Post on 25-Feb-2016
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Compartment model based analytical PET simulator for
PVELab
L. Balkay, I. Valastyán, M. Emri, L. TrónUDMHSC, PET Center, Debrecen, Hungary
Monte Carlo simulators
(Eidolon PET simulator, SimSET package,…) • tracks each individual photons from the annihilation to the final absorption or escape
• it can take into consideration the PMT characteristics and the whole coincidence signal processing
• conceptually precise, versatile, but not fast
Analytical simulators(AS)
(McConnell Brain Imaging Center ,…) • analytically models the most important photon interactions (attenuation, scatter, randoms)
• adding poisson noise to sinograms • although less versatile, very fast (~1min/slice) allowing repeated simulation as often as necessary
Analytical PET simulator
segmented MRI
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activity distribution
Pk = (TkAk+Sk)Nk+Rk
• Tk – true counts• Ak – attenuation factors• Sk – scatter counts• Rk – random counts• Nk – normalization factors
forward projection
distortion effects on sinograms
Correction, reconstruction
* convolving with the PET PSF
*
Option: kinetic model based simulation
segmented MRI
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k1, k2, … mapsinputs
tracer kinetic information
•model •kinetic const.•blood curve
k1
k2
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.
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time
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frames of true activity
distortion effects on sinograms
forward projection
Correction, reconstruction
distortions …
Implementation of kinetic modeling
)(ˆ tCPBXAX • Generalized matrix representation of dynamic system models
X – conc. vector; ,B – matrix, vector of kin. const. The general solution:
A
)()())1((0
ˆˆ TkCdeTkeTk P
TT
BXX AA
• Examples: ,A B
k k2 100 0 0
( )
,A B
k k k k kk kk k
k2 3 5 4 6
3 4
5 6
100 0
0 01 1 1 0
000
Selectable analytical blood curves:
Generate the radioactivity distribution and the statistical error of the radioactive decay
Simulate the instrumental and physical effects as Poisson processes
Correct the distortions of the acquisition
Reconstruction, simulated PET image
Theoretical activity
distribution
Simulate the attenuationof the source object
Simulate the Compton scattering
Simulate the random coincidences
Apply the random correction
Apply the scatter correction
Apply the attenuation correction
Add the statistical noise (Poisson distribution)
Transform to the sinogram spaceSpatial blur with PSF
Main steps during the simulation
The Matlab GUI
GUI to explore the input volume.
The GUI for kinetic model definition.
The Matlab GUI
Validation using the Hoffman slice phantom.
Differences (in %) between simulated and measured parameters
11 %4.4 %4.5 %Mean activity concentration
9 %3.4 %5.2 %SD/M
Region3Region2Region1
Differences (in %) between simulated and measured parameters
11 %4.4 %4.5 %Mean activity concentration
9 %3.4 %5.2 %SD/M
Region3Region2Region1
Measured and simulated images
The simulation time of one dynamic slice took approximately 5 minutes on one 2.8 GHz processor.
Simulating C11[FCWAY] accumulation
0,0130,0730,0770,061GM segment
0,10,010,0770,013WM segment
k4 (1/min)k3 (1/min)k2(1/min)k1(ml/mg/min)
0,0130,0730,0770,061GM segment
0,10,010,0770,013WM segment
k4 (1/min)k3 (1/min)k2(1/min)k1(ml/mg/min)
T=5 min
T=60 minT=35 min
T=6 min T=13 min
T=75 min
Simulating FDG accumulation
T=1.5 min T=2 min T=7 min
T=35 min T=60 min T=120 min
0,006
0,005
k4 (1/min)
0.1
0.1
vf
0,0620,130,102GM segment
0,0450,1090,054WM segment
k3 (1/min)k2(1/min)k1(ml/mg/min)
0,006
0,005
k4 (1/min)
0.1
0.1
vf
0,0620,130,102GM segment
0,0450,1090,054WM segment
k3 (1/min)k2(1/min)k1(ml/mg/min)
Simulating F18-L-Dopa accumulation
Summed image slice from 40 min to 80 min of simulated dynamic frames
The program can be downloaded from:http:\\pet.dote.hu\pveout
Compartment model based analytical PET simulator for PVELab