PET: Physics Principles and Equipment Design · 2012-07-01 · 1. PET transmission source (68Ge/68Ga): Coincident annihilation photons (mono-energetic @ 511 keV), 265 day half life

AAPM 2012 Summer School on Medical Imaging using Ionizing Radiation

PET: Physics Principles and Equipment Design

Paul Kinahan, PhD, FIEEE

Director of PET/CT PhysicsImaging Research LaboratoryDepartment of RadiologyUniversity of Washington, Seattle, WA


Paul Kinahan

Disclosures• Research Contract, GE Healthcare• Advisory Board, Aposense Inc.


Paul Kinahan

Objectives1. Review physics of positron emission and detection of

annihilation photons2. Understand quantitative corrections that are needed3. Learn context of PET imaging in clinical practice

Outlinedecay and scintillation

• Coincidence event detection• Quantitative corrections• The PET imaging equation• CT-based attenuation correction• Image reconstruction• Patient imaging process• Scanner calibration, SUVs• Resolution versus noise tradeoffs


Paul Kinahan

PET/CT Imaging is a powerful tool for detection, diagnosis, and staging of cancer

PET Image of Function

Function+Anatomy CT Image of Anatomy


Paul Kinahan

Diagnostic Accuracy of PET/CT exceeds CT or PET only

Weber et al. Nature Reviews Clinical Oncology 2008


Paul Kinahan

• A nucleus is made of neutrons (N) and protons (Z) with mass number A = N+Z• Element X (i.e. the chemistry) is determined by the # protons Z• Symbolically • Black dots on plot are stable combinations of N and Z• N increases faster than Z for stable atoms• Combinations of N and Z away from the line of stability decay to the line

ZA X

Nuclear Stability and Decay

ISOTOPE LINE Z=50


Paul Kinahan

Decay modes when there are not enough neutrons• Positron emission: a proton converts to a neutron and emits

a positron (to conserve charge)

• For example: The positron then combines with a free electron and annihilates, producing 2 annihilation photons of 511 keV each

• Electron capture: an orbital electron (typically from inner K or L shells) combines with a proton to form a neutron

and also typically generating a characteristic x-ray

p n v

ZA X Z1

A X vor

918F 8

18O v

e 2 (E mc2 )

p e n v


Paul Kinahan

Positron Emission

Radioactive decay• start with neutron-deficient

isotope• decays to stable form by

converting a proton to a neutron and ejects a 'positron' to conserve electric charge

• positron annihilates with an electron, releasing two anti-colinear high-energy photons

npnp

n

pnp n

pn

pn p

p

pn

p n

pn

p

n

p n npnp

n

pnp n

pn

pn p

n

pn

p n

pn

p

n

p n

~2 mm

18F 18O

~180 deg

E = mc2

= 511 keV

+

e-


Paul Kinahan

Energy Spectrum of Positrons in Isotopes

Levin PMB 1999


Paul Kinahan

Calculated spatial resolution

20 cm system diameter and 2 mm wide detectors (pre-clinical scanner)

80 cm system diameter with 4 mm detectors (clinical scanner)

Resolution is typically at least 2x worse than this in practice• detector multiplexing• sinogram sampling• smoothing applied during/after image reconstruction to suppress noise• Formula by Moses:

d = detector width, D = ring diameter, R = positron range, b = 'block factor'

Levin PMB 1999

FWHM 1.25 d / 2 2 0.0022D 2 R2 b2


Paul Kinahan

Useful Positron Emitting Isotopes

Isotope Half life (min)

Most probable energy (keV)

FWHM of positron range* in water (mm)

109.7 203 0.102

1.3 1384 0.169

20.3 326 0.111

10.0 432 0.142

2.0 696 0.149

918F

3782Rb

611C

713N

815O

* very long tails> 90% of all clinical studies


Paul Kinahan

Scintillation Detectors

high energy511 keV photon

optical photons (~ 1eV)

scintillator(e.g. BGO Dense yet transparent)

current pulse for each UV photon

detected

photomultipliertubes (PMTs)gain of ~ 106


Paul Kinahan

Scintillators tried in PET

Used in commercial scanners


Paul Kinahan

PET Detector Block

Reflective lightsealing tape

Two dual photocathode PMTs

gamma raysscintillation light

signal out to processing

• PET scanners are assembled in block modules

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


Paul Kinahan

Block matrix6 x 8 crystals (axial by transaxial)Each crystal:

6.3 mm axial4.7 mm transaxial

Scanner constructionAxial:

4 blocks axially = 24 rings15.7 cm axial extent

Transaxial:70 blocks around = 560 crystals88 cm BGO ring diameter70 cm patient port

13,440 individual crystals

Block formation for a current PET scanner


Paul Kinahan

Line of response collimation by coincidence timing

t < 10 ns?

detector A

detector B

record coincident event for this line

of response (LOR)

scannerFOV

+ + e-

annihilation

• In SPECT this is achieved though use of a collimator• In CT the known source-detector geometry is used


Paul Kinahan

PET Imaging Equation• With enough coincident events for each line of

response, we can approximate measures as line-integral data of the radioisotope concentration

g(l,) f (x(s), y(s))ds

The integral is along a lineL(l, ) (x, y) x cos ysin l With rotated coordinates (l,s)x(s) l cos ssiny(s) l sin s cos

s

f (x, y)


Paul Kinahan

Sinograms• We can represent the projection data g(l,), as a 2-D image, which is

called a sinogram• Each row is a projection at a fixed angle , with an intensity of g(l,• A point in the object projects to a sine wave in the sinogram• Useful for understanding scanner problems

l

object sinogram

scanner FOV


Paul Kinahan

More complex sinogram example

l

x

y

l

s


Paul Kinahan

“2D” versus “Fully-3D” PET imaging

2D Emission Scan Fully-3D Emission Scan

detectedphotons absorbed

by septa

detecteddetected

• lower sensitivity, simpler to reconstruct

septa

• lower sensitivity, simpler to reconstruct

• higher sensitivity, harder to reconstruct

end shield

scintillator

tracer accumulation


Paul Kinahan

Quantitative errors in measurement

Lost (attenuated)event

Scattered coincidenceevent

Random coincidenceevent

incorrectly determined LORs

Compton scatter

no LOR

• Corrections have to be applied for these effects


Paul Kinahan

QuestionWhat physical property has the biggest impact on PET image quality?

1. Type of scintillator material2. Attenuation3. Scatter4. Random coincidences5. Amount of injected FDG6. Scanner calibration and QA/QC


Paul Kinahan

Answer: Attenuation

Scans performed using the same scanner and protocols

Thin not Thin


Paul Kinahan

Effects of Attenuation: Patient Study

PET: without attenuation correction

PET: with attenuation correction (accurate)

CT image (accurate)

Enhanced skin uptake

reduced mediastinal

uptake

Non-uniform liver

'hot' lungs

Attenuation, and errors in attenuation correction, can dominate image quality


Paul Kinahan

Attenuation in PET Imaging• A key issue is that there are 2 photons along the line of response (LOR)

so that total attenuation is always the same (unlike case for SPECT)

annihilation location

detector A

detector B

attenuation distance from annihilation location to detector B

NA N0 exp (x( s ), y( s );E)d sS0

R

NB N0 exp (x( s ), y( s );E)d s

R

S0

photons detected from a single

annihilation location at s0


Paul Kinahan

Attenuation in PET Imaging• Total number of annihilation photons arriving in

coincidence is the product of the attenuation factors

• If we now allow for a distributed source of positrons

even better, we have attenuation as a simple multiplication

NC N0 exp (x( s ), y( s );E)d sS0

R

exp (x( s ), y( s );E)d sR

S0

N0 exp (x( s ), y( s );E)d s

R

R

(l,) K A(x(s), y(s))exp (x( s ), y( s );E)d sR

R

dsR

R

(l,) K A(x(s), y(s))dsR

R

exp (x(s), y(s);E)dsR

R


Paul Kinahan

Types of transmission imaging

1. PET transmission source (68Ge/68Ga): Coincident annihilation photons (mono-energetic @ 511 keV), 265 day half life

2. Single photon source (137Cs): Single -rays (mono energetic @ 662 keV), 20 yr half-life

3. X-ray CT scan: X-rays with a distribution of energies from ~30 to 130 keV (effective energy of ~70 keV)

E

I0(E) X-ray source spectra


Paul Kinahan

Comparing X-ray, -camera (SPECT) and PET

SPECT:

X-ray CT:

PET:L1L2

L1

Attenuation only, but with complicated energy weighting

Uncoupled mono-energetic attenuation and emission

Coupled mono-energetic attenuation and emission

I0(E)

(x,y,E)

I I 0 (E)e (x .y ,E )dL

0

L

0

dE

I I 0 (x, y)

dL

e

(x .y ,511keV )dL

I0 (x, y)

I I0 (x, y)0

L

e (x .y ,EO )dL

0

L

dL

E

I0(E)

I0 (x, y)

L1 L2 Lconstant attenuation length:

L1variable attenuation length:

emission (sinogram) dataattenuation factors


Paul Kinahan

PET Transmission imaging

• Using 3-point coincidences, we can reject TX scatter• (x,y) is measured at needed value of 511 keV• Near-side detectors, however, suffer from deadtime due to high countrates• Subject to bias from emission photons from patient

orbiting 68Ge/68Ga

source

PET scanner

scattered TX photon

near-side detectors

511 keV annihilation

photon


Paul Kinahan

Single-photon transmission imaging

• We cannot reject TX scatter with 3-point method, so additional scatter corrections needed• (x,y) is measured at 662 keV, so scaling or segmentation is needed (to impose correct

value), which can add bias• no deadtime for near-side detectors, so much higher source strengths can be used

orbiting 137Cs source

PET scanner

scattered TX photon

662 keV g-ray photonshielding for near-

side detectors


Paul Kinahan

X-ray CT transmission imaging

• Scatter is suppressed with rejection grid, although beam-hardening occurs• (x,y,E) is measured as an (unknown) weighted average from ~30-130 keV, so some other method to get

(x,y,511keV), potentially introducing bias. Such as the hybrid method [Kinahan et al, Med Phys, 25:2046-2053, 1998], but which has bias problems.

• photon flux is very high, so very low noise, but much higher patient dose• greatly improved contrast

orbiting X-ray tube

X-ray detectors

30-130 keV X-ray photon

scatter-rejection grid


Paul Kinahan

PET TX: 3min511 keVbest quantitationhighest noise

singles TX: 3min662 keV

X-ray CT TX: 20 s~30-120 keVworst quantitationlowest noise

Comparison of transmission imaging methods

• Due to the diagnostic superiority of PET/CT over PET, all attenuation correction is done use CT-based methods


Paul Kinahan

CT-based Attenuation Correction• The mass-attenuation coefficient () is similar for all non-bone

materials since Compton scatter dominates for these materials• Bone has a higher photoelectric absorption cross-section due to

presence of calcium• Can use two different scaling factors: one for bone and one for

everything else

0.01

0.10

1.00

10.00

100.00

10 100 1000keV

Bone, Cortical

Muscle,SkeletalAir

bone

everything else

70 511


Paul Kinahan

0.00

0.05

0.10

0.15

0.20

-1000 -500 0 500 1000 1500

CT Hounsfield Units

CT-based Attenuation Correction• Bi-linear scaling methods apply different scale factors for bone and non-

bone materials• Should be calibrated for every kVp and/or contrast agent

air-water mixture

water-bone mixture

air soft tissue dense bone


Paul Kinahan

PET/CT Anatomy

All 3 (couch, CT and PET) must be in accurate alignment


Paul Kinahan

• CT images are also used for calibration (attenuation correction) of the PET data

• Note that images are not really fused, but are displayed as fused or side-by-side with linked cursors

• Note also that the CT is used for attenuation correction, thus a significant potential for error

Data Flow and Processing

X-ray acquisition

Anatomical (CT) Reconstruction

PET Emission Acquisition

CT Image

Translate CT to PET Energy (511 keV)

Smooth to PET Resolution

Attenuation Correct PET Emission Data

Functional (PET) Reconstruction

PET Image

Display of PET and CT DICOM image stacks


Paul Kinahan

Respiratory Artifacts: Propagation of CT breathing artifacts via CT-based attenuation correction

Attenuation artifacts can dominate true tracer uptake values


Paul Kinahan

• Examples of respiratory and gross motion artifacts• As a check, compare PET image without attenuation correction

Coronal section of attenuation-corrected FDG-PET image

PET image (now in hot metal color scale) overlaid on CT image

Coronal section of FDG-PET image without attenuation-correction

Motion Artifacts


Paul Kinahan

Commercial/Clinical PET/CT ScannerPET detector blocksthermal barrierrotating CT system

unit

hum

an


Paul Kinahan

GE Discovery 690 Siemens mCT Philips Gemini TF

Some Current Scanners


Paul Kinahan

Some Current Scanners Specifications*

*May have errors or be obsolete in some categories


Paul Kinahan

Quantitative Corrections• Attenuation• Scattered coincidences• Random coincidences• Detector efficiency corrections• Deadtime corrections• Scanner calibration• Image reconstruction

In principle corrections for these effects can be performed accurately, but any errors will produce errors in the PET image.

Attenuation correction errors are the most significant in generalCalibration errors have typically received the least attention


Paul Kinahan

PET Image Reconstruction• We have an inverse problem since the scanner

measures

• In other words, given g(l,), what is f(x,y)?

• There are two main classes of image reconstruction– Analytic: Using the Filtered-backprojection algorithm (FBP)

– Iterative: Based on statistical modeling of the data, which is Poisson distributed

• Iterative methods are most commonly used– Typically some variant of expectation maximization (EM)

used for maximum likelihood estimation

g(l,) f (x(s), y(s))ds


Clinical Considerations


Paul Kinahan

Clinical Applications

IMV 2008 PET Imaging Market Summary Report


Paul Kinahan

PET Scanning Process

QuickTime™ and a decompressor

are needed to see this picture.

Imageinterpre‐tation



Patient

preparation



Scan

acquisition



Image

recon-

struction



Image

analysis


Paul Kinahan

1. Scout scan (5-10 sec)

CT PET

4. Whole-body PET (15-30 min)

CT PET

Typical PET/CT Scan Protocol

3. Helical CT (30 sec)

CT PET

2. Selection of scan region

Scout scan image


Paul Kinahan

Typical Radiation Doses


Paul Kinahan

What Do PET Scans Measure?• If everything goes well, the role of the PET scanner is to measure the

radioactivity per unit volume• Typically measured as kBq/ml or Ci/ml• Start with a simple example:

10 mCi = 370 MBq 70 kg water = 70 L inject

concentration = 370,000 kBq / 70,000 ml= 5.3 kBq/ml

suppose there is a very small object that takes up 5x the local concentration, so its concentration = 26.5 kBq/ml


Paul Kinahan

What if there are different activities or distribution volumes?

• Injecting different amounts or changing the volume will change the concentration

10 mCi = 370 MBq inject

concentration = 5.3 kBq/ml





35 kg = 35 L

26.5 kBq/ml

13.3 kBq/ml

53.0 kBq/ml

The hot spot has different uptake values in kBq/ml even though it has the same relative uptake compared to background


Paul Kinahan

Standardized uptake values (SUVs)• Normalize by amounts injected per volume (i.e. weight) to get the same

relative distribution with SUV = 1.0 for a uniform distribution


SUV = 5.3 kBq/ml / (370MBq/70 Kg)= 1.0 gm/ml


SUV = 1.0 gm/ml


SUV = 1.0 gm/ml

35 kg = 35 L

SUV = 5.0

SUV = 5.0

SUV = 5.0

The hot spot now has the same SUV uptake values independent in activity injected or volume of distribution (i.e. patient size)


Paul Kinahan

Sources of Error in SUV Values

It is important to minimize SUV errors for serial (e.g. response to Rx) or multi-center studies

Some potential sources of error are:• High blood glucose levels• Variations in dose uptake time• Uncalibrated clocks (including scanner) and cross calibration of scanner with dose

calibrator• Errors in radioactive dose assay• Variations in image reconstruction and other processing protocols and parameters• Variations in images analysis methods: E.g. how ROIs are drawn and whether max or

mean SUV values are reported

SUV PETROI

DINJ / V

PET = measured PET activity concentrationD' = decay-corrected injected doseV' = surrogate for volume of distribution


Paul Kinahan

SUV calculation chain for PET

9.6 mCi

dose calibrator

pre- and post injection assays

decay correctednet activity

PET scanner scanner global

calibration factor

patient weight (& height)

scanner units Bq/ml SUVs

SUV scale factor s


Paul Kinahan

• Modified NEMA NU-2 Image Quality Phantom (30 cm x 23 cm cross section)

• Sphere diameters:1.0, 1.3, 1.7, 2.2, 2.8, 3.7 cm• 4:1 target:background ratio and typical patient activity• RC = measured / true

Resolution Effects

Recovery Coeffcient (RC) with 2D FBP

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4Diameter (cm)

Mean RC for ROI

Max RC for ROI


Paul Kinahan

Variations in resolution loss vs. size and smoothingM

ean

Max

FBP OSEM

Incr smoothing


Paul Kinahan

Resolution versus noise

10 mm smoothing4 mm smoothing 7 mm smoothing

RC for 1 cm spheres

0.85

0.92

0.52

0.80

0.40

0.72SNM Chest phantom: True RC is 1.0


Paul Kinahan

QuestionWhat is the goal of a combined PET/CT scanner?1. Accurate attenuation correction2. Accurate image alignment3. Revitalize nuclear medicine4. Job security for physicists


Paul Kinahan

References• Cherry SR, Sorenson JA, Phelps ME. Physics in

Nuclear Medicine. Saunders: Philadelphia, PA, 2003• Positron Emission Tomography: Basic Science and

Clinical Practice. Peter E Valk, Dale L Bailey, David W Townsend and Michael N Maisey Eds., London, Springer Verlag, 2003


Extra slides


Paul Kinahan

• An atomic nucleus is made of neutrons (N) and protons (Z) with mass number A = N+Z

• Element X (i.e. the chemistry) is determined by the # protons Z

• Symbolically • Black dots on plot are stable

combinations of N and Z• N increases faster than Z for

stable atoms• Combinations of N and Z away

from the line of stability decay to the line

ZA X

Nuclear Stability and Decay

ISOTOPE LINE Z=50


Paul Kinahan

PET Image Reconstruction• From the sinograms, or line integral data collected as

large numbers of coincident events, we can solve the inverse problem


Paul Kinahan

Size-Dependent Resolution Losses

• Hot sphere diameters of 10, 13, 17, 22, 28, and 37-mm

• Target/background ratio 4:1

• Max and mean activity concentrations measured via 10-mm diameter ROIs

similar to abdominal x-section

Modified NEMA NU-2 IQ Phantom


Paul Kinahan

Not meant as a "Consumer's Report" evaluation, but rather to facilitate multi-center comparisons

SNM Validation Phantom Study• Sample images of the IDENTICAL object from 12 different PET and PET/CT

scanners


Paul Kinahan

‘Coffee Break’ Repeat PET/CT scans with Repositioning

GE DSTE-16 PET/CT Scanner Siemens Biograph HI-REZ-16 PET/CT Scanner

20%

30%

40%

50%

60%

70%

80%

90%

100%

5 10 15 20 25 30 35Sphere Diameter (mm

Max

Mean

20%

30%

40%

50%

60%

70%

80%

90%

100%

5 10 15 20 25 30 35Sphere Diameter (mm)

Max

Mean

SUVs from 20 3D-OSEM scans with 7-mm smoothing

• Intra-scanner short-term variability is 3% - 4%


Paul Kinahan

SNM Phantom: Key results of SUV measurements

Variations are introduced by the scanner type,acquisition protocol, calibration differences,processing (e.g. image reconstruction methodor smoothing) and ROI definition method.

averaged coefficients of variation

mean SUV: 8.6%, max SUV: 11.1%

Plots of recovery coefficient (RC) = measured in ROI/true


Paul Kinahan

2 cm sphere

5 cm sphere

33 cm

profile

Resolution Effects


Paul Kinahan

Image Reconstruction: Modeling Detector BlurringInter-crystal scattering Parallax error

true LOR

variable depth of

interactionassigned line of

response (LOR)

Shape of detector blurring point spread function (PSF) • Radially variant• Asymmetric in transaxial direction• Two-fold symmetric about FOV center

crystal thickness

true event crystal

assigned event crystal due to scattering

scintillation(Compton scatter)

light collection

annihilation photon


Paul Kinahan

Spatially‐Variant Image Resolution

standard OSEM

OSEM with detector blurring

modeled


Paul Kinahan

Typical PET Scanner Detector Ring


Paul Kinahan

X-ray and Annihilation Photon Transmission Imaging for Attenuation Correction

0

25,000

50,000

75,000

100,000

0 100 200 300 400 500 600

keV

I

X-ray (~30-120 keV) PET Transmission (511 keV)Low noise Noisy

Fast SlowPotential for bias when

scaled to 511 keVQuantitatively accurate

for 511 keV

Transform?

Documents

PET: Physics Principles and Equipment Design · 2012-07-01 · 1. PET transmission source (68Ge/68Ga): Coincident annihilation photons (mono-energetic @ 511 keV), 265 day half life