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

Objective: To validate a newly proposed stochastic differential equation (SDE)-based model for proton beam energy deposition by comparing its predictions with those from Geant4 in simplified phantom scenarios. Approach: Building on previous work in Crossley et al. (2025), where energy deposition from a proton beam was modelled using an SDE framework, we implemented the model with standard approximations to interaction cross sections and mean excitation energies, which makes simulations easily adaptable to new materials and configurations. The model was benchmarked against Geant4 in homogeneous and heterogeneous phantoms. Main results: The SDE-based dose distributions agreed well with Geant4, showing range differences within 0.4 mm and 3D gamma pass rates exceeding 98% under 3%/2 mm criteria with a 1% dose threshold. The model achieved a computational speed-up of approximately fivefold relative to Geant4, consistent across different Geant4 physics lists. Significance: These results demonstrate that the SDE approach can reproduce accuracy comparable to high-fidelity Monte Carlo for proton therapy at a fraction of the computational cost, highlighting its potential for accelerating dose calculations and treatment planning.