Path-Length-Based Monte Carlo Simulation for Primary Proton Fluence In Dose Calculation
Abstract
Purpose
Proton therapy offers superior therapeutic ratio due to its favorable dose distribution, but accurate dose calculation remains challenging. Current methods rely on either pencil-beam algorithms (fast but inaccurate in heterogeneous media) or Monte Carlo simulations (accurate but computationally expensive). This work introduces a primary proton model and a fluence calculation method to enable faster, accurate dose calculation in clinical applications.
Methods
Particles in proton therapy exhibit distinct propagation characteristics. We classify them as primary protons (continuous small-scale energy loss and direction changes) and secondary particles (wider directional distribution). Following the collapsed-cone convolution/superposition framework, secondary particle fluence is derived from primary proton fluence. Using Geant4 as ground truth, we define primary protons by energy loss per step in a homogeneous medium using a threshold of 1.2×(2×P₉₉−P₉₈), where P₉₉ and P₉₈ are the 99th and 98th percentiles of stepwise energy loss. We traced 250 MeV protons and collected comprehensive energy and directional statistics. Scattering angular distributions were approximated as a function of path length despite a moderate energy spread at equal path lengths. We validated our approach against Geant4 using a custom Monte Carlo program that traces primary protons by path length and samples directional changes from collected statistics.
Results
We calculated the primary proton fluence of a 250 MeV infinitesimal incident beam using both Geant4 and our custom Monte Carlo method in a water phantom. Our simulation achieved an 18.36× speedup over Geant4 (14 vs. 257 seconds). Due to rapid beam spreading, fluence values beyond the incident region are low; we benchmarked using logarithmic scale. Our method achieved gamma passing rates of 95.11%, 98.18%, and 99.78% at criteria 1.5%/1.5 mm, 2.0%/2.0 mm, and 3.0%/3.0 mm, respectively.
Conclusion
We successfully developed a path-length-based Monte Carlo simulation for primary proton fluence, achieving a significant computational speedup while maintaining high accuracy.