Implementation of a simplified analytical random walk model dose calculation algorithm with nuclear interaction for treatment planning of scanning-beam proton therapy

Abstract

Our recently proposed simplified analytical random walk model (SaRWM) dose calculation algorithm without the nuclear interaction component gives an analytical solution of the proton dose by treating each medium voxel as a proton source. It was validated against Monte Carlo simulation. In this work, we included the nuclear interactions into SaRWM and implemented SaRWM with the measured proton range in water, beam source divergence, and spot size for our proton pencil-beam scanning system at St. Jude Children’s Research Hospital. The proton relative fluence in SaRWM was calibrated to the measured relative output of our treatment machine, and the absolute proton fluence per system’s monitor unit (MU) was calibrated by the calculated dose against the absolute dose at the center of a spread-out Bragg peak (SOBP, in depth from 10 cm to 20 cm and field size 10 × 10 cm2) in water. The accuracy of SaRWM was evaluated by the measured integral depth dose (IDD) of each energy in water, the measured point dose in an SOBP region, and gamma test of the calculated 3D dose delivered from treatment plans in solid water against the measured 2D dose at depths corresponding to the proximal, middle, and distal SOBP region. The mean relative difference of IDDs was within 3% before the Bragg peak, and the distance between IDDs after the Bragg peak, calculated at the depth where the relative difference was maximal, was within 0.4 mm. The point dose difference was within 1.68% in the plateau SOBP region and within 1.26% before the SOBP region. The gamma test (2%/2 mm with 10% threshold dose) pass rates for the 235 planes of patient plans examined were 96.97% ± 2.82% for those without a range shifter and 98.03 ± 2.29% for those with a 4 cm range shifter. The results indicate high accuracy of SaRWM for proton dose calculation. Approximately 75% of calculation time was for the nuclear interaction.