Polar voxelization schemes combined with a Monte-Carlo based system matrix for image reconstruction in high resolution PET

Iterative methods are currently accepted as the gold standard image reconstruction methods in nuclear medicine. The quality of the final reconstructed image greatly depends on how good the physical processes are modelled in the System-Response-Matrix (SRM). Monte-Carlo based methods are a promising approach to calculate the SRM. However, the increasing granularity used in the detector and image space of high resolution small animal scanners has a direct impact on the time needed to calculate the matrix and its file size. The more physical processes are included in the SRM, or the better these processes are modelled, has a significant impact on the simulation time and the number of non-zero SRM elements. The use of polar voxels is an alternative to tackle this problem. In this work, a study on the performance and image quality of reconstructed images using polar voxels is compared to the traditional approach of cubic voxels, both based on a Monte-Carlo generated SRM. Several alternatives for polar voxelization, and comparison with cubic voxels are also studied in this work. The results obtained show that polar voxels produce reconstructed images with similar image quality, at the cost of reduced spatial resolution in the centre of the field of view (FOV), due to the elongated shape of the voxels in that region. This problem is of great importance, given that the centre of the FOV usually is the region of a PET scanner with highest sensitivity, and high spatial resolution in preclinical studies in this region is vital. A solution to this problem is proposed, introducing a different polar voxelization scheme for the central region of the FOV. It is demonstrated that the spatial resolution is fully recovered in this region, compared to Cartesian voxelization.