Nuclear Medicine Basic Science Lectures Stephen  Bowen  

October  18,  2011  Email:  srbowen@uw.edu  

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Stephen Bowen, Ph.D.

Nuclear Medicine Basic Science Lectures October 18, 2011

srbowen@uw.edu

Introduction to Positron Emission Tomography

Planar and SPECT Cameras Summary

  System components: –  Collimator Detector Electronics

  Collimator –  Types: Parallel, Converging, Diverging, Pinhole, Multi-pinhole –  Performance: Penetration, Resolution, Efficiency

  Detector: –  Components: Scintillator crystal, Optical spacer, PMTs –  Performance: Efficiency, Intrinsic (spatial) resolution, Energy resolution

  Acquisition modes: –  Frame vs List mode –  Static (time-averaged), Dynamic (TAC), Gated (cardiac / respiration)

  Camera QA corrections: –  Uniformity, Linearity, Photo-peak window, Multi-energy registration

  SPECT QA/QC: –  Center-of-rotation, Head tilt, uniformity

PET Definition

  Positron –  Uses positron (+) emitting radio-isotopes to label physiologic

tracers (e.g. glucose metabolism, cell proliferation, hypoxia) –  Positrons are unstable in that they annihilate with electrons,

resulting in two anti-parallel photons each with energy 511 keV –  PET scanners measure coincident annihilation photons and

collimate the source of the decay via coincidence detection

  Emission –  The source of the signal is emission of annihilation photons from

within the patient, as opposed to photons transmitted through the patient in x-ray imaging

  Tomography –  Three-dimensional volume image reconstruction through collection

of projection data from all angles around the patient

Positron Annihilation

~ 1 mm

N N

N P

P P P

P P N N

Parent nucleus: unstable due to excessive P/N ratio (18F, 11C, 13N, 15O, 124I)

positron emission

two anti-parallel annihilation

photons

positron annihilates with an electron: mass energy is converted to electromagnetic energy resulting in

positron may scatter

e- e+

N N

N P

P P P

P N N N

proton decays to neutron

(18O, 11B, 13C, 15N, 124Te) + + +

neutrino also emitted

(inconsequential to PET)

e+

Nuclear Medicine Basic Science Lectures Stephen  Bowen  

October  18,  2011  Email:  srbowen@uw.edu  

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detector i

detector j

detector i-j coincidence

coincidence events

Emission Coincidence Detection

time

i

j

Random rate determined from i, j singles rates

Tomographic Data Acquisition

All coincidence events acquired over time allows dynamic imaging

Sort LOR into sinograms and/or save list-mode data

Group coincidence data into parallel projections (LOR) for tomographic reconstruction

LOR  

Projection  Angle  

Coincidence Events: Signal and Noise

True coincidence:

anti-parallel photons travel directly to and are absorbed

by detectors

PET detectors seek simultaneous gamma ray absorptions (“simultaneous” → within ~ 5-10 ns)

Random coincidence:

photons from different nuclear decays are detected

simultaneously

NOTE: scattered and random coincidence lines-of-response need not pass through object!

Scattered coincidence:

one or both photons change direction from a scatter before

detection

PET signal components

  S and R has to be estimated and removed

  Estimation challenges –  R estimation accurate and efficient (singles method) –  S estimation can have significant errors (e.g. lung)

P = T + S + RMeasured  Projections  

True  Signal  

Noise  from  Scatter  

Noise  from  Random  

T !"t # rij ! activity

R!"t # ri # rj ! activity2 ri  =  single  photon  

detection  rate  in  pixel  i

rij =  photon  pair  detection  rate  in  detector  pixels  i,j

Nuclear Medicine Basic Science Lectures Stephen  Bowen  

October  18,  2011  Email:  srbowen@uw.edu  

3  

PET Acquisition: 2D vs. 3D Mode Form of collimation (septa) that separate axial slices in 2D PET

- reduces scattered and random events (also reduces trues!)

2D PET uses axial septa 3D PET uses no septa

detector crystals

septa & end shielding

blocked

scatter & randoms

PET Contrast and Quantitation   Noise from Scattered Coincidence

–  Predominantly Compton scatter. Gamma rays scatter off of electrons, change direction and lose energy.

•  results in misplaced events due to change in photon direction (loss of contrast)

•  energy discrimination can eliminate scatter (but not all) •  correction based on scatter equations, scatter object (CT), measured

data

  Noise from Random Coincidence –  Random events proportional to singles rates squared –  Mean random events estimated in two ways:

•  measured with delayed coincidence window (direct measure, high noise due to random rate)

•  calculated based on system singles rates (low noise singles-based calculation)

  Attenuation of Signal –  Gamma rays are absorbed in the patient

•  Variability due to heterogeneity of attenuating tissue –  Correctable with properly aligned attenuation map

Signal and Noise Estimates

NEC = T 2

T + S +!R

 depends  on  randoms  estimation  method  

Noise  Equivalent  Counts  (NEC)  

Scatter  Fraction  (SF)  

SF = ST + S

SNR = T! P( )

!T

T + S +!R

Signal  to  Noise  Ratio  (SNR)  

NEC = T 2

T + S +!R

0

100

200

300

400

0 5 10 15 20

DSTE Count Rates: NEMA Cylinder Phantom

Cou

nt ra

te (k

cps)

Phantom activity (mCi)

3D  R  

3D  T  

2D  S  

3D  S  2D  T  

2D  R  

0

20

40

60

80

100

0 5 10 15 20

DSTE Measured NEC

NE

C ra

te (k

cps)

Phantom activity (mCi)

3D  NEC  

2D  NEC  

2D  =  20%  3D  =  34%  

FDG  oncology  patient  activity:  

PET Contrast: 2D vs. 3D mode

SF = ST + S

Ascan = Ainj !e"! tscan"tinj( )

Ascan = 10"15mCi( ) ! 12

60min110min

# 7"10mCi

Nuclear Medicine Basic Science Lectures Stephen  Bowen  

October  18,  2011  Email:  srbowen@uw.edu  

4  

Annihilation Photon Attenuation   Anti-parallel gamma ray coincidence detection means that attenuation is

independent of position along any line of response.

P1 = e− µ x( )dx0

′x

∫P2 = e

− µ x( )dx′x

a

∫

PC = P1P2 = e− µ x( )dx0

a

∫

detector  1   detector  2  

x  x’   a  0  

Attn.  of  photon  1:   Attn.  of  photon  2:  

Total  attn.  of  coincidence  pair:  

Pc  is  independent  of  annihilation  position  x’  

PET/CT Scanners"  CT scan used for PET AC"  CT image is downsampled to PET resolution"

–  Advantages"•  Fast acquisition"•  Low image noise"

–  Disadvantages"•  Higher dose"•  Attn. coeff. measured with poly-energetic

photons < 140 keV"

Consequences of CTAC!  More accurate quantitation"

PET/CT Attenuation Correction (AC)

CT  (diagnostic)  

same  CT,  re-­‐sampled  to  PET  resolution  

PET/CT Scanners

Micro  PET/CT  Clinical  PET/CT  

PET Detector Block

Reflective light sealing tape

Two dual photocathode PMTs

•  PET  scanners  are  assembled  in  block  modules  

•  Each  block  uses  a  limited  number  of  PMTs  to  decode  an  array  of  scintillation  crystals

gamma  rays  scintillation  light  

signal  out  to  processing  

Nuclear Medicine Basic Science Lectures Stephen  Bowen  

October  18,  2011  Email:  srbowen@uw.edu  

5  

Block matrix: BGO crystals""6 x 8 crystals (axial by transaxial)""Each crystal:"" "6.3 mm axial"" "4.7 mm transaxial"

"Scanner construction""Axial:"" "4 blocks axially = 24 rings"" "15.7 cm axial extent""Transaxial:"" "70 blocks around = 560 xtals"" "88 cm BGO ring diameter"" "70 cm patient port"

13,440 individual crystals"

Inside GE Discovery STE PET/CT   Positron Physics

–  Positron Range –  Photon Non-colinearity

  Detectors –  Response function

  Ring Geometry –  Non-uniform LOR sampling –  Depth-of-interaction

  Reconstruction Filters

PET Spatial Resolution

Rsystem = Rpos. phys.2 + Rdet

2 + Rsampl2 + Rrecon

2

Resolution components add in quadrature

Positron Physics Resolution

  Positron range •  maximum energy of isotope •  scatter medium

  Photon non-colinearity –  Non-colinearity: Rnon-colin = 0.0022 x Ring Diameter –  Clinical scanner: Diam. ~ 80 - 90 cm; Rnon-col. ~ 2 mm –  Small animal scanner ~ 15 - 20 cm; Rnon-col. ~ 0.4 mm

data from Derenzo, et al. IEEE TNS 33:565-569, 1986

0

0.5

1

1.5

2

2.5

3

0 0.5 1 1.5 2 2.5 3 3.5

Pos

itron

rms

rang

e (m

m)

Maximum positron kinetic energy (MeV)

82Rb

18F 11C

68Ga

13N 15O

Tran

sver

se Axial

A

B

C

D

Signal  Decoding  Energy, E = A + B + C + D

Axial position, Z = (C +D) / E Transverse position, X = (B + D) / E

Radial position: not determined (no DOI)  

Light  Sharing  Relative PMTs signal heights

depend on crystal of interaction

PMTs

A C

Rad

ial

Axial

Detector Signal Decoding

Nuclear Medicine Basic Science Lectures Stephen  Bowen  

October  18,  2011  Email:  srbowen@uw.edu  

6  

Detector Resolution

•  Peaks for different crystals at different positions"•  Window center and width adjusted for each crystal"

PET Ring Geometry Effect on Resolution

center

edge

entrance position and true line-of-response

detection position and assigned line-of-response

photon penetration

Depth-of-Interaction error:

w/2

w

Data Sampling Error:   Coincidence lines-of-response are not uniformly spaced across a ring detector

  Interpolate to uniform spacing, or account for non-uniformity in reconstruction

Resolution Effect of Smoothing vs. Noise with FBP Human abdomen simulation with 2cm diam. lesion 2:1 contrast

more  counts  (less  noise)  

less  smoothing  (more  noise)  

1.  Absorption efficiency of detectors –  scintillation crystal attenuation coefficient –  scintillation crystal thickness –  detector response uniformity

2.  Solid angle coverage of object by detectors –  PET ring diameter –  smaller diameter

•  pro: increases solid angle and sensitivity, reduces system cost

•  con: leads to DOI resolution degradation •  con: limits patient size

–  PET ring axial length larger axial extent •  pro: increases solid angle and sensitivity •  con: increases system cost

PET Sensitivity

Nuclear Medicine Basic Science Lectures Stephen  Bowen  

October  18,  2011  Email:  srbowen@uw.edu  

7  

Detector Sensitivity vs. Resolution Tradeoff

sensitivity  

energy  &  spatial  resolution  

counting  speed  (randoms  rate,  dead-­‐time  

photo-­‐sensor  matching,  manufacturing  cost  

relevant  PET  scanner  property  

Inorganic  scintillation  crystals  

*crystal  thickness,  t:  typically  BGO  scanners  use  t  =  3cm,  LSO  scanners  use  t  =  2cm  for  cost  reasons.  PET  scanners  are  not  made  from  NaI(Tl)  or  BaF2  due  to  low  sensitivity,  despite  other  advantages  

Geometric Efficiency vs. Sensitivity

sensitivity qmax

Graph from “Emission Tomography”, Eds. Wernick, Aarsvold, pg.186

Limited q

PET scanner axis

Full q

max

max

axial center plane

axial end plane

PET scanner sensitivity scales with the number of detectable coincidence events, which in turn scales as max.

This results in lower sensitivity at the end of any PET scanner

scanner axis

edge = 0o

edge

source

QA for PET Scanners: Evaluation of Performance Metrics

•  Sensitivity - both system and per transaxial slice (measured with a line source)

•  Spatial resolution - measured with a point source and an analytical image reconstruction algorithm at several positions in the scanner FOV (x,y,z resolution)

•  Uniformity - measured with a uniform cylinder of activity

•  Count rate - measured with a decaying line source in a solid, cold cylinder

•  Dead time correction accuracy - measured from the count rate data

•  Scatter fraction - measured from the count rate data

•  Attenuation correction accuracy, contrast performance - from a non-cylindrical phantom with hot and cold spheres.

Current  specifications  based  on  National  Electrical  Manufacturers  Association  (NEMA)  Standard  

PET Image Formation Workflow

Primary Detection Decoding Detector

corrections

Coincidence Processing

Data Binning

Data Corrections

Image Reconstruction

Nuclear Medicine Basic Science Lectures Stephen  Bowen  

October  18,  2011  Email:  srbowen@uw.edu  

8  

Analytic Reconstruction

  FBP assumes linear projections and does not account for many sources of variability in LOR

  Backprojection leads to streak artifacts in PET images

Backprojection Filtered Backprojection

From WikiBooks Basic Physics of Digital Radiography •  There are many ways to: –  model the system (and the noise) –  compare measured and estimated projection data –  update the image estimate based on the differences between measured

and estimated projection data –  decide when to stop iterating

Iterative Reconstruction

measured data

p(k) =Hf (k) + n

compute estimated projection data

f (k )

compare measured and

estimated projection data

initial image estimate

p

pp(k )

f (k) → f (k+1)

update image estimate based

on ratio or difference

f (0 )

Reconstructed PET/CT images

No AC

OS-EM

kVCT AC-CT

FBP fused

AC: Attenuation Correction OS-EM: Ordered Subsets Expectation Maximization FBP: Filtered Back-Projection

Modern Times: Time-of-Flight   Time-of-flight capability is now offered in many new PET scanners"

–  Measure time difference of detection of coincidence gammas"–  Defines a line segment in space, shorter than distance between detectors"

–  Improves image signal to noise that is a function of the object size."

TOF  Gaussian  SOR  Conventional  LOR  

segment  length  x  =  cDt/2  c  =  speed  of  light  

Dt  =  timing  resolution  

x  =  7.5  cm  for  the  Dt  ~  0.5  ns  typical  of  TOF  PET  scanners  

x  

Nuclear Medicine Basic Science Lectures Stephen  Bowen  

October  18,  2011  Email:  srbowen@uw.edu  

9  

PET Introduction Summary   PET concept

–  Physics of positron emission, photon annihilation, coincidence detection

  PET components –  2D collimated vs. 3D acquisition mode, detector block

  PET resolution –  Positron range, detector response, line-of-response sampling, depth-of-interaction –  Take home 1: clinical PET resolution ~ 5 mm, small animal PET ~ 1 mm

  PET quantitation –  CT attenuation correction –  Take home 2: separable attenuation correction makes PET more quantitative

than SPECT or MRI

  PET sensitivity –  Absorption efficiency, geometric efficiency –  Take home 3: PET sensitivity 103 greater than SPECT, 106 greater than MRI

  PET image formation –  Acquisition –  Reconstruction