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

50 100 150 200 250

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100

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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

50 100 150 200 250

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100

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k1, k2, … mapsinputs

tracer kinetic information

•model •kinetic const.•blood curve

k1

k2

.

.

.

50 100 150 200 250

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100

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250

50 100 150 200 250

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100

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time

50 100 150 200 250

50

100

150

200

250

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