Free flight angular acceptance (FFAA) variance reduction technique for SPECT Monte Carlo simulations

Objective.While several variance reduction techniques (VRTs) exist for SPECT Monte Carlo simulations, many require system-specific pre-calculations (e.g. angular response function) or patient-specific training (e.g. generative adversarial networks), limiting their flexibility for novel detector design and research. To address this, we introduce free flight angular acceptance (FFAA), a novel VRT that integrates methods into an on-the-fly, pre-calculation-free framework.Approach.The method utilizes a two-step approach to separately handle primary and scattered photons. Primary photons are emitted with a forced direction towards the detector and transported using a free flight (FF) biasing method, with their statistical weights adjusted to account for attenuation. For scatter, the technique employs splitting at each Compton and Rayleigh interaction site, where scattered photons are only tracked further if they satisfy an angular acceptance criterion before being transported with FF. By deactivating FF transport at the entrance to the SPECT head and reverting to a conventional analog Monte Carlo simulation for passage through the collimator and detector, the method accurately models complex physical interactions without relying on pre-calculated detector response functions.Main results.When compared with analog Monte Carlo simulations, FFAA achieves mean voxel speedup of about 200 in high-count regions and 100 in low-count regions. The method preserves high fidelity for critical effects, such as collimator scatter and septal penetration, ensuring that the speedup does not compromise the accuracy of complex physical interactions.Significance.This makes FFAA particularly suitable for the development and optimization of novel SPECT collimator designs. To facilitate adoption, FFAA is integrated into the open-source GATE 10 software and is accessible via simple Python functions.