Adaptive step size algorithm to increase efficiency of proton macro Monte Carlo dose calculation

PURPOSE: To provide fast and accurate dose calculation in voxelized geometries for proton radiation therapy by implementing an adaptive step size algorithm in the proton macro Monte Carlo (pMMC) method. METHODS: The in-house developed local-to-global MMC method for proton dose calculation is extended with an adaptive step size algorithm for efficient proton transport through a voxelized geometry by sampling transport parameters from a pre-simulated database. Adaptive choice of an adequate slab size in dependence of material interfaces in the proton’s longitudinal and lateral vicinity is investigated. The dose calculation algorithm is validated against the non-adaptive pMMC and full MC simulation for pencil and broad beams with various energies impinging on academic phantoms as well as a head and neck patient CT. RESULTS: For material interfaces perpendicular to a proton’s direction, choice of nearest neighbor slab thickness shows best trade-off between dosimetric accuracy and calculation efficiency. Adaptive reduction of chosen slab size is shown to be required for material interfaces closer than 0.5 mm in lateral direction. For the academic phantoms, dose differences of within 1% or 1 mm compared to full Geant4 MC simulation are found, while achieving an efficiency gain of up to a factor of 5.6 compared to the non-adaptive algorithm and 284 compared to Geant4. For the head and neck patient CT, dose differences are within 1% or 1 mm with an efficiency gain factor of up to 3.4 compared to the non-adaptive algorithm and 145 compared to Geant4. CONCLUSION: An adaptive step size algorithm for proton macro Monte Carlo was implemented and evaluated. The dose calculation provides the accuracy of full MC simulations, while achieving an efficiency gain factor of three compared to the non-adaptive algorithm and two orders of magnitude compared to full MC for a complex patient CT.