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

Recently, SPECT and positron emission tomography 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. Several authors have developed methods to calculate line-of-response and voxel sensitivities, known as rotational and geometric weights, respectively. These weights are important for use as normalization factors in iterative image reconstruction, as well as to provide insight into the nonuniformity of voxel sensitivity across the reconstructed field-of-view. 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 may affect the voxel sensitivity in that the accuracy and speed of such a discrete calculation are heavily dependent on the mesh size used. The authors´ alternative approach, that does not rely on the numerical approximation, is to directly calculate the solid angle subtended by each voxel with the detectors over all detector positions. They include results for two camera heads 180° apart (DUAL), three camera heads 120° apart (TRI), and three camera heads 90° and 180° apart (C-SHAPE), with and without axial collimation.