SDE-based Monte Carlo dose calculation for proton therapy validated against Geant4

Objective.To systematically assess the accuracy and computational performance of a newly proposed stochastic differential equation (SDE)-based model for proton beam dose calculation by benchmarking it against Geant4 in a set of simplified but increasingly challenging phantom geometries.Approach.Building on previous work in Crossleyet al(2025Proc. R. Soc. A48120240687), where energy deposition from a proton beam was modelled using an SDE framework, we implemented the model using standard approximations to interaction cross sections and mean excitation energies, enabling straightforward adaptation to new materials and configurations. The model was benchmarked against Geant4 in homogeneous, longitudinally heterogeneous and laterally heterogeneous phantoms, for assessment of depth-dose behaviour, lateral transport and impact of material heterogeneities.Main results.Across all phantom configurations and beam energies, the SDE model reproduced the main depth-dose characteristics predicted by Geant4, with proton range agreement within 0.2 mm for 100 MeV beams and within 0.6 mm for 150 MeV beams. Voxel-wise comparisons yielded gamma pass rates exceeding 95% for all cases under strict 2%/0.5 mm criteria with a 1% dose threshold. Differences between the two approaches were spatially localised and primarily associated with regions of steep dose gradients or material heterogeneities, while overall lateral beam dispersion was well reproduced. In terms of computational performance, the SDE model achieved speed-up factors of approximately 2.5-3 relative to single-threaded Geant4, consistently across different Geant4 physics lists.Significance.These results demonstrate that the SDE-based approach can reproduce key dosimetric features predicted by high-fidelity Monte Carlo simulations with good accuracy while already offering a moderate reduction in computational cost. Owing to its formulation, the method is naturally amenable to parallel and GPU-accelerated implementations, suggesting potential for substantial further speed improvements. This makes the approach a promising candidate for fast dose calculations in proton therapy.