Outline
Basic Physics of PET and PET/CT
Frederic H. Fahey DSc
Children’s Hospital Boston
Harvard Medical School
frederic.fahey@childrens.harvard.edu
Positron Emission
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Basics of PET Scanner Design
Data Acquisition
Scintillation Materials
Reconstruction Methods
PET/CT
Time-of-Flight (TOF) PET
MicroPET
Detector Ring
18F
+
511 keV
e511 keV
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Detector Blocks (GE Advance NXi)
PET Sinograms
Sinogram
PET Sinograms
Brain
Projection View
Slice
Angle
Point Source
Image for Each Angle
Image for Each Slice
Note: Sinograms and projection
views are different ways or
showing the same data.
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True, Scatter and Random
Coincidence Detections
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Scatter
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Span of 3 Michelogram
(R = 2 τ N1 N2)
2D Detector
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Span of 7 Michelogram
Scintillator
Crystals
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PMTs
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Axial Direction
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End
Shields
Septa
511 kev photon
Courtesy of M. Graham, M. Madsen, U Iowa
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Acquisition Modes
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2D
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Segment 2
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Segment 1
Segment 3
GE 3D Projection view and Michelogram
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3D PET
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Sensitivity drops off towards edges
4-5X increased sensitivity overall
Increased scatter (15% to 40%)
Increased randoms from out-of-field activity
Rebinning algorithms to apply 2D
reconstruction
• Some devices can acquire in 2D or 3D whereas
some can only acquire in 3D
• 3D in Brain, 2D (or 3D) in Whole Body
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Criteria for Scintillation Material
Crystal Identification
• Detection Efficiency (Stopping Power)
– High Effective Z
– High Density
• Light Output
– Good energy resolution
– Good crystal identification
• Decay Time
– Reduction of random coincidences
– Time-of-Flight PET
Feedback Loop
New Detector Materials
SCINTILLATOR
Rel. Light Output
NaI(Tl)
100
BGO
LSO
GSO
15-20
75
20-25
Peak Wavelength (nm) 410
480
420
440
Decay Constant (ns)
230
300
12,42
30-60
Density (g/mL)
3.67
7.13
7.40
6.71
Effective Z
51
75
66
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Index of Refraction
1.85
2.15
1.82
1.85
Hygroscopic ?
Yes
No
No
No
Current Estimate
Actual
Projections
Simulated Projections
Use to
improve
current
estimate
Compare
Backprojection
Error
Courtesy of Jerold W. Wallis, M.D.
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Maximum Likelihood
Reconstruction (ML-EM)
aij is the
probability
that a photon
emitted
from pixelj is
detected at
projection
bini.
pixelj
• Maximize the likelihood that the estimated
activity distribution in the body (the
reconstructed transaxial slices) would lead
to the measured projections
• Use the expectation maximization (EM)
algorithm to iteratively estimate the activity
distribution
projection bini
ML-EM Algorithm
EM-ML Reconstruction
• aij can contain physical information (effects
of spatial resolution, scatter, attenuation…)
• EM-ML algorithm takes into account the
nature of the noise (quantum mottle) in the
projection data
• Can yield a more accurate reconstruction
λ’(k)j = λ’(k -1)j Σ [aij {d/ Σ [aij] λ’(k -1)j }]
Σ [aij]
λ’(k)j is the newest estimate of the object pixel value
λ’(k -1)j is estimate of the object at last iteration
d is the projection data
d’ = Σ [aij] λ’(k -1)j is the calculated projection data
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ML-EM Algorithm (added corrections)
Advantages of Iterative Reconstruction
λ’(k)j = λ’(k -1)j Σ [aij {d/ (Σ [aij] λ’(k -1)j+acj(rj nj + cj) }]
Σ [aij/nj acj]
• Correct physics can be included in the
reconstruction and Poission statistics
• Attenuation correction
• Reduction of streak artifact
• Overall quality
ac is photon attenuation data
r is random data
n is normalization data
c is scatter data
Accurate characterization of
the point spread functions
(PSFs) throughout the files of
view allows for an accurate
estimation of the “aij” matrix
leading to improvement in
spatial resolution and signalto-noise.
Improved Image Quality with Accurate Specification
Of the PSF Throughout the Field of View
FBP
Courtesy of Siemens Medical Solutions
HD
Courtesy of Siemens Medical Solutions
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Disadvantages of Iterative
Reconstruction
OS-EM Algorithm
• Ordered-subset expectation maximization
• At each step, project and backproject at only some
angles (i.e. a subset)
• Perform the steps in an ordered way to include all
angles
• Data start to converge even before the 1st iteration
is complete
• Convergence achieved in 3 - 10 iterations
• Computation time of a few minutes
• Slow convergence to the desired solution
(e.g. tens - hundreds of iterations)
• Computationally demanding - number of
iterations and inclusion of the physics
Ways to Increase the Rate of Convergence
• Stopping rules
• Regularization
• OS-EM
OSEM Iterative Reconstruction
OSEM Iterative Reconstruction
First Subset
Assume 80 angles (rows)
Divided into 8 subsets
Thus, 10 rows/subset.
Angle
Angle
Assume 80 angles (rows)
Divided into 8 subsets
Thus, 10 rows/subset.
Second Subset
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OSEM Iterative Reconstruction
Angle
Assume 80 angles (rows)
Divided into 8 subsets
Thus, 10 rows/subset.
Third Subset
By the time one has
processed all of the
projections (rows) once,
the estimate of the object
has been updated 8 times.
Single Slice Rebinning (SSRB)
OSEM Iterative Reconstruction
• Filtered Back-Projection
– Fast
– Robust
– Subject to noise & streaks
• OSEM
– Almost as fast
– Handles noise & streaks
Example: 28 subsets (12
projections per subset) and
2 iterations)
Fourier Rebinning
• More accurate approach to rebinning
• Better estimate of determining into which
parallel plane oblique data should be placed
• Based on the frequency-distance
relationship (Value of Fourier transform of
a sinogram receives contributions mainly
from sources at a fixed distance t=-k/ )
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GE Discovery ST PET/CT
PET/CT
• State-of-the-art PET combined with
state-of-the-art CT (up to 64 slice)
• Anatomical correlation
• CT-based attenuation correction
CT
PET Attenuation Correction
PET
PET-CT Attenuation Correction
P2 = e-µ(L-x)
X
P1 = e-µx
L
PTOT = P1 x P2
= e-µL
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PET-CT Attenuation Correction
PET-CT Attenuation Correction
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Dose from CT of PET-CT
Acquire CT Scan and reconstruct
Apply energy transformation
Reproject to generate correction matrix
Smooth to resolution of PET
Apply during reconstruction
Quality of CTAC
CTADIvol (160 m A, 0.8 s , 1.5:1 pitch)
3000.00
CTADIvol (mrad)
2500.00
New Born
2000.00
1 Y ear Old
1500.00
5 Y ear Old
10 Y ear Old
1000.00
Med Adult
80 kVp
10 mA
0.5 s/rot
1.5:1
140 kVp
160 mA
0.8 s/rot
1.5:1
500.00
0.00
70
90
110
130
Tube V oltage (k V p)
150
ED from
14 mCi of FDG
1 rad
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Effect of Patient Size
80 kVp, 10 mA, 0.5 s/rotation
Quality of CTAC
Accuracy of Atte nuation Correction w ith Patie nt Size
0.0920
80 kVp
10 mA
0.5 s/rot
1.5:1
140 kVp
160 mA
0.8 s/rot
1.5:1
Linear Attenuation Coefficient (cm-1)
0.0900
New born
0.0880
1 YO
5 YO
0.0860
10 Y O
15 Y O
0.0840
Small A dult
Med Adult
0.0820
Large A dult
0.0800
0.0780
80/10/.5
PET-CT Scanners
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Siemens Biograph
GE Discovery ST
GE Discovery STE
Philips Gemini
PET-CT Scanners
Detector Dimension (mm)
# of PET Detectors
PET Detector Material
Spatial Resolution
2D/3D
Atten Corr
Detector Dimension (mm)
# of PET Detectors
PET Detector Material
Spatial Resolution
2D/3D
Atten Corr
GE Discovery STE
4.7 x 6.3 x 30
13,440
BGO
5.0
2D/3D
CT
GE Discovery ST
6.2 x 6.2 x 30
10,080
BGO
6.1
2D/3D
CT
Philips Gemini
4 x 6 x 20
17,864
GSO
4.9
3D
CT&Cs-137
Siemens Biograph LSO Siemens Hi-Rez LSO
6.5 x 6.5 x 25
4 x 4 x 20
9,216
23,336
LSO
LSO
6.3
4.6
3D
3D
CT
CT
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Time-of-Flight PET
Time-of-Flight PET
x = c t/2
Speed of Light
Time (ns)
Distance (cm)
c=3x
1010
cm/s
Where x is the time-of-flight spatial
uncertainty and t is the timing resolution.
0.1
0.5
1.0
5.0
t (ns)
0.1
0.3
0.5
1.0
3
15
30
150
x (cm)
1.5
4.5
7.5
15.0
Time-of-Flight PET
Time-of-Flight PET
Assume t of 0.5 ns => x of 7.5 cm
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Philips Gemini TF
PET/CT scanner
Time-of-Flight PET
SNR Gain from Time-of-Flight PET
D/1.6 x
2 D/ 1.6 c t
PET scanner
CT scanner
70-cm bore
18-cm axial FOV
Brilliance 16-slice
LYSO crystals
where D is the diameter of the object
D (cm)
20
30
40
SNR Gain
1.6
2.5
3.3
Intrinsic
Energy resolution: 11.5% fwhm, Timing resolution: 585 ps
NEMA NU-2
Spatial resolution: 4.8 mm at 1 cm, 5.2 mm at 10 cm
Sensitivity: 6.6 cps/kBq
Scatter fraction (at 440 keV): 27% for 20-cm x 70-cm
Peak NEC: 125 kcps @ 0.42µCi/ml
Courtesy of Joel Karp, PhD, Univ of Penn
Measurements: 35-cm lesion phantom
TOF
non TOF
Gemini TF
6-to-1 contrast
300s
similar noise
and scan time
180s
TOF
higher
CRC
60s
Courtesy of
Joel Karp, PhD,
Univ of Penn
Heavy-weight patient study
13 mCi
2 hr post-inj
3 min/bed
Colon cancer
119 kg
BMI = 46.5
MIP
LDCT
non-TOF
TOF
Courtesy of Joel Karp, PhD, Univ of Penn
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non-Hodgkin’s lymphoma 136 kg (45 BMI) Courtesy of Joel Karp, PhD, Univ of Penn
nonTOF 30 min
TOF
30 min
TOF
CHB MicroPET
10 min
TOF tumor contrast (SUV) higher than non-TOF by 1.5
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Installed 8/16/06
Siemens Focus 120
1.5 mm spatial resolution
7 % Sensitivity
TOF tumor contrast superior to non-TOF for 10 min as well as 30 min scan
Summary
• Modern scanners designed for oncologic imaging
• Practically all PET sales are PET/CT scanners
• New scintillation crystals combine excellent
detection efficiency with short decay times
• Appropriate choice of reconstruction algorithm
can lead to better image quality
• Shorter decay times leads to possibility of time-offlight PET.
• MicroPET scanners can provide very high spatial
resolution with high sensitivity in a small foot
print and easy access to the research animals.
Now for the SAM questions!!
Acquiring a PET scan in 3D mode
leads to
0%
0%
0%
0%
1.
2.
3.
4.
Shorter reconstruction times
Less scatter and random coincidences
Improved spatial resolution
Improved sensitivity
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Time-of-flight PET improves image
quality, particularly in
Answer
4. Improved sensitivity
0%
0%
Reference: Cherry SR, Sorenson JA, Phelps ME,
“Physics in Nuclear Medicine, Saunders,
Philadelphia PA. page 351-352.
Explanation: 3D PET has approximately the same spatial resolution
as 2D PET with increased scatter and random coincidences. It is
also more complicated to reconstruct. However, the removal of the
inter-plane septa leads to a large increase in the lines-of-response
(LORs) and thus a 4 to 5 fold increase in sensitivity.
0%
0%
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2.
3.
4.
Fast scans
Larger patients
Small animals
Time sequences of scans
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Answer
2. Larger Patients
Reference: Suleman Surti, Austin Kuhn, Matthew E. Werner,
Amy E. Perkins, Jeffrey Kolthammer and Joel S. Karp,
“Performance of Philips Gemini TF PET/CT Scanner with Special
Consideration for Its Time-of-Flight Imaging Capabilities”,
J Nucl Med 48: 471-480, 2007.
Explanation: Time-of-flight PET involves both data acquisition and
reconstruction. It allows one to locate the annihilation event along
the line-of-response which leads to reduced noise and higher
contrast in the image data. With current technology, the event can
be localized to within about 7-8 cm which leads to better image
improvement in larger patients but not for small patients or small
animals. It is not at all related to the duration of the scan or whether
the study is acquired as a time sequence.
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