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Fundamentals of Nuclear

Medicine Physics: PET

Curtis B. Caldwell, Ph.D., MCCPM

TG217 SHSC

(416) 480-5736

curtis.caldwell@sunnybrook.ca

Advanced Imaging MBP1024Y

Physics of PET; Radioactive Decay

Why positron emitters for tracers?

• Many of the positron emitters occur naturally in

biological molecules (C, N, O, etc.)

• Many have small molecular weights relative to the

biological molecules they may be used to label

(e.g., F) even if they aren’t found there naturally.

• Consequently, radioactive isotopes can be attached

to biologically interesting molecules with no or

minimal impact on the behavior of those

molecules in the body.

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General Positron Characteristics

• Created by accelerated particle bombardment of specific target materials in a

cyclotron (or linear accelerator)

• Short physical half life

– Fluorine-18 110 Minutes

• Fluorodeoxyglucose

• Variety of new tagged compounds

– Oxygen-15 122 Seconds

• Water

– Nitrogen-13 10 Minutes

• Nitrogen Ammonia

– Carbon-11 20 Minutes

• Variety of tagged biological markers

– Rubidium-82 85 Seconds

Physics of PET; Radioactive Decay

Selected PET tracer compoundsCOMPOUND USE

18F-2-deoxyglucose metabolic imaging

13NH3 (ammonia) blood flow

11C-palmitate myocardial metabolism

11C labeled amino acids protein synthesis, pancreatic

imaging, tumor metabolism 11C-butanol myocardial flow/perfusion

15O2, H2

15O blood flow

C15O2 blood volume

82Rb-chloride myocardial perfusion

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Positron Annihilation

γγγγ

γγγγβ+

PETTRACE Cyclotron from GE

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Typical PET System

• Multiple rings of LSO,

BGO (18-32)

• Ring diameter 80 to 92 cm

• Transverse FOV 60 cm

• Axial FOV 15-18 cm

• Retractable septa/no septa

• Rotating rod/point

sources/x-ray CT

Coincidence Detection

11C13N15O18F

...

positron range

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Electronic Collimation

Types of Coincident Events

True Scatter Randoms

“Prompts” = true + scatter+ randoms

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Random Coincidences• Simultaneous decays can cause

erroneous coincident events called

“randoms”

• For 3D PET, randoms can be as high

as 50% of the image

• Randoms reduced by narrowing the

coincidence window, ∆t

• Random rate is rate1x rate2 x 2∆t

• Time of flight across tomograph

requires ∆t > 2 ns

Random rate α (activity density)2

Scattered Events

• Compton scatter in

patient produces

erroneous coincident

events

• ~15% of events are

scattered in 2-D PET

• ~40% of events are

scattered in 3D whole

body PET

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Scattered and Unscattered Spectra Overlap

Use energy to reduce (not eliminate) scatter

2D Sinogram

• Sinogram:

– collection of projections for one slice

– arranged by radial distance and angle

4 point sources Radial distance

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Resolution limits for PET

• Two assumptions are made in PET:

– The positron originated on a line defined by the

two annihilation photons

– Annihilation photons travel at exactly 180

degrees to each other

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Resolution Limits for PET:

Positron Range

1.72.63.10Rb-82

0.31.10.97C-11

0.21.00.64F-18

Effect on

Resolution

FWHM

(mm)

Range

FWHM

(mm)

Max energy

(MeV)

Isotope

Resolution Limits for PET

• Non-collinearity of 511 keV gamma rays

(180º ± 0.25º)

– Positional inaccuracy of 2 to 3 mm for a 100

cm diameter system

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Other factors affecting resolution

• Size of detector elements

– FWHM is ½ of the size of the detector element

at the centre of the ring (e.g., crystals 4 mm �

FWHM 2 mm)

Other factors affecting resolution

• Transverse position

– Radial resolution degrades as the source is

moved away from the centre (radial elongation)

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Radial Elongation

• Penetration of 511 keV

photons into crystal ring

blurs measured position

• Known as radial

elongation, parallax error,

radial astigmatism

• Can be removed (in

theory) by measuring the

depth of interaction

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Scintillator Properties

812158Energy Resolution(%)

6040300230Decay cst (ns)

267515100Light yield (%NaI)

0.670.870.940.34µ511keV (cm-1)

6.77.47.13.7Density

58667450Effective Atomic #

GSOLSOBGONaIProperty

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PET Block Detector Module

• Saw cuts direct light toward PMTs

• Depth of cut determines light spread at PMTs

• Crystal of interaction found with Anger logic

• 8x8 array; 6mmx6mm

Good performance, less expensive, easier to pack

Block Detectors

• 2D array of crystals attached to 4 PMTs

– Light guides define the pattern of light

distribution in the block crystal

– Determines light output (sharing) to the PMTs

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Physics of PET; photon detection - I

Block detector event positioning

x

y

A C

B D

Event locations are determined

taking by weighting the

amplitudes of the signals from

the four photomultiplier tubes

xA B

A B C D=

+

+ + +

yA C

A B C D=

+

+ + +

BGO Crystals, Blocks and

Modules • 1 BGO crystal: 4 mm x 8

mm x 30 mm

• 36 crystals in a block (6x6) x 6 blocks in a module (2x3) x 56 modules in the scanner = 12096 crystals in the scanner

• 2 dual cathode PMTs in a block = 672 PMTs in the scanner

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Continuous Detector Design

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Three-Dimensional PET

• Colsher – theory of 3D PET reconstruction

(1980)

• Townsend – 3D PET imaging (1988)

• Why? Improved sensitivity.

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2D vs 3D: Sensitivity Profile

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Randoms

• Trues α activity

• Randoms α activity2

• Estimate randoms:– using delayed coincidence window

– calculate based on singles rate and timing window

• Subtract randoms from raw sinogram

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T= rate of

True

coincidences

S=rate of

Scattered

Coincidences

R=rate of

Random

coincidences

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Noise Equivalent Count Rate: A figure of

merit relating scanner performance to image

SNR after randoms and scatter corrections

Sunnybrook PET/CT

0

50000

100000

150000

200000

250000

300000

350000

0 0.5 1 1.5 2

Activity Concentration (microCi/ml)

Count Rate (cps)

Trues

Randoms

Scatter

Total events

NEC

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(US$)

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Sunnybrook PET/CT + Physicists

Sunnybrook PET/CT Images

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