Fast analytical modeling of Compton scatter using point clouds and graphics processing unit (GPU)

Quantitative SPECT and PET is not possible without accurate modeling of Compton scatter. The physics of this interaction is well-understood and Monte Carlo and analytical calculations are possible. However, such approaches require exorbitant computing times that limit their practical value in the clinical setting. We present a novel computational model that considerably reduces the computation time needed to estimate Compton scatter by using efficient geometrical models and parallel computational architecture of the graphics processing unit (GPU). The method is based on the use of the point cloud image representation we have previously demonstrated. In this representation, an image is defined as a group of points with unrestricted locations. By allowing free localization of the points, the volumetric image sampling can be optimized. Image volume is represented as a set of non-overlapping tetrahedrons that are defined unambiguously by the points. By tailoring the number of points used in this representation to the resolution level required for the computation of scatter of different orders, we exploit a natural advantage of the point cloud representation. The point cloud model is particularly useful for scatter calculation since n only low spatial frequencies are present The image model thus reduces the computation time significantly. Our computational framework is well-suited for the parallel processing architecture of the NVIDIA Quadro FX 4500 GPU on which the algorithm is implemented. We performed computer simulations to evaluate calculation speed. Our results show that the analytical calculation is very fast at 0.5-1 second per SPECT projection with a scattering point cloud of 30,000 points. The number of points can be further decreased, hence increasing significantly the calculation speed. Further work will optimize the number of points, and investigate strategies for distributing these points optimally in 3D space to obtain a compromise between speed and the accuracy of the calculations. Results of our method will be compared to Monte Carlo simulations to determine the accuracy.