Acceleration of Monte Carlo SPECT simulation using convolution-based forced detection

Monte Carlo (MC) simulation is an established tool to calculate photon transport through tissue in Emission Computed Tomography (ECT). Since the first appearance of MC a large variety of variance reduction techniques (VRT) have been introduced to speed up these notoriously slow simulations. One example of a very effective and established VRT is known as forced detection (FD). In standard FD the path from the photon's scatter position to the camera is chosen stochastically from the appropriate probability density function (PDF), modeling the distance-dependent detector response. In order to speed up MC we propose a convolution-based FD (CFD) which involves replacing the sampling of the PDF by a convolution with a kernel which depends on the position of the scatter event. We validated CFD for parallel-hole Single Photon Emission Computed Tomography (SPECT) using a digital thorax phantom. Comparison of projections estimated with CFD and standard FD shows that both estimates converge to practically identical projections (maximum bias 0.9% of peak projection value), despite the slightly different photon paths used in CFD and standard FD. Projections generated with CFD converge, however, to a noise-free projection up to one or two orders of magnitude faster, which is extremely useful in many applications such as model-based image reconstruction.