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
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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)
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
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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)
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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MTF
Spatial Freq (mm)
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Spatial Freq (mm)
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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
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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
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1E-4
00 05 10 15 20 25 30 35
NNPS
Spatial Freq (mm)
NNPS
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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
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NNPS
Spatial Freq (mm-1)
NNPS (1 mR)
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Spatial Freq (mm-1)
NNPS (1 mR)
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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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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)
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Spatial Freq (mm-1)
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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)
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)
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
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00 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
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04
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06
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08
00 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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04
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00 05 10 15 20 25 30 35
DQE
Spatial Freq (mm)
DQE
enl0-h
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enl2-h
enl2-v
00
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DQE
Spatial Freq (mm)
DQE
enl0-h
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enl2-v
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DQE
Spatial Freq (mm)
DQE
enl0-h
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enl2-v
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DQE
Spatial Freq (mm)
DQE
enl0-h
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enl2-v
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DQE
Spatial Freq (mm)
DQE
enl0-h
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enl2-v
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00 05 10 15 20 25 30 35
DQE
Spatial Freq (mm)
DQE
enl0-h
enl0-v
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enl2-h
enl2-v
00
01
02
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06
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00 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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04
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00 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
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00 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)
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)
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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MTF
Spatial Freq (mm)
MTF
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vert
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MTF
Spatial Freq (mm)
MTF
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MTF
Spatial Freq (mm)
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Spatial Freq (mm)
MTF
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Spatial Freq (mm)
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Spatial Freq (mm)
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Spatial Freq (mm)
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MTF
Spatial Freq (mm)
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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
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
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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
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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
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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
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1E-4
00 05 10 15 20 25 30 35
NNPS
Spatial Freq (mm)
NNPS
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1E-6
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NNPS
Spatial Freq (mm)
NNPS
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1E-7
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00 05 10 15 20 25 30 35
NNPS
Spatial Freq (mm)
NNPS
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NNPS
Spatial Freq (mm)
NNPS
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00 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
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DQE
Spatial Freq (mm)
DQE
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Spatial Freq (mm)
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Spatial Freq (mm)
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Spatial Freq (mm)
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Spatial Freq (mm)
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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
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)
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)
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
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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
horiz
vert
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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
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03
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06
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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
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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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enl1-v
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enl2-v
1E-7
1E-6
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00 05 10 15 20 25 30 35
NNPS
Spatial Freq (mm)
NNPS
enl0-h
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1E-7
1E-6
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00 05 10 15 20 25 30 35
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Spatial Freq (mm)
NNPS
enl0-h
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1E-6
1E-5
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00 05 10 15 20 25 30 35
NNPS
Spatial Freq (mm)
NNPS
enl0-h
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enl2-v
1E-7
1E-6
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00 05 10 15 20 25 30 35
NNPS
Spatial Freq (mm)
NNPS
enl0-h
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1E-7
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00 05 10 15 20 25 30 35
NNPS
Spatial Freq (mm)
NNPS
enl0-h
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1E-7
1E-6
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00 05 10 15 20 25 30 35
NNPS
Spatial Freq (mm)
NNPS
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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
1E-7
1E-6
1E-5
1E-4
00 05 10 15 20 25 30 35
NNPS
Spatial Freq (mm)
NNPS
enl0-h
enl0-v
enl1-h
enl1-v
enl2-h
enl2-v
1E-7
1E-6
1E-5
1E-4
00 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
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01
02
03
04
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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
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06
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08
00 05 10 15 20 25 30 35
DQE
Spatial Freq (mm)
DQE
enl0-h
enl0-v
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enl2-v
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00 05 10 15 20 25 30 35
DQE
Spatial Freq (mm)
DQE
enl0-h
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enl2-v
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03
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DQE
Spatial Freq (mm)
DQE
enl0-h
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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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01
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03
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DQE
Spatial Freq (mm)
DQE
enl0-h
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enl2-v
00
01
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04
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00 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)
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
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(2005)
8 Samei E and Flynn MJ An experimental comparison of detector performance
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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)
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)
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
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01
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
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00 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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06
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00 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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00 05 10 15 20 25 30 35
DQE
Spatial Freq (mm)
DQE
enl0-h
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enl2-h
enl2-v
00
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DQE
Spatial Freq (mm)
DQE
enl0-h
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enl2-v
00
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DQE
Spatial Freq (mm)
DQE
enl0-h
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enl2-v
00
01
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DQE
Spatial Freq (mm)
DQE
enl0-h
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enl2-v
00
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DQE
Spatial Freq (mm)
DQE
enl0-h
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enl2-v
00
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00 05 10 15 20 25 30 35
DQE
Spatial Freq (mm)
DQE
enl0-h
enl0-v
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enl1-v
enl2-h
enl2-v
00
01
02
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04
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06
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00 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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04
05
06
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00 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
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00 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)
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
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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)
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)
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
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08
09
10
00 05 10 15 20 25 30 35
MTF
Spatial Freq (mm)
MTF
horiz
vert
00
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10
00 05 10 15 20 25 30 35
MTF
Spatial Freq (mm)
MTF
horiz
vert
00
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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
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enl2-v
1E-7
1E-6
1E-5
1E-4
00 05 10 15 20 25 30 35
NNPS
Spatial Freq (mm)
NNPS
enl0-h
enl0-v
enl1-h
enl1-v
enl2-h
enl2-v
1E-7
1E-6
1E-5
1E-4
00 05 10 15 20 25 30 35
NNPS
Spatial Freq (mm)
NNPS
enl0-h
enl0-v
enl1-h
enl1-v
enl2-h
enl2-v
1E-7
1E-6
1E-5
1E-4
00 05 10 15 20 25 30 35
NNPS
Spatial Freq (mm)
NNPS
enl0-h
enl0-v
enl1-h
enl1-v
enl2-h
enl2-v
1E-7
1E-6
1E-5
1E-4
00 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
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enl2-v
00
01
02
03
04
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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
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)
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)
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
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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
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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
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8 Samei E and Flynn MJ An experimental comparison of detector performance
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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)
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
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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)
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)
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)
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)
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
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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)
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
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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
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(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)
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)
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
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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
RQ
A5C
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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)
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)
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
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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
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(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)