Compartment model based analytical PET simulator for PVELab L. Balkay, I. Valastyán, M. Emri, L. Trón UDMHSC, 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 activity distribution P k = (T k A k +S k )N k +R k T k – true counts A k – attenuation factors S k – scatter counts R k – random counts N k – normalization factors forward projection distortion effects on sinograms Correction, reconstruction * convolving with the PET PSF *

Option: kinetic model based simulation segmented MRI k1, k2, … maps inputs tracer kinetic information model kinetic const. blood curve k1 k time frames of true activity distortion effects on sinograms forward projection Correction, reconstruction distortions …

Implementation of kinetic modeling Generalized matrix representation of dynamic system models X – conc. vector;,B – matrix, vector of kin. const. The general solution: Examples:

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 attenuation of 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 space Spatial 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. 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 k1(ml/mg/min)k2(1/min)k3 (1/min)k4 (1/min) WM segment0,0130,0770,010,1 GM segment0,0610,0770,0730,013 k1(ml/mg/min)k2(1/min)k3 (1/min)k4 (1/min) WM segment0,0130,0770,010,1 GM segment0,0610,0770,0730,013 k1(ml/mg/min)k2(1/min)k3 (1/min)k4 (1/min) WM segment0,0130,0770,010,1 GM segment0,0610,0770,0730,013

Simulating FDG accumulation T=1.5 minT=2 minT=7 min T=35 minT=60 minT=120 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: Compartment model based analytical PET simulator for PVELab