120 150 190 250 355

RQA9C 130 160 210 265 360

DRX-1

RQA5A 110 135 160 205 280

RQA5C 110 135 170 210 285

RQA9A 105 125 155 195 270

RQA9C 110 135 165 210 285

Table 5 Estimated DQE values for 1 mR exposure by frequency bins

Detector Filtration DQE(00 mm-1) DQE(10 mm-1) DQE(20 mm-1) DQE(30 mm-1)

Pixium

4600

RQA5A 62 42 32 21

RQA5C 63 45 36 25

RQA9A 41 27 30 13

RQA9C 43 33 27 19

DRX-1C

RQA5A 72 52 35 21

RQA5C 76 55 41 24

RQA9A 49 33 23 15

RQA9C 51 40 31 20

DRX-1

RQA5A 38 24 12 4

RQA5C 38 25 14 5

RQA9A 28 18 9 4

RQA9C 28 19 12 5

DQE values at the zero-frequency axis were estimated by the intercept of a linear fit of low-frequency data

but excluding most proximal to the axis due to large fluctuations Other estimated values are grouped into

frequency bins due to the noisiness of the data

23

considerable differences in the spatial resolutions of the detectors as expected The noise

responses for each filtration were also similar except at the lower frequencies of the

NNPS especially near the zero-frequency axis There observing the NNPS responses at

RQA5 for Pixium 4600 and DRX-1C in Figure 8 the NNPS for the IEC-based filtration

(solid lines) tend to drop faster than the NNPS for the alternative filtration This

subsequently appears as a drop in DQE near the zero-frequency axis shown for those

detectors in Figure 10 Overall as indicated in Table 5 the DQEs of the two filtrations

while similar in trend indicate that the alternative filtration increases the DQE by a

small amount of 3-5 Part of this may be explained by the slightly higher beam

energy which may be more optimal for the energy response of the detectors or may

weigh the pixel responses slightly considering that they are energy-integrating types

The most probable explanation is the gain map correction for the alternative filtration

where fixed pattern noise is more sufficiently reduced

A previous study [6] had discussed the choice of filter material in the analysis of

DQE when achieving the beam conditions defined by IEC It found that visible

nonuniformities were present with the higher purity aluminum filter (type-11999 alloy)

The low frequency mottle in the flat-field images for NPS measurements were also

attributed to structured noise from the grain size in the IEC-based filter with an

attenuating thickness that would reveal nonuniformities The mottle in the current study

was only observable under very narrow windowing as shown in Figure 11 Such low

24

frequency artifacts which are not readily noticeable may also be caused by shading

artifacts inverse square law or even the heel effect A possible method to correct for this

is a subtraction method by taking the average of the flat-field images for an exposure

level and then subtracting that from each of them This would remove nonuniformities

that were not corrected using a suboptimal gain map calibration

Figure 11 DRX1-C NNPS images at 1 mR for RQA5 with IEC filtration (left) and

alternative filtration (right) Images are equally windowed at 45 and leveled at 980

One convenient aspect of the copper and aluminum filtration is that it requires

much less tube current to achieve the same amount of exposure at the detector than the

much thicker aluminum filtration As shown in the non-normalized spectra in Figure 2

the exiting photon fluence exiting the copper and aluminum filtration is substantially

higher than that of the IEC-specified filtration This is due to the smaller total filtration

25

attenuation For extensive DQE analysis multiple sets of exposures may be acquired

before tube overheating becomes a concern

One limitation to the comparison of the two filtrations is that calibration

procedures specified copper and aluminum filtration at 80 kVp (for all detectors 05 mm

Cu and 10 mm Al) This may have influenced the results in favor of the alternative

filtration A further investigation involving the calibration procedures and performing

DQE measurements is encouraged Another factor may be influenced by the fact that the

tests were performed at 70 kVp and 120 kVp different from the recommended

calibration tube potential Clearly there would be differences in the linear attenuation

coefficients of the filters and different energy responses of the detectors themselves This

must be considered when interpreting DQE results The current results support a

previous study decades ago that described filtration of different material types in terms

of an aluminum equivalent [16] The results show that the two filtration schemes are

essentially equivalent when considering beam qualities and spatial resolutions The

NNPS and DQE results can be seen as close enough where their small differences are

insignificant when performing quality assurance tests in a clinical setting Overall our

results indicate that the alternative filtration with copper and aluminum may be more

convenient to use than the current IEC standard filtration

26

I4iii Implications of Wireless DR

This study has shown that wireless image receptors can have the same DQE

performance if not better than conventional flat-panel detectors They operate on the

same basic physical principles the new features offered by the DRX-1C and DRX-1 are

wireless communication with the workstation and electronics packaging technology

The latter feature may pose limitations for these units in terms of possible degradation

in the detectors in routine clinical conditions A consideration for future work would be

to longitudinally track DQE performance of the wireless detectors over time while being

utilized in a clinical environment In the end one must consider risks versus benefits of

choosing portable DR technology over CR one of which includes the cost and fragility

of DR detectors

The DQE performance of one wireless system is just as good as or better than

conventional systems as seen by the DRX-1C performance compared to the Pixium

4600 Wireless systems can also reduce the need for CR readers especially in portable

applications in other regions of the world (eg military hospitals developing countries)

However while DQE performance indicates the physical performance of the detector

system it is still unknown how it relates to observer performance

I5 Conclusions

Two wireless image receptors DRX-1C and DRX-1 were evaluated and

compared with the conventional DR flat-panel Pixium 4600 in terms of DQE

27

performance along with MTF and NNPS performances The detectors have similar

resolution properties although the DRX-1 is inferior at higher spatial frequencies The

NNPS and DQE results both indicate that the DRX-1C is superior to the DRX-1 and

comparable if not better to the Pixium 4600

The results from the filtration comparison indicate no substantial differences

between the IEC-based filtration and the copper-based alternative filtration Only slight

differences were found in the low frequency components of the NNPS and the DQE due

to the inherent nonuniformities of the IEC specified filtration Given the similarity of the

results and low attenuation advantage of the copper and aluminum filter its use is

encouraged

28

II Directional MTF for Breast Tomosynthesis

II1 Introduction

Breast tomosynthesis is an emerging 3D imaging modality that has potential use

for screening and diagnosis of breast cancer Breast tomosynthesis along with other 3D

techniques is preferable to planar imaging methods (eg mammography) because they

reduce anatomical noise by removing overlying structures above and below the plane of

an image slice [17-20] Recent advances in detectors and computer technology have

made digital tomosynthesis feasible

An image quality metric of particular importance in breast tomosynthesis is

spatial resolution Resolution is important to know in order to assess small-detail

structures such as microcalcifications A descriptive metric for characterizing spatial

resolution in the Fourier (or frequency) domain is the modulation transfer function

(MTF) Affected by reconstruction filters [21] the limited angular projections involved in

breast tomosynthesis results in highly anisotropic (or nonuniform) resolution Many

studies have looked only at characterizing the in-plane spatial resolution (ie in an

individual slice) with an elevated angled edge phantom [2223] A few studies have

looked at characterizing a more comprehensive 3D spatial resolution by using a

phantom with angled wires or tubes [24-26] However such studies require precise

mechanical alignment of the phantoms Several studies have explored a method using a

29

sphere phantom for the directional 3D MTF evaluation for microtomography [27] and

multi-slice CT [2829] This method has not yet been extended to breast tomosynthesis

This chapter focuses on breast tomosynthesis because it is highly anisotropic in

spatial resolution and like its predecessor mammography requires high spatial

resolution Additionally breast tomosynthesis acquisitions and reconstructions produce

several types of artifacts The use of a cone-based method using a sphere phantom [28] is

explored to characterize the directional 3D spatial resolution of simulated images from

breast tomosynthesis A technique for removing out-of-plane artifacts of the ESFs for the

in-plane axes is investigated to yield a modified MTF in a method that separates artifact

information from resolution information

II2 Materials and Methods

II2i Image Simulation

Breast tomosynthesis images were simulated by using a virtual imaging system

depicted in Figure 12 A volumetric breast phantom was voxelized as a rectangular mass

of uniform breast equivalent tissue of 4 cm thickness embedded with fifteen evenly

spaced plastic sphere inserts of 12 mm diameter The spheres were placed in a grid

formation within the central plane of the phantom The x-ray fluence was modeled from

a 28 kVp beam incident upon an indirect flat-panel detector with 200 micro m pixel size

Twenty-three projections within an angular range of 44deg were simulated using cascaded

systems analysis to generate characteristic 2D noise and spatial blurring [29] Each

30

projection was simulated to have an exposure of 174 mR with a fluence of 79 times 105

photonsmm-2 A standard filtered backprojection technique based on the Feldkamp

reconstruction algorithm [29] was used to reconstruct the projections and produce a

volumetric dataset with an isotropic voxel size of 200 micro m

Figure 12 Depiction of the virtual image system

II2ii Uncorrected MTF

To enable comparison of multiple spheres the reconstructed volume was

initially homogenized by performing a background subtraction based on a portion of the

volume devoid of spheres The voxel values were rescaled between one and zero to

eliminate negative values

31

The volumetric data were segmented to extract individual regions of interest

(ROIs) each containing a single sphere The ROIs extended along the full range of the z-

axis A thresholded ROI was generated by determining the exterior and interior voxels

relative to the sphere in the ROI The threshold value was set at 45 of the maximum

voxel value prior to thresholding The exterior and interior voxel values were then set to

values of 0 and 1 respectively Using the thresholded volume the center of mass was

calculated to determine the centroid The voxel values from the original ROI were

subsequently tabulated with the associated distances azimuthal angles and polar

angles relative to the centroid

Conical regions were prescribed along the positive and negative directions along

the three major axes extending from the centroid of the sphere as depicted in Figure 13

The axes about which the extent of the cone angle was delineated were defined with

the azimuthal and polar angles

Voxels with centers within the angular range of the cone were considered for

generating the edge spread function (ESF) To improve regularity of the distance

sampling interval the ESF values were rebinned to discrete distances corresponding to a

fraction of the voxel size Only voxels with distances ranging from the voxel size (ie

200 micro m) to the maximum distance were considered The ESFs from multiple spheres

were averaged together for each of the three major axes to produce an averaged ESF

which was further smoothed utilizing a Gaussian filter

32

Figure 13 Example of 30-degree cone prescribed along z axis of the sphere

The resulting ESF was then differentiated using the central difference method to

produce the line spread function (LSF) A Hanning filter with the same length as the LSF

was applied to zero out the tails of the LSF The presampled MTF was subsequently

computed as the amplitude of the Fourier transform of the LSF The MTF was

normalized with respect to the maximum value occurring within the range of the cutoff

frequency Binning size and conical range for the ESF were considered for maximizing

accuracy and minimizing noise of the MTF verified by comparison against the

theoretical MTF as determined in the previous section

II2iii Theoretical Directional MTF

The theoretical 3D MTF was calculated using a priori knowledge of the transfer

function of the virtual imaging system described in the previous section A phantom

was created with a set of point objects in a uniform and noise-free background with the

objects spanning across the volume of the breast [29] Twenty-one realizations were

33

generated from the reconstructed images of the point objects to yield a set of 3D point

spread functions (PSFs) The 3D fast Fourier transform (FFT) was performed for each 3D

PSF and averaged to give an ldquoexpectationrdquo 3D MTF [29] The theoretical directional

MTFs in the three major spatial axes were determined by line profiles along each of the

corresponding spatial frequency axes in the 3D MTF An additional theoretical MTF for

each direction was determined by using the application of conical regions along the axes

in frequency-space to take into account the contributions of MTF information from other

planes

II2iv Modified MTF

The tomosynthesis reconstruction is known to have edge enhancements which

affect the overall MTF by shifting the peaks of the MTF toward the higher frequencies

[23] The presence of this artifact complicates the interpretation of the actual spatial

resolution of the images Several steps were performed to remove the artifact

contribution to the resolution information particularly for the in-plane x and y

directions with the assumption that resolution information was contained immediately

near the edge

For the x-direction averaged ESF only values that were detected to be inside the

edge of the sphere were considered Those values were previously determined via

thresholding for calculating the centroid The ESF information corresponding to these

values was inversed and flipped about the detected edge to produce a symmetric

34

modified ESF The modified MTF was subsequently calculated from this modified ESF

as described in the previous section

For the y-direction averaged ESF an upward trend was found in the initial part

of the ESF This section was detrended with a polynomial fit and subtracted to produce a

flatter curve in that region The resulting detrended ESF was used to calculate the y axis

modified MTF

Figure 14 Photograph of the imaging system with the acrylic sphere phantom

embedded in oil

II2v Preliminary Experimental Validation

A clinical breast tomosynthesis system (Mammomat Inspiration Siemens AG

Munich Germany) was used to perform a preliminary evaluation of the cone-based

MTF technique The phantom for the experiment consisted of a single acrylic ball of 075

in diameter (SmallParts Seattle WA) suspended by a 0029 in diameter plastic filament

35

(Omniflex Zebco Tulsa OK) in an acrylic frame filled up to 4 in with vegetable oil

(Target Brands Inc Minneapolis MN) The system and phantom are shown in Figure

14 Twenty-five projections with an angular range of 44deg were acquired and subsequently

reconstructed to produce a volume with a voxel size of 01times01times10 mm3 The voxels were

reformatted to have an isotropic size of 01 mm The uncorrected ESF LSF and MTF

were calculated as described in the previous section

II3 Results

II3i Reconstruction

The reconstructed volume is shown in Figure 15 Notice the edge enhancement

along the x-direction as indicated by the sharp shadowing artifacts on either side of the

spheres The background was effectively homogenized using the background

subtraction technique This also took account of the curved edges of the breast phantom

With the close spacing of the spheres in the phantom the shadows along the x direction

for the fifteen spheres overlap with each other As the nine centrally located spheres

experience this effect the same way they were used for determining the ESF

A 3D rendering of the ROI containing a sphere shown in Figure 16 indicates the

anisotropic resolution of the reconstruction Note that the sphere is not accurately

reconstructed and has an oblong shape especially along the z axis Cross sectional views

of the ROI also in Figure 16 clearly demonstrate the edge enhancement causing a

shadow artifact in the x direction caused by the incomplete angular sampling of

36

tomosynthesis The sampling also introduces the triangular reconstruction of the sphere

as seen in the x-z plane Note the gradual edge drop-off in the z direction much beyond

the sphere radius

Figure 15 View of the central slice of the breast phantom reconstruction before (top)

and after (bottom) background subtraction The z axis is through the page

37

Figure 16 3D rendering of the ROI volume (left) and cross-sectional views of the most

centrally located sphere with centroid indicated with red circle (right)

II3ii Theoretical MTF

The theoretical MTFs for x y and z directions as determined from the line

profiles of the 3D MTF are shown in Figure 17 The theoretical MTF in the x direction

has a maximum value that is toward higher frequencies Its 10 response occurs at

about 125 cyclesmm which is at 50 of the cutoff frequency The rapid increase from

the zero-frequency intercept to the peak corresponds to the ramp filter used in filtered

backprojection which decreases the weighting of low frequency contributions due to the

incomplete angular sampling of the frequency-space The MTF does not reach a value of

0 at the zero-frequency intercept as it is very difficult to assess the zero-frequency

intercept due to the finite size of the phantom The theoretical MTF in the y direction

peaks at the zero-frequency intercept and reaches 20 proximal to the cutoff frequency

38

The 10 MTF is well beyond the cutoff frequency The theoretical MTF in the z direction

has a rapid drop-off at very low spatial frequencies indicating the lack of resolution in

that dimension

Figure 17 Theoretical 3D MTF results along the three major planes (top) and along x

y and z directions (bottom) Also note that the angular spread seen in the fx-fz plane is

equal to the angular range of 44deg for the acquisition

II3iii Uncorrected MTF

The ESF LSF and MTF using the cone-based method are shown for the x y and

z directions in Figure 18 It was found that a bin size of one-tenth the voxel size (002

mm) and a cone angle of 30deg to establish the ESF were enough to minimize noise and

maximize accuracy in the uncorrected MTFs considering the reasonable comparison of

the shapes of the MTF curves with the theoretical results in Figure 17 The LSFs are

generally noisy because differentiation of the ESF increases the amplitude of the noise

39

The data shown reflect a convolution with a smoothing Gaussian filter which was later

further corrected for in the reported MTF Nevertheless the high frequency components

of the noise are well beyond the MTF cutoff frequency of 25 cyclesmm and do not

impact the MTF results greatly

For the ESF in the x direction the shadow effect evident at the edge of the sphere

is visible as a steep decline followed by an increase Due to the finite distance range

provided by the ROI the ESF beyond the edge did not asymptotically reach the

background value The corresponding LSF demonstrates a low frequency modulation

that is indicated by the shift of 03 cyclesmm in the x direction for the peak of the MTF

The MTF exhibits a zero-frequency intercept that is non-zero unlike the theoretical MTF

and a 10 value at approximately 1 cyclesmm These features may be a direct

consequence of MTF information ldquocontaminationrdquo from y and z directions Furthermore

the ESF in the y direction demonstrates a reasonably shaped curve except for the slight

upward trend within the radius of the sphere which can be attributed to the shadow

artifact overlapping with the sphere volume The associated MTF has a peak shifted by

approximately 01 cyclesmm away from the axis and a 10 MTF occurring at

approximately 15 cyclesmm Both features which are not present in the theoretical

results may also be attributed to contaminant MTF information from x and z directions

The ESF in the z direction has a drop-off that occurs at a small fraction of the cutoff

frequency similar to that demonstrated by the theoretical MTF

40

Uncorrected ESF LSF and MTF

Figure 18 Uncorrected ESF (top) LSF (middle) and MTF (bottom) for x y and z

directions

41

Figure 19 Comparisons of the directional MTFs as calculated by the sphere method

(dashed line) by theoretical line profiles (light-weight line) by theoretical cone

regions (heavy-weight line)

II3iv Comparison of Theoretical and Simulated MTFs

The theoretical MTF results obtained from line profiles through the 3D MTF and

the simulated MTFs using the cone-based technique did not match very well except for

the general shape of the curves It was assumed in the previous section that the cone-

based technique contains information from other planes Figure 19 compares MTFs in

each direction for the two methods described in the methods and an additional method

based on conical regions of the 3D MTF The latter computes the MTF by averaging

contributions of the 3D MTF using the same cone prescription method used to define the

ESFs Comparison of the curves indicate some interesting correlations aside from the

fact that using conical regions with the 3D MTF results produce more noisy MTF results

partly due to the low sampling provided by the theoretical calculations The same

conclusions regarding the z direction MTF can be confirmed regardless of either

theoretical MTF procedures The experimental x direction MTF seems to agree best with

42

the line profile method whereas the y direction MTF agrees better with the cone region

method The fact that the experimental x direction MTF has a drop-off frequency that is

lower than those of either of the theoretical MTFs in Figure 19 suggests that this might

be due to integration of the z-direction in the in-plane slices considering how slices are

essentially averages of z direction information contained within it [33]

II3v Modified MTF for x and y

Modified ESF LSF and MTF curves for x and y directions are shown in Figure

20 The modified ESF and the resulting LSF in the x direction appear symmetric as

expected from the inverse and flip operation of the interior ESF about the detected edge

The modified MTF appears with less variation than the uncorrected MTF and the MTF

peak occurs at the zero-frequency axis The correction yields a 10 MTF at about 15

cyclesmm an improvement from the uncorrected MTF but still distant from the cutoff

frequency The modified ESF in the y direction demonstrates the detrended curve within

the sphere radius after a quadratic polynomial fit The resulting modified MTF still

appears similar to the uncorrected MTF except that the peak now coincides with the

zero-frequency axis For both x and y directions the low response of the modified MTFs

at the higher frequencies suggests that the contamination from other directions is

substantial due to the angular range of the cone

43

Modified ESF LSF and MTF

Figure 20 Modified ESF (top) LSF (middle) and MTF (bottom) for x and y directions

44

II3v Preliminary Experimental Validation

Cross-sections of the reconstructed sphere volume are shown in Figure 21

Relative to the simulation reconstructions the reconstructions of the experimental

phantom images produce lower contrast and higher noise The preliminary results

shown in Figure 22 indicate that our technique can be applied to actual experimental

breast tomosynthesis reconstructions However due to the noise exhibited by the MTF

curves for the x and y directions we did not determine the modified MTFs to separate

resolution and artifact information

Figure 21 Cross sectional views of the experimental sphere image with centroid

indicated with red circle

45

Uncorrected ESF LSF and MTF for Real Image

Figure 22 ESF (top) LSF (middle) and MTF (bottom) of real image for x y

and z directions

46

II4 Discussion

II4i Evaluation of Cone-based Method

The cone-based MTF technique was introduced by Thornton and Flynn [28] for

evaluation of volumetric CT images To utilize this technique as a characterization of a

3D system spatial resolution one must first consider the validity of the assumption of

shift invariance such that the same MTF result may be obtained regardless of the

location of the sphere The study by Zhao et al [23] found that there was no shift

variance for the MTF measurements along the vertical axis but this was only considering

the in-plane resolution along one axis On the other hand this study evaluated the MTF

with images simulated with cascaded systems analysis which includes conditions of

linearity and shift invariance Additionally the MTF was calculated by averaging the

ESF from several spheres in the same volume only after performing a background

subtraction This step was essential to account for the sensitivity of centroid calculations

as well as ensuring symmetric ESFs for opposing axes of the sphere ROIs

The measurement of MTF with the cone-based technique inherently

supersamples the edge of the sphere to increase signal-to-noise-ratio (SNR) of edge

information by averaging the contributions of each voxel to the ESF [713] This method

also takes into account the discrete sampling of the voxels by accounting for various

shifts of the edge in the voxel (also known as the partial volume effect) However using

the curved surface of the sphere phantom to approximate an edge along a given

47

direction naturally leads to contamination of information from other directions aside

from the one of interest Preferably a directional ESF should be created by using a single

radial line but this would limit the available voxels to obtain edge information An ideal

situation theoretically would be to use a larger-sized sphere such that the surface is

nearly flat and perpendicular to the axes of interest This would also permit a reduction

in the angular range of the cone and thus the introduction of out-of-plane information in

the resulting MTF However sphere size is a limitation in breast tomosynthesis and the

use of a large phantom might void the assumption of shift invariance of the spatial

resolution

The choice of a sphere phantom nevertheless may be based on the clinical need

to quickly acquire a single image for MTF evaluation especially for multiple directions

without presenting extra logistical challenges The use of a wire or edge phantom

requires more precise mechanical alignment to achieve the correct set up The edge

phantom [23] would require at least two images to sample all three dimensions In the

case of the three wire phantom [2425] all three dimensions of the frame must be aligned

simultaneously with respect to the axis of rotation A similar situation would be

encountered when considering a cubic phantom with the planes normal to the axis of

interest In contrast to these phantoms the sphere eliminates the need for precise

alignment especially with respect to three spatial dimensions simultaneously A sphere

48

has ideal symmetry in all directions and can be used to evaluate MTF in any arbitrary

direction

This study unlike others [242532] did not explore the effects of physical

parameters such as scatter or contrast on the final MTF result but it demonstrated the

feasibility of using the cone-based method with an actual breast tomosynthesis image of

a sphere phantom as shown in Error Reference source not found and Error Reference

source not found These effects should be addressed in future works A further look

into deriving the principles of comparing the theoretical MTF with the experimental

MTF using the cone-based method is further warranted

II4ii Separation of Artifact and Resolution Information

The focus of this study was to develop a technique for measuring spatial

resolution of tomosynthesis images The intrinsic artifacts from tomosynthesis

reconstructions however lead to uncharacteristic MTFs and possible misinterpretation

of the effective resolution information When considering previous techniques for

calculating the presampled MTF [713152328] the analysis was performed using an

edge or a line to produce the corresponding ESF The resolution information is

essentially contained only along the edge indicated by the need to calculate the LSF In a

way the method of extracting artifact information is to focus the analysis only on the

edge part of the ESF to calculate the modified MTF This will lead to a better

understanding of the limiting size of objects that may be seen in the reconstructed 3D

49

image The presampled MTF without correction should still be analyzed to understand

the entire system response Note that the ESFs attempt to reflect information only at the

detected edge of the sphere

II5 Conclusions

The directional MTF of a simulated breast tomosynthesis reconstruction was

determined by using the cone-based MTF technique demonstrating the feasibility of a

single phantom for MTF evaluation This study further presented methods of analyzing

only the edge information in the ESF to create a modified MTF along in-slice (x and y)

axes It can provide insight into the actual spatial resolution information contained in the

image while separating the resolution information from the information introduced by

artifacts caused by the reconstruction and insufficient volumetric sampling The idea of

separating the resolution and artifacts from the measured ESF are expected to facilitate

the interpretation of MTF measurements in breast tomosynthesis Similar methods may

be applied to characterize the resolution of other 3D imaging modalities

50

References

1 Garmer M Hannigs SP Jaumlger HJ et al ldquoDigital Radiography Versus

Conventional Radiology in Chest Imaging Diagnostic Performance of a Large-

Area Silicon Flat-Panel Detector in a Clinical CT-Controlled Studyrdquo American

Journal of Roentgenology Volume 74 75-80 (2000)

2 Cowen AR Kengyelics SM and Davies AG ldquoSolid-state flat-panel digital

radiography detectors and their physical imaging characteristics rdquoClinical

Radiology Volume 63 487-498 (2008)

3 Chotas HG Dobbins III JT and Ravin CE ldquoPrinciples of Digital

Radiography with Large-Area Electronically Readable Detectors A Review of

the Basicsrdquo Radiology Volume 210 Number 3 595-599 (1999)

4 Flynn MJ and Samei E Experimental comparison of noise and resolution for

2k and 4k storage phosphor radiography systems Medical Physics Volume 26

Number 8 1612-1623 (1999)

5 Rong XJ Shaw CC Liu X Lemacks MR and Thompson SK

ldquoComparison of an amorphous siliconcesium iodide flat-panel digital chest

radiography system with screenfilm and computed radiography systems ndash A

contrast-detail phantom studyrdquo Medical Physics Volume 28 Number 11 2328-

2335 (2001)

6 Ranger NT Samei E Dobbins III JT and Ravin CE Measurement of the

detective quantum efficiency in digital detectors consistent with the IEC 62220-1

standard Practical considerations regarding the choice of filter material

Medical Physics Volume 30 Number 7 2305-2311 (2005)

7 Samei E Buhr E Granfors P Vandenbroucke D and Wang X Comparison

of edge analysis techniques for the determination of the MTF of digital

radiographic systems Physics in Medicine and Biology Volume 50 3613-3625

(2005)

8 Samei E and Flynn MJ An experimental comparison of detector performance

for computed radiography systems Medical Physics Volume 29 Number 4 447-

459 (2002)

51

9 Samei E and Flynn MJ An experimental comparison of detector performance

for direct and indirect digital radiography systems Medical Physics Volume 30

Number 4 608-622 (2003)

10 Samei E Ranger NT MacKenzie A Honey ID Dobbins III JT and Ravin

CE Effective DQE (eDQE) and speed of digital radiographic systems An

experimental methodology Medical Physics Volume 36 Number 8 3806-3817

(2009)

11 Samei E Ranger NT MacKenzie A Honey ID Dobbins III JT and Ravin

CE Detector or System Extending the Concept of Detective Quantum

Efficiency to Characterize the Performance of Digital Radiographic Imaging

Systems Radiology Volume 249 Number 3 926-937 (2008)

12 ldquoIEC 62220-1 Medical Electrical Equipment ndash Characteristics of Digital X-Ray

Imaging Devices ndash Part 1 Determination of the Detective Quantum Efficiencyrdquo

International Electrotechnical Commission Geneva Switzerland (2003)

13 Samei E Ranger NT Dobbins III JT and Chen Y Intercomparison of

methods for image quality characterization I Modulation transfer function

Medical Physics Volume 33 Number 5 1454-1465 (2006)

14 Dobbins III JT Samei E Ranger NT and Chen Y Intercomparison of

methods for image quality characterization II Noise power spectrum Medical

Physics Volume 33 Number 5 1466-1475 (2006)

15 Samei E Flynn MJ and Reimann DA A method for measuring the

presampled MTF of digital radiographic systems using an edge test device

Medical Physics Volume 25 Number 1 102-113 (1998)

16 Nagel HD ldquoAluminum equivalence of materials used in diagnostic radiology

and its dependence on beam qualityrdquo Physics in Medicine and Biology Volume

31 Number 12 1381-1399 (1986)

17 Niklason LT Christian BT Niklason LE et al ldquoDigital Tomosynthesis in

Breast Imagingrdquo Radiology Volume 205 399-406 (1997)

18 Gur D ldquoTomosynthesis Potential Clinical Role in Breast Imagingrdquo American

Journal of Roentgenology Volume 189 614-615 (2007)

52

19 Park JM Franken Jr EA Garg M Fajardo LL and Niklason LT ldquoBreast

Tomosynthesis Present Considerations and Future Applicationsrdquo

RadioGraphics Volume 27 S231-S240 (2007)

20 Good WF Abrams GS Catullo VJ Chough DM Ganott MA Hakim

CM and Gur D ldquoDigital Breast Tomosynthesis A Pilot Observer Studyrdquo

American Journal of Roentgenology Volume 190 865-869 (2008)

21 Hu Y-H Zhao W Mertelmeier T and Ludwig J ldquoImage Artifact in Digital

Breast Tomosynthesis and Its Dependence on System and Reconstruction

Parametersrdquo IWDM 2008 LNCS 5116 628-634 (2008)

22 Chen Y Lo JY Ranger NT Samei E Dobbins III JT ldquoMethodology of

NEQ(f) analysis for optimization and comparison of digital breast tomosynthesis

acquisition techniques and reconstruction algorithmsrdquo Proceedings of SPIE

Volume 6510 65101I (2007)

23 Zhao B Zhou J Hu Y-H Mertelmeier T Ludwig J and Zhao W

ldquoExperimental validation of a three-dimensional linear system model for breast

tomosynthesisrdquo Medical Physics Volume 36 Number 1 240-251 (2009)

24 Madhav P Brzymialkiewicz CN Cutler SJ Bowsher JE and Tornai MP

ldquoCharacterizing the MTF in 3D for a Quantized SPECT Camera Having Arbitrary

Trajectoriesrdquo 2005 IEEE Nuclear Science Symposium Conference Record 1722-

1726 (2005)

25 Madhav P McKinley RL Samei E Bowsher JE and Tornai MP ldquoA Novel

Method to Characterize the MTF in 3D for Computed Mammotomographyrdquo

Proceedings of SPIE Volume 6142 61421Y (2006)

26 Hu Y-H Zhao B and Zhao W ldquoImage artifacts in digital breast

tomosynthesis Investigation of the effects of system geometry and

reconstruction parameters using a linear system approachrdquo Medical Physics

Volume 35 Number 12 5242-5252 (2008)

27 Seifert A and Flynn MJ ldquoResolving power of 3D x-ray microtomography

systemsrdquo Proceedings of SPIE Volume 4682 407-413 (2002)

28 Thornton MM and Flynn MJ Measurement of the spatial resolution of a

clinical volumetric computed tomography scanner using a sphere phantom

Proceedings of SPIE Volume 6142 61421Z (2006)

53

29 Baek J Pelc NJ ldquoUse of sphere phantoms to measure the 3D MTF of FDK

reconstructionsrdquo Proceedings of SPIE Volume 7961 79610D (2011)

30 Richard S and Samei E ldquoQuantitative imaging in breast tomosynthesis and CT

Comparison of detection and estimation task performancerdquo Medical Physics

Volume 37 Number 6 2627-2637 (2010)

31 Chen Y Lo JY and Dobbins III JT ldquoImpulse response analysis for several

digital tomosynthesis mammography reconstruction algorithmsrdquo Proceedings of

SPIE Volume 5745 541-549 (2005)

32 Zhao B and Zhao W ldquoThree-dimensional linear system analysis for breast

tomosynthesisrdquo Medical Physics Volume 35 Number 12 5219-5232 (2008)

33 Wu G Mainprize JG Boone JM and Yaffe MJ ldquoEvaluation of scatter

effects on image quality for breast tomosynthesisrdquo Medical Physics Volume 36

Number 10 4425-4432 (2009)

Page 23: Development and Evaluation of 2D and 3D Image Quality ...

10

Pixium 4600 Original System

Response

Pixium 4600 Linearized System

Response R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 3 Original (left) and linearized (right) system responses for Pixium 4600 The

linearized system responses were measured from actual images The offsets are small

with respect to the slope sufficient enough for zero-offset conditions

y = 13971x - 13236

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x - 00106Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 13576x + 28292

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

7000

0000 1000 2000 3000 4000 5000

AD

U

Exposure (mR)

y = 99997x - 00067Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0000 1000 2000 3000 4000 5000

AD

U

Exposure (mR)

y = 13644x + 16167Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x + 00044

Rsup2 = 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 13845x + 13541

Rsup2 = 1

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5

AD

U

Exposure (mR)

y = 1000x - 00177

Rsup2= 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

AD

U

Exposure (mR)

11

Table 3 Spectral Simulation Results

Beam Quality Filtration

Mean Energy

(kV)

Photon Fluence

(mRmm2)

RQA5A 21 mm Al 5243 259543

RQA5C 05 mm Cu + 10 mm Al 5214 259554

diff 055 0004

RQA9A 40 mm Al 7619 273281

RQA9C 104 mm Cu + 10 mm Al 7579 273964

diff 052 025

Figure 4 Spectral simulations for RQA5 (top) and RQA9 (bottom) conditions Note

the similarities of spectral shapes of the normalized spectra (right) Also note the

significant differences in fluence between filtrations in the simulated spectra (left)

00E+00

50E+04

10E+05

15E+05

20E+05

25E+05

30E+05

35E+05

40E+05

45E+05

0 20 40 60 80

ph

oto

ns

mA

s-1

cm

-2

keV

RQA5 Spectra Comparison

21 mm Al

05 mm Cu + 10 mm Al

00

02

04

06

08

10

12

0 20 40 60 80

keV

RQA5 Normalized Spectra Comparison

21 mm Al

05 mm Cu +

10 mm Al

00E+00

50E+05

10E+06

15E+06

20E+06

25E+06

30E+06

35E+06

40E+06

45E+06

50E+06

0 50 100 150

ph

oto

ns

mA

s-1

cm

-2

keV

RQA9 Spectra Comparison

40 mm Al

104 mm Cu +

10 mm Al

00

02

04

06

08

10

12

0 50 100 150

keV

RQA9 Normalized Spectra Comparison

40 mm Al104 mm Cu + 10 mm Al

12

I3iii Modulation Transfer Function

The limiting spatial resolutions of the systems were indicated by the cutoff

frequencies which were approximately 35 cyclesmm for all three detectors The spatial

resolutions also demonstrated a good degree of isotropy as confirmed by the close

alignment of MTF curves between vertical and horizontal directions differentiated in

Figure 5 by dashed and solid lines respectively The MTF curves for the Pixium 4600

and DRX-1C were nearly equal to each other whereas the DRX-1 MTF curve showed a

more rapid decrease at high frequencies as shown in Figure 6 This difference may be

due to the differences in the inherent optical properties of the scintillating materials

where finer image details are provided by structured CsI more than by granulated GOS

There were no significant differences in MTF curves across beam qualities and filtrations

as shown by the curve comparisons in Figure 6 although the alternative filtration

produced slightly higher MTF curves as seen in Figure 4 Table 4 lists the experimental

specific spatial frequencies for varying levels of MTF

I3iv Noise Power Spectrum

The noise characteristics are indicated by the NNPS curves shown in Figure 7

The noise was similar for both horizontal and vertical directions As exposure increased

the NNPS decreased consistent with the characteristics of Poisson noise describing the

relationship between signal and noise in the presence of increased photon fluence At

13

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 5 MTF results by detector (columns) and beam quality (rows)

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

horizontal

vertical

14

Figure 6 Plots of MTF for RQA5 (top) and RQA9 (bottom) showing the relationships

between detectors (blue red and green) and by filtration (solid and dashed)

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm-1)

MTF

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm-1)

MTF

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

15

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 7 NNPS results by detector (columns) and beam quality (rows)

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

05 mR - horizontal

05 mR - vertical

10 mR - horizontal

10 mR - vertical

20 mR - horizontal

20 mR - vertical

16

Figure 8 Plots of NNPS for RQA5 (top) and RQA9 (bottom) at 1 mR exposure

showing the relationships between detectors (blue red and green) and by filtration

(solid and dashed)

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm-1)

NNPS (1 mR)

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm-1)

NNPS (1 mR)

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

17

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 9 DQE results by detector (columns) and beam quality (rows)

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

05 mR - horizontal

05 mR - vertical

10 mR - horizontal

10 mR - vertical

20 mR - horizontal

20 mR - vertical

18

Figure 10 Plots of DQE for RQA5 (top) and RQA9 (bottom) at 1 mR exposure showing

the relationships between detectors (blue red and green) and by filtration (solid and

dashed)

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm-1)

DQE (1 mR)

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm-1)

DQE

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

19

higher frequencies the NNPS curves of the Pixium 4600 and DRX-1 diverge slightly for

the different directions illustrating increased noise in the readout direction (vertical)

Differences in the noise characteristics were more apparent among detectors as

shown for 1 mR in Figure 8 The NNPS curve for the DRX-1 was higher in magnitude

across the entire frequency range than either the Pixium 4600 or DRX-1C which both

seemed to demonstrate reasonably similar NNPS curves The higher magnitude noise of

the DRX-1 indicates higher relative noise content overall Closer inspection of the NNPS

curves of the Pixium 4600 and DRX-1C detectors in Figure 7 revealed differences in the

spacing between the three exposure levels The gaps between the Pixium 4600 NNPS

curves do not correspond to the factor of two differences between each exposure level

especially at low- to mid- spatial frequencies suggesting a higher level of fixed pattern

noise additional noise with increasing exposure levels due to ineffective gain map

corrections Between filtration schemes the differences in NNPS curves for a given beam

quality were not substantial as shown in Figure 7

I3v Detective Quantum Efficiency

The DQE results are shown in Figure 9 DQE curves across exposure levels were

almost collinear except for Pixium 4600 and in general could be inferred from the

NNPS results Additionally the DQE curves demonstrated a relatively linear response

with spatial frequencies as expected for flat-panel detectors [9] Differences in DQE

among detectors were consistent for the most part with the type of scintillating material

20

As depicted for 1 mR exposure in Figure 10 differences between Pixium 4600 and DRX-

1C DQE curves correspond to the differences in their NNPS curves DRX-1 DQE curves

were consistently lower than either the Pixium 4600 or DRX-1C curves The DQE curves

for the alternative filtration were consistently higher than those for the IEC filtration

and the most noticeable differences were near the zero-frequency axis These effects can

be both attributed to ineffective gain map correction DQE values for 1 mR exposure are

listed in Table 5

I4 Discussion

I4i Comparisons of Detectors

The limiting spatial resolutions of all three detectors were almost exactly the

same considering that their pixel areas were similar in size The decrease in high-

frequency MTF of the DRX-1 compared to the other detectors is probably a result of

increased optical blurring due to the differences in the powdered structure of GOS

versus the needle-like structure of CsI [2] The fact that the DRX-1C and Pixium 4600

have comparable MTFs suggests similar scintillator thicknesses assuming that the

materials were processed alike

The noise of the three detectors demonstrated similar trends with each other The

higher NNPS curves of the DRX-1 detector are probably due also to the scintillating

material and its operation in converting photons into signal The conversion process is

less efficient because of the less favorable stopping power of the GOS compared to CsI

21

especially with higher energy beams The noise of the Pixium 4600 and DRX-1C were

similar except for the spacing between exposures The DRX-1C NNPS curve spacing is

consistent with a factor of two difference in exposure levels but the Pixium 4600 has a

smaller spacing The 05 mR NNPS curve of the Pixium 4600 is closer to that of the 05

mR NNPS curve of the DRX-1C This demonstrates that at higher exposures the Pixium

4600 produces a larger amount of additional noise beyond that explained by simple

stochastic effects It suggests bad performance in the gain map corrections

The DQE results indicate SNR properties of each detector The Pixium 4600 and

DRX-1C are comparable for the most part with the DRX-1C performing slightly better

The DRX-1 as predicted from MTF and NNPS results has a DQE much lower than

either of the previous two This is a reflection of the detection properties as provided by

its scintillator material The DQE of the DRX-1 however is comparable to CR image

receptors [2] The mid-frequency dips in the DQE for Pixium 4600 may be due to the

optical properties of the CsI phosphor layer which can affect the MTF in this manner

Because the DQE is calculated by squaring the MTF this effect at the mid-range

frequencies becomes more apparent The dips may also be further evidence of bad gain

map corrections

I4ii Comparisons of Filtrations

The alternative filtration closely matches for the most part the IEC-based

filtration for MTF NNPS and DQEs at RQA5 but not at RQA9 The filters do not have

22

Table 4 Experimental MTF frequency locations for 1 mR exposure

Detector Filtration

50 MTF

(mm-1)

40 MTF

(mm-1)

30 MTF

(mm-1)

20 MTF

(mm-1)

10 MTF

(mm-1)

Pixium

4600

RQA5A 115 145 185 245 330

RQA5C 125 155 195 250 345

RQA9A 110 175 175 235 330

RQA9C 125 155 195 255 345

DRX-1C

RQA5A 120 150 185 245 350

RQA5C 125 155 195 255 355

RQA9A 120 150 190 250 355

RQA9C 130 160 210 265 360

DRX-1

RQA5A 110 135 160 205 280

RQA5C 110 135 170 210 285

RQA9A 105 125 155 195 270

RQA9C 110 135 165 210 285

Table 5 Estimated DQE values for 1 mR exposure by frequency bins

Detector Filtration DQE(00 mm-1) DQE(10 mm-1) DQE(20 mm-1) DQE(30 mm-1)

Pixium

4600

RQA5A 62 42 32 21

RQA5C 63 45 36 25

RQA9A 41 27 30 13

RQA9C 43 33 27 19

DRX-1C

RQA5A 72 52 35 21

RQA5C 76 55 41 24

RQA9A 49 33 23 15

RQA9C 51 40 31 20

DRX-1

RQA5A 38 24 12 4

RQA5C 38 25 14 5

RQA9A 28 18 9 4

RQA9C 28 19 12 5

DQE values at the zero-frequency axis were estimated by the intercept of a linear fit of low-frequency data

but excluding most proximal to the axis due to large fluctuations Other estimated values are grouped into

frequency bins due to the noisiness of the data

23

considerable differences in the spatial resolutions of the detectors as expected The noise

responses for each filtration were also similar except at the lower frequencies of the

NNPS especially near the zero-frequency axis There observing the NNPS responses at

RQA5 for Pixium 4600 and DRX-1C in Figure 8 the NNPS for the IEC-based filtration

(solid lines) tend to drop faster than the NNPS for the alternative filtration This

subsequently appears as a drop in DQE near the zero-frequency axis shown for those

detectors in Figure 10 Overall as indicated in Table 5 the DQEs of the two filtrations

while similar in trend indicate that the alternative filtration increases the DQE by a

small amount of 3-5 Part of this may be explained by the slightly higher beam

energy which may be more optimal for the energy response of the detectors or may

weigh the pixel responses slightly considering that they are energy-integrating types

The most probable explanation is the gain map correction for the alternative filtration

where fixed pattern noise is more sufficiently reduced

A previous study [6] had discussed the choice of filter material in the analysis of

DQE when achieving the beam conditions defined by IEC It found that visible

nonuniformities were present with the higher purity aluminum filter (type-11999 alloy)

The low frequency mottle in the flat-field images for NPS measurements were also

attributed to structured noise from the grain size in the IEC-based filter with an

attenuating thickness that would reveal nonuniformities The mottle in the current study

was only observable under very narrow windowing as shown in Figure 11 Such low

24

frequency artifacts which are not readily noticeable may also be caused by shading

artifacts inverse square law or even the heel effect A possible method to correct for this

is a subtraction method by taking the average of the flat-field images for an exposure

level and then subtracting that from each of them This would remove nonuniformities

that were not corrected using a suboptimal gain map calibration

Figure 11 DRX1-C NNPS images at 1 mR for RQA5 with IEC filtration (left) and

alternative filtration (right) Images are equally windowed at 45 and leveled at 980

One convenient aspect of the copper and aluminum filtration is that it requires

much less tube current to achieve the same amount of exposure at the detector than the

much thicker aluminum filtration As shown in the non-normalized spectra in Figure 2

the exiting photon fluence exiting the copper and aluminum filtration is substantially

higher than that of the IEC-specified filtration This is due to the smaller total filtration

25

attenuation For extensive DQE analysis multiple sets of exposures may be acquired

before tube overheating becomes a concern

One limitation to the comparison of the two filtrations is that calibration

procedures specified copper and aluminum filtration at 80 kVp (for all detectors 05 mm

Cu and 10 mm Al) This may have influenced the results in favor of the alternative

filtration A further investigation involving the calibration procedures and performing

DQE measurements is encouraged Another factor may be influenced by the fact that the

tests were performed at 70 kVp and 120 kVp different from the recommended

calibration tube potential Clearly there would be differences in the linear attenuation

coefficients of the filters and different energy responses of the detectors themselves This

must be considered when interpreting DQE results The current results support a

previous study decades ago that described filtration of different material types in terms

of an aluminum equivalent [16] The results show that the two filtration schemes are

essentially equivalent when considering beam qualities and spatial resolutions The

NNPS and DQE results can be seen as close enough where their small differences are

insignificant when performing quality assurance tests in a clinical setting Overall our

results indicate that the alternative filtration with copper and aluminum may be more

convenient to use than the current IEC standard filtration

26

I4iii Implications of Wireless DR

This study has shown that wireless image receptors can have the same DQE

performance if not better than conventional flat-panel detectors They operate on the

same basic physical principles the new features offered by the DRX-1C and DRX-1 are

wireless communication with the workstation and electronics packaging technology

The latter feature may pose limitations for these units in terms of possible degradation

in the detectors in routine clinical conditions A consideration for future work would be

to longitudinally track DQE performance of the wireless detectors over time while being

utilized in a clinical environment In the end one must consider risks versus benefits of

choosing portable DR technology over CR one of which includes the cost and fragility

of DR detectors

The DQE performance of one wireless system is just as good as or better than

conventional systems as seen by the DRX-1C performance compared to the Pixium

4600 Wireless systems can also reduce the need for CR readers especially in portable

applications in other regions of the world (eg military hospitals developing countries)

However while DQE performance indicates the physical performance of the detector

system it is still unknown how it relates to observer performance

I5 Conclusions

Two wireless image receptors DRX-1C and DRX-1 were evaluated and

compared with the conventional DR flat-panel Pixium 4600 in terms of DQE

27

performance along with MTF and NNPS performances The detectors have similar

resolution properties although the DRX-1 is inferior at higher spatial frequencies The

NNPS and DQE results both indicate that the DRX-1C is superior to the DRX-1 and

comparable if not better to the Pixium 4600

The results from the filtration comparison indicate no substantial differences

between the IEC-based filtration and the copper-based alternative filtration Only slight

differences were found in the low frequency components of the NNPS and the DQE due

to the inherent nonuniformities of the IEC specified filtration Given the similarity of the

results and low attenuation advantage of the copper and aluminum filter its use is

encouraged

28

II Directional MTF for Breast Tomosynthesis

II1 Introduction

Breast tomosynthesis is an emerging 3D imaging modality that has potential use

for screening and diagnosis of breast cancer Breast tomosynthesis along with other 3D

techniques is preferable to planar imaging methods (eg mammography) because they

reduce anatomical noise by removing overlying structures above and below the plane of

an image slice [17-20] Recent advances in detectors and computer technology have

made digital tomosynthesis feasible

An image quality metric of particular importance in breast tomosynthesis is

spatial resolution Resolution is important to know in order to assess small-detail

structures such as microcalcifications A descriptive metric for characterizing spatial

resolution in the Fourier (or frequency) domain is the modulation transfer function

(MTF) Affected by reconstruction filters [21] the limited angular projections involved in

breast tomosynthesis results in highly anisotropic (or nonuniform) resolution Many

studies have looked only at characterizing the in-plane spatial resolution (ie in an

individual slice) with an elevated angled edge phantom [2223] A few studies have

looked at characterizing a more comprehensive 3D spatial resolution by using a

phantom with angled wires or tubes [24-26] However such studies require precise

mechanical alignment of the phantoms Several studies have explored a method using a

29

sphere phantom for the directional 3D MTF evaluation for microtomography [27] and

multi-slice CT [2829] This method has not yet been extended to breast tomosynthesis

This chapter focuses on breast tomosynthesis because it is highly anisotropic in

spatial resolution and like its predecessor mammography requires high spatial

resolution Additionally breast tomosynthesis acquisitions and reconstructions produce

several types of artifacts The use of a cone-based method using a sphere phantom [28] is

explored to characterize the directional 3D spatial resolution of simulated images from

breast tomosynthesis A technique for removing out-of-plane artifacts of the ESFs for the

in-plane axes is investigated to yield a modified MTF in a method that separates artifact

information from resolution information

II2 Materials and Methods

II2i Image Simulation

Breast tomosynthesis images were simulated by using a virtual imaging system

depicted in Figure 12 A volumetric breast phantom was voxelized as a rectangular mass

of uniform breast equivalent tissue of 4 cm thickness embedded with fifteen evenly

spaced plastic sphere inserts of 12 mm diameter The spheres were placed in a grid

formation within the central plane of the phantom The x-ray fluence was modeled from

a 28 kVp beam incident upon an indirect flat-panel detector with 200 micro m pixel size

Twenty-three projections within an angular range of 44deg were simulated using cascaded

systems analysis to generate characteristic 2D noise and spatial blurring [29] Each

30

projection was simulated to have an exposure of 174 mR with a fluence of 79 times 105

photonsmm-2 A standard filtered backprojection technique based on the Feldkamp

reconstruction algorithm [29] was used to reconstruct the projections and produce a

volumetric dataset with an isotropic voxel size of 200 micro m

Figure 12 Depiction of the virtual image system

II2ii Uncorrected MTF

To enable comparison of multiple spheres the reconstructed volume was

initially homogenized by performing a background subtraction based on a portion of the

volume devoid of spheres The voxel values were rescaled between one and zero to

eliminate negative values

31

The volumetric data were segmented to extract individual regions of interest

(ROIs) each containing a single sphere The ROIs extended along the full range of the z-

axis A thresholded ROI was generated by determining the exterior and interior voxels

relative to the sphere in the ROI The threshold value was set at 45 of the maximum

voxel value prior to thresholding The exterior and interior voxel values were then set to

values of 0 and 1 respectively Using the thresholded volume the center of mass was

calculated to determine the centroid The voxel values from the original ROI were

subsequently tabulated with the associated distances azimuthal angles and polar

angles relative to the centroid

Conical regions were prescribed along the positive and negative directions along

the three major axes extending from the centroid of the sphere as depicted in Figure 13

The axes about which the extent of the cone angle was delineated were defined with

the azimuthal and polar angles

Voxels with centers within the angular range of the cone were considered for

generating the edge spread function (ESF) To improve regularity of the distance

sampling interval the ESF values were rebinned to discrete distances corresponding to a

fraction of the voxel size Only voxels with distances ranging from the voxel size (ie

200 micro m) to the maximum distance were considered The ESFs from multiple spheres

were averaged together for each of the three major axes to produce an averaged ESF

which was further smoothed utilizing a Gaussian filter

32

Figure 13 Example of 30-degree cone prescribed along z axis of the sphere

The resulting ESF was then differentiated using the central difference method to

produce the line spread function (LSF) A Hanning filter with the same length as the LSF

was applied to zero out the tails of the LSF The presampled MTF was subsequently

computed as the amplitude of the Fourier transform of the LSF The MTF was

normalized with respect to the maximum value occurring within the range of the cutoff

frequency Binning size and conical range for the ESF were considered for maximizing

accuracy and minimizing noise of the MTF verified by comparison against the

theoretical MTF as determined in the previous section

II2iii Theoretical Directional MTF

The theoretical 3D MTF was calculated using a priori knowledge of the transfer

function of the virtual imaging system described in the previous section A phantom

was created with a set of point objects in a uniform and noise-free background with the

objects spanning across the volume of the breast [29] Twenty-one realizations were

33

generated from the reconstructed images of the point objects to yield a set of 3D point

spread functions (PSFs) The 3D fast Fourier transform (FFT) was performed for each 3D

PSF and averaged to give an ldquoexpectationrdquo 3D MTF [29] The theoretical directional

MTFs in the three major spatial axes were determined by line profiles along each of the

corresponding spatial frequency axes in the 3D MTF An additional theoretical MTF for

each direction was determined by using the application of conical regions along the axes

in frequency-space to take into account the contributions of MTF information from other

planes

II2iv Modified MTF

The tomosynthesis reconstruction is known to have edge enhancements which

affect the overall MTF by shifting the peaks of the MTF toward the higher frequencies

[23] The presence of this artifact complicates the interpretation of the actual spatial

resolution of the images Several steps were performed to remove the artifact

contribution to the resolution information particularly for the in-plane x and y

directions with the assumption that resolution information was contained immediately

near the edge

For the x-direction averaged ESF only values that were detected to be inside the

edge of the sphere were considered Those values were previously determined via

thresholding for calculating the centroid The ESF information corresponding to these

values was inversed and flipped about the detected edge to produce a symmetric

34

modified ESF The modified MTF was subsequently calculated from this modified ESF

as described in the previous section

For the y-direction averaged ESF an upward trend was found in the initial part

of the ESF This section was detrended with a polynomial fit and subtracted to produce a

flatter curve in that region The resulting detrended ESF was used to calculate the y axis

modified MTF

Figure 14 Photograph of the imaging system with the acrylic sphere phantom

embedded in oil

II2v Preliminary Experimental Validation

A clinical breast tomosynthesis system (Mammomat Inspiration Siemens AG

Munich Germany) was used to perform a preliminary evaluation of the cone-based

MTF technique The phantom for the experiment consisted of a single acrylic ball of 075

in diameter (SmallParts Seattle WA) suspended by a 0029 in diameter plastic filament

35

(Omniflex Zebco Tulsa OK) in an acrylic frame filled up to 4 in with vegetable oil

(Target Brands Inc Minneapolis MN) The system and phantom are shown in Figure

14 Twenty-five projections with an angular range of 44deg were acquired and subsequently

reconstructed to produce a volume with a voxel size of 01times01times10 mm3 The voxels were

reformatted to have an isotropic size of 01 mm The uncorrected ESF LSF and MTF

were calculated as described in the previous section

II3 Results

II3i Reconstruction

The reconstructed volume is shown in Figure 15 Notice the edge enhancement

along the x-direction as indicated by the sharp shadowing artifacts on either side of the

spheres The background was effectively homogenized using the background

subtraction technique This also took account of the curved edges of the breast phantom

With the close spacing of the spheres in the phantom the shadows along the x direction

for the fifteen spheres overlap with each other As the nine centrally located spheres

experience this effect the same way they were used for determining the ESF

A 3D rendering of the ROI containing a sphere shown in Figure 16 indicates the

anisotropic resolution of the reconstruction Note that the sphere is not accurately

reconstructed and has an oblong shape especially along the z axis Cross sectional views

of the ROI also in Figure 16 clearly demonstrate the edge enhancement causing a

shadow artifact in the x direction caused by the incomplete angular sampling of

36

tomosynthesis The sampling also introduces the triangular reconstruction of the sphere

as seen in the x-z plane Note the gradual edge drop-off in the z direction much beyond

the sphere radius

Figure 15 View of the central slice of the breast phantom reconstruction before (top)

and after (bottom) background subtraction The z axis is through the page

37

Figure 16 3D rendering of the ROI volume (left) and cross-sectional views of the most

centrally located sphere with centroid indicated with red circle (right)

II3ii Theoretical MTF

The theoretical MTFs for x y and z directions as determined from the line

profiles of the 3D MTF are shown in Figure 17 The theoretical MTF in the x direction

has a maximum value that is toward higher frequencies Its 10 response occurs at

about 125 cyclesmm which is at 50 of the cutoff frequency The rapid increase from

the zero-frequency intercept to the peak corresponds to the ramp filter used in filtered

backprojection which decreases the weighting of low frequency contributions due to the

incomplete angular sampling of the frequency-space The MTF does not reach a value of

0 at the zero-frequency intercept as it is very difficult to assess the zero-frequency

intercept due to the finite size of the phantom The theoretical MTF in the y direction

peaks at the zero-frequency intercept and reaches 20 proximal to the cutoff frequency

38

The 10 MTF is well beyond the cutoff frequency The theoretical MTF in the z direction

has a rapid drop-off at very low spatial frequencies indicating the lack of resolution in

that dimension

Figure 17 Theoretical 3D MTF results along the three major planes (top) and along x

y and z directions (bottom) Also note that the angular spread seen in the fx-fz plane is

equal to the angular range of 44deg for the acquisition

II3iii Uncorrected MTF

The ESF LSF and MTF using the cone-based method are shown for the x y and

z directions in Figure 18 It was found that a bin size of one-tenth the voxel size (002

mm) and a cone angle of 30deg to establish the ESF were enough to minimize noise and

maximize accuracy in the uncorrected MTFs considering the reasonable comparison of

the shapes of the MTF curves with the theoretical results in Figure 17 The LSFs are

generally noisy because differentiation of the ESF increases the amplitude of the noise

39

The data shown reflect a convolution with a smoothing Gaussian filter which was later

further corrected for in the reported MTF Nevertheless the high frequency components

of the noise are well beyond the MTF cutoff frequency of 25 cyclesmm and do not

impact the MTF results greatly

For the ESF in the x direction the shadow effect evident at the edge of the sphere

is visible as a steep decline followed by an increase Due to the finite distance range

provided by the ROI the ESF beyond the edge did not asymptotically reach the

background value The corresponding LSF demonstrates a low frequency modulation

that is indicated by the shift of 03 cyclesmm in the x direction for the peak of the MTF

The MTF exhibits a zero-frequency intercept that is non-zero unlike the theoretical MTF

and a 10 value at approximately 1 cyclesmm These features may be a direct

consequence of MTF information ldquocontaminationrdquo from y and z directions Furthermore

the ESF in the y direction demonstrates a reasonably shaped curve except for the slight

upward trend within the radius of the sphere which can be attributed to the shadow

artifact overlapping with the sphere volume The associated MTF has a peak shifted by

approximately 01 cyclesmm away from the axis and a 10 MTF occurring at

approximately 15 cyclesmm Both features which are not present in the theoretical

results may also be attributed to contaminant MTF information from x and z directions

The ESF in the z direction has a drop-off that occurs at a small fraction of the cutoff

frequency similar to that demonstrated by the theoretical MTF

40

Uncorrected ESF LSF and MTF

Figure 18 Uncorrected ESF (top) LSF (middle) and MTF (bottom) for x y and z

directions

41

Figure 19 Comparisons of the directional MTFs as calculated by the sphere method

(dashed line) by theoretical line profiles (light-weight line) by theoretical cone

regions (heavy-weight line)

II3iv Comparison of Theoretical and Simulated MTFs

The theoretical MTF results obtained from line profiles through the 3D MTF and

the simulated MTFs using the cone-based technique did not match very well except for

the general shape of the curves It was assumed in the previous section that the cone-

based technique contains information from other planes Figure 19 compares MTFs in

each direction for the two methods described in the methods and an additional method

based on conical regions of the 3D MTF The latter computes the MTF by averaging

contributions of the 3D MTF using the same cone prescription method used to define the

ESFs Comparison of the curves indicate some interesting correlations aside from the

fact that using conical regions with the 3D MTF results produce more noisy MTF results

partly due to the low sampling provided by the theoretical calculations The same

conclusions regarding the z direction MTF can be confirmed regardless of either

theoretical MTF procedures The experimental x direction MTF seems to agree best with

42

the line profile method whereas the y direction MTF agrees better with the cone region

method The fact that the experimental x direction MTF has a drop-off frequency that is

lower than those of either of the theoretical MTFs in Figure 19 suggests that this might

be due to integration of the z-direction in the in-plane slices considering how slices are

essentially averages of z direction information contained within it [33]

II3v Modified MTF for x and y

Modified ESF LSF and MTF curves for x and y directions are shown in Figure

20 The modified ESF and the resulting LSF in the x direction appear symmetric as

expected from the inverse and flip operation of the interior ESF about the detected edge

The modified MTF appears with less variation than the uncorrected MTF and the MTF

peak occurs at the zero-frequency axis The correction yields a 10 MTF at about 15

cyclesmm an improvement from the uncorrected MTF but still distant from the cutoff

frequency The modified ESF in the y direction demonstrates the detrended curve within

the sphere radius after a quadratic polynomial fit The resulting modified MTF still

appears similar to the uncorrected MTF except that the peak now coincides with the

zero-frequency axis For both x and y directions the low response of the modified MTFs

at the higher frequencies suggests that the contamination from other directions is

substantial due to the angular range of the cone

43

Modified ESF LSF and MTF

Figure 20 Modified ESF (top) LSF (middle) and MTF (bottom) for x and y directions

44

II3v Preliminary Experimental Validation

Cross-sections of the reconstructed sphere volume are shown in Figure 21

Relative to the simulation reconstructions the reconstructions of the experimental

phantom images produce lower contrast and higher noise The preliminary results

shown in Figure 22 indicate that our technique can be applied to actual experimental

breast tomosynthesis reconstructions However due to the noise exhibited by the MTF

curves for the x and y directions we did not determine the modified MTFs to separate

resolution and artifact information

Figure 21 Cross sectional views of the experimental sphere image with centroid

indicated with red circle

45

Uncorrected ESF LSF and MTF for Real Image

Figure 22 ESF (top) LSF (middle) and MTF (bottom) of real image for x y

and z directions

46

II4 Discussion

II4i Evaluation of Cone-based Method

The cone-based MTF technique was introduced by Thornton and Flynn [28] for

evaluation of volumetric CT images To utilize this technique as a characterization of a

3D system spatial resolution one must first consider the validity of the assumption of

shift invariance such that the same MTF result may be obtained regardless of the

location of the sphere The study by Zhao et al [23] found that there was no shift

variance for the MTF measurements along the vertical axis but this was only considering

the in-plane resolution along one axis On the other hand this study evaluated the MTF

with images simulated with cascaded systems analysis which includes conditions of

linearity and shift invariance Additionally the MTF was calculated by averaging the

ESF from several spheres in the same volume only after performing a background

subtraction This step was essential to account for the sensitivity of centroid calculations

as well as ensuring symmetric ESFs for opposing axes of the sphere ROIs

The measurement of MTF with the cone-based technique inherently

supersamples the edge of the sphere to increase signal-to-noise-ratio (SNR) of edge

information by averaging the contributions of each voxel to the ESF [713] This method

also takes into account the discrete sampling of the voxels by accounting for various

shifts of the edge in the voxel (also known as the partial volume effect) However using

the curved surface of the sphere phantom to approximate an edge along a given

47

direction naturally leads to contamination of information from other directions aside

from the one of interest Preferably a directional ESF should be created by using a single

radial line but this would limit the available voxels to obtain edge information An ideal

situation theoretically would be to use a larger-sized sphere such that the surface is

nearly flat and perpendicular to the axes of interest This would also permit a reduction

in the angular range of the cone and thus the introduction of out-of-plane information in

the resulting MTF However sphere size is a limitation in breast tomosynthesis and the

use of a large phantom might void the assumption of shift invariance of the spatial

resolution

The choice of a sphere phantom nevertheless may be based on the clinical need

to quickly acquire a single image for MTF evaluation especially for multiple directions

without presenting extra logistical challenges The use of a wire or edge phantom

requires more precise mechanical alignment to achieve the correct set up The edge

phantom [23] would require at least two images to sample all three dimensions In the

case of the three wire phantom [2425] all three dimensions of the frame must be aligned

simultaneously with respect to the axis of rotation A similar situation would be

encountered when considering a cubic phantom with the planes normal to the axis of

interest In contrast to these phantoms the sphere eliminates the need for precise

alignment especially with respect to three spatial dimensions simultaneously A sphere

48

has ideal symmetry in all directions and can be used to evaluate MTF in any arbitrary

direction

This study unlike others [242532] did not explore the effects of physical

parameters such as scatter or contrast on the final MTF result but it demonstrated the

feasibility of using the cone-based method with an actual breast tomosynthesis image of

a sphere phantom as shown in Error Reference source not found and Error Reference

source not found These effects should be addressed in future works A further look

into deriving the principles of comparing the theoretical MTF with the experimental

MTF using the cone-based method is further warranted

II4ii Separation of Artifact and Resolution Information

The focus of this study was to develop a technique for measuring spatial

resolution of tomosynthesis images The intrinsic artifacts from tomosynthesis

reconstructions however lead to uncharacteristic MTFs and possible misinterpretation

of the effective resolution information When considering previous techniques for

calculating the presampled MTF [713152328] the analysis was performed using an

edge or a line to produce the corresponding ESF The resolution information is

essentially contained only along the edge indicated by the need to calculate the LSF In a

way the method of extracting artifact information is to focus the analysis only on the

edge part of the ESF to calculate the modified MTF This will lead to a better

understanding of the limiting size of objects that may be seen in the reconstructed 3D

49

image The presampled MTF without correction should still be analyzed to understand

the entire system response Note that the ESFs attempt to reflect information only at the

detected edge of the sphere

II5 Conclusions

The directional MTF of a simulated breast tomosynthesis reconstruction was

determined by using the cone-based MTF technique demonstrating the feasibility of a

single phantom for MTF evaluation This study further presented methods of analyzing

only the edge information in the ESF to create a modified MTF along in-slice (x and y)

axes It can provide insight into the actual spatial resolution information contained in the

image while separating the resolution information from the information introduced by

artifacts caused by the reconstruction and insufficient volumetric sampling The idea of

separating the resolution and artifacts from the measured ESF are expected to facilitate

the interpretation of MTF measurements in breast tomosynthesis Similar methods may

be applied to characterize the resolution of other 3D imaging modalities

50

References

1 Garmer M Hannigs SP Jaumlger HJ et al ldquoDigital Radiography Versus

Conventional Radiology in Chest Imaging Diagnostic Performance of a Large-

Area Silicon Flat-Panel Detector in a Clinical CT-Controlled Studyrdquo American

Journal of Roentgenology Volume 74 75-80 (2000)

2 Cowen AR Kengyelics SM and Davies AG ldquoSolid-state flat-panel digital

radiography detectors and their physical imaging characteristics rdquoClinical

Radiology Volume 63 487-498 (2008)

3 Chotas HG Dobbins III JT and Ravin CE ldquoPrinciples of Digital

Radiography with Large-Area Electronically Readable Detectors A Review of

the Basicsrdquo Radiology Volume 210 Number 3 595-599 (1999)

4 Flynn MJ and Samei E Experimental comparison of noise and resolution for

2k and 4k storage phosphor radiography systems Medical Physics Volume 26

Number 8 1612-1623 (1999)

5 Rong XJ Shaw CC Liu X Lemacks MR and Thompson SK

ldquoComparison of an amorphous siliconcesium iodide flat-panel digital chest

radiography system with screenfilm and computed radiography systems ndash A

contrast-detail phantom studyrdquo Medical Physics Volume 28 Number 11 2328-

2335 (2001)

6 Ranger NT Samei E Dobbins III JT and Ravin CE Measurement of the

detective quantum efficiency in digital detectors consistent with the IEC 62220-1

standard Practical considerations regarding the choice of filter material

Medical Physics Volume 30 Number 7 2305-2311 (2005)

7 Samei E Buhr E Granfors P Vandenbroucke D and Wang X Comparison

of edge analysis techniques for the determination of the MTF of digital

radiographic systems Physics in Medicine and Biology Volume 50 3613-3625

(2005)

8 Samei E and Flynn MJ An experimental comparison of detector performance

for computed radiography systems Medical Physics Volume 29 Number 4 447-

459 (2002)

51

9 Samei E and Flynn MJ An experimental comparison of detector performance

for direct and indirect digital radiography systems Medical Physics Volume 30

Number 4 608-622 (2003)

10 Samei E Ranger NT MacKenzie A Honey ID Dobbins III JT and Ravin

CE Effective DQE (eDQE) and speed of digital radiographic systems An

experimental methodology Medical Physics Volume 36 Number 8 3806-3817

(2009)

11 Samei E Ranger NT MacKenzie A Honey ID Dobbins III JT and Ravin

CE Detector or System Extending the Concept of Detective Quantum

Efficiency to Characterize the Performance of Digital Radiographic Imaging

Systems Radiology Volume 249 Number 3 926-937 (2008)

12 ldquoIEC 62220-1 Medical Electrical Equipment ndash Characteristics of Digital X-Ray

Imaging Devices ndash Part 1 Determination of the Detective Quantum Efficiencyrdquo

International Electrotechnical Commission Geneva Switzerland (2003)

13 Samei E Ranger NT Dobbins III JT and Chen Y Intercomparison of

methods for image quality characterization I Modulation transfer function

Medical Physics Volume 33 Number 5 1454-1465 (2006)

14 Dobbins III JT Samei E Ranger NT and Chen Y Intercomparison of

methods for image quality characterization II Noise power spectrum Medical

Physics Volume 33 Number 5 1466-1475 (2006)

15 Samei E Flynn MJ and Reimann DA A method for measuring the

presampled MTF of digital radiographic systems using an edge test device

Medical Physics Volume 25 Number 1 102-113 (1998)

16 Nagel HD ldquoAluminum equivalence of materials used in diagnostic radiology

and its dependence on beam qualityrdquo Physics in Medicine and Biology Volume

31 Number 12 1381-1399 (1986)

17 Niklason LT Christian BT Niklason LE et al ldquoDigital Tomosynthesis in

Breast Imagingrdquo Radiology Volume 205 399-406 (1997)

18 Gur D ldquoTomosynthesis Potential Clinical Role in Breast Imagingrdquo American

Journal of Roentgenology Volume 189 614-615 (2007)

52

19 Park JM Franken Jr EA Garg M Fajardo LL and Niklason LT ldquoBreast

Tomosynthesis Present Considerations and Future Applicationsrdquo

RadioGraphics Volume 27 S231-S240 (2007)

20 Good WF Abrams GS Catullo VJ Chough DM Ganott MA Hakim

CM and Gur D ldquoDigital Breast Tomosynthesis A Pilot Observer Studyrdquo

American Journal of Roentgenology Volume 190 865-869 (2008)

21 Hu Y-H Zhao W Mertelmeier T and Ludwig J ldquoImage Artifact in Digital

Breast Tomosynthesis and Its Dependence on System and Reconstruction

Parametersrdquo IWDM 2008 LNCS 5116 628-634 (2008)

22 Chen Y Lo JY Ranger NT Samei E Dobbins III JT ldquoMethodology of

NEQ(f) analysis for optimization and comparison of digital breast tomosynthesis

acquisition techniques and reconstruction algorithmsrdquo Proceedings of SPIE

Volume 6510 65101I (2007)

23 Zhao B Zhou J Hu Y-H Mertelmeier T Ludwig J and Zhao W

ldquoExperimental validation of a three-dimensional linear system model for breast

tomosynthesisrdquo Medical Physics Volume 36 Number 1 240-251 (2009)

24 Madhav P Brzymialkiewicz CN Cutler SJ Bowsher JE and Tornai MP

ldquoCharacterizing the MTF in 3D for a Quantized SPECT Camera Having Arbitrary

Trajectoriesrdquo 2005 IEEE Nuclear Science Symposium Conference Record 1722-

1726 (2005)

25 Madhav P McKinley RL Samei E Bowsher JE and Tornai MP ldquoA Novel

Method to Characterize the MTF in 3D for Computed Mammotomographyrdquo

Proceedings of SPIE Volume 6142 61421Y (2006)

26 Hu Y-H Zhao B and Zhao W ldquoImage artifacts in digital breast

tomosynthesis Investigation of the effects of system geometry and

reconstruction parameters using a linear system approachrdquo Medical Physics

Volume 35 Number 12 5242-5252 (2008)

27 Seifert A and Flynn MJ ldquoResolving power of 3D x-ray microtomography

systemsrdquo Proceedings of SPIE Volume 4682 407-413 (2002)

28 Thornton MM and Flynn MJ Measurement of the spatial resolution of a

clinical volumetric computed tomography scanner using a sphere phantom

Proceedings of SPIE Volume 6142 61421Z (2006)

53

29 Baek J Pelc NJ ldquoUse of sphere phantoms to measure the 3D MTF of FDK

reconstructionsrdquo Proceedings of SPIE Volume 7961 79610D (2011)

30 Richard S and Samei E ldquoQuantitative imaging in breast tomosynthesis and CT

Comparison of detection and estimation task performancerdquo Medical Physics

Volume 37 Number 6 2627-2637 (2010)

31 Chen Y Lo JY and Dobbins III JT ldquoImpulse response analysis for several

digital tomosynthesis mammography reconstruction algorithmsrdquo Proceedings of

SPIE Volume 5745 541-549 (2005)

32 Zhao B and Zhao W ldquoThree-dimensional linear system analysis for breast

tomosynthesisrdquo Medical Physics Volume 35 Number 12 5219-5232 (2008)

33 Wu G Mainprize JG Boone JM and Yaffe MJ ldquoEvaluation of scatter

effects on image quality for breast tomosynthesisrdquo Medical Physics Volume 36

Number 10 4425-4432 (2009)

Page 24: Development and Evaluation of 2D and 3D Image Quality ...

11

Table 3 Spectral Simulation Results

Beam Quality Filtration

Mean Energy

(kV)

Photon Fluence

(mRmm2)

RQA5A 21 mm Al 5243 259543

RQA5C 05 mm Cu + 10 mm Al 5214 259554

diff 055 0004

RQA9A 40 mm Al 7619 273281

RQA9C 104 mm Cu + 10 mm Al 7579 273964

diff 052 025

Figure 4 Spectral simulations for RQA5 (top) and RQA9 (bottom) conditions Note

the similarities of spectral shapes of the normalized spectra (right) Also note the

significant differences in fluence between filtrations in the simulated spectra (left)

00E+00

50E+04

10E+05

15E+05

20E+05

25E+05

30E+05

35E+05

40E+05

45E+05

0 20 40 60 80

ph

oto

ns

mA

s-1

cm

-2

keV

RQA5 Spectra Comparison

21 mm Al

05 mm Cu + 10 mm Al

00

02

04

06

08

10

12

0 20 40 60 80

keV

RQA5 Normalized Spectra Comparison

21 mm Al

05 mm Cu +

10 mm Al

00E+00

50E+05

10E+06

15E+06

20E+06

25E+06

30E+06

35E+06

40E+06

45E+06

50E+06

0 50 100 150

ph

oto

ns

mA

s-1

cm

-2

keV

RQA9 Spectra Comparison

40 mm Al

104 mm Cu +

10 mm Al

00

02

04

06

08

10

12

0 50 100 150

keV

RQA9 Normalized Spectra Comparison

40 mm Al104 mm Cu + 10 mm Al

12

I3iii Modulation Transfer Function

The limiting spatial resolutions of the systems were indicated by the cutoff

frequencies which were approximately 35 cyclesmm for all three detectors The spatial

resolutions also demonstrated a good degree of isotropy as confirmed by the close

alignment of MTF curves between vertical and horizontal directions differentiated in

Figure 5 by dashed and solid lines respectively The MTF curves for the Pixium 4600

and DRX-1C were nearly equal to each other whereas the DRX-1 MTF curve showed a

more rapid decrease at high frequencies as shown in Figure 6 This difference may be

due to the differences in the inherent optical properties of the scintillating materials

where finer image details are provided by structured CsI more than by granulated GOS

There were no significant differences in MTF curves across beam qualities and filtrations

as shown by the curve comparisons in Figure 6 although the alternative filtration

produced slightly higher MTF curves as seen in Figure 4 Table 4 lists the experimental

specific spatial frequencies for varying levels of MTF

I3iv Noise Power Spectrum

The noise characteristics are indicated by the NNPS curves shown in Figure 7

The noise was similar for both horizontal and vertical directions As exposure increased

the NNPS decreased consistent with the characteristics of Poisson noise describing the

relationship between signal and noise in the presence of increased photon fluence At

13

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 5 MTF results by detector (columns) and beam quality (rows)

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

horizontal

vertical

14

Figure 6 Plots of MTF for RQA5 (top) and RQA9 (bottom) showing the relationships

between detectors (blue red and green) and by filtration (solid and dashed)

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm-1)

MTF

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm-1)

MTF

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

15

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 7 NNPS results by detector (columns) and beam quality (rows)

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

05 mR - horizontal

05 mR - vertical

10 mR - horizontal

10 mR - vertical

20 mR - horizontal

20 mR - vertical

16

Figure 8 Plots of NNPS for RQA5 (top) and RQA9 (bottom) at 1 mR exposure

showing the relationships between detectors (blue red and green) and by filtration

(solid and dashed)

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm-1)

NNPS (1 mR)

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm-1)

NNPS (1 mR)

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

17

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 9 DQE results by detector (columns) and beam quality (rows)

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

05 mR - horizontal

05 mR - vertical

10 mR - horizontal

10 mR - vertical

20 mR - horizontal

20 mR - vertical

18

Figure 10 Plots of DQE for RQA5 (top) and RQA9 (bottom) at 1 mR exposure showing

the relationships between detectors (blue red and green) and by filtration (solid and

dashed)

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm-1)

DQE (1 mR)

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm-1)

DQE

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

19

higher frequencies the NNPS curves of the Pixium 4600 and DRX-1 diverge slightly for

the different directions illustrating increased noise in the readout direction (vertical)

Differences in the noise characteristics were more apparent among detectors as

shown for 1 mR in Figure 8 The NNPS curve for the DRX-1 was higher in magnitude

across the entire frequency range than either the Pixium 4600 or DRX-1C which both

seemed to demonstrate reasonably similar NNPS curves The higher magnitude noise of

the DRX-1 indicates higher relative noise content overall Closer inspection of the NNPS

curves of the Pixium 4600 and DRX-1C detectors in Figure 7 revealed differences in the

spacing between the three exposure levels The gaps between the Pixium 4600 NNPS

curves do not correspond to the factor of two differences between each exposure level

especially at low- to mid- spatial frequencies suggesting a higher level of fixed pattern

noise additional noise with increasing exposure levels due to ineffective gain map

corrections Between filtration schemes the differences in NNPS curves for a given beam

quality were not substantial as shown in Figure 7

I3v Detective Quantum Efficiency

The DQE results are shown in Figure 9 DQE curves across exposure levels were

almost collinear except for Pixium 4600 and in general could be inferred from the

NNPS results Additionally the DQE curves demonstrated a relatively linear response

with spatial frequencies as expected for flat-panel detectors [9] Differences in DQE

among detectors were consistent for the most part with the type of scintillating material

20

As depicted for 1 mR exposure in Figure 10 differences between Pixium 4600 and DRX-

1C DQE curves correspond to the differences in their NNPS curves DRX-1 DQE curves

were consistently lower than either the Pixium 4600 or DRX-1C curves The DQE curves

for the alternative filtration were consistently higher than those for the IEC filtration

and the most noticeable differences were near the zero-frequency axis These effects can

be both attributed to ineffective gain map correction DQE values for 1 mR exposure are

listed in Table 5

I4 Discussion

I4i Comparisons of Detectors

The limiting spatial resolutions of all three detectors were almost exactly the

same considering that their pixel areas were similar in size The decrease in high-

frequency MTF of the DRX-1 compared to the other detectors is probably a result of

increased optical blurring due to the differences in the powdered structure of GOS

versus the needle-like structure of CsI [2] The fact that the DRX-1C and Pixium 4600

have comparable MTFs suggests similar scintillator thicknesses assuming that the

materials were processed alike

The noise of the three detectors demonstrated similar trends with each other The

higher NNPS curves of the DRX-1 detector are probably due also to the scintillating

material and its operation in converting photons into signal The conversion process is

less efficient because of the less favorable stopping power of the GOS compared to CsI

21

especially with higher energy beams The noise of the Pixium 4600 and DRX-1C were

similar except for the spacing between exposures The DRX-1C NNPS curve spacing is

consistent with a factor of two difference in exposure levels but the Pixium 4600 has a

smaller spacing The 05 mR NNPS curve of the Pixium 4600 is closer to that of the 05

mR NNPS curve of the DRX-1C This demonstrates that at higher exposures the Pixium

4600 produces a larger amount of additional noise beyond that explained by simple

stochastic effects It suggests bad performance in the gain map corrections

The DQE results indicate SNR properties of each detector The Pixium 4600 and

DRX-1C are comparable for the most part with the DRX-1C performing slightly better

The DRX-1 as predicted from MTF and NNPS results has a DQE much lower than

either of the previous two This is a reflection of the detection properties as provided by

its scintillator material The DQE of the DRX-1 however is comparable to CR image

receptors [2] The mid-frequency dips in the DQE for Pixium 4600 may be due to the

optical properties of the CsI phosphor layer which can affect the MTF in this manner

Because the DQE is calculated by squaring the MTF this effect at the mid-range

frequencies becomes more apparent The dips may also be further evidence of bad gain

map corrections

I4ii Comparisons of Filtrations

The alternative filtration closely matches for the most part the IEC-based

filtration for MTF NNPS and DQEs at RQA5 but not at RQA9 The filters do not have

22

Table 4 Experimental MTF frequency locations for 1 mR exposure

Detector Filtration

50 MTF

(mm-1)

40 MTF

(mm-1)

30 MTF

(mm-1)

20 MTF

(mm-1)

10 MTF

(mm-1)

Pixium

4600

RQA5A 115 145 185 245 330

RQA5C 125 155 195 250 345

RQA9A 110 175 175 235 330

RQA9C 125 155 195 255 345

DRX-1C

RQA5A 120 150 185 245 350

RQA5C 125 155 195 255 355

RQA9A 120 150 190 250 355

RQA9C 130 160 210 265 360

DRX-1

RQA5A 110 135 160 205 280

RQA5C 110 135 170 210 285

RQA9A 105 125 155 195 270

RQA9C 110 135 165 210 285

Table 5 Estimated DQE values for 1 mR exposure by frequency bins

Detector Filtration DQE(00 mm-1) DQE(10 mm-1) DQE(20 mm-1) DQE(30 mm-1)

Pixium

4600

RQA5A 62 42 32 21

RQA5C 63 45 36 25

RQA9A 41 27 30 13

RQA9C 43 33 27 19

DRX-1C

RQA5A 72 52 35 21

RQA5C 76 55 41 24

RQA9A 49 33 23 15

RQA9C 51 40 31 20

DRX-1

RQA5A 38 24 12 4

RQA5C 38 25 14 5

RQA9A 28 18 9 4

RQA9C 28 19 12 5

DQE values at the zero-frequency axis were estimated by the intercept of a linear fit of low-frequency data

but excluding most proximal to the axis due to large fluctuations Other estimated values are grouped into

frequency bins due to the noisiness of the data

23

considerable differences in the spatial resolutions of the detectors as expected The noise

responses for each filtration were also similar except at the lower frequencies of the

NNPS especially near the zero-frequency axis There observing the NNPS responses at

RQA5 for Pixium 4600 and DRX-1C in Figure 8 the NNPS for the IEC-based filtration

(solid lines) tend to drop faster than the NNPS for the alternative filtration This

subsequently appears as a drop in DQE near the zero-frequency axis shown for those

detectors in Figure 10 Overall as indicated in Table 5 the DQEs of the two filtrations

while similar in trend indicate that the alternative filtration increases the DQE by a

small amount of 3-5 Part of this may be explained by the slightly higher beam

energy which may be more optimal for the energy response of the detectors or may

weigh the pixel responses slightly considering that they are energy-integrating types

The most probable explanation is the gain map correction for the alternative filtration

where fixed pattern noise is more sufficiently reduced

A previous study [6] had discussed the choice of filter material in the analysis of

DQE when achieving the beam conditions defined by IEC It found that visible

nonuniformities were present with the higher purity aluminum filter (type-11999 alloy)

The low frequency mottle in the flat-field images for NPS measurements were also

attributed to structured noise from the grain size in the IEC-based filter with an

attenuating thickness that would reveal nonuniformities The mottle in the current study

was only observable under very narrow windowing as shown in Figure 11 Such low

24

frequency artifacts which are not readily noticeable may also be caused by shading

artifacts inverse square law or even the heel effect A possible method to correct for this

is a subtraction method by taking the average of the flat-field images for an exposure

level and then subtracting that from each of them This would remove nonuniformities

that were not corrected using a suboptimal gain map calibration

Figure 11 DRX1-C NNPS images at 1 mR for RQA5 with IEC filtration (left) and

alternative filtration (right) Images are equally windowed at 45 and leveled at 980

One convenient aspect of the copper and aluminum filtration is that it requires

much less tube current to achieve the same amount of exposure at the detector than the

much thicker aluminum filtration As shown in the non-normalized spectra in Figure 2

the exiting photon fluence exiting the copper and aluminum filtration is substantially

higher than that of the IEC-specified filtration This is due to the smaller total filtration

25

attenuation For extensive DQE analysis multiple sets of exposures may be acquired

before tube overheating becomes a concern

One limitation to the comparison of the two filtrations is that calibration

procedures specified copper and aluminum filtration at 80 kVp (for all detectors 05 mm

Cu and 10 mm Al) This may have influenced the results in favor of the alternative

filtration A further investigation involving the calibration procedures and performing

DQE measurements is encouraged Another factor may be influenced by the fact that the

tests were performed at 70 kVp and 120 kVp different from the recommended

calibration tube potential Clearly there would be differences in the linear attenuation

coefficients of the filters and different energy responses of the detectors themselves This

must be considered when interpreting DQE results The current results support a

previous study decades ago that described filtration of different material types in terms

of an aluminum equivalent [16] The results show that the two filtration schemes are

essentially equivalent when considering beam qualities and spatial resolutions The

NNPS and DQE results can be seen as close enough where their small differences are

insignificant when performing quality assurance tests in a clinical setting Overall our

results indicate that the alternative filtration with copper and aluminum may be more

convenient to use than the current IEC standard filtration

26

I4iii Implications of Wireless DR

This study has shown that wireless image receptors can have the same DQE

performance if not better than conventional flat-panel detectors They operate on the

same basic physical principles the new features offered by the DRX-1C and DRX-1 are

wireless communication with the workstation and electronics packaging technology

The latter feature may pose limitations for these units in terms of possible degradation

in the detectors in routine clinical conditions A consideration for future work would be

to longitudinally track DQE performance of the wireless detectors over time while being

utilized in a clinical environment In the end one must consider risks versus benefits of

choosing portable DR technology over CR one of which includes the cost and fragility

of DR detectors

The DQE performance of one wireless system is just as good as or better than

conventional systems as seen by the DRX-1C performance compared to the Pixium

4600 Wireless systems can also reduce the need for CR readers especially in portable

applications in other regions of the world (eg military hospitals developing countries)

However while DQE performance indicates the physical performance of the detector

system it is still unknown how it relates to observer performance

I5 Conclusions

Two wireless image receptors DRX-1C and DRX-1 were evaluated and

compared with the conventional DR flat-panel Pixium 4600 in terms of DQE

27

performance along with MTF and NNPS performances The detectors have similar

resolution properties although the DRX-1 is inferior at higher spatial frequencies The

NNPS and DQE results both indicate that the DRX-1C is superior to the DRX-1 and

comparable if not better to the Pixium 4600

The results from the filtration comparison indicate no substantial differences

between the IEC-based filtration and the copper-based alternative filtration Only slight

differences were found in the low frequency components of the NNPS and the DQE due

to the inherent nonuniformities of the IEC specified filtration Given the similarity of the

results and low attenuation advantage of the copper and aluminum filter its use is

encouraged

28

II Directional MTF for Breast Tomosynthesis

II1 Introduction

Breast tomosynthesis is an emerging 3D imaging modality that has potential use

for screening and diagnosis of breast cancer Breast tomosynthesis along with other 3D

techniques is preferable to planar imaging methods (eg mammography) because they

reduce anatomical noise by removing overlying structures above and below the plane of

an image slice [17-20] Recent advances in detectors and computer technology have

made digital tomosynthesis feasible

An image quality metric of particular importance in breast tomosynthesis is

spatial resolution Resolution is important to know in order to assess small-detail

structures such as microcalcifications A descriptive metric for characterizing spatial

resolution in the Fourier (or frequency) domain is the modulation transfer function

(MTF) Affected by reconstruction filters [21] the limited angular projections involved in

breast tomosynthesis results in highly anisotropic (or nonuniform) resolution Many

studies have looked only at characterizing the in-plane spatial resolution (ie in an

individual slice) with an elevated angled edge phantom [2223] A few studies have

looked at characterizing a more comprehensive 3D spatial resolution by using a

phantom with angled wires or tubes [24-26] However such studies require precise

mechanical alignment of the phantoms Several studies have explored a method using a

29

sphere phantom for the directional 3D MTF evaluation for microtomography [27] and

multi-slice CT [2829] This method has not yet been extended to breast tomosynthesis

This chapter focuses on breast tomosynthesis because it is highly anisotropic in

spatial resolution and like its predecessor mammography requires high spatial

resolution Additionally breast tomosynthesis acquisitions and reconstructions produce

several types of artifacts The use of a cone-based method using a sphere phantom [28] is

explored to characterize the directional 3D spatial resolution of simulated images from

breast tomosynthesis A technique for removing out-of-plane artifacts of the ESFs for the

in-plane axes is investigated to yield a modified MTF in a method that separates artifact

information from resolution information

II2 Materials and Methods

II2i Image Simulation

Breast tomosynthesis images were simulated by using a virtual imaging system

depicted in Figure 12 A volumetric breast phantom was voxelized as a rectangular mass

of uniform breast equivalent tissue of 4 cm thickness embedded with fifteen evenly

spaced plastic sphere inserts of 12 mm diameter The spheres were placed in a grid

formation within the central plane of the phantom The x-ray fluence was modeled from

a 28 kVp beam incident upon an indirect flat-panel detector with 200 micro m pixel size

Twenty-three projections within an angular range of 44deg were simulated using cascaded

systems analysis to generate characteristic 2D noise and spatial blurring [29] Each

30

projection was simulated to have an exposure of 174 mR with a fluence of 79 times 105

photonsmm-2 A standard filtered backprojection technique based on the Feldkamp

reconstruction algorithm [29] was used to reconstruct the projections and produce a

volumetric dataset with an isotropic voxel size of 200 micro m

Figure 12 Depiction of the virtual image system

II2ii Uncorrected MTF

To enable comparison of multiple spheres the reconstructed volume was

initially homogenized by performing a background subtraction based on a portion of the

volume devoid of spheres The voxel values were rescaled between one and zero to

eliminate negative values

31

The volumetric data were segmented to extract individual regions of interest

(ROIs) each containing a single sphere The ROIs extended along the full range of the z-

axis A thresholded ROI was generated by determining the exterior and interior voxels

relative to the sphere in the ROI The threshold value was set at 45 of the maximum

voxel value prior to thresholding The exterior and interior voxel values were then set to

values of 0 and 1 respectively Using the thresholded volume the center of mass was

calculated to determine the centroid The voxel values from the original ROI were

subsequently tabulated with the associated distances azimuthal angles and polar

angles relative to the centroid

Conical regions were prescribed along the positive and negative directions along

the three major axes extending from the centroid of the sphere as depicted in Figure 13

The axes about which the extent of the cone angle was delineated were defined with

the azimuthal and polar angles

Voxels with centers within the angular range of the cone were considered for

generating the edge spread function (ESF) To improve regularity of the distance

sampling interval the ESF values were rebinned to discrete distances corresponding to a

fraction of the voxel size Only voxels with distances ranging from the voxel size (ie

200 micro m) to the maximum distance were considered The ESFs from multiple spheres

were averaged together for each of the three major axes to produce an averaged ESF

which was further smoothed utilizing a Gaussian filter

32

Figure 13 Example of 30-degree cone prescribed along z axis of the sphere

The resulting ESF was then differentiated using the central difference method to

produce the line spread function (LSF) A Hanning filter with the same length as the LSF

was applied to zero out the tails of the LSF The presampled MTF was subsequently

computed as the amplitude of the Fourier transform of the LSF The MTF was

normalized with respect to the maximum value occurring within the range of the cutoff

frequency Binning size and conical range for the ESF were considered for maximizing

accuracy and minimizing noise of the MTF verified by comparison against the

theoretical MTF as determined in the previous section

II2iii Theoretical Directional MTF

The theoretical 3D MTF was calculated using a priori knowledge of the transfer

function of the virtual imaging system described in the previous section A phantom

was created with a set of point objects in a uniform and noise-free background with the

objects spanning across the volume of the breast [29] Twenty-one realizations were

33

generated from the reconstructed images of the point objects to yield a set of 3D point

spread functions (PSFs) The 3D fast Fourier transform (FFT) was performed for each 3D

PSF and averaged to give an ldquoexpectationrdquo 3D MTF [29] The theoretical directional

MTFs in the three major spatial axes were determined by line profiles along each of the

corresponding spatial frequency axes in the 3D MTF An additional theoretical MTF for

each direction was determined by using the application of conical regions along the axes

in frequency-space to take into account the contributions of MTF information from other

planes

II2iv Modified MTF

The tomosynthesis reconstruction is known to have edge enhancements which

affect the overall MTF by shifting the peaks of the MTF toward the higher frequencies

[23] The presence of this artifact complicates the interpretation of the actual spatial

resolution of the images Several steps were performed to remove the artifact

contribution to the resolution information particularly for the in-plane x and y

directions with the assumption that resolution information was contained immediately

near the edge

For the x-direction averaged ESF only values that were detected to be inside the

edge of the sphere were considered Those values were previously determined via

thresholding for calculating the centroid The ESF information corresponding to these

values was inversed and flipped about the detected edge to produce a symmetric

34

modified ESF The modified MTF was subsequently calculated from this modified ESF

as described in the previous section

For the y-direction averaged ESF an upward trend was found in the initial part

of the ESF This section was detrended with a polynomial fit and subtracted to produce a

flatter curve in that region The resulting detrended ESF was used to calculate the y axis

modified MTF

Figure 14 Photograph of the imaging system with the acrylic sphere phantom

embedded in oil

II2v Preliminary Experimental Validation

A clinical breast tomosynthesis system (Mammomat Inspiration Siemens AG

Munich Germany) was used to perform a preliminary evaluation of the cone-based

MTF technique The phantom for the experiment consisted of a single acrylic ball of 075

in diameter (SmallParts Seattle WA) suspended by a 0029 in diameter plastic filament

35

(Omniflex Zebco Tulsa OK) in an acrylic frame filled up to 4 in with vegetable oil

(Target Brands Inc Minneapolis MN) The system and phantom are shown in Figure

14 Twenty-five projections with an angular range of 44deg were acquired and subsequently

reconstructed to produce a volume with a voxel size of 01times01times10 mm3 The voxels were

reformatted to have an isotropic size of 01 mm The uncorrected ESF LSF and MTF

were calculated as described in the previous section

II3 Results

II3i Reconstruction

The reconstructed volume is shown in Figure 15 Notice the edge enhancement

along the x-direction as indicated by the sharp shadowing artifacts on either side of the

spheres The background was effectively homogenized using the background

subtraction technique This also took account of the curved edges of the breast phantom

With the close spacing of the spheres in the phantom the shadows along the x direction

for the fifteen spheres overlap with each other As the nine centrally located spheres

experience this effect the same way they were used for determining the ESF

A 3D rendering of the ROI containing a sphere shown in Figure 16 indicates the

anisotropic resolution of the reconstruction Note that the sphere is not accurately

reconstructed and has an oblong shape especially along the z axis Cross sectional views

of the ROI also in Figure 16 clearly demonstrate the edge enhancement causing a

shadow artifact in the x direction caused by the incomplete angular sampling of

36

tomosynthesis The sampling also introduces the triangular reconstruction of the sphere

as seen in the x-z plane Note the gradual edge drop-off in the z direction much beyond

the sphere radius

Figure 15 View of the central slice of the breast phantom reconstruction before (top)

and after (bottom) background subtraction The z axis is through the page

37

Figure 16 3D rendering of the ROI volume (left) and cross-sectional views of the most

centrally located sphere with centroid indicated with red circle (right)

II3ii Theoretical MTF

The theoretical MTFs for x y and z directions as determined from the line

profiles of the 3D MTF are shown in Figure 17 The theoretical MTF in the x direction

has a maximum value that is toward higher frequencies Its 10 response occurs at

about 125 cyclesmm which is at 50 of the cutoff frequency The rapid increase from

the zero-frequency intercept to the peak corresponds to the ramp filter used in filtered

backprojection which decreases the weighting of low frequency contributions due to the

incomplete angular sampling of the frequency-space The MTF does not reach a value of

0 at the zero-frequency intercept as it is very difficult to assess the zero-frequency

intercept due to the finite size of the phantom The theoretical MTF in the y direction

peaks at the zero-frequency intercept and reaches 20 proximal to the cutoff frequency

38

The 10 MTF is well beyond the cutoff frequency The theoretical MTF in the z direction

has a rapid drop-off at very low spatial frequencies indicating the lack of resolution in

that dimension

Figure 17 Theoretical 3D MTF results along the three major planes (top) and along x

y and z directions (bottom) Also note that the angular spread seen in the fx-fz plane is

equal to the angular range of 44deg for the acquisition

II3iii Uncorrected MTF

The ESF LSF and MTF using the cone-based method are shown for the x y and

z directions in Figure 18 It was found that a bin size of one-tenth the voxel size (002

mm) and a cone angle of 30deg to establish the ESF were enough to minimize noise and

maximize accuracy in the uncorrected MTFs considering the reasonable comparison of

the shapes of the MTF curves with the theoretical results in Figure 17 The LSFs are

generally noisy because differentiation of the ESF increases the amplitude of the noise

39

The data shown reflect a convolution with a smoothing Gaussian filter which was later

further corrected for in the reported MTF Nevertheless the high frequency components

of the noise are well beyond the MTF cutoff frequency of 25 cyclesmm and do not

impact the MTF results greatly

For the ESF in the x direction the shadow effect evident at the edge of the sphere

is visible as a steep decline followed by an increase Due to the finite distance range

provided by the ROI the ESF beyond the edge did not asymptotically reach the

background value The corresponding LSF demonstrates a low frequency modulation

that is indicated by the shift of 03 cyclesmm in the x direction for the peak of the MTF

The MTF exhibits a zero-frequency intercept that is non-zero unlike the theoretical MTF

and a 10 value at approximately 1 cyclesmm These features may be a direct

consequence of MTF information ldquocontaminationrdquo from y and z directions Furthermore

the ESF in the y direction demonstrates a reasonably shaped curve except for the slight

upward trend within the radius of the sphere which can be attributed to the shadow

artifact overlapping with the sphere volume The associated MTF has a peak shifted by

approximately 01 cyclesmm away from the axis and a 10 MTF occurring at

approximately 15 cyclesmm Both features which are not present in the theoretical

results may also be attributed to contaminant MTF information from x and z directions

The ESF in the z direction has a drop-off that occurs at a small fraction of the cutoff

frequency similar to that demonstrated by the theoretical MTF

40

Uncorrected ESF LSF and MTF

Figure 18 Uncorrected ESF (top) LSF (middle) and MTF (bottom) for x y and z

directions

41

Figure 19 Comparisons of the directional MTFs as calculated by the sphere method

(dashed line) by theoretical line profiles (light-weight line) by theoretical cone

regions (heavy-weight line)

II3iv Comparison of Theoretical and Simulated MTFs

The theoretical MTF results obtained from line profiles through the 3D MTF and

the simulated MTFs using the cone-based technique did not match very well except for

the general shape of the curves It was assumed in the previous section that the cone-

based technique contains information from other planes Figure 19 compares MTFs in

each direction for the two methods described in the methods and an additional method

based on conical regions of the 3D MTF The latter computes the MTF by averaging

contributions of the 3D MTF using the same cone prescription method used to define the

ESFs Comparison of the curves indicate some interesting correlations aside from the

fact that using conical regions with the 3D MTF results produce more noisy MTF results

partly due to the low sampling provided by the theoretical calculations The same

conclusions regarding the z direction MTF can be confirmed regardless of either

theoretical MTF procedures The experimental x direction MTF seems to agree best with

42

the line profile method whereas the y direction MTF agrees better with the cone region

method The fact that the experimental x direction MTF has a drop-off frequency that is

lower than those of either of the theoretical MTFs in Figure 19 suggests that this might

be due to integration of the z-direction in the in-plane slices considering how slices are

essentially averages of z direction information contained within it [33]

II3v Modified MTF for x and y

Modified ESF LSF and MTF curves for x and y directions are shown in Figure

20 The modified ESF and the resulting LSF in the x direction appear symmetric as

expected from the inverse and flip operation of the interior ESF about the detected edge

The modified MTF appears with less variation than the uncorrected MTF and the MTF

peak occurs at the zero-frequency axis The correction yields a 10 MTF at about 15

cyclesmm an improvement from the uncorrected MTF but still distant from the cutoff

frequency The modified ESF in the y direction demonstrates the detrended curve within

the sphere radius after a quadratic polynomial fit The resulting modified MTF still

appears similar to the uncorrected MTF except that the peak now coincides with the

zero-frequency axis For both x and y directions the low response of the modified MTFs

at the higher frequencies suggests that the contamination from other directions is

substantial due to the angular range of the cone

43

Modified ESF LSF and MTF

Figure 20 Modified ESF (top) LSF (middle) and MTF (bottom) for x and y directions

44

II3v Preliminary Experimental Validation

Cross-sections of the reconstructed sphere volume are shown in Figure 21

Relative to the simulation reconstructions the reconstructions of the experimental

phantom images produce lower contrast and higher noise The preliminary results

shown in Figure 22 indicate that our technique can be applied to actual experimental

breast tomosynthesis reconstructions However due to the noise exhibited by the MTF

curves for the x and y directions we did not determine the modified MTFs to separate

resolution and artifact information

Figure 21 Cross sectional views of the experimental sphere image with centroid

indicated with red circle

45

Uncorrected ESF LSF and MTF for Real Image

Figure 22 ESF (top) LSF (middle) and MTF (bottom) of real image for x y

and z directions

46

II4 Discussion

II4i Evaluation of Cone-based Method

The cone-based MTF technique was introduced by Thornton and Flynn [28] for

evaluation of volumetric CT images To utilize this technique as a characterization of a

3D system spatial resolution one must first consider the validity of the assumption of

shift invariance such that the same MTF result may be obtained regardless of the

location of the sphere The study by Zhao et al [23] found that there was no shift

variance for the MTF measurements along the vertical axis but this was only considering

the in-plane resolution along one axis On the other hand this study evaluated the MTF

with images simulated with cascaded systems analysis which includes conditions of

linearity and shift invariance Additionally the MTF was calculated by averaging the

ESF from several spheres in the same volume only after performing a background

subtraction This step was essential to account for the sensitivity of centroid calculations

as well as ensuring symmetric ESFs for opposing axes of the sphere ROIs

The measurement of MTF with the cone-based technique inherently

supersamples the edge of the sphere to increase signal-to-noise-ratio (SNR) of edge

information by averaging the contributions of each voxel to the ESF [713] This method

also takes into account the discrete sampling of the voxels by accounting for various

shifts of the edge in the voxel (also known as the partial volume effect) However using

the curved surface of the sphere phantom to approximate an edge along a given

47

direction naturally leads to contamination of information from other directions aside

from the one of interest Preferably a directional ESF should be created by using a single

radial line but this would limit the available voxels to obtain edge information An ideal

situation theoretically would be to use a larger-sized sphere such that the surface is

nearly flat and perpendicular to the axes of interest This would also permit a reduction

in the angular range of the cone and thus the introduction of out-of-plane information in

the resulting MTF However sphere size is a limitation in breast tomosynthesis and the

use of a large phantom might void the assumption of shift invariance of the spatial

resolution

The choice of a sphere phantom nevertheless may be based on the clinical need

to quickly acquire a single image for MTF evaluation especially for multiple directions

without presenting extra logistical challenges The use of a wire or edge phantom

requires more precise mechanical alignment to achieve the correct set up The edge

phantom [23] would require at least two images to sample all three dimensions In the

case of the three wire phantom [2425] all three dimensions of the frame must be aligned

simultaneously with respect to the axis of rotation A similar situation would be

encountered when considering a cubic phantom with the planes normal to the axis of

interest In contrast to these phantoms the sphere eliminates the need for precise

alignment especially with respect to three spatial dimensions simultaneously A sphere

48

has ideal symmetry in all directions and can be used to evaluate MTF in any arbitrary

direction

This study unlike others [242532] did not explore the effects of physical

parameters such as scatter or contrast on the final MTF result but it demonstrated the

feasibility of using the cone-based method with an actual breast tomosynthesis image of

a sphere phantom as shown in Error Reference source not found and Error Reference

source not found These effects should be addressed in future works A further look

into deriving the principles of comparing the theoretical MTF with the experimental

MTF using the cone-based method is further warranted

II4ii Separation of Artifact and Resolution Information

The focus of this study was to develop a technique for measuring spatial

resolution of tomosynthesis images The intrinsic artifacts from tomosynthesis

reconstructions however lead to uncharacteristic MTFs and possible misinterpretation

of the effective resolution information When considering previous techniques for

calculating the presampled MTF [713152328] the analysis was performed using an

edge or a line to produce the corresponding ESF The resolution information is

essentially contained only along the edge indicated by the need to calculate the LSF In a

way the method of extracting artifact information is to focus the analysis only on the

edge part of the ESF to calculate the modified MTF This will lead to a better

understanding of the limiting size of objects that may be seen in the reconstructed 3D

49

image The presampled MTF without correction should still be analyzed to understand

the entire system response Note that the ESFs attempt to reflect information only at the

detected edge of the sphere

II5 Conclusions

The directional MTF of a simulated breast tomosynthesis reconstruction was

determined by using the cone-based MTF technique demonstrating the feasibility of a

single phantom for MTF evaluation This study further presented methods of analyzing

only the edge information in the ESF to create a modified MTF along in-slice (x and y)

axes It can provide insight into the actual spatial resolution information contained in the

image while separating the resolution information from the information introduced by

artifacts caused by the reconstruction and insufficient volumetric sampling The idea of

separating the resolution and artifacts from the measured ESF are expected to facilitate

the interpretation of MTF measurements in breast tomosynthesis Similar methods may

be applied to characterize the resolution of other 3D imaging modalities

50

References

1 Garmer M Hannigs SP Jaumlger HJ et al ldquoDigital Radiography Versus

Conventional Radiology in Chest Imaging Diagnostic Performance of a Large-

Area Silicon Flat-Panel Detector in a Clinical CT-Controlled Studyrdquo American

Journal of Roentgenology Volume 74 75-80 (2000)

2 Cowen AR Kengyelics SM and Davies AG ldquoSolid-state flat-panel digital

radiography detectors and their physical imaging characteristics rdquoClinical

Radiology Volume 63 487-498 (2008)

3 Chotas HG Dobbins III JT and Ravin CE ldquoPrinciples of Digital

Radiography with Large-Area Electronically Readable Detectors A Review of

the Basicsrdquo Radiology Volume 210 Number 3 595-599 (1999)

4 Flynn MJ and Samei E Experimental comparison of noise and resolution for

2k and 4k storage phosphor radiography systems Medical Physics Volume 26

Number 8 1612-1623 (1999)

5 Rong XJ Shaw CC Liu X Lemacks MR and Thompson SK

ldquoComparison of an amorphous siliconcesium iodide flat-panel digital chest

radiography system with screenfilm and computed radiography systems ndash A

contrast-detail phantom studyrdquo Medical Physics Volume 28 Number 11 2328-

2335 (2001)

6 Ranger NT Samei E Dobbins III JT and Ravin CE Measurement of the

detective quantum efficiency in digital detectors consistent with the IEC 62220-1

standard Practical considerations regarding the choice of filter material

Medical Physics Volume 30 Number 7 2305-2311 (2005)

7 Samei E Buhr E Granfors P Vandenbroucke D and Wang X Comparison

of edge analysis techniques for the determination of the MTF of digital

radiographic systems Physics in Medicine and Biology Volume 50 3613-3625

(2005)

8 Samei E and Flynn MJ An experimental comparison of detector performance

for computed radiography systems Medical Physics Volume 29 Number 4 447-

459 (2002)

51

9 Samei E and Flynn MJ An experimental comparison of detector performance

for direct and indirect digital radiography systems Medical Physics Volume 30

Number 4 608-622 (2003)

10 Samei E Ranger NT MacKenzie A Honey ID Dobbins III JT and Ravin

CE Effective DQE (eDQE) and speed of digital radiographic systems An

experimental methodology Medical Physics Volume 36 Number 8 3806-3817

(2009)

11 Samei E Ranger NT MacKenzie A Honey ID Dobbins III JT and Ravin

CE Detector or System Extending the Concept of Detective Quantum

Efficiency to Characterize the Performance of Digital Radiographic Imaging

Systems Radiology Volume 249 Number 3 926-937 (2008)

12 ldquoIEC 62220-1 Medical Electrical Equipment ndash Characteristics of Digital X-Ray

Imaging Devices ndash Part 1 Determination of the Detective Quantum Efficiencyrdquo

International Electrotechnical Commission Geneva Switzerland (2003)

13 Samei E Ranger NT Dobbins III JT and Chen Y Intercomparison of

methods for image quality characterization I Modulation transfer function

Medical Physics Volume 33 Number 5 1454-1465 (2006)

14 Dobbins III JT Samei E Ranger NT and Chen Y Intercomparison of

methods for image quality characterization II Noise power spectrum Medical

Physics Volume 33 Number 5 1466-1475 (2006)

15 Samei E Flynn MJ and Reimann DA A method for measuring the

presampled MTF of digital radiographic systems using an edge test device

Medical Physics Volume 25 Number 1 102-113 (1998)

16 Nagel HD ldquoAluminum equivalence of materials used in diagnostic radiology

and its dependence on beam qualityrdquo Physics in Medicine and Biology Volume

31 Number 12 1381-1399 (1986)

17 Niklason LT Christian BT Niklason LE et al ldquoDigital Tomosynthesis in

Breast Imagingrdquo Radiology Volume 205 399-406 (1997)

18 Gur D ldquoTomosynthesis Potential Clinical Role in Breast Imagingrdquo American

Journal of Roentgenology Volume 189 614-615 (2007)

52

19 Park JM Franken Jr EA Garg M Fajardo LL and Niklason LT ldquoBreast

Tomosynthesis Present Considerations and Future Applicationsrdquo

RadioGraphics Volume 27 S231-S240 (2007)

20 Good WF Abrams GS Catullo VJ Chough DM Ganott MA Hakim

CM and Gur D ldquoDigital Breast Tomosynthesis A Pilot Observer Studyrdquo

American Journal of Roentgenology Volume 190 865-869 (2008)

21 Hu Y-H Zhao W Mertelmeier T and Ludwig J ldquoImage Artifact in Digital

Breast Tomosynthesis and Its Dependence on System and Reconstruction

Parametersrdquo IWDM 2008 LNCS 5116 628-634 (2008)

22 Chen Y Lo JY Ranger NT Samei E Dobbins III JT ldquoMethodology of

NEQ(f) analysis for optimization and comparison of digital breast tomosynthesis

acquisition techniques and reconstruction algorithmsrdquo Proceedings of SPIE

Volume 6510 65101I (2007)

23 Zhao B Zhou J Hu Y-H Mertelmeier T Ludwig J and Zhao W

ldquoExperimental validation of a three-dimensional linear system model for breast

tomosynthesisrdquo Medical Physics Volume 36 Number 1 240-251 (2009)

24 Madhav P Brzymialkiewicz CN Cutler SJ Bowsher JE and Tornai MP

ldquoCharacterizing the MTF in 3D for a Quantized SPECT Camera Having Arbitrary

Trajectoriesrdquo 2005 IEEE Nuclear Science Symposium Conference Record 1722-

1726 (2005)

25 Madhav P McKinley RL Samei E Bowsher JE and Tornai MP ldquoA Novel

Method to Characterize the MTF in 3D for Computed Mammotomographyrdquo

Proceedings of SPIE Volume 6142 61421Y (2006)

26 Hu Y-H Zhao B and Zhao W ldquoImage artifacts in digital breast

tomosynthesis Investigation of the effects of system geometry and

reconstruction parameters using a linear system approachrdquo Medical Physics

Volume 35 Number 12 5242-5252 (2008)

27 Seifert A and Flynn MJ ldquoResolving power of 3D x-ray microtomography

systemsrdquo Proceedings of SPIE Volume 4682 407-413 (2002)

28 Thornton MM and Flynn MJ Measurement of the spatial resolution of a

clinical volumetric computed tomography scanner using a sphere phantom

Proceedings of SPIE Volume 6142 61421Z (2006)

53

29 Baek J Pelc NJ ldquoUse of sphere phantoms to measure the 3D MTF of FDK

reconstructionsrdquo Proceedings of SPIE Volume 7961 79610D (2011)

30 Richard S and Samei E ldquoQuantitative imaging in breast tomosynthesis and CT

Comparison of detection and estimation task performancerdquo Medical Physics

Volume 37 Number 6 2627-2637 (2010)

31 Chen Y Lo JY and Dobbins III JT ldquoImpulse response analysis for several

digital tomosynthesis mammography reconstruction algorithmsrdquo Proceedings of

SPIE Volume 5745 541-549 (2005)

32 Zhao B and Zhao W ldquoThree-dimensional linear system analysis for breast

tomosynthesisrdquo Medical Physics Volume 35 Number 12 5219-5232 (2008)

33 Wu G Mainprize JG Boone JM and Yaffe MJ ldquoEvaluation of scatter

effects on image quality for breast tomosynthesisrdquo Medical Physics Volume 36

Number 10 4425-4432 (2009)

Page 25: Development and Evaluation of 2D and 3D Image Quality ...

12

I3iii Modulation Transfer Function

The limiting spatial resolutions of the systems were indicated by the cutoff

frequencies which were approximately 35 cyclesmm for all three detectors The spatial

resolutions also demonstrated a good degree of isotropy as confirmed by the close

alignment of MTF curves between vertical and horizontal directions differentiated in

Figure 5 by dashed and solid lines respectively The MTF curves for the Pixium 4600

and DRX-1C were nearly equal to each other whereas the DRX-1 MTF curve showed a

more rapid decrease at high frequencies as shown in Figure 6 This difference may be

due to the differences in the inherent optical properties of the scintillating materials

where finer image details are provided by structured CsI more than by granulated GOS

There were no significant differences in MTF curves across beam qualities and filtrations

as shown by the curve comparisons in Figure 6 although the alternative filtration

produced slightly higher MTF curves as seen in Figure 4 Table 4 lists the experimental

specific spatial frequencies for varying levels of MTF

I3iv Noise Power Spectrum

The noise characteristics are indicated by the NNPS curves shown in Figure 7

The noise was similar for both horizontal and vertical directions As exposure increased

the NNPS decreased consistent with the characteristics of Poisson noise describing the

relationship between signal and noise in the presence of increased photon fluence At

13

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 5 MTF results by detector (columns) and beam quality (rows)

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

horizontal

vertical

14

Figure 6 Plots of MTF for RQA5 (top) and RQA9 (bottom) showing the relationships

between detectors (blue red and green) and by filtration (solid and dashed)

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm-1)

MTF

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm-1)

MTF

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

15

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 7 NNPS results by detector (columns) and beam quality (rows)

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

05 mR - horizontal

05 mR - vertical

10 mR - horizontal

10 mR - vertical

20 mR - horizontal

20 mR - vertical

16

Figure 8 Plots of NNPS for RQA5 (top) and RQA9 (bottom) at 1 mR exposure

showing the relationships between detectors (blue red and green) and by filtration

(solid and dashed)

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm-1)

NNPS (1 mR)

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm-1)

NNPS (1 mR)

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

17

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 9 DQE results by detector (columns) and beam quality (rows)

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

05 mR - horizontal

05 mR - vertical

10 mR - horizontal

10 mR - vertical

20 mR - horizontal

20 mR - vertical

18

Figure 10 Plots of DQE for RQA5 (top) and RQA9 (bottom) at 1 mR exposure showing

the relationships between detectors (blue red and green) and by filtration (solid and

dashed)

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm-1)

DQE (1 mR)

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm-1)

DQE

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

19

higher frequencies the NNPS curves of the Pixium 4600 and DRX-1 diverge slightly for

the different directions illustrating increased noise in the readout direction (vertical)

Differences in the noise characteristics were more apparent among detectors as

shown for 1 mR in Figure 8 The NNPS curve for the DRX-1 was higher in magnitude

across the entire frequency range than either the Pixium 4600 or DRX-1C which both

seemed to demonstrate reasonably similar NNPS curves The higher magnitude noise of

the DRX-1 indicates higher relative noise content overall Closer inspection of the NNPS

curves of the Pixium 4600 and DRX-1C detectors in Figure 7 revealed differences in the

spacing between the three exposure levels The gaps between the Pixium 4600 NNPS

curves do not correspond to the factor of two differences between each exposure level

especially at low- to mid- spatial frequencies suggesting a higher level of fixed pattern

noise additional noise with increasing exposure levels due to ineffective gain map

corrections Between filtration schemes the differences in NNPS curves for a given beam

quality were not substantial as shown in Figure 7

I3v Detective Quantum Efficiency

The DQE results are shown in Figure 9 DQE curves across exposure levels were

almost collinear except for Pixium 4600 and in general could be inferred from the

NNPS results Additionally the DQE curves demonstrated a relatively linear response

with spatial frequencies as expected for flat-panel detectors [9] Differences in DQE

among detectors were consistent for the most part with the type of scintillating material

20

As depicted for 1 mR exposure in Figure 10 differences between Pixium 4600 and DRX-

1C DQE curves correspond to the differences in their NNPS curves DRX-1 DQE curves

were consistently lower than either the Pixium 4600 or DRX-1C curves The DQE curves

for the alternative filtration were consistently higher than those for the IEC filtration

and the most noticeable differences were near the zero-frequency axis These effects can

be both attributed to ineffective gain map correction DQE values for 1 mR exposure are

listed in Table 5

I4 Discussion

I4i Comparisons of Detectors

The limiting spatial resolutions of all three detectors were almost exactly the

same considering that their pixel areas were similar in size The decrease in high-

frequency MTF of the DRX-1 compared to the other detectors is probably a result of

increased optical blurring due to the differences in the powdered structure of GOS

versus the needle-like structure of CsI [2] The fact that the DRX-1C and Pixium 4600

have comparable MTFs suggests similar scintillator thicknesses assuming that the

materials were processed alike

The noise of the three detectors demonstrated similar trends with each other The

higher NNPS curves of the DRX-1 detector are probably due also to the scintillating

material and its operation in converting photons into signal The conversion process is

less efficient because of the less favorable stopping power of the GOS compared to CsI

21

especially with higher energy beams The noise of the Pixium 4600 and DRX-1C were

similar except for the spacing between exposures The DRX-1C NNPS curve spacing is

consistent with a factor of two difference in exposure levels but the Pixium 4600 has a

smaller spacing The 05 mR NNPS curve of the Pixium 4600 is closer to that of the 05

mR NNPS curve of the DRX-1C This demonstrates that at higher exposures the Pixium

4600 produces a larger amount of additional noise beyond that explained by simple

stochastic effects It suggests bad performance in the gain map corrections

The DQE results indicate SNR properties of each detector The Pixium 4600 and

DRX-1C are comparable for the most part with the DRX-1C performing slightly better

The DRX-1 as predicted from MTF and NNPS results has a DQE much lower than

either of the previous two This is a reflection of the detection properties as provided by

its scintillator material The DQE of the DRX-1 however is comparable to CR image

receptors [2] The mid-frequency dips in the DQE for Pixium 4600 may be due to the

optical properties of the CsI phosphor layer which can affect the MTF in this manner

Because the DQE is calculated by squaring the MTF this effect at the mid-range

frequencies becomes more apparent The dips may also be further evidence of bad gain

map corrections

I4ii Comparisons of Filtrations

The alternative filtration closely matches for the most part the IEC-based

filtration for MTF NNPS and DQEs at RQA5 but not at RQA9 The filters do not have

22

Table 4 Experimental MTF frequency locations for 1 mR exposure

Detector Filtration

50 MTF

(mm-1)

40 MTF

(mm-1)

30 MTF

(mm-1)

20 MTF

(mm-1)

10 MTF

(mm-1)

Pixium

4600

RQA5A 115 145 185 245 330

RQA5C 125 155 195 250 345

RQA9A 110 175 175 235 330

RQA9C 125 155 195 255 345

DRX-1C

RQA5A 120 150 185 245 350

RQA5C 125 155 195 255 355

RQA9A 120 150 190 250 355

RQA9C 130 160 210 265 360

DRX-1

RQA5A 110 135 160 205 280

RQA5C 110 135 170 210 285

RQA9A 105 125 155 195 270

RQA9C 110 135 165 210 285

Table 5 Estimated DQE values for 1 mR exposure by frequency bins

Detector Filtration DQE(00 mm-1) DQE(10 mm-1) DQE(20 mm-1) DQE(30 mm-1)

Pixium

4600

RQA5A 62 42 32 21

RQA5C 63 45 36 25

RQA9A 41 27 30 13

RQA9C 43 33 27 19

DRX-1C

RQA5A 72 52 35 21

RQA5C 76 55 41 24

RQA9A 49 33 23 15

RQA9C 51 40 31 20

DRX-1

RQA5A 38 24 12 4

RQA5C 38 25 14 5

RQA9A 28 18 9 4

RQA9C 28 19 12 5

DQE values at the zero-frequency axis were estimated by the intercept of a linear fit of low-frequency data

but excluding most proximal to the axis due to large fluctuations Other estimated values are grouped into

frequency bins due to the noisiness of the data

23

considerable differences in the spatial resolutions of the detectors as expected The noise

responses for each filtration were also similar except at the lower frequencies of the

NNPS especially near the zero-frequency axis There observing the NNPS responses at

RQA5 for Pixium 4600 and DRX-1C in Figure 8 the NNPS for the IEC-based filtration

(solid lines) tend to drop faster than the NNPS for the alternative filtration This

subsequently appears as a drop in DQE near the zero-frequency axis shown for those

detectors in Figure 10 Overall as indicated in Table 5 the DQEs of the two filtrations

while similar in trend indicate that the alternative filtration increases the DQE by a

small amount of 3-5 Part of this may be explained by the slightly higher beam

energy which may be more optimal for the energy response of the detectors or may

weigh the pixel responses slightly considering that they are energy-integrating types

The most probable explanation is the gain map correction for the alternative filtration

where fixed pattern noise is more sufficiently reduced

A previous study [6] had discussed the choice of filter material in the analysis of

DQE when achieving the beam conditions defined by IEC It found that visible

nonuniformities were present with the higher purity aluminum filter (type-11999 alloy)

The low frequency mottle in the flat-field images for NPS measurements were also

attributed to structured noise from the grain size in the IEC-based filter with an

attenuating thickness that would reveal nonuniformities The mottle in the current study

was only observable under very narrow windowing as shown in Figure 11 Such low

24

frequency artifacts which are not readily noticeable may also be caused by shading

artifacts inverse square law or even the heel effect A possible method to correct for this

is a subtraction method by taking the average of the flat-field images for an exposure

level and then subtracting that from each of them This would remove nonuniformities

that were not corrected using a suboptimal gain map calibration

Figure 11 DRX1-C NNPS images at 1 mR for RQA5 with IEC filtration (left) and

alternative filtration (right) Images are equally windowed at 45 and leveled at 980

One convenient aspect of the copper and aluminum filtration is that it requires

much less tube current to achieve the same amount of exposure at the detector than the

much thicker aluminum filtration As shown in the non-normalized spectra in Figure 2

the exiting photon fluence exiting the copper and aluminum filtration is substantially

higher than that of the IEC-specified filtration This is due to the smaller total filtration

25

attenuation For extensive DQE analysis multiple sets of exposures may be acquired

before tube overheating becomes a concern

One limitation to the comparison of the two filtrations is that calibration

procedures specified copper and aluminum filtration at 80 kVp (for all detectors 05 mm

Cu and 10 mm Al) This may have influenced the results in favor of the alternative

filtration A further investigation involving the calibration procedures and performing

DQE measurements is encouraged Another factor may be influenced by the fact that the

tests were performed at 70 kVp and 120 kVp different from the recommended

calibration tube potential Clearly there would be differences in the linear attenuation

coefficients of the filters and different energy responses of the detectors themselves This

must be considered when interpreting DQE results The current results support a

previous study decades ago that described filtration of different material types in terms

of an aluminum equivalent [16] The results show that the two filtration schemes are

essentially equivalent when considering beam qualities and spatial resolutions The

NNPS and DQE results can be seen as close enough where their small differences are

insignificant when performing quality assurance tests in a clinical setting Overall our

results indicate that the alternative filtration with copper and aluminum may be more

convenient to use than the current IEC standard filtration

26

I4iii Implications of Wireless DR

This study has shown that wireless image receptors can have the same DQE

performance if not better than conventional flat-panel detectors They operate on the

same basic physical principles the new features offered by the DRX-1C and DRX-1 are

wireless communication with the workstation and electronics packaging technology

The latter feature may pose limitations for these units in terms of possible degradation

in the detectors in routine clinical conditions A consideration for future work would be

to longitudinally track DQE performance of the wireless detectors over time while being

utilized in a clinical environment In the end one must consider risks versus benefits of

choosing portable DR technology over CR one of which includes the cost and fragility

of DR detectors

The DQE performance of one wireless system is just as good as or better than

conventional systems as seen by the DRX-1C performance compared to the Pixium

4600 Wireless systems can also reduce the need for CR readers especially in portable

applications in other regions of the world (eg military hospitals developing countries)

However while DQE performance indicates the physical performance of the detector

system it is still unknown how it relates to observer performance

I5 Conclusions

Two wireless image receptors DRX-1C and DRX-1 were evaluated and

compared with the conventional DR flat-panel Pixium 4600 in terms of DQE

27

performance along with MTF and NNPS performances The detectors have similar

resolution properties although the DRX-1 is inferior at higher spatial frequencies The

NNPS and DQE results both indicate that the DRX-1C is superior to the DRX-1 and

comparable if not better to the Pixium 4600

The results from the filtration comparison indicate no substantial differences

between the IEC-based filtration and the copper-based alternative filtration Only slight

differences were found in the low frequency components of the NNPS and the DQE due

to the inherent nonuniformities of the IEC specified filtration Given the similarity of the

results and low attenuation advantage of the copper and aluminum filter its use is

encouraged

28

II Directional MTF for Breast Tomosynthesis

II1 Introduction

Breast tomosynthesis is an emerging 3D imaging modality that has potential use

for screening and diagnosis of breast cancer Breast tomosynthesis along with other 3D

techniques is preferable to planar imaging methods (eg mammography) because they

reduce anatomical noise by removing overlying structures above and below the plane of

an image slice [17-20] Recent advances in detectors and computer technology have

made digital tomosynthesis feasible

An image quality metric of particular importance in breast tomosynthesis is

spatial resolution Resolution is important to know in order to assess small-detail

structures such as microcalcifications A descriptive metric for characterizing spatial

resolution in the Fourier (or frequency) domain is the modulation transfer function

(MTF) Affected by reconstruction filters [21] the limited angular projections involved in

breast tomosynthesis results in highly anisotropic (or nonuniform) resolution Many

studies have looked only at characterizing the in-plane spatial resolution (ie in an

individual slice) with an elevated angled edge phantom [2223] A few studies have

looked at characterizing a more comprehensive 3D spatial resolution by using a

phantom with angled wires or tubes [24-26] However such studies require precise

mechanical alignment of the phantoms Several studies have explored a method using a

29

sphere phantom for the directional 3D MTF evaluation for microtomography [27] and

multi-slice CT [2829] This method has not yet been extended to breast tomosynthesis

This chapter focuses on breast tomosynthesis because it is highly anisotropic in

spatial resolution and like its predecessor mammography requires high spatial

resolution Additionally breast tomosynthesis acquisitions and reconstructions produce

several types of artifacts The use of a cone-based method using a sphere phantom [28] is

explored to characterize the directional 3D spatial resolution of simulated images from

breast tomosynthesis A technique for removing out-of-plane artifacts of the ESFs for the

in-plane axes is investigated to yield a modified MTF in a method that separates artifact

information from resolution information

II2 Materials and Methods

II2i Image Simulation

Breast tomosynthesis images were simulated by using a virtual imaging system

depicted in Figure 12 A volumetric breast phantom was voxelized as a rectangular mass

of uniform breast equivalent tissue of 4 cm thickness embedded with fifteen evenly

spaced plastic sphere inserts of 12 mm diameter The spheres were placed in a grid

formation within the central plane of the phantom The x-ray fluence was modeled from

a 28 kVp beam incident upon an indirect flat-panel detector with 200 micro m pixel size

Twenty-three projections within an angular range of 44deg were simulated using cascaded

systems analysis to generate characteristic 2D noise and spatial blurring [29] Each

30

projection was simulated to have an exposure of 174 mR with a fluence of 79 times 105

photonsmm-2 A standard filtered backprojection technique based on the Feldkamp

reconstruction algorithm [29] was used to reconstruct the projections and produce a

volumetric dataset with an isotropic voxel size of 200 micro m

Figure 12 Depiction of the virtual image system

II2ii Uncorrected MTF

To enable comparison of multiple spheres the reconstructed volume was

initially homogenized by performing a background subtraction based on a portion of the

volume devoid of spheres The voxel values were rescaled between one and zero to

eliminate negative values

31

The volumetric data were segmented to extract individual regions of interest

(ROIs) each containing a single sphere The ROIs extended along the full range of the z-

axis A thresholded ROI was generated by determining the exterior and interior voxels

relative to the sphere in the ROI The threshold value was set at 45 of the maximum

voxel value prior to thresholding The exterior and interior voxel values were then set to

values of 0 and 1 respectively Using the thresholded volume the center of mass was

calculated to determine the centroid The voxel values from the original ROI were

subsequently tabulated with the associated distances azimuthal angles and polar

angles relative to the centroid

Conical regions were prescribed along the positive and negative directions along

the three major axes extending from the centroid of the sphere as depicted in Figure 13

The axes about which the extent of the cone angle was delineated were defined with

the azimuthal and polar angles

Voxels with centers within the angular range of the cone were considered for

generating the edge spread function (ESF) To improve regularity of the distance

sampling interval the ESF values were rebinned to discrete distances corresponding to a

fraction of the voxel size Only voxels with distances ranging from the voxel size (ie

200 micro m) to the maximum distance were considered The ESFs from multiple spheres

were averaged together for each of the three major axes to produce an averaged ESF

which was further smoothed utilizing a Gaussian filter

32

Figure 13 Example of 30-degree cone prescribed along z axis of the sphere

The resulting ESF was then differentiated using the central difference method to

produce the line spread function (LSF) A Hanning filter with the same length as the LSF

was applied to zero out the tails of the LSF The presampled MTF was subsequently

computed as the amplitude of the Fourier transform of the LSF The MTF was

normalized with respect to the maximum value occurring within the range of the cutoff

frequency Binning size and conical range for the ESF were considered for maximizing

accuracy and minimizing noise of the MTF verified by comparison against the

theoretical MTF as determined in the previous section

II2iii Theoretical Directional MTF

The theoretical 3D MTF was calculated using a priori knowledge of the transfer

function of the virtual imaging system described in the previous section A phantom

was created with a set of point objects in a uniform and noise-free background with the

objects spanning across the volume of the breast [29] Twenty-one realizations were

33

generated from the reconstructed images of the point objects to yield a set of 3D point

spread functions (PSFs) The 3D fast Fourier transform (FFT) was performed for each 3D

PSF and averaged to give an ldquoexpectationrdquo 3D MTF [29] The theoretical directional

MTFs in the three major spatial axes were determined by line profiles along each of the

corresponding spatial frequency axes in the 3D MTF An additional theoretical MTF for

each direction was determined by using the application of conical regions along the axes

in frequency-space to take into account the contributions of MTF information from other

planes

II2iv Modified MTF

The tomosynthesis reconstruction is known to have edge enhancements which

affect the overall MTF by shifting the peaks of the MTF toward the higher frequencies

[23] The presence of this artifact complicates the interpretation of the actual spatial

resolution of the images Several steps were performed to remove the artifact

contribution to the resolution information particularly for the in-plane x and y

directions with the assumption that resolution information was contained immediately

near the edge

For the x-direction averaged ESF only values that were detected to be inside the

edge of the sphere were considered Those values were previously determined via

thresholding for calculating the centroid The ESF information corresponding to these

values was inversed and flipped about the detected edge to produce a symmetric

34

modified ESF The modified MTF was subsequently calculated from this modified ESF

as described in the previous section

For the y-direction averaged ESF an upward trend was found in the initial part

of the ESF This section was detrended with a polynomial fit and subtracted to produce a

flatter curve in that region The resulting detrended ESF was used to calculate the y axis

modified MTF

Figure 14 Photograph of the imaging system with the acrylic sphere phantom

embedded in oil

II2v Preliminary Experimental Validation

A clinical breast tomosynthesis system (Mammomat Inspiration Siemens AG

Munich Germany) was used to perform a preliminary evaluation of the cone-based

MTF technique The phantom for the experiment consisted of a single acrylic ball of 075

in diameter (SmallParts Seattle WA) suspended by a 0029 in diameter plastic filament

35

(Omniflex Zebco Tulsa OK) in an acrylic frame filled up to 4 in with vegetable oil

(Target Brands Inc Minneapolis MN) The system and phantom are shown in Figure

14 Twenty-five projections with an angular range of 44deg were acquired and subsequently

reconstructed to produce a volume with a voxel size of 01times01times10 mm3 The voxels were

reformatted to have an isotropic size of 01 mm The uncorrected ESF LSF and MTF

were calculated as described in the previous section

II3 Results

II3i Reconstruction

The reconstructed volume is shown in Figure 15 Notice the edge enhancement

along the x-direction as indicated by the sharp shadowing artifacts on either side of the

spheres The background was effectively homogenized using the background

subtraction technique This also took account of the curved edges of the breast phantom

With the close spacing of the spheres in the phantom the shadows along the x direction

for the fifteen spheres overlap with each other As the nine centrally located spheres

experience this effect the same way they were used for determining the ESF

A 3D rendering of the ROI containing a sphere shown in Figure 16 indicates the

anisotropic resolution of the reconstruction Note that the sphere is not accurately

reconstructed and has an oblong shape especially along the z axis Cross sectional views

of the ROI also in Figure 16 clearly demonstrate the edge enhancement causing a

shadow artifact in the x direction caused by the incomplete angular sampling of

36

tomosynthesis The sampling also introduces the triangular reconstruction of the sphere

as seen in the x-z plane Note the gradual edge drop-off in the z direction much beyond

the sphere radius

Figure 15 View of the central slice of the breast phantom reconstruction before (top)

and after (bottom) background subtraction The z axis is through the page

37

Figure 16 3D rendering of the ROI volume (left) and cross-sectional views of the most

centrally located sphere with centroid indicated with red circle (right)

II3ii Theoretical MTF

The theoretical MTFs for x y and z directions as determined from the line

profiles of the 3D MTF are shown in Figure 17 The theoretical MTF in the x direction

has a maximum value that is toward higher frequencies Its 10 response occurs at

about 125 cyclesmm which is at 50 of the cutoff frequency The rapid increase from

the zero-frequency intercept to the peak corresponds to the ramp filter used in filtered

backprojection which decreases the weighting of low frequency contributions due to the

incomplete angular sampling of the frequency-space The MTF does not reach a value of

0 at the zero-frequency intercept as it is very difficult to assess the zero-frequency

intercept due to the finite size of the phantom The theoretical MTF in the y direction

peaks at the zero-frequency intercept and reaches 20 proximal to the cutoff frequency

38

The 10 MTF is well beyond the cutoff frequency The theoretical MTF in the z direction

has a rapid drop-off at very low spatial frequencies indicating the lack of resolution in

that dimension

Figure 17 Theoretical 3D MTF results along the three major planes (top) and along x

y and z directions (bottom) Also note that the angular spread seen in the fx-fz plane is

equal to the angular range of 44deg for the acquisition

II3iii Uncorrected MTF

The ESF LSF and MTF using the cone-based method are shown for the x y and

z directions in Figure 18 It was found that a bin size of one-tenth the voxel size (002

mm) and a cone angle of 30deg to establish the ESF were enough to minimize noise and

maximize accuracy in the uncorrected MTFs considering the reasonable comparison of

the shapes of the MTF curves with the theoretical results in Figure 17 The LSFs are

generally noisy because differentiation of the ESF increases the amplitude of the noise

39

The data shown reflect a convolution with a smoothing Gaussian filter which was later

further corrected for in the reported MTF Nevertheless the high frequency components

of the noise are well beyond the MTF cutoff frequency of 25 cyclesmm and do not

impact the MTF results greatly

For the ESF in the x direction the shadow effect evident at the edge of the sphere

is visible as a steep decline followed by an increase Due to the finite distance range

provided by the ROI the ESF beyond the edge did not asymptotically reach the

background value The corresponding LSF demonstrates a low frequency modulation

that is indicated by the shift of 03 cyclesmm in the x direction for the peak of the MTF

The MTF exhibits a zero-frequency intercept that is non-zero unlike the theoretical MTF

and a 10 value at approximately 1 cyclesmm These features may be a direct

consequence of MTF information ldquocontaminationrdquo from y and z directions Furthermore

the ESF in the y direction demonstrates a reasonably shaped curve except for the slight

upward trend within the radius of the sphere which can be attributed to the shadow

artifact overlapping with the sphere volume The associated MTF has a peak shifted by

approximately 01 cyclesmm away from the axis and a 10 MTF occurring at

approximately 15 cyclesmm Both features which are not present in the theoretical

results may also be attributed to contaminant MTF information from x and z directions

The ESF in the z direction has a drop-off that occurs at a small fraction of the cutoff

frequency similar to that demonstrated by the theoretical MTF

40

Uncorrected ESF LSF and MTF

Figure 18 Uncorrected ESF (top) LSF (middle) and MTF (bottom) for x y and z

directions

41

Figure 19 Comparisons of the directional MTFs as calculated by the sphere method

(dashed line) by theoretical line profiles (light-weight line) by theoretical cone

regions (heavy-weight line)

II3iv Comparison of Theoretical and Simulated MTFs

The theoretical MTF results obtained from line profiles through the 3D MTF and

the simulated MTFs using the cone-based technique did not match very well except for

the general shape of the curves It was assumed in the previous section that the cone-

based technique contains information from other planes Figure 19 compares MTFs in

each direction for the two methods described in the methods and an additional method

based on conical regions of the 3D MTF The latter computes the MTF by averaging

contributions of the 3D MTF using the same cone prescription method used to define the

ESFs Comparison of the curves indicate some interesting correlations aside from the

fact that using conical regions with the 3D MTF results produce more noisy MTF results

partly due to the low sampling provided by the theoretical calculations The same

conclusions regarding the z direction MTF can be confirmed regardless of either

theoretical MTF procedures The experimental x direction MTF seems to agree best with

42

the line profile method whereas the y direction MTF agrees better with the cone region

method The fact that the experimental x direction MTF has a drop-off frequency that is

lower than those of either of the theoretical MTFs in Figure 19 suggests that this might

be due to integration of the z-direction in the in-plane slices considering how slices are

essentially averages of z direction information contained within it [33]

II3v Modified MTF for x and y

Modified ESF LSF and MTF curves for x and y directions are shown in Figure

20 The modified ESF and the resulting LSF in the x direction appear symmetric as

expected from the inverse and flip operation of the interior ESF about the detected edge

The modified MTF appears with less variation than the uncorrected MTF and the MTF

peak occurs at the zero-frequency axis The correction yields a 10 MTF at about 15

cyclesmm an improvement from the uncorrected MTF but still distant from the cutoff

frequency The modified ESF in the y direction demonstrates the detrended curve within

the sphere radius after a quadratic polynomial fit The resulting modified MTF still

appears similar to the uncorrected MTF except that the peak now coincides with the

zero-frequency axis For both x and y directions the low response of the modified MTFs

at the higher frequencies suggests that the contamination from other directions is

substantial due to the angular range of the cone

43

Modified ESF LSF and MTF

Figure 20 Modified ESF (top) LSF (middle) and MTF (bottom) for x and y directions

44

II3v Preliminary Experimental Validation

Cross-sections of the reconstructed sphere volume are shown in Figure 21

Relative to the simulation reconstructions the reconstructions of the experimental

phantom images produce lower contrast and higher noise The preliminary results

shown in Figure 22 indicate that our technique can be applied to actual experimental

breast tomosynthesis reconstructions However due to the noise exhibited by the MTF

curves for the x and y directions we did not determine the modified MTFs to separate

resolution and artifact information

Figure 21 Cross sectional views of the experimental sphere image with centroid

indicated with red circle

45

Uncorrected ESF LSF and MTF for Real Image

Figure 22 ESF (top) LSF (middle) and MTF (bottom) of real image for x y

and z directions

46

II4 Discussion

II4i Evaluation of Cone-based Method

The cone-based MTF technique was introduced by Thornton and Flynn [28] for

evaluation of volumetric CT images To utilize this technique as a characterization of a

3D system spatial resolution one must first consider the validity of the assumption of

shift invariance such that the same MTF result may be obtained regardless of the

location of the sphere The study by Zhao et al [23] found that there was no shift

variance for the MTF measurements along the vertical axis but this was only considering

the in-plane resolution along one axis On the other hand this study evaluated the MTF

with images simulated with cascaded systems analysis which includes conditions of

linearity and shift invariance Additionally the MTF was calculated by averaging the

ESF from several spheres in the same volume only after performing a background

subtraction This step was essential to account for the sensitivity of centroid calculations

as well as ensuring symmetric ESFs for opposing axes of the sphere ROIs

The measurement of MTF with the cone-based technique inherently

supersamples the edge of the sphere to increase signal-to-noise-ratio (SNR) of edge

information by averaging the contributions of each voxel to the ESF [713] This method

also takes into account the discrete sampling of the voxels by accounting for various

shifts of the edge in the voxel (also known as the partial volume effect) However using

the curved surface of the sphere phantom to approximate an edge along a given

47

direction naturally leads to contamination of information from other directions aside

from the one of interest Preferably a directional ESF should be created by using a single

radial line but this would limit the available voxels to obtain edge information An ideal

situation theoretically would be to use a larger-sized sphere such that the surface is

nearly flat and perpendicular to the axes of interest This would also permit a reduction

in the angular range of the cone and thus the introduction of out-of-plane information in

the resulting MTF However sphere size is a limitation in breast tomosynthesis and the

use of a large phantom might void the assumption of shift invariance of the spatial

resolution

The choice of a sphere phantom nevertheless may be based on the clinical need

to quickly acquire a single image for MTF evaluation especially for multiple directions

without presenting extra logistical challenges The use of a wire or edge phantom

requires more precise mechanical alignment to achieve the correct set up The edge

phantom [23] would require at least two images to sample all three dimensions In the

case of the three wire phantom [2425] all three dimensions of the frame must be aligned

simultaneously with respect to the axis of rotation A similar situation would be

encountered when considering a cubic phantom with the planes normal to the axis of

interest In contrast to these phantoms the sphere eliminates the need for precise

alignment especially with respect to three spatial dimensions simultaneously A sphere

48

has ideal symmetry in all directions and can be used to evaluate MTF in any arbitrary

direction

This study unlike others [242532] did not explore the effects of physical

parameters such as scatter or contrast on the final MTF result but it demonstrated the

feasibility of using the cone-based method with an actual breast tomosynthesis image of

a sphere phantom as shown in Error Reference source not found and Error Reference

source not found These effects should be addressed in future works A further look

into deriving the principles of comparing the theoretical MTF with the experimental

MTF using the cone-based method is further warranted

II4ii Separation of Artifact and Resolution Information

The focus of this study was to develop a technique for measuring spatial

resolution of tomosynthesis images The intrinsic artifacts from tomosynthesis

reconstructions however lead to uncharacteristic MTFs and possible misinterpretation

of the effective resolution information When considering previous techniques for

calculating the presampled MTF [713152328] the analysis was performed using an

edge or a line to produce the corresponding ESF The resolution information is

essentially contained only along the edge indicated by the need to calculate the LSF In a

way the method of extracting artifact information is to focus the analysis only on the

edge part of the ESF to calculate the modified MTF This will lead to a better

understanding of the limiting size of objects that may be seen in the reconstructed 3D

49

image The presampled MTF without correction should still be analyzed to understand

the entire system response Note that the ESFs attempt to reflect information only at the

detected edge of the sphere

II5 Conclusions

The directional MTF of a simulated breast tomosynthesis reconstruction was

determined by using the cone-based MTF technique demonstrating the feasibility of a

single phantom for MTF evaluation This study further presented methods of analyzing

only the edge information in the ESF to create a modified MTF along in-slice (x and y)

axes It can provide insight into the actual spatial resolution information contained in the

image while separating the resolution information from the information introduced by

artifacts caused by the reconstruction and insufficient volumetric sampling The idea of

separating the resolution and artifacts from the measured ESF are expected to facilitate

the interpretation of MTF measurements in breast tomosynthesis Similar methods may

be applied to characterize the resolution of other 3D imaging modalities

50

References

1 Garmer M Hannigs SP Jaumlger HJ et al ldquoDigital Radiography Versus

Conventional Radiology in Chest Imaging Diagnostic Performance of a Large-

Area Silicon Flat-Panel Detector in a Clinical CT-Controlled Studyrdquo American

Journal of Roentgenology Volume 74 75-80 (2000)

2 Cowen AR Kengyelics SM and Davies AG ldquoSolid-state flat-panel digital

radiography detectors and their physical imaging characteristics rdquoClinical

Radiology Volume 63 487-498 (2008)

3 Chotas HG Dobbins III JT and Ravin CE ldquoPrinciples of Digital

Radiography with Large-Area Electronically Readable Detectors A Review of

the Basicsrdquo Radiology Volume 210 Number 3 595-599 (1999)

4 Flynn MJ and Samei E Experimental comparison of noise and resolution for

2k and 4k storage phosphor radiography systems Medical Physics Volume 26

Number 8 1612-1623 (1999)

5 Rong XJ Shaw CC Liu X Lemacks MR and Thompson SK

ldquoComparison of an amorphous siliconcesium iodide flat-panel digital chest

radiography system with screenfilm and computed radiography systems ndash A

contrast-detail phantom studyrdquo Medical Physics Volume 28 Number 11 2328-

2335 (2001)

6 Ranger NT Samei E Dobbins III JT and Ravin CE Measurement of the

detective quantum efficiency in digital detectors consistent with the IEC 62220-1

standard Practical considerations regarding the choice of filter material

Medical Physics Volume 30 Number 7 2305-2311 (2005)

7 Samei E Buhr E Granfors P Vandenbroucke D and Wang X Comparison

of edge analysis techniques for the determination of the MTF of digital

radiographic systems Physics in Medicine and Biology Volume 50 3613-3625

(2005)

8 Samei E and Flynn MJ An experimental comparison of detector performance

for computed radiography systems Medical Physics Volume 29 Number 4 447-

459 (2002)

51

9 Samei E and Flynn MJ An experimental comparison of detector performance

for direct and indirect digital radiography systems Medical Physics Volume 30

Number 4 608-622 (2003)

10 Samei E Ranger NT MacKenzie A Honey ID Dobbins III JT and Ravin

CE Effective DQE (eDQE) and speed of digital radiographic systems An

experimental methodology Medical Physics Volume 36 Number 8 3806-3817

(2009)

11 Samei E Ranger NT MacKenzie A Honey ID Dobbins III JT and Ravin

CE Detector or System Extending the Concept of Detective Quantum

Efficiency to Characterize the Performance of Digital Radiographic Imaging

Systems Radiology Volume 249 Number 3 926-937 (2008)

12 ldquoIEC 62220-1 Medical Electrical Equipment ndash Characteristics of Digital X-Ray

Imaging Devices ndash Part 1 Determination of the Detective Quantum Efficiencyrdquo

International Electrotechnical Commission Geneva Switzerland (2003)

13 Samei E Ranger NT Dobbins III JT and Chen Y Intercomparison of

methods for image quality characterization I Modulation transfer function

Medical Physics Volume 33 Number 5 1454-1465 (2006)

14 Dobbins III JT Samei E Ranger NT and Chen Y Intercomparison of

methods for image quality characterization II Noise power spectrum Medical

Physics Volume 33 Number 5 1466-1475 (2006)

15 Samei E Flynn MJ and Reimann DA A method for measuring the

presampled MTF of digital radiographic systems using an edge test device

Medical Physics Volume 25 Number 1 102-113 (1998)

16 Nagel HD ldquoAluminum equivalence of materials used in diagnostic radiology

and its dependence on beam qualityrdquo Physics in Medicine and Biology Volume

31 Number 12 1381-1399 (1986)

17 Niklason LT Christian BT Niklason LE et al ldquoDigital Tomosynthesis in

Breast Imagingrdquo Radiology Volume 205 399-406 (1997)

18 Gur D ldquoTomosynthesis Potential Clinical Role in Breast Imagingrdquo American

Journal of Roentgenology Volume 189 614-615 (2007)

52

19 Park JM Franken Jr EA Garg M Fajardo LL and Niklason LT ldquoBreast

Tomosynthesis Present Considerations and Future Applicationsrdquo

RadioGraphics Volume 27 S231-S240 (2007)

20 Good WF Abrams GS Catullo VJ Chough DM Ganott MA Hakim

CM and Gur D ldquoDigital Breast Tomosynthesis A Pilot Observer Studyrdquo

American Journal of Roentgenology Volume 190 865-869 (2008)

21 Hu Y-H Zhao W Mertelmeier T and Ludwig J ldquoImage Artifact in Digital

Breast Tomosynthesis and Its Dependence on System and Reconstruction

Parametersrdquo IWDM 2008 LNCS 5116 628-634 (2008)

22 Chen Y Lo JY Ranger NT Samei E Dobbins III JT ldquoMethodology of

NEQ(f) analysis for optimization and comparison of digital breast tomosynthesis

acquisition techniques and reconstruction algorithmsrdquo Proceedings of SPIE

Volume 6510 65101I (2007)

23 Zhao B Zhou J Hu Y-H Mertelmeier T Ludwig J and Zhao W

ldquoExperimental validation of a three-dimensional linear system model for breast

tomosynthesisrdquo Medical Physics Volume 36 Number 1 240-251 (2009)

24 Madhav P Brzymialkiewicz CN Cutler SJ Bowsher JE and Tornai MP

ldquoCharacterizing the MTF in 3D for a Quantized SPECT Camera Having Arbitrary

Trajectoriesrdquo 2005 IEEE Nuclear Science Symposium Conference Record 1722-

1726 (2005)

25 Madhav P McKinley RL Samei E Bowsher JE and Tornai MP ldquoA Novel

Method to Characterize the MTF in 3D for Computed Mammotomographyrdquo

Proceedings of SPIE Volume 6142 61421Y (2006)

26 Hu Y-H Zhao B and Zhao W ldquoImage artifacts in digital breast

tomosynthesis Investigation of the effects of system geometry and

reconstruction parameters using a linear system approachrdquo Medical Physics

Volume 35 Number 12 5242-5252 (2008)

27 Seifert A and Flynn MJ ldquoResolving power of 3D x-ray microtomography

systemsrdquo Proceedings of SPIE Volume 4682 407-413 (2002)

28 Thornton MM and Flynn MJ Measurement of the spatial resolution of a

clinical volumetric computed tomography scanner using a sphere phantom

Proceedings of SPIE Volume 6142 61421Z (2006)

53

29 Baek J Pelc NJ ldquoUse of sphere phantoms to measure the 3D MTF of FDK

reconstructionsrdquo Proceedings of SPIE Volume 7961 79610D (2011)

30 Richard S and Samei E ldquoQuantitative imaging in breast tomosynthesis and CT

Comparison of detection and estimation task performancerdquo Medical Physics

Volume 37 Number 6 2627-2637 (2010)

31 Chen Y Lo JY and Dobbins III JT ldquoImpulse response analysis for several

digital tomosynthesis mammography reconstruction algorithmsrdquo Proceedings of

SPIE Volume 5745 541-549 (2005)

32 Zhao B and Zhao W ldquoThree-dimensional linear system analysis for breast

tomosynthesisrdquo Medical Physics Volume 35 Number 12 5219-5232 (2008)

33 Wu G Mainprize JG Boone JM and Yaffe MJ ldquoEvaluation of scatter

effects on image quality for breast tomosynthesisrdquo Medical Physics Volume 36

Number 10 4425-4432 (2009)

Page 26: Development and Evaluation of 2D and 3D Image Quality ...

13

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 5 MTF results by detector (columns) and beam quality (rows)

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm)

MTF

horiz

vert

horizontal

vertical

14

Figure 6 Plots of MTF for RQA5 (top) and RQA9 (bottom) showing the relationships

between detectors (blue red and green) and by filtration (solid and dashed)

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm-1)

MTF

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm-1)

MTF

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

15

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 7 NNPS results by detector (columns) and beam quality (rows)

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

05 mR - horizontal

05 mR - vertical

10 mR - horizontal

10 mR - vertical

20 mR - horizontal

20 mR - vertical

16

Figure 8 Plots of NNPS for RQA5 (top) and RQA9 (bottom) at 1 mR exposure

showing the relationships between detectors (blue red and green) and by filtration

(solid and dashed)

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm-1)

NNPS (1 mR)

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm-1)

NNPS (1 mR)

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

17

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 9 DQE results by detector (columns) and beam quality (rows)

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

05 mR - horizontal

05 mR - vertical

10 mR - horizontal

10 mR - vertical

20 mR - horizontal

20 mR - vertical

18

Figure 10 Plots of DQE for RQA5 (top) and RQA9 (bottom) at 1 mR exposure showing

the relationships between detectors (blue red and green) and by filtration (solid and

dashed)

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm-1)

DQE (1 mR)

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm-1)

DQE

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

19

higher frequencies the NNPS curves of the Pixium 4600 and DRX-1 diverge slightly for

the different directions illustrating increased noise in the readout direction (vertical)

Differences in the noise characteristics were more apparent among detectors as

shown for 1 mR in Figure 8 The NNPS curve for the DRX-1 was higher in magnitude

across the entire frequency range than either the Pixium 4600 or DRX-1C which both

seemed to demonstrate reasonably similar NNPS curves The higher magnitude noise of

the DRX-1 indicates higher relative noise content overall Closer inspection of the NNPS

curves of the Pixium 4600 and DRX-1C detectors in Figure 7 revealed differences in the

spacing between the three exposure levels The gaps between the Pixium 4600 NNPS

curves do not correspond to the factor of two differences between each exposure level

especially at low- to mid- spatial frequencies suggesting a higher level of fixed pattern

noise additional noise with increasing exposure levels due to ineffective gain map

corrections Between filtration schemes the differences in NNPS curves for a given beam

quality were not substantial as shown in Figure 7

I3v Detective Quantum Efficiency

The DQE results are shown in Figure 9 DQE curves across exposure levels were

almost collinear except for Pixium 4600 and in general could be inferred from the

NNPS results Additionally the DQE curves demonstrated a relatively linear response

with spatial frequencies as expected for flat-panel detectors [9] Differences in DQE

among detectors were consistent for the most part with the type of scintillating material

20

As depicted for 1 mR exposure in Figure 10 differences between Pixium 4600 and DRX-

1C DQE curves correspond to the differences in their NNPS curves DRX-1 DQE curves

were consistently lower than either the Pixium 4600 or DRX-1C curves The DQE curves

for the alternative filtration were consistently higher than those for the IEC filtration

and the most noticeable differences were near the zero-frequency axis These effects can

be both attributed to ineffective gain map correction DQE values for 1 mR exposure are

listed in Table 5

I4 Discussion

I4i Comparisons of Detectors

The limiting spatial resolutions of all three detectors were almost exactly the

same considering that their pixel areas were similar in size The decrease in high-

frequency MTF of the DRX-1 compared to the other detectors is probably a result of

increased optical blurring due to the differences in the powdered structure of GOS

versus the needle-like structure of CsI [2] The fact that the DRX-1C and Pixium 4600

have comparable MTFs suggests similar scintillator thicknesses assuming that the

materials were processed alike

The noise of the three detectors demonstrated similar trends with each other The

higher NNPS curves of the DRX-1 detector are probably due also to the scintillating

material and its operation in converting photons into signal The conversion process is

less efficient because of the less favorable stopping power of the GOS compared to CsI

21

especially with higher energy beams The noise of the Pixium 4600 and DRX-1C were

similar except for the spacing between exposures The DRX-1C NNPS curve spacing is

consistent with a factor of two difference in exposure levels but the Pixium 4600 has a

smaller spacing The 05 mR NNPS curve of the Pixium 4600 is closer to that of the 05

mR NNPS curve of the DRX-1C This demonstrates that at higher exposures the Pixium

4600 produces a larger amount of additional noise beyond that explained by simple

stochastic effects It suggests bad performance in the gain map corrections

The DQE results indicate SNR properties of each detector The Pixium 4600 and

DRX-1C are comparable for the most part with the DRX-1C performing slightly better

The DRX-1 as predicted from MTF and NNPS results has a DQE much lower than

either of the previous two This is a reflection of the detection properties as provided by

its scintillator material The DQE of the DRX-1 however is comparable to CR image

receptors [2] The mid-frequency dips in the DQE for Pixium 4600 may be due to the

optical properties of the CsI phosphor layer which can affect the MTF in this manner

Because the DQE is calculated by squaring the MTF this effect at the mid-range

frequencies becomes more apparent The dips may also be further evidence of bad gain

map corrections

I4ii Comparisons of Filtrations

The alternative filtration closely matches for the most part the IEC-based

filtration for MTF NNPS and DQEs at RQA5 but not at RQA9 The filters do not have

22

Table 4 Experimental MTF frequency locations for 1 mR exposure

Detector Filtration

50 MTF

(mm-1)

40 MTF

(mm-1)

30 MTF

(mm-1)

20 MTF

(mm-1)

10 MTF

(mm-1)

Pixium

4600

RQA5A 115 145 185 245 330

RQA5C 125 155 195 250 345

RQA9A 110 175 175 235 330

RQA9C 125 155 195 255 345

DRX-1C

RQA5A 120 150 185 245 350

RQA5C 125 155 195 255 355

RQA9A 120 150 190 250 355

RQA9C 130 160 210 265 360

DRX-1

RQA5A 110 135 160 205 280

RQA5C 110 135 170 210 285

RQA9A 105 125 155 195 270

RQA9C 110 135 165 210 285

Table 5 Estimated DQE values for 1 mR exposure by frequency bins

Detector Filtration DQE(00 mm-1) DQE(10 mm-1) DQE(20 mm-1) DQE(30 mm-1)

Pixium

4600

RQA5A 62 42 32 21

RQA5C 63 45 36 25

RQA9A 41 27 30 13

RQA9C 43 33 27 19

DRX-1C

RQA5A 72 52 35 21

RQA5C 76 55 41 24

RQA9A 49 33 23 15

RQA9C 51 40 31 20

DRX-1

RQA5A 38 24 12 4

RQA5C 38 25 14 5

RQA9A 28 18 9 4

RQA9C 28 19 12 5

DQE values at the zero-frequency axis were estimated by the intercept of a linear fit of low-frequency data

but excluding most proximal to the axis due to large fluctuations Other estimated values are grouped into

frequency bins due to the noisiness of the data

23

considerable differences in the spatial resolutions of the detectors as expected The noise

responses for each filtration were also similar except at the lower frequencies of the

NNPS especially near the zero-frequency axis There observing the NNPS responses at

RQA5 for Pixium 4600 and DRX-1C in Figure 8 the NNPS for the IEC-based filtration

(solid lines) tend to drop faster than the NNPS for the alternative filtration This

subsequently appears as a drop in DQE near the zero-frequency axis shown for those

detectors in Figure 10 Overall as indicated in Table 5 the DQEs of the two filtrations

while similar in trend indicate that the alternative filtration increases the DQE by a

small amount of 3-5 Part of this may be explained by the slightly higher beam

energy which may be more optimal for the energy response of the detectors or may

weigh the pixel responses slightly considering that they are energy-integrating types

The most probable explanation is the gain map correction for the alternative filtration

where fixed pattern noise is more sufficiently reduced

A previous study [6] had discussed the choice of filter material in the analysis of

DQE when achieving the beam conditions defined by IEC It found that visible

nonuniformities were present with the higher purity aluminum filter (type-11999 alloy)

The low frequency mottle in the flat-field images for NPS measurements were also

attributed to structured noise from the grain size in the IEC-based filter with an

attenuating thickness that would reveal nonuniformities The mottle in the current study

was only observable under very narrow windowing as shown in Figure 11 Such low

24

frequency artifacts which are not readily noticeable may also be caused by shading

artifacts inverse square law or even the heel effect A possible method to correct for this

is a subtraction method by taking the average of the flat-field images for an exposure

level and then subtracting that from each of them This would remove nonuniformities

that were not corrected using a suboptimal gain map calibration

Figure 11 DRX1-C NNPS images at 1 mR for RQA5 with IEC filtration (left) and

alternative filtration (right) Images are equally windowed at 45 and leveled at 980

One convenient aspect of the copper and aluminum filtration is that it requires

much less tube current to achieve the same amount of exposure at the detector than the

much thicker aluminum filtration As shown in the non-normalized spectra in Figure 2

the exiting photon fluence exiting the copper and aluminum filtration is substantially

higher than that of the IEC-specified filtration This is due to the smaller total filtration

25

attenuation For extensive DQE analysis multiple sets of exposures may be acquired

before tube overheating becomes a concern

One limitation to the comparison of the two filtrations is that calibration

procedures specified copper and aluminum filtration at 80 kVp (for all detectors 05 mm

Cu and 10 mm Al) This may have influenced the results in favor of the alternative

filtration A further investigation involving the calibration procedures and performing

DQE measurements is encouraged Another factor may be influenced by the fact that the

tests were performed at 70 kVp and 120 kVp different from the recommended

calibration tube potential Clearly there would be differences in the linear attenuation

coefficients of the filters and different energy responses of the detectors themselves This

must be considered when interpreting DQE results The current results support a

previous study decades ago that described filtration of different material types in terms

of an aluminum equivalent [16] The results show that the two filtration schemes are

essentially equivalent when considering beam qualities and spatial resolutions The

NNPS and DQE results can be seen as close enough where their small differences are

insignificant when performing quality assurance tests in a clinical setting Overall our

results indicate that the alternative filtration with copper and aluminum may be more

convenient to use than the current IEC standard filtration

26

I4iii Implications of Wireless DR

This study has shown that wireless image receptors can have the same DQE

performance if not better than conventional flat-panel detectors They operate on the

same basic physical principles the new features offered by the DRX-1C and DRX-1 are

wireless communication with the workstation and electronics packaging technology

The latter feature may pose limitations for these units in terms of possible degradation

in the detectors in routine clinical conditions A consideration for future work would be

to longitudinally track DQE performance of the wireless detectors over time while being

utilized in a clinical environment In the end one must consider risks versus benefits of

choosing portable DR technology over CR one of which includes the cost and fragility

of DR detectors

The DQE performance of one wireless system is just as good as or better than

conventional systems as seen by the DRX-1C performance compared to the Pixium

4600 Wireless systems can also reduce the need for CR readers especially in portable

applications in other regions of the world (eg military hospitals developing countries)

However while DQE performance indicates the physical performance of the detector

system it is still unknown how it relates to observer performance

I5 Conclusions

Two wireless image receptors DRX-1C and DRX-1 were evaluated and

compared with the conventional DR flat-panel Pixium 4600 in terms of DQE

27

performance along with MTF and NNPS performances The detectors have similar

resolution properties although the DRX-1 is inferior at higher spatial frequencies The

NNPS and DQE results both indicate that the DRX-1C is superior to the DRX-1 and

comparable if not better to the Pixium 4600

The results from the filtration comparison indicate no substantial differences

between the IEC-based filtration and the copper-based alternative filtration Only slight

differences were found in the low frequency components of the NNPS and the DQE due

to the inherent nonuniformities of the IEC specified filtration Given the similarity of the

results and low attenuation advantage of the copper and aluminum filter its use is

encouraged

28

II Directional MTF for Breast Tomosynthesis

II1 Introduction

Breast tomosynthesis is an emerging 3D imaging modality that has potential use

for screening and diagnosis of breast cancer Breast tomosynthesis along with other 3D

techniques is preferable to planar imaging methods (eg mammography) because they

reduce anatomical noise by removing overlying structures above and below the plane of

an image slice [17-20] Recent advances in detectors and computer technology have

made digital tomosynthesis feasible

An image quality metric of particular importance in breast tomosynthesis is

spatial resolution Resolution is important to know in order to assess small-detail

structures such as microcalcifications A descriptive metric for characterizing spatial

resolution in the Fourier (or frequency) domain is the modulation transfer function

(MTF) Affected by reconstruction filters [21] the limited angular projections involved in

breast tomosynthesis results in highly anisotropic (or nonuniform) resolution Many

studies have looked only at characterizing the in-plane spatial resolution (ie in an

individual slice) with an elevated angled edge phantom [2223] A few studies have

looked at characterizing a more comprehensive 3D spatial resolution by using a

phantom with angled wires or tubes [24-26] However such studies require precise

mechanical alignment of the phantoms Several studies have explored a method using a

29

sphere phantom for the directional 3D MTF evaluation for microtomography [27] and

multi-slice CT [2829] This method has not yet been extended to breast tomosynthesis

This chapter focuses on breast tomosynthesis because it is highly anisotropic in

spatial resolution and like its predecessor mammography requires high spatial

resolution Additionally breast tomosynthesis acquisitions and reconstructions produce

several types of artifacts The use of a cone-based method using a sphere phantom [28] is

explored to characterize the directional 3D spatial resolution of simulated images from

breast tomosynthesis A technique for removing out-of-plane artifacts of the ESFs for the

in-plane axes is investigated to yield a modified MTF in a method that separates artifact

information from resolution information

II2 Materials and Methods

II2i Image Simulation

Breast tomosynthesis images were simulated by using a virtual imaging system

depicted in Figure 12 A volumetric breast phantom was voxelized as a rectangular mass

of uniform breast equivalent tissue of 4 cm thickness embedded with fifteen evenly

spaced plastic sphere inserts of 12 mm diameter The spheres were placed in a grid

formation within the central plane of the phantom The x-ray fluence was modeled from

a 28 kVp beam incident upon an indirect flat-panel detector with 200 micro m pixel size

Twenty-three projections within an angular range of 44deg were simulated using cascaded

systems analysis to generate characteristic 2D noise and spatial blurring [29] Each

30

projection was simulated to have an exposure of 174 mR with a fluence of 79 times 105

photonsmm-2 A standard filtered backprojection technique based on the Feldkamp

reconstruction algorithm [29] was used to reconstruct the projections and produce a

volumetric dataset with an isotropic voxel size of 200 micro m

Figure 12 Depiction of the virtual image system

II2ii Uncorrected MTF

To enable comparison of multiple spheres the reconstructed volume was

initially homogenized by performing a background subtraction based on a portion of the

volume devoid of spheres The voxel values were rescaled between one and zero to

eliminate negative values

31

The volumetric data were segmented to extract individual regions of interest

(ROIs) each containing a single sphere The ROIs extended along the full range of the z-

axis A thresholded ROI was generated by determining the exterior and interior voxels

relative to the sphere in the ROI The threshold value was set at 45 of the maximum

voxel value prior to thresholding The exterior and interior voxel values were then set to

values of 0 and 1 respectively Using the thresholded volume the center of mass was

calculated to determine the centroid The voxel values from the original ROI were

subsequently tabulated with the associated distances azimuthal angles and polar

angles relative to the centroid

Conical regions were prescribed along the positive and negative directions along

the three major axes extending from the centroid of the sphere as depicted in Figure 13

The axes about which the extent of the cone angle was delineated were defined with

the azimuthal and polar angles

Voxels with centers within the angular range of the cone were considered for

generating the edge spread function (ESF) To improve regularity of the distance

sampling interval the ESF values were rebinned to discrete distances corresponding to a

fraction of the voxel size Only voxels with distances ranging from the voxel size (ie

200 micro m) to the maximum distance were considered The ESFs from multiple spheres

were averaged together for each of the three major axes to produce an averaged ESF

which was further smoothed utilizing a Gaussian filter

32

Figure 13 Example of 30-degree cone prescribed along z axis of the sphere

The resulting ESF was then differentiated using the central difference method to

produce the line spread function (LSF) A Hanning filter with the same length as the LSF

was applied to zero out the tails of the LSF The presampled MTF was subsequently

computed as the amplitude of the Fourier transform of the LSF The MTF was

normalized with respect to the maximum value occurring within the range of the cutoff

frequency Binning size and conical range for the ESF were considered for maximizing

accuracy and minimizing noise of the MTF verified by comparison against the

theoretical MTF as determined in the previous section

II2iii Theoretical Directional MTF

The theoretical 3D MTF was calculated using a priori knowledge of the transfer

function of the virtual imaging system described in the previous section A phantom

was created with a set of point objects in a uniform and noise-free background with the

objects spanning across the volume of the breast [29] Twenty-one realizations were

33

generated from the reconstructed images of the point objects to yield a set of 3D point

spread functions (PSFs) The 3D fast Fourier transform (FFT) was performed for each 3D

PSF and averaged to give an ldquoexpectationrdquo 3D MTF [29] The theoretical directional

MTFs in the three major spatial axes were determined by line profiles along each of the

corresponding spatial frequency axes in the 3D MTF An additional theoretical MTF for

each direction was determined by using the application of conical regions along the axes

in frequency-space to take into account the contributions of MTF information from other

planes

II2iv Modified MTF

The tomosynthesis reconstruction is known to have edge enhancements which

affect the overall MTF by shifting the peaks of the MTF toward the higher frequencies

[23] The presence of this artifact complicates the interpretation of the actual spatial

resolution of the images Several steps were performed to remove the artifact

contribution to the resolution information particularly for the in-plane x and y

directions with the assumption that resolution information was contained immediately

near the edge

For the x-direction averaged ESF only values that were detected to be inside the

edge of the sphere were considered Those values were previously determined via

thresholding for calculating the centroid The ESF information corresponding to these

values was inversed and flipped about the detected edge to produce a symmetric

34

modified ESF The modified MTF was subsequently calculated from this modified ESF

as described in the previous section

For the y-direction averaged ESF an upward trend was found in the initial part

of the ESF This section was detrended with a polynomial fit and subtracted to produce a

flatter curve in that region The resulting detrended ESF was used to calculate the y axis

modified MTF

Figure 14 Photograph of the imaging system with the acrylic sphere phantom

embedded in oil

II2v Preliminary Experimental Validation

A clinical breast tomosynthesis system (Mammomat Inspiration Siemens AG

Munich Germany) was used to perform a preliminary evaluation of the cone-based

MTF technique The phantom for the experiment consisted of a single acrylic ball of 075

in diameter (SmallParts Seattle WA) suspended by a 0029 in diameter plastic filament

35

(Omniflex Zebco Tulsa OK) in an acrylic frame filled up to 4 in with vegetable oil

(Target Brands Inc Minneapolis MN) The system and phantom are shown in Figure

14 Twenty-five projections with an angular range of 44deg were acquired and subsequently

reconstructed to produce a volume with a voxel size of 01times01times10 mm3 The voxels were

reformatted to have an isotropic size of 01 mm The uncorrected ESF LSF and MTF

were calculated as described in the previous section

II3 Results

II3i Reconstruction

The reconstructed volume is shown in Figure 15 Notice the edge enhancement

along the x-direction as indicated by the sharp shadowing artifacts on either side of the

spheres The background was effectively homogenized using the background

subtraction technique This also took account of the curved edges of the breast phantom

With the close spacing of the spheres in the phantom the shadows along the x direction

for the fifteen spheres overlap with each other As the nine centrally located spheres

experience this effect the same way they were used for determining the ESF

A 3D rendering of the ROI containing a sphere shown in Figure 16 indicates the

anisotropic resolution of the reconstruction Note that the sphere is not accurately

reconstructed and has an oblong shape especially along the z axis Cross sectional views

of the ROI also in Figure 16 clearly demonstrate the edge enhancement causing a

shadow artifact in the x direction caused by the incomplete angular sampling of

36

tomosynthesis The sampling also introduces the triangular reconstruction of the sphere

as seen in the x-z plane Note the gradual edge drop-off in the z direction much beyond

the sphere radius

Figure 15 View of the central slice of the breast phantom reconstruction before (top)

and after (bottom) background subtraction The z axis is through the page

37

Figure 16 3D rendering of the ROI volume (left) and cross-sectional views of the most

centrally located sphere with centroid indicated with red circle (right)

II3ii Theoretical MTF

The theoretical MTFs for x y and z directions as determined from the line

profiles of the 3D MTF are shown in Figure 17 The theoretical MTF in the x direction

has a maximum value that is toward higher frequencies Its 10 response occurs at

about 125 cyclesmm which is at 50 of the cutoff frequency The rapid increase from

the zero-frequency intercept to the peak corresponds to the ramp filter used in filtered

backprojection which decreases the weighting of low frequency contributions due to the

incomplete angular sampling of the frequency-space The MTF does not reach a value of

0 at the zero-frequency intercept as it is very difficult to assess the zero-frequency

intercept due to the finite size of the phantom The theoretical MTF in the y direction

peaks at the zero-frequency intercept and reaches 20 proximal to the cutoff frequency

38

The 10 MTF is well beyond the cutoff frequency The theoretical MTF in the z direction

has a rapid drop-off at very low spatial frequencies indicating the lack of resolution in

that dimension

Figure 17 Theoretical 3D MTF results along the three major planes (top) and along x

y and z directions (bottom) Also note that the angular spread seen in the fx-fz plane is

equal to the angular range of 44deg for the acquisition

II3iii Uncorrected MTF

The ESF LSF and MTF using the cone-based method are shown for the x y and

z directions in Figure 18 It was found that a bin size of one-tenth the voxel size (002

mm) and a cone angle of 30deg to establish the ESF were enough to minimize noise and

maximize accuracy in the uncorrected MTFs considering the reasonable comparison of

the shapes of the MTF curves with the theoretical results in Figure 17 The LSFs are

generally noisy because differentiation of the ESF increases the amplitude of the noise

39

The data shown reflect a convolution with a smoothing Gaussian filter which was later

further corrected for in the reported MTF Nevertheless the high frequency components

of the noise are well beyond the MTF cutoff frequency of 25 cyclesmm and do not

impact the MTF results greatly

For the ESF in the x direction the shadow effect evident at the edge of the sphere

is visible as a steep decline followed by an increase Due to the finite distance range

provided by the ROI the ESF beyond the edge did not asymptotically reach the

background value The corresponding LSF demonstrates a low frequency modulation

that is indicated by the shift of 03 cyclesmm in the x direction for the peak of the MTF

The MTF exhibits a zero-frequency intercept that is non-zero unlike the theoretical MTF

and a 10 value at approximately 1 cyclesmm These features may be a direct

consequence of MTF information ldquocontaminationrdquo from y and z directions Furthermore

the ESF in the y direction demonstrates a reasonably shaped curve except for the slight

upward trend within the radius of the sphere which can be attributed to the shadow

artifact overlapping with the sphere volume The associated MTF has a peak shifted by

approximately 01 cyclesmm away from the axis and a 10 MTF occurring at

approximately 15 cyclesmm Both features which are not present in the theoretical

results may also be attributed to contaminant MTF information from x and z directions

The ESF in the z direction has a drop-off that occurs at a small fraction of the cutoff

frequency similar to that demonstrated by the theoretical MTF

40

Uncorrected ESF LSF and MTF

Figure 18 Uncorrected ESF (top) LSF (middle) and MTF (bottom) for x y and z

directions

41

Figure 19 Comparisons of the directional MTFs as calculated by the sphere method

(dashed line) by theoretical line profiles (light-weight line) by theoretical cone

regions (heavy-weight line)

II3iv Comparison of Theoretical and Simulated MTFs

The theoretical MTF results obtained from line profiles through the 3D MTF and

the simulated MTFs using the cone-based technique did not match very well except for

the general shape of the curves It was assumed in the previous section that the cone-

based technique contains information from other planes Figure 19 compares MTFs in

each direction for the two methods described in the methods and an additional method

based on conical regions of the 3D MTF The latter computes the MTF by averaging

contributions of the 3D MTF using the same cone prescription method used to define the

ESFs Comparison of the curves indicate some interesting correlations aside from the

fact that using conical regions with the 3D MTF results produce more noisy MTF results

partly due to the low sampling provided by the theoretical calculations The same

conclusions regarding the z direction MTF can be confirmed regardless of either

theoretical MTF procedures The experimental x direction MTF seems to agree best with

42

the line profile method whereas the y direction MTF agrees better with the cone region

method The fact that the experimental x direction MTF has a drop-off frequency that is

lower than those of either of the theoretical MTFs in Figure 19 suggests that this might

be due to integration of the z-direction in the in-plane slices considering how slices are

essentially averages of z direction information contained within it [33]

II3v Modified MTF for x and y

Modified ESF LSF and MTF curves for x and y directions are shown in Figure

20 The modified ESF and the resulting LSF in the x direction appear symmetric as

expected from the inverse and flip operation of the interior ESF about the detected edge

The modified MTF appears with less variation than the uncorrected MTF and the MTF

peak occurs at the zero-frequency axis The correction yields a 10 MTF at about 15

cyclesmm an improvement from the uncorrected MTF but still distant from the cutoff

frequency The modified ESF in the y direction demonstrates the detrended curve within

the sphere radius after a quadratic polynomial fit The resulting modified MTF still

appears similar to the uncorrected MTF except that the peak now coincides with the

zero-frequency axis For both x and y directions the low response of the modified MTFs

at the higher frequencies suggests that the contamination from other directions is

substantial due to the angular range of the cone

43

Modified ESF LSF and MTF

Figure 20 Modified ESF (top) LSF (middle) and MTF (bottom) for x and y directions

44

II3v Preliminary Experimental Validation

Cross-sections of the reconstructed sphere volume are shown in Figure 21

Relative to the simulation reconstructions the reconstructions of the experimental

phantom images produce lower contrast and higher noise The preliminary results

shown in Figure 22 indicate that our technique can be applied to actual experimental

breast tomosynthesis reconstructions However due to the noise exhibited by the MTF

curves for the x and y directions we did not determine the modified MTFs to separate

resolution and artifact information

Figure 21 Cross sectional views of the experimental sphere image with centroid

indicated with red circle

45

Uncorrected ESF LSF and MTF for Real Image

Figure 22 ESF (top) LSF (middle) and MTF (bottom) of real image for x y

and z directions

46

II4 Discussion

II4i Evaluation of Cone-based Method

The cone-based MTF technique was introduced by Thornton and Flynn [28] for

evaluation of volumetric CT images To utilize this technique as a characterization of a

3D system spatial resolution one must first consider the validity of the assumption of

shift invariance such that the same MTF result may be obtained regardless of the

location of the sphere The study by Zhao et al [23] found that there was no shift

variance for the MTF measurements along the vertical axis but this was only considering

the in-plane resolution along one axis On the other hand this study evaluated the MTF

with images simulated with cascaded systems analysis which includes conditions of

linearity and shift invariance Additionally the MTF was calculated by averaging the

ESF from several spheres in the same volume only after performing a background

subtraction This step was essential to account for the sensitivity of centroid calculations

as well as ensuring symmetric ESFs for opposing axes of the sphere ROIs

The measurement of MTF with the cone-based technique inherently

supersamples the edge of the sphere to increase signal-to-noise-ratio (SNR) of edge

information by averaging the contributions of each voxel to the ESF [713] This method

also takes into account the discrete sampling of the voxels by accounting for various

shifts of the edge in the voxel (also known as the partial volume effect) However using

the curved surface of the sphere phantom to approximate an edge along a given

47

direction naturally leads to contamination of information from other directions aside

from the one of interest Preferably a directional ESF should be created by using a single

radial line but this would limit the available voxels to obtain edge information An ideal

situation theoretically would be to use a larger-sized sphere such that the surface is

nearly flat and perpendicular to the axes of interest This would also permit a reduction

in the angular range of the cone and thus the introduction of out-of-plane information in

the resulting MTF However sphere size is a limitation in breast tomosynthesis and the

use of a large phantom might void the assumption of shift invariance of the spatial

resolution

The choice of a sphere phantom nevertheless may be based on the clinical need

to quickly acquire a single image for MTF evaluation especially for multiple directions

without presenting extra logistical challenges The use of a wire or edge phantom

requires more precise mechanical alignment to achieve the correct set up The edge

phantom [23] would require at least two images to sample all three dimensions In the

case of the three wire phantom [2425] all three dimensions of the frame must be aligned

simultaneously with respect to the axis of rotation A similar situation would be

encountered when considering a cubic phantom with the planes normal to the axis of

interest In contrast to these phantoms the sphere eliminates the need for precise

alignment especially with respect to three spatial dimensions simultaneously A sphere

48

has ideal symmetry in all directions and can be used to evaluate MTF in any arbitrary

direction

This study unlike others [242532] did not explore the effects of physical

parameters such as scatter or contrast on the final MTF result but it demonstrated the

feasibility of using the cone-based method with an actual breast tomosynthesis image of

a sphere phantom as shown in Error Reference source not found and Error Reference

source not found These effects should be addressed in future works A further look

into deriving the principles of comparing the theoretical MTF with the experimental

MTF using the cone-based method is further warranted

II4ii Separation of Artifact and Resolution Information

The focus of this study was to develop a technique for measuring spatial

resolution of tomosynthesis images The intrinsic artifacts from tomosynthesis

reconstructions however lead to uncharacteristic MTFs and possible misinterpretation

of the effective resolution information When considering previous techniques for

calculating the presampled MTF [713152328] the analysis was performed using an

edge or a line to produce the corresponding ESF The resolution information is

essentially contained only along the edge indicated by the need to calculate the LSF In a

way the method of extracting artifact information is to focus the analysis only on the

edge part of the ESF to calculate the modified MTF This will lead to a better

understanding of the limiting size of objects that may be seen in the reconstructed 3D

49

image The presampled MTF without correction should still be analyzed to understand

the entire system response Note that the ESFs attempt to reflect information only at the

detected edge of the sphere

II5 Conclusions

The directional MTF of a simulated breast tomosynthesis reconstruction was

determined by using the cone-based MTF technique demonstrating the feasibility of a

single phantom for MTF evaluation This study further presented methods of analyzing

only the edge information in the ESF to create a modified MTF along in-slice (x and y)

axes It can provide insight into the actual spatial resolution information contained in the

image while separating the resolution information from the information introduced by

artifacts caused by the reconstruction and insufficient volumetric sampling The idea of

separating the resolution and artifacts from the measured ESF are expected to facilitate

the interpretation of MTF measurements in breast tomosynthesis Similar methods may

be applied to characterize the resolution of other 3D imaging modalities

50

References

1 Garmer M Hannigs SP Jaumlger HJ et al ldquoDigital Radiography Versus

Conventional Radiology in Chest Imaging Diagnostic Performance of a Large-

Area Silicon Flat-Panel Detector in a Clinical CT-Controlled Studyrdquo American

Journal of Roentgenology Volume 74 75-80 (2000)

2 Cowen AR Kengyelics SM and Davies AG ldquoSolid-state flat-panel digital

radiography detectors and their physical imaging characteristics rdquoClinical

Radiology Volume 63 487-498 (2008)

3 Chotas HG Dobbins III JT and Ravin CE ldquoPrinciples of Digital

Radiography with Large-Area Electronically Readable Detectors A Review of

the Basicsrdquo Radiology Volume 210 Number 3 595-599 (1999)

4 Flynn MJ and Samei E Experimental comparison of noise and resolution for

2k and 4k storage phosphor radiography systems Medical Physics Volume 26

Number 8 1612-1623 (1999)

5 Rong XJ Shaw CC Liu X Lemacks MR and Thompson SK

ldquoComparison of an amorphous siliconcesium iodide flat-panel digital chest

radiography system with screenfilm and computed radiography systems ndash A

contrast-detail phantom studyrdquo Medical Physics Volume 28 Number 11 2328-

2335 (2001)

6 Ranger NT Samei E Dobbins III JT and Ravin CE Measurement of the

detective quantum efficiency in digital detectors consistent with the IEC 62220-1

standard Practical considerations regarding the choice of filter material

Medical Physics Volume 30 Number 7 2305-2311 (2005)

7 Samei E Buhr E Granfors P Vandenbroucke D and Wang X Comparison

of edge analysis techniques for the determination of the MTF of digital

radiographic systems Physics in Medicine and Biology Volume 50 3613-3625

(2005)

8 Samei E and Flynn MJ An experimental comparison of detector performance

for computed radiography systems Medical Physics Volume 29 Number 4 447-

459 (2002)

51

9 Samei E and Flynn MJ An experimental comparison of detector performance

for direct and indirect digital radiography systems Medical Physics Volume 30

Number 4 608-622 (2003)

10 Samei E Ranger NT MacKenzie A Honey ID Dobbins III JT and Ravin

CE Effective DQE (eDQE) and speed of digital radiographic systems An

experimental methodology Medical Physics Volume 36 Number 8 3806-3817

(2009)

11 Samei E Ranger NT MacKenzie A Honey ID Dobbins III JT and Ravin

CE Detector or System Extending the Concept of Detective Quantum

Efficiency to Characterize the Performance of Digital Radiographic Imaging

Systems Radiology Volume 249 Number 3 926-937 (2008)

12 ldquoIEC 62220-1 Medical Electrical Equipment ndash Characteristics of Digital X-Ray

Imaging Devices ndash Part 1 Determination of the Detective Quantum Efficiencyrdquo

International Electrotechnical Commission Geneva Switzerland (2003)

13 Samei E Ranger NT Dobbins III JT and Chen Y Intercomparison of

methods for image quality characterization I Modulation transfer function

Medical Physics Volume 33 Number 5 1454-1465 (2006)

14 Dobbins III JT Samei E Ranger NT and Chen Y Intercomparison of

methods for image quality characterization II Noise power spectrum Medical

Physics Volume 33 Number 5 1466-1475 (2006)

15 Samei E Flynn MJ and Reimann DA A method for measuring the

presampled MTF of digital radiographic systems using an edge test device

Medical Physics Volume 25 Number 1 102-113 (1998)

16 Nagel HD ldquoAluminum equivalence of materials used in diagnostic radiology

and its dependence on beam qualityrdquo Physics in Medicine and Biology Volume

31 Number 12 1381-1399 (1986)

17 Niklason LT Christian BT Niklason LE et al ldquoDigital Tomosynthesis in

Breast Imagingrdquo Radiology Volume 205 399-406 (1997)

18 Gur D ldquoTomosynthesis Potential Clinical Role in Breast Imagingrdquo American

Journal of Roentgenology Volume 189 614-615 (2007)

52

19 Park JM Franken Jr EA Garg M Fajardo LL and Niklason LT ldquoBreast

Tomosynthesis Present Considerations and Future Applicationsrdquo

RadioGraphics Volume 27 S231-S240 (2007)

20 Good WF Abrams GS Catullo VJ Chough DM Ganott MA Hakim

CM and Gur D ldquoDigital Breast Tomosynthesis A Pilot Observer Studyrdquo

American Journal of Roentgenology Volume 190 865-869 (2008)

21 Hu Y-H Zhao W Mertelmeier T and Ludwig J ldquoImage Artifact in Digital

Breast Tomosynthesis and Its Dependence on System and Reconstruction

Parametersrdquo IWDM 2008 LNCS 5116 628-634 (2008)

22 Chen Y Lo JY Ranger NT Samei E Dobbins III JT ldquoMethodology of

NEQ(f) analysis for optimization and comparison of digital breast tomosynthesis

acquisition techniques and reconstruction algorithmsrdquo Proceedings of SPIE

Volume 6510 65101I (2007)

23 Zhao B Zhou J Hu Y-H Mertelmeier T Ludwig J and Zhao W

ldquoExperimental validation of a three-dimensional linear system model for breast

tomosynthesisrdquo Medical Physics Volume 36 Number 1 240-251 (2009)

24 Madhav P Brzymialkiewicz CN Cutler SJ Bowsher JE and Tornai MP

ldquoCharacterizing the MTF in 3D for a Quantized SPECT Camera Having Arbitrary

Trajectoriesrdquo 2005 IEEE Nuclear Science Symposium Conference Record 1722-

1726 (2005)

25 Madhav P McKinley RL Samei E Bowsher JE and Tornai MP ldquoA Novel

Method to Characterize the MTF in 3D for Computed Mammotomographyrdquo

Proceedings of SPIE Volume 6142 61421Y (2006)

26 Hu Y-H Zhao B and Zhao W ldquoImage artifacts in digital breast

tomosynthesis Investigation of the effects of system geometry and

reconstruction parameters using a linear system approachrdquo Medical Physics

Volume 35 Number 12 5242-5252 (2008)

27 Seifert A and Flynn MJ ldquoResolving power of 3D x-ray microtomography

systemsrdquo Proceedings of SPIE Volume 4682 407-413 (2002)

28 Thornton MM and Flynn MJ Measurement of the spatial resolution of a

clinical volumetric computed tomography scanner using a sphere phantom

Proceedings of SPIE Volume 6142 61421Z (2006)

53

29 Baek J Pelc NJ ldquoUse of sphere phantoms to measure the 3D MTF of FDK

reconstructionsrdquo Proceedings of SPIE Volume 7961 79610D (2011)

30 Richard S and Samei E ldquoQuantitative imaging in breast tomosynthesis and CT

Comparison of detection and estimation task performancerdquo Medical Physics

Volume 37 Number 6 2627-2637 (2010)

31 Chen Y Lo JY and Dobbins III JT ldquoImpulse response analysis for several

digital tomosynthesis mammography reconstruction algorithmsrdquo Proceedings of

SPIE Volume 5745 541-549 (2005)

32 Zhao B and Zhao W ldquoThree-dimensional linear system analysis for breast

tomosynthesisrdquo Medical Physics Volume 35 Number 12 5219-5232 (2008)

33 Wu G Mainprize JG Boone JM and Yaffe MJ ldquoEvaluation of scatter

effects on image quality for breast tomosynthesisrdquo Medical Physics Volume 36

Number 10 4425-4432 (2009)

Page 27: Development and Evaluation of 2D and 3D Image Quality ...

14

Figure 6 Plots of MTF for RQA5 (top) and RQA9 (bottom) showing the relationships

between detectors (blue red and green) and by filtration (solid and dashed)

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm-1)

MTF

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

00

01

02

03

04

05

06

07

08

09

10

00 05 10 15 20 25 30 35

MTF

Spatial Freq (mm-1)

MTF

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

15

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 7 NNPS results by detector (columns) and beam quality (rows)

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm)

NNPS

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

05 mR - horizontal

05 mR - vertical

10 mR - horizontal

10 mR - vertical

20 mR - horizontal

20 mR - vertical

16

Figure 8 Plots of NNPS for RQA5 (top) and RQA9 (bottom) at 1 mR exposure

showing the relationships between detectors (blue red and green) and by filtration

(solid and dashed)

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm-1)

NNPS (1 mR)

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

1E-7

1E-6

1E-5

1E-4

00 05 10 15 20 25 30 35

NNPS

Spatial Freq (mm-1)

NNPS (1 mR)

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

17

Pixium 4600 DRX-1C DRX-1 R

QA

5A

RQ

A5C

RQ

A9A

RQ

A9C

Figure 9 DQE results by detector (columns) and beam quality (rows)

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm)

DQE

enl0-h

enl0-v

enl1-h

enl1-v

enl2-h

enl2-v

05 mR - horizontal

05 mR - vertical

10 mR - horizontal

10 mR - vertical

20 mR - horizontal

20 mR - vertical

18

Figure 10 Plots of DQE for RQA5 (top) and RQA9 (bottom) at 1 mR exposure showing

the relationships between detectors (blue red and green) and by filtration (solid and

dashed)

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm-1)

DQE (1 mR)

RQA5A-Pixium

RQA5C-Pixium

RQA5A-DRX-1C

RQA5C-DRX-1C

RQA5A-DRX-1

RQA5C-DRX-1

00

01

02

03

04

05

06

07

08

00 05 10 15 20 25 30 35

DQE

Spatial Freq (mm-1)

DQE

RQA9A-Pixium

RQA9C-Pixium

RQA9A-DRX-1C

RQA9C-DRX-1C

RQA9A-DRX-1

RQA9C-DRX-1

19

higher frequencies the NNPS curves of the Pixium 4600 and DRX-1 diverge slightly for

the different directions illustrating increased noise in the readout direction (vertical)

Differences in the noise characteristics were more apparent among detectors as

shown for 1 mR in Figure 8 The NNPS curve for the DRX-1 was higher in magnitude

across the entire frequency range than either the Pixium 4600 or DRX-1C which both

seemed to demonstrate reasonably similar NNPS curves The higher magnitude noise of

the DRX-1 indicates higher relative noise content overall Closer inspection of the NNPS

curves of the Pixium 4600 and DRX-1C detectors in Figure 7 revealed differences in the

spacing between the three exposure levels The gaps between the Pixium 4600 NNPS

curves do not correspond to the factor of two differences between each exposure level

especially at low- to mid- spatial frequencies suggesting a higher level of fixed pattern

noise additional noise with increasing exposure levels due to ineffective gain map

corrections Between filtration schemes the differences in NNPS curves for a given beam

quality were not substantial as shown in Figure 7

I3v Detective Quantum Efficiency

The DQE results are shown in Figure 9 DQE curves across exposure levels were

almost collinear except for Pixium 4600 and in general could be inferred from the

NNPS results Additionally the DQE curves demonstrated a relatively linear response

with spatial frequencies as expected for flat-panel detectors [9] Differences in DQE

among detectors were consistent for the most part with the type of scintillating material

20

As depicted for 1 mR exposure in Figure 10 differences between Pixium 4600 and DRX-

1C DQE curves correspond to the differences in their NNPS curves DRX-1 DQE curves

were consistently lower than either the Pixium 4600 or DRX-1C curves The DQE curves

for the alternative filtration were consistently higher than those for the IEC filtration

and the most noticeable differences were near the zero-frequency axis These effects can

be both attributed to ineffective gain map correction DQE values for 1 mR exposure are

listed in Table 5

I4 Discussion

I4i Comparisons of Detectors

The limiting spatial resolutions of all three detectors were almost exactly the

same considering that their pixel areas were similar in size The decrease in high-

frequency MTF of the DRX-1 compared to the other detectors is probably a result of

increased optical blurring due to the differences in the powdered structure of GOS

versus the needle-like structure of CsI [2] The fact that the DRX-1C and Pixium 4600

have comparable MTFs suggests similar scintillator thicknesses assuming that the

materials were processed alike

The noise of the three detectors demonstrated similar trends with each other The

higher NNPS curves of the DRX-1 detector are probably due also to the scintillating

material and its operation in converting photons into signal The conversion process is

less efficient because of the less favorable stopping power of the GOS compared to CsI

21

especially with higher energy beams The noise of the Pixium 4600 and DRX-1C were

similar except for the spacing between exposures The DRX-1C NNPS curve spacing is

consistent with a factor of two difference in exposure levels but the Pixium 4600 has a

smaller spacing The 05 mR NNPS curve of the Pixium 4600 is closer to that of the 05

mR NNPS curve of the DRX-1C This demonstrates that at higher exposures the Pixium

4600 produces a larger amount of additional noise beyond that explained by simple

stochastic effects It suggests bad performance in the gain map corrections

The DQE results indicate SNR properties of each detector The Pixium 4600 and

DRX-1C are comparable for the most part with the DRX-1C performing slightly better

The DRX-1 as predicted from MTF and NNPS results has a DQE much lower than

either of the previous two This is a reflection of the detection properties as provided by

its scintillator material The DQE of the DRX-1 however is comparable to CR image

receptors [2] The mid-frequency dips in the DQE for Pixium 4600 may be due to the

optical properties of the CsI phosphor layer which can affect the MTF in this manner

Because the DQE is calculated by squaring the MTF this effect at the mid-range

frequencies becomes more apparent The dips may also be further evidence of bad gain

map corrections

I4ii Comparisons of Filtrations

The alternative filtration closely matches for the most part the IEC-based

filtration for MTF NNPS and DQEs at RQA5 but not at RQA9 The filters do not have

22

Table 4 Experimental MTF frequency locations for 1 mR exposure

Detector Filtration

50 MTF

(mm-1)

40 MTF

(mm-1)

30 MTF

(mm-1)

20 MTF

(mm-1)

10 MTF

(mm-1)

Pixium

4600

RQA5A 115 145 185 245 330

RQA5C 125 155 195 250 345

RQA9A 110 175 175 235 330

RQA9C 125 155 195 255 345

DRX-1C

RQA5A 120 150 185 245 350

RQA5C 125 155 195 255 355

RQA9A 120 150 190 250 355

RQA9C 130 160 210 265 360

DRX-1

RQA5A 110 135 160 205 280

RQA5C 110 135 170 210 285

RQA9A 105 125 155 195 270

RQA9C 110 135 165 210 285

Table 5 Estimated DQE values for 1 mR exposure by frequency bins

Detector Filtration DQE(00 mm-1) DQE(10 mm-1) DQE(20 mm-1) DQE(30 mm-1)

Pixium

4600

RQA5A 62 42 32 21

RQA5C 63 45 36 25

RQA9A 41 27 30 13

RQA9C 43 33 27 19

DRX-1C

RQA5A 72 52 35 21

RQA5C 76 55 41 24

RQA9A 49 33 23 15

RQA9C 51 40 31 20

DRX-1

RQA5A 38 24 12 4

RQA5C 38 25 14 5

RQA9A 28 18 9 4

RQA9C 28 19 12 5

DQE values at the zero-frequency axis were estimated by the intercept of a linear fit of low-frequency data

but excluding most proximal to the axis due to large fluctuations Other estimated values are grouped into

frequency bins due to the noisiness of the data

23

considerable differences in the spatial resolutions of the detectors as expected The noise

responses for each filtration were also similar except at the lower frequencies of the

NNPS especially near the zero-frequency axis There observing the NNPS responses at

RQA5 for Pixium 4600 and DRX-1C in Figure 8 the NNPS for the IEC-based filtration

(solid lines) tend to drop faster than the NNPS for the alternative filtration This

subsequently appears as a drop in DQE near the zero-frequency axis shown for those

detectors in Figure 10 Overall as indicated in Table 5 the DQEs of the two filtrations

while similar in trend indicate that the alternative filtration increases the DQE by a

small amount of 3-5 Part of this may be explained by the slightly higher beam

energy which may be more optimal for the energy response of the detectors or may

weigh the pixel responses slightly considering that they are energy-integrating types

The most probable explanation is the gain map correction for the alternative filtration

where fixed pattern noise is more sufficiently reduced

A previous study [6] had discussed the choice of filter material in the analysis of

DQE when achieving the beam conditions defined by IEC It found that visible

nonuniformities were present with the higher purity aluminum filter (type-11999 alloy)

The low frequency mottle in the flat-field images for NPS measurements were also

attributed to structured noise from the grain size in the IEC-based filter with an

attenuating thickness that would reveal nonuniformities The mottle in the current study

was only observable under very narrow windowing as shown in Figure 11 Such low

24

frequency artifacts which are not readily noticeable may also be caused by shading

artifacts inverse square law or even the heel effect A possible method to correct for this

is a subtraction method by taking the average of the flat-field images for an exposure

level and then subtracting that from each of them This would remove nonuniformities

that were not corrected using a suboptimal gain map calibration

Figure 11 DRX1-C NNPS images at 1 mR for RQA5 with IEC filtration (left) and

alternative filtration (right) Images are equally windowed at 45 and leveled at 980

One convenient aspect of the copper and aluminum filtration is that it requires

much less tube current to achieve the same amount of exposure at the detector than the

much thicker aluminum filtration As shown in the non-normalized spectra in Figure 2

the exiting photon fluence exiting the copper and aluminum filtration is substantially

higher than that of the IEC-specified filtration This is due to the smaller total filtration

25

attenuation For extensive DQE analysis multiple sets of exposures may be acquired

before tube overheating becomes a concern

One limitation to the comparison of the two filtrations is that calibration

procedures specified copper and aluminum filtration at 80 kVp (for all detectors 05 mm

Cu and 10 mm Al) This may have influenced the results in favor of the alternative

filtration A further investigation involving the calibration procedures and performing

DQE measurements is encouraged Another factor may be influenced by the fact that the

tests were performed at 70 kVp and 120 kVp different from the recommended

calibration tube potential Clearly there would be differences in the linear attenuation

coefficients of the filters and different energy responses of the detectors themselves This

must be considered when interpreting DQE results The current results support a

previous study decades ago that described filtration of different material types in terms

of an aluminum equivalent [16] The results show that the two filtration schemes are

essentially equivalent when considering beam qualities and spatial resolutions The

NNPS and DQE results can be seen as close enough where their small differences are

insignificant when performing quality assurance tests in a clinical setting Overall our

results indicate that the alternative filtration with copper and aluminum may be more

convenient to use than the current IEC standard filtration

26

I4iii Implications of Wireless DR

This study has shown that wireless image receptors can have the same DQE

performance if not better than conventional flat-panel detectors They operate on the

same basic physical principles the new features offered by the DRX-1C and DRX-1 are

wireless communication with the workstation and electronics packaging technology

The latter feature may pose limitations for these units in terms of possible degradation

in the detectors in routine clinical conditions A consideration for future work would be

to longitudinally track DQE performance of the wireless detectors over time while being

utilized in a clinical environment In the end one must consider risks versus benefits of

choosing portable DR technology over CR one of which includes the cost and fragility

of DR detectors

The DQE performance of one wireless system is just as good as or better than

conventional systems as seen by the DRX-1C performance compared to the Pixium

4600 Wireless systems can also reduce the need for CR readers especially in portable

applications in other regions of the world (eg military hospitals developing countries)

However while DQE performance indicates the physical performance of the detector

system it is still unknown how it relates to observer performance

I5 Conclusions

Two wireless image receptors DRX-1C and DRX-1 were evaluated and

compared with the conventional DR flat-panel Pixium 4600 in terms of DQE

27

performance along with MTF and NNPS performances The detectors have similar

resolution properties although the DRX-1 is inferior at higher spatial frequencies The

NNPS and DQE results both indicate that the DRX-1C is superior to the DRX-1 and

comparable if not better to the Pixium 4600

The results from the filtration comparison indicate no substantial differences

between the IEC-based filtration and the copper-based alternative filtration Only slight

differences were found in the low frequency components of the NNPS and the DQE due

to the inherent nonuniformities of the IEC specified filtration Given the similarity of the

results and low attenuation advantage of the copper and aluminum filter its use is

encouraged

28

II Directional MTF for Breast Tomosynthesis

II1 Introduction

Breast tomosynthesis is an emerging 3D imaging modality that has potential use

for screening and diagnosis of breast cancer Breast tomosynthesis along with other 3D

techniques is preferable to planar imaging methods (eg mammography) because they

reduce anatomical noise by removing overlying structures above and below the plane of

an image slice [17-20] Recent advances in detectors and computer technology have

made digital tomosynthesis feasible

An image quality metric of particular importance in breast tomosynthesis is

spatial resolution Resolution is important to know in order to assess small-detail

structures such as microcalcifications A descriptive metric for characterizing spatial

resolution in the Fourier (or frequency) domain is the modulation transfer function

(MTF) Affected by reconstruction filters [21] the limited angular projections involved in

breast tomosynthesis results in highly anisotropic (or nonuniform) resolution Many

studies have looked only at characterizing the in-plane spatial resolution (ie in an

individual slice) with an elevated angled edge phantom [2223] A few studies have

looked at characterizing a more comprehensive 3D spatial resolution by using a

phantom with angled wires or tubes [24-26] However such studies require precise

mechanical alignment of the phantoms Several studies have explored a method using a

29

sphere phantom for the directional 3D MTF evaluation for microtomography [27] and

multi-slice CT [2829] This method has not yet been extended to breast tomosynthesis

This chapter focuses on breast tomosynthesis because it is highly anisotropic in

spatial resolution and like its predecessor mammography requires high spatial

resolution Additionally breast tomosynthesis acquisitions and reconstructions produce

several types of artifacts The use of a cone-based method using a sphere phantom [28] is

explored to characterize the directional 3D spatial resolution of simulated images from

breast tomosynthesis A technique for removing out-of-plane artifacts of the ESFs for the

in-plane axes is investigated to yield a modified MTF in a method that separates artifact

information from resolution information

II2 Materials and Methods

II2i Image Simulation

Breast tomosynthesis images were simulated by using a virtual imaging system

depicted in Figure 12 A volumetric breast phantom was voxelized as a rectangular mass

of uniform breast equivalent tissue of 4 cm thickness embedded with fifteen evenly

spaced plastic sphere inserts of 12 mm diameter The spheres were placed in a grid

formation within the central plane of the phantom The x-ray fluence was modeled from

a 28 kVp beam incident upon an indirect flat-panel detector with 200 micro m pixel size

Twenty-three projections within an angular range of 44deg were simulated using cascaded

systems analysis to generate characteristic 2D noise and spatial blurring [29] Each

30

projection was simulated to have an exposure of 174 mR with a fluence of 79 times 105

photonsmm-2 A standard filtered backprojection technique based on the Feldkamp

reconstruction algorithm [29] was used to reconstruct the projections and produce a

volumetric dataset with an isotropic voxel size of 200 micro m

Figure 12 Depiction of the virtual image system

II2ii Uncorrected MTF

To enable comparison of multiple spheres the reconstructed volume was

initially homogenized by performing a background subtraction based on a portion of the

volume devoid of spheres The voxel values were rescaled between one and zero to

eliminate negative values

31

The volumetric data were segmented to extract individual regions of interest

(ROIs) each containing a single sphere The ROIs extended along the full range of the z-

axis A thresholded ROI was generated by determining the exterior and interior voxels

relative to the sphere in the ROI The threshold value was set at 45 of the maximum

voxel value prior to thresholding The exterior and interior voxel values were then set to

values of 0 and 1 respectively Using the thresholded volume the center of mass was

calculated to determine the centroid The voxel values from the original ROI were

subsequently tabulated with the associated distances azimuthal angles and polar

angles relative to the centroid

Conical regions were prescribed along the positive and negative directions along

the three major axes extending from the centroid of the sphere as depicted in Figure 13

The axes about which the extent of the cone angle was delineated were defined with

the azimuthal and polar angles

Voxels with centers within the angular range of the cone were considered for

generating the edge spread function (ESF) To improve regularity of the distance

sampling interval the ESF values were rebinned to discrete distances corresponding to a

fraction of the voxel size Only voxels with distances ranging from the voxel size (ie

200 micro m) to the maximum distance were considered The ESFs from multiple spheres

were averaged together for each of the three major axes to produce an averaged ESF

which was further smoothed utilizing a Gaussian filter

32

Figure 13 Example of 30-degree cone prescribed along z axis of the sphere

The resulting ESF was then differentiated using the central difference method to

produce the line spread function (LSF) A Hanning filter with the same length as the LSF

was applied to zero out the tails of the LSF The presampled MTF was subsequently

computed as the amplitude of the Fourier transform of the LSF The MTF was

normalized with respect to the maximum value occurring within the range of the cutoff

frequency Binning size and conical range for the ESF were considered for maximizing

accuracy and minimizing noise of the MTF verified by comparison against the

theoretical MTF as determined in the previous section

II2iii Theoretical Directional MTF

The theoretical 3D MTF was calculated using a priori knowledge of the transfer

function of the virtual imaging system described in the previous section A phantom

was created with a set of point objects in a uniform and noise-free background with the

objects spanning across the volume of the breast [29] Twenty-one realizations were

33

generated from the reconstructed images of the point objects to yield a set of 3D point

spread functions (PSFs) The 3D fast Fourier transform (FFT) was performed for each 3D

PSF and averaged to give an ldquoexpectationrdquo 3D MTF [29] The theoretical directional

MTFs in the three major spatial axes were determined by line profiles along each of the

corresponding spatial frequency axes in the 3D MTF An additional theoretical MTF for

each direction was determined by using the application of conical regions along the axes

in frequency-space to take into account the contributions of MTF information from other

planes

II2iv Modified MTF

The tomosynthesis reconstruction is known to have edge enhancements which

affect the overall MTF by shifting the peaks of the MTF toward the higher frequencies

[23] The presence of this artifact complicates the interpretation of the actual spatial

resolution of the images Several steps were performed to remove the artifact

contribution to the resolution information particularly for the in-plane x and y

directions with the assumption that resolution information was contained immediately

near the edge

For the x-direction averaged ESF only values that were detected to be inside the

edge of the sphere were considered Those values were previously determined via

thresholding for calculating the centroid The ESF information corresponding to these

values was inversed and flipped about the detected edge to produce a symmetric

34

modified ESF The modified MTF was subsequently calculated from this modified ESF

as described in the previous section

For the y-direction averaged ESF an upward trend was found in the initial part

of the ESF This section was detrended with a polynomial fit and subtracted to produce a

flatter curve in that region The resulting detrended ESF was used to calculate the y axis

modified MTF

Figure 14 Photograph of the imaging system with the acrylic sphere phantom

embedded in oil

II2v Preliminary Experimental Validation

A clinical breast tomosynthesis system (Mammomat Inspiration Siemens AG

Munich Germany) was used to perform a preliminary evaluation of the cone-based

MTF technique The phantom for the experiment consisted of a single acrylic ball of 075

in diameter (SmallParts Seattle WA) suspended by a 0029 in diameter plastic filament

35

(Omniflex Zebco Tulsa OK) in an acrylic frame filled up to 4 in with vegetable oil

(Target Brands Inc Minneapolis MN) The system and phantom are shown in Figure

14 Twenty-five projections with an angular range of 44deg were acquired and subsequently

reconstructed to produce a volume with a voxel size of 01times01times10 mm3 The voxels were

reformatted to have an isotropic size of 01 mm The uncorrected ESF LSF and MTF

were calculated as described in the previous section

II3 Results

II3i Reconstruction

The reconstructed volume is shown in Figure 15 Notice the edge enhancement

along the x-direction as indicated by the sharp shadowing artifacts on either side of the

spheres The background was effectively homogenized using the background

subtraction technique This also took account of the curved edges of the breast phantom

With the close spacing of the spheres in the phantom the shadows along the x direction

for the fifteen spheres overlap with each other As the nine centrally located spheres

experience this effect the same way they were used for determining the ESF

A 3D rendering of the ROI containing a sphere shown in Figure 16 indicates the

anisotropic resolution of the reconstruction Note that the sphere is not accurately

reconstructed and has an oblong shape especially along the z axis Cross sectional views

of the ROI also in Figure 16 clearly demonstrate the edge enhancement causing a

shadow artifact in the x direction caused by the incomplete angular sampling of

36

tomosynthesis The sampling also introduces the triangular reconstruction of the sphere

as seen in the x-z plane Note the gradual edge drop-off in the z direction much beyond

the sphere radius

Figure 15 View of the central slice of the breast phantom reconstruction before (top)

and after (bottom) background subtraction The z axis is through the page

37

Figure 16 3D rendering of the ROI volume (left) and cross-sectional views of the most

centrally located sphere with centroid indicated with red circle (right)

II3ii Theoretical MTF

The theoretical MTFs for x y and z directions as determined from the line

profiles of the 3D MTF are shown in Figure 17 The theoretical MTF in the x direction

has a maximum value that is toward higher frequencies Its 10 response occurs at

about 125 cyclesmm which is at 50 of the cutoff frequency The rapid increase from

the zero-frequency intercept to the peak corresponds to the ramp filter used in filtered

backprojection which decreases the weighting of low frequency contributions due to the

incomplete angular sampling of the frequency-space The MTF does not reach a value of

0 at the zero-frequency intercept as it is very difficult to assess the zero-frequency

intercept due to the finite size of the phantom The theoretical MTF in the y direction

peaks at the zero-frequency intercept and reaches 20 proximal to the cutoff frequency

38

The 10 MTF is well beyond the cutoff frequency The theoretical MTF in the z direction

has a rapid drop-off at very low spatial frequencies indicating the lack of resolution in

that dimension

Figure 17 Theoretical 3D MTF results along the three major planes (top) and along x

y and z directions (bottom) Also note that the angular spread seen in the fx-fz plane is

equal to the angular range of 44deg for the acquisition

II3iii Uncorrected MTF

The ESF LSF and MTF using the cone-based method are shown for the x y and

z directions in Figure 18 It was found that a bin size of one-tenth the voxel size (002

mm) and a cone angle of 30deg to establish the ESF were enough to minimize noise and

maximize accuracy in the uncorrected MTFs considering the reasonable comparison of

the shapes of the MTF curves with the theoretical results in Figure 17 The LSFs are

generally noisy because differentiation of the ESF increases the amplitude of the noise

39

The data shown reflect a convolution with a smoothing Gaussian filter which was later

further corrected for in the reported MTF Nevertheless the high frequency components

of the noise are well beyond the MTF cutoff frequency of 25 cyclesmm and do not

impact the MTF results greatly

For the ESF in the x direction the shadow effect evident at the edge of the sphere

is visible as a steep decline followed by an increase Due to the finite distance range

provided by the ROI the ESF beyond the edge did not asymptotically reach the

background value The corresponding LSF demonstrates a low frequency modulation

that is indicated by the shift of 03 cyclesmm in the x direction for the peak of the MTF

The MTF exhibits a zero-frequency intercept that is non-zero unlike the theoretical MTF

and a 10 value at approximately 1 cyclesmm These features may be a direct

consequence of MTF information ldquocontaminationrdquo from y and z directions Furthermore

the ESF in the y direction demonstrates a reasonably shaped curve except for the slight

upward trend within the radius of the sphere which can be attributed to the shadow

artifact overlapping with the sphere volume The associated MTF has a peak shifted by

approximately 01 cyclesmm away from the axis and a 10 MTF occurring at

approximately 15 cyclesmm Both features which are not present in the theoretical

results may also be attributed to contaminant MTF information from x and z directions

The ESF in the z direction has a drop-off that occurs at a small fraction of the cutoff

frequency similar to that demonstrated by the theoretical MTF

40

Uncorrected ESF LSF and MTF

Figure 18 Uncorrected ESF (top) LSF (middle) and MTF (bottom) for x y and z

directions

41

Figure 19 Comparisons of the directional MTFs as calculated by the sphere method

(dashed line) by theoretical line profiles (light-weight line) by theoretical cone

regions (heavy-weight line)

II3iv Comparison of Theoretical and Simulated MTFs

The theoretical MTF results obtained from line profiles through the 3D MTF and

the simulated MTFs using the cone-based technique did not match very well except for

the general shape of the curves It was assumed in the previous section that the cone-

based technique contains information from other planes Figure 19 compares MTFs in

each direction for the two methods described in the methods and an additional method

based on conical regions of the 3D MTF The latter computes the MTF by averaging

contributions of the 3D MTF using the same cone prescription method used to define the

ESFs Comparison of the curves indicate some interesting correlations aside from the

fact that using conical regions with the 3D MTF results produce more noisy MTF results

partly due to the low sampling provided by the theoretical calculations The same

conclusions regarding the z direction MTF can be confirmed regardless of either

theoretical MTF procedures The experimental x direction MTF seems to agree best with

42

the line profile method whereas the y direction MTF agrees better with the cone region

method The fact that the experimental x direction MTF has a drop-off frequency that is

lower than those of either of the theoretical MTFs in Figure 19 suggests that this might

be due to integration of the z-direction in the in-plane slices considering how slices are

essentially averages of z direction information contained within it [33]

II3v Modified MTF for x and y

Modified ESF LSF and MTF curves for x and y directions are shown in Figure

20 The modified ESF and the resulting LSF in the x direction appear symmetric as

expected from the inverse and flip operation of the interior ESF about the detected edge

The modified MTF appears with less variation than the uncorrected MTF and the MTF

peak occurs at the zero-frequency axis The correction yields a 10 MTF at about 15

cyclesmm an improvement from the uncorrected MTF but still distant from the cutoff

frequency The modified ESF in the y direction demonstrates the detrended curve within

the sphere radius after a quadratic polynomial fit The resulting modified MTF still

appears similar to the uncorrected MTF except that the peak now coincides with the

zero-frequency axis For both x and y directions the low response of the modified MTFs

at the higher frequencies suggests that the contamination from other directions is

substantial due to the angular range of the cone

43

Modified ESF LSF and MTF

Figure 20 Modified ESF (top) LSF (middle) and MTF (bottom) for x and y directions

44

II3v Preliminary Experimental Validation

Cross-sections of the reconstructed sphere volume are shown in Figure 21

Relative to the simulation reconstructions the reconstructions of the experimental

phantom images produce lower contrast and higher noise The preliminary results

shown in Figure 22 indicate that our technique can be applied to actual experimental

breast tomosynthesis reconstructions However due to the noise exhibited by the MTF

curves for the x and y directions we did not determine the modified MTFs to separate

resolution and artifact information

Figure 21 Cross sectional views of the experimental sphere image with centroid

indicated with red circle

45

Uncorrected ESF LSF and MTF for Real Image

Figure 22 ESF (top) LSF (middle) and MTF (bottom) of real image for x y

and z directions

46

II4 Discussion

II4i Evaluation of Cone-based Method

The cone-based MTF technique was introduced by Thornton and Flynn [28] for

evaluation of volumetric CT images To utilize this technique as a characterization of a

3D system spatial resolution one must first consider the validity of the assumption of

shift invariance such that the same MTF result may be obtained regardless of the

location of the sphere The study by Zhao et al [23] found that there was no shift

variance for the MTF measurements along the vertical axis but this was only considering

the in-plane resolution along one axis On the other hand this study evaluated the MTF

with images simulated with cascaded systems analysis which includes conditions of

linearity and shift invariance Additionally the MTF was calculated by averaging the

ESF from several spheres in the same volume only after performing a background

subtraction This step was essential to account for the sensitivity of centroid calculations

as well as ensuring symmetric ESFs for opposing axes of the sphere ROIs

The measurement of MTF with the cone-based technique inherently

supersamples the edge of the sphere to increase signal-to-noise-ratio (SNR) of edge

information by averaging the contributions of each voxel to the ESF [713] This method

also takes into account the discrete sampling of the voxels by accounting for various

shifts of the edge in the voxel (also known as the partial volume effect) However using

the curved surface of the sphere phantom to approximate an edge along a given

47

direction naturally leads to contamination of information from other directions aside

from the one of interest Preferably a directional ESF should be created by using a single

radial line but this would limit the available voxels to obtain edge information An ideal

situation theoretically would be to use a larger-sized sphere such that the surface is

nearly flat and perpendicular to the axes of interest This would also permit a reduction

in the angular range of the cone and thus the introduction of out-of-plane information in

the resulting MTF However sphere size is a limitation in breast tomosynthesis and the

use of a large phantom might void the assumption of shift invariance of the spatial

resolution

The choice of a sphere phantom nevertheless may be based on the clinical need

to quickly acquire a single image for MTF evaluation especially for multiple directions

without presenting extra logistical challenges The use of a wire or edge phantom

requires more precise mechanical alignment to achieve the correct set up The edge

phantom [23] would require at least two images to sample all three dimensions In the

case of the three wire phantom [2425] all three dimensions of the frame must be aligned

simultaneously with respect to the axis of rotation A similar situation would be

encountered when considering a cubic phantom with the planes normal to the axis of

interest In contrast to these phantoms the sphere eliminates the need for precise

alignment especially with respect to three spatial dimensions simultaneously A sphere

48

has ideal symmetry in all directions and can be used to evaluate MTF in any arbitrary

direction

This study unlike others [242532] did not explore the effects of physical

parameters such as scatter or contrast on the final MTF result but it demonstrated the

feasibility of using the cone-based method with an actual breast tomosynthesis image of

a sphere phantom as shown in Error Reference source not found and Error Reference

source not found These effects should be addressed in future works A further look

into deriving the principles of comparing the theoretical MTF with the experimental

MTF using the cone-based method is further warranted

II4ii Separation of Artifact and Resolution Information

The focus of this study was to develop a technique for measuring spatial

resolution of tomosynthesis images The intrinsic artifacts from tomosynthesis

reconstructions however lead to uncharacteristic MTFs and possible misinterpretation

of the effective resolution information When considering previous techniques for

calculating the presampled MTF [713152328] the analysis was performed using an

edge or a line to produce the corresponding ESF The resolution information is

essentially contained only along the edge indicated by the need to calculate the LSF In a

way the method of extracting artifact information is to focus the analysis only on the

edge part of the ESF to calculate the modified MTF This will lead to a better

understanding of the limiting size of objects that may be seen in the reconstructed 3D

49

image The presampled MTF without correction should still be analyzed to understand

the entire system response Note that the ESFs attempt to reflect information only at the

detected edge of the sphere

II5 Conclusions

The directional MTF of a simulated breast tomosynthesis reconstruction was

determined by using the cone-based MTF technique demonstrating the feasibility of a

single phantom for MTF evaluation This study further presented methods of analyzing

only the edge information in the ESF to create a modified MTF along in-slice (x and y)

axes It can provide insight into the actual spatial resolution information contained in the

image while separating the resolution information from the information introduced by

artifacts caused by the reconstruction and insufficient volumetric sampling The idea of

separating the resolution and artifacts from the measured ESF are expected to facilitate

the interpretation of MTF measurements in breast tomosynthesis Similar methods may

be applied to characterize the resolution of other 3D imaging modalities

50

References

1 Garmer M Hannigs SP Jaumlger HJ et al ldquoDigital Radiography Versus

Conventional Radiology in Chest Imaging Diagnostic Performance of a Large-

Area Silicon Flat-Panel Detector in a Clinical CT-Controlled Studyrdquo American

Journal of Roentgenology Volume 74 75-80 (2000)

2 Cowen AR Kengyelics SM and Davies AG ldquoSolid-state flat-panel digital

radiography detectors and their physical imaging characteristics rdquoClinical

Radiology Volume 63 487-498 (2008)

3 Chotas HG Dobbins III JT and Ravin CE ldquoPrinciples of Digital

Radiography with Large-Area Electronically Readable Detectors A Review of

the Basicsrdquo Radiology Volume 210 Number 3 595-599 (1999)

4 Flynn MJ and Samei E Experimental comparison of noise and resolution for

2k and 4k storage phosphor radiography systems Medical Physics Volume 26

Number 8 1612-1623 (1999)

5 Rong XJ Shaw CC Liu X Lemacks MR and Thompson SK

ldquoComparison of an amorphous siliconcesium iodide flat-panel digital chest

radiography system with screenfilm and computed radiography systems ndash A

contrast-detail phantom studyrdquo Medical Physics Volume 28 Number 11 2328-

2335 (2001)

6 Ranger NT Samei E Dobbins III JT and Ravin CE Measurement of the

detective quantum efficiency in digital detectors consistent with the IEC 62220-1

standard Practical considerations regarding the choice of filter material

Medical Physics Volume 30 Number 7 2305-2311 (2005)

7 Samei E Buhr E Granfors P Vandenbroucke D and Wang X Comparison

of edge analysis techniques for the determination of the MTF of digital

radiographic systems Physics in Medicine and Biology Volume 50 3613-3625

(2005)

8 Samei E and Flynn MJ An experimental comparison of detector performance

for computed radiography systems Medical Physics Volume 29 Number 4 447-

459 (2002)

51

9 Samei E and Flynn MJ An experimental comparison of detector performance

for direct and indirect digital radiography systems Medical Physics Volume 30

Number 4 608-622 (2003)

10 Samei E Ranger NT MacKenzie A Honey ID Dobbins III JT and Ravin

CE Effective DQE (eDQE) and speed of digital radiographic systems An

experimental methodology Medical Physics Volume 36 Number 8 3806-3817

(2009)

11 Samei E Ranger NT MacKenzie A Honey ID Dobbins III JT and Ravin

CE Detector or System Extending the Concept of Detective Quantum

Efficiency to Characterize the Performance of Digital Radiographic Imaging

Systems Radiology Volume 249 Number 3 926-937 (2008)

12 ldquoIEC 62220-1 Medical Electrical Equipment ndash Characteristics of Digital X-Ray

Imaging Devices ndash Part 1 Determination of the Detective Quantum Efficiencyrdquo

International Electrotechnical Commission Geneva Switzerland (2003)

13 Samei E Ranger NT Dobbins III JT and Chen Y Intercomparison of

methods for image quality characterization I Modulation transfer function

Medical Physics Volume 33 Number 5 1454-1465 (2006)

14 Dobbins III JT Samei E Ranger NT and Chen Y Intercomparison of

methods for image quality characterization II Noise power spectrum Medical

Physics Volume 33 Number 5 1466-1475 (2006)

15 Samei E Flynn MJ and Reimann DA A method for measuring the

presampled MTF of digital radiographic systems using an edge test device

Medical Physics Volume 25 Number 1 102-113 (1998)

16 Nagel HD ldquoAluminum equivalence of materials used in diagnostic radiology

and its dependence on beam qualityrdquo Physics in Medicine and Biology Volume

31 Number 12 1381-1399 (1986)

17 Niklason LT Christian BT Niklason LE et al ldquoDigital Tomosynthesis in

Breast Imagingrdquo Radiology Volume 205 399-406 (1997)

18 Gur D ldquoTomosynthesis Potential Clinical Role in Breast Imagingrdquo American

Journal of Roentgenology Volume 189 614-615 (2007)

52

19 Park JM Franken Jr EA Garg M Fajardo LL and Niklason LT ldquoBreast

Tomosynthesis Present Considerations and Future Applicationsrdquo

RadioGraphics Volume 27 S231-S240 (2007)

20 Good WF Abrams GS Catullo VJ Chough DM Ganott MA Hakim

CM and Gur D ldquoDigital Breast Tomosynthesis A Pilot Observer Studyrdquo

American Journal of Roentgenology Volume 190 865-869 (2008)

21 Hu Y-H Zhao W Mertelmeier T and Ludwig J ldquoImage Artifact in Digital

Breast Tomosynthesis and Its Dependence on System and Reconstruction

Parametersrdquo IWDM 2008 LNCS 5116 628-634 (2008)

22 Chen Y Lo JY Ranger NT Samei E Dobbins III JT ldquoMethodology of

NEQ(f) analysis for optimization and comparison of digital breast tomosynthesis

acquisition techniques and reconstruction algorithmsrdquo Proceedings of SPIE

Volume 6510 65101I (2007)

23 Zhao B Zhou J Hu Y-H Mertelmeier T Ludwig J and Zhao W

ldquoExperimental validation of a three-dimensional linear system model for breast

tomosynthesisrdquo Medical Physics Volume 36 Number 1 240-251 (2009)

24 Madhav P Brzymialkiewicz CN Cutler SJ Bowsher JE and Tornai MP

ldquoCharacterizing the MTF in 3D for a Quantized SPECT Camera Having Arbitrary

Trajectoriesrdquo 2005 IEEE Nuclear Science Symposium Conference Record 1722-

1726 (2005)

25 Madhav P McKinley RL Samei E Bowsher JE and Tornai MP ldquoA Novel

Method to Characterize the MTF in 3D for Computed Mammotomographyrdquo

Proceedings of SPIE Volume 6142 61421Y (2006)

26 Hu Y-H Zhao B and Zhao W ldquoImage artifacts in digital breast

tomosynthesis Investigation of the effects of system geometry and

reconstruction parameters using a linear system approachrdquo Medical Physics

Volume 35 Number 12 5242-5252 (2008)

27 Seifert A and Flynn MJ ldquoResolving power of 3D x-ray microtomography

systemsrdquo Proceedings of SPIE Volume 4682 407-413 (2002)

28 Thornton MM and Flynn MJ Measurement of the spatial resolution of a

clinical volumetric computed tomography scanner using a sphere phantom

Proceedings of SPIE Volume 6142 61421Z (2006)

53

29 Baek J Pelc NJ ldquoUse of sphere phantoms to measure the 3D MTF of FDK

reconstructionsrdquo Proceedings of SPIE Volume 7961 79610D (2011)

30 Richard S and Samei E ldquoQuantitative imaging in breast tomosynthesis and CT

Comparison of detection and estimation task performancerdquo Medical Physics

Volume 37 Number 6 2627-2637 (2010)

31 Chen Y Lo JY and Dobbins III JT ldquoImpulse response analysis for several

digital tomosynthesis mammography reconstruction algorithmsrdquo Proceedings of

SPIE Volume 5745 541-549 (2005)

32 Zhao B and Zhao W ldquoThree-dimensional linear system analysis for breast

tomosynthesisrdquo Medical Physics Volume 35 Number 12 5219-5232 (2008)

33 Wu G Mainprize JG Boone JM and Yaffe MJ ldquoEvaluation of scatter

effects on image quality for breast tomosynthesisrdquo Medical Physics Volume 36

Number 10 4425-4432 (2009)

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