Gamma Photon Transport on the GPU for PET

This paper proposes a Monte Carlo algorithm for gammaphoton transport, that partially reuses random paths and is appropriate for parallel GPU implementation. According to the requirements of the application of the simulation results in reconstruction algorithms, the method aims at similar relative rather than absolute errors of the detectors. The resulting algorithm is SIMD-like, which is a requirement of efficient GPU implementation, i.e. all random paths are built with the same sequence of instructions, thus can be simulated on parallel threads that practically have no conditional branches. The algorithm is a combined method that separates the low-dimensional part that cannot be well mimicked by importance sampling and computes it by a deterministic quadrature, while the high-dimensional part that is made low-variation by importance sampling is handled by the Monte Carlo method. The deterministic quadrature is based on a geometric interpretation of a direct, i.e. non-scattered effect of a photon on all detectors.