Determination of three-dimensional voxel sensitivity for two- and three-headed coincidence imaging

Recently, SPECT and PET imaging modalities have been hybridized, so that positron coincidence detection can be accomplished with SPECT systems. Originally, only systems with two opposing camera heads were employed. Recent developments to improve sensitivity include the addition of a third camera head. Other authors have developed methods to calculate line-of-response (LOR) and voxel sensitivities, known as rotational and geometric weights, respectively. These weights are important for list-mode image reconstruction. Although their formulations use analytic expressions, the equations derived for the voxel sensitivities involve an integral which cannot be computed in closed form, that is, one must use a numerical approximation. This further impacts the voxel sensitivity, in that a discrete calculation of the integral means that the weighting may not accurately represent the total number of LORs that pass through the voxel. Our alternative approach, that does not rely on the numerical approximation, is to calculate the solid angle subtended by each voxel and the detectors directly. We include results for two camera heads 180degrees apart (DUAL), three camera heads 120degrees apart (EQUI), and three camera heads 90degrees and 180degrees apart (C-SHAPE).