Comparison of different Monte-Carlo based approaches to calculating the system matrix for small animal PET

This study focuses on Monte-Carlo (MC) based techniques to calculate the system matrix (SM) for iterative image reconstruction of small animal PET data. Our goal is to determine in advance if some simplifications can be done to accelerate the MC simulation without jeopardizing the accuracy of the system model. For most PET scanners, the calculation of the SM would imply extremely long simulation times, even when considering symmetries. Our small animal scanner prototype consists of a continuous LSO crystal (42 times 42 times 10 mm³ ) attached to a flat panel position sensitive photomultiplier tube which was simulated using GATE. To compute the SM elements, we investigated three different radioactivity distribution models: (a) homogeneous distribution within the voxel, (b) one unique emission point at the center of the voxel and (c) eight point sources distributed within the voxel. Each of these models was simulated for five representative voxel positions inside the field of view (FOV), two of these voxels in the inner region of the FOV and the other three voxels were in the peripheral region of the FOV. The storage and discretization of the SM elements was performed by means of: (i) tube-of-response (TOR) histograms and (ii) sinograms. By comparing the SM´s elements generated for each distribution model at each voxel´s position, the accuracy of the models was studied. The results show that in the inner region of the FOV, model C distribution yields the best trade-off between simulation time and SM accuracy. Whereas, for the peripheral region of the FOV, model B yields the best compromise. These results are independent of the discretization process considered. Since the scanner is capable to yield depth-of-interaction (DOI) information, the study was performed taking DOI into account