1
Fundamentals of Nuclear
Medicine Physics: PET
Curtis B. Caldwell, Ph.D., MCCPM
TG217 SHSC
(416) 480-5736
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.
2
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
3
Positron Annihilation
γγγγ
γγγγβ+
PETTRACE Cyclotron from GE
4
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
5
Electronic Collimation
Types of Coincident Events
True Scatter Randoms
“Prompts” = true + scatter+ randoms
6
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
7
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
8
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
9
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
10
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)
11
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
12
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
13
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
14
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
15
Continuous Detector Design
16
Three-Dimensional PET
• Colsher – theory of 3D PET reconstruction
(1980)
• Townsend – 3D PET imaging (1988)
• Why? Improved sensitivity.
17
2D vs 3D: Sensitivity Profile
18
19
20
21
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
22
T= rate of
True
coincidences
S=rate of
Scattered
Coincidences
R=rate of
Random
coincidences
23
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
24
25
26
(US$)
27
28
Sunnybrook PET/CT + Physicists
Sunnybrook PET/CT Images
29
30
