Flagged uniform particle splitting for variance reduction in proton and carbon ion track-structure simulations

Flagged uniform particle splitting was implemented with two methods to improve the computational efficiency of Monte Carlo track structure simulations with TOPAS-nBio by enhancing the production of secondary electrons in ionization events. In method 1 the Geant4 kernel was modified. In method 2 Geant4 was not modified. In both methods a unique flag number assigned to each new split electron was inherited by its progeny, permitting reclassification of the split events as if produced by independent histories. Computational efficiency and accuracy were evaluated for simulations of 0.5-20 MeV protons and 1-20 MeV u^-1 carbon ions for three endpoints: (1) mean of the ionization cluster size distribution, (2) mean number of DNA single-strand breaks (SSBs) and double-strand breaks (DSBs) classified with DBSCAN, and (3) mean number of SSBs and DSBs classified with a geometry-based algorithm. For endpoint (1), simulation efficiency was 3 times lower when splitting electrons generated by direct ionization events of primary particles than when splitting electrons generated by the first ionization events of secondary electrons. The latter technique was selected for further investigation. The following results are for method 2, with relative efficiencies about 4.5 times lower for method 1. For endpoint (1), relative efficiency at 128 split electrons approached maximum, increasing with energy from 47.2 ± 0.2 to 66.9 ± 0.2 for protons, decreasing with energy from 51.3 ± 0.4 to 41.7 ± 0.2 for carbon. For endpoint (2), relative efficiency increased with energy, from 20.7 ± 0.1 to 50.2 ± 0.3 for protons, 15.6 ± 0.1 to 20.2 ± 0.1 for carbon. For endpoint (3) relative efficiency increased with energy, from 31.0 ± 0.2 to 58.2 ± 0.4 for protons, 23.9 ± 0.1 to 26.2 ± 0.2 for carbon. Simulation results with and without splitting agreed within 1% (2 standard deviations) for endpoints (1) and (2), within 2% (1 standard deviation) for endpoint (3). In conclusion, standard particle splitting variance reduction techniques can be successfully implemented in Monte Carlo track structure codes.