Hybrid 3D analytical linear energy transfer calculation algorithm based on precalculated data from Monte Carlo simulations

Purpose: The dose-averaged linear energy transfer (LET_d) for intensity-modulated proton therapy (IMPT) calculated by one-dimensional (1D) analytical models deviates from more accurate but time-consuming Monte Carlo (MC) simulations. We developed a fast hybrid three-dimensional (3D) analytical LET_d calculation that is more accurate than 1D analytical model. Methods: We used the Geant4 MC code to generate 3D LET_d distributions of monoenergetic proton beams in water for all energies and used a customized error function to fit the LET_d lateral profiles at various depths to the MC simulation. The 3D LET_d calculation kernel was a lookup table of these fitted coefficients, and LET_d was determined directly from spot energies and voxel coordinates during analytical dose calculations. We validated our new method by comparing the calculated LET_d distributions to MC results using 3D Gamma index analysis with 3%/2 mm criteria in 12 patient geometries. The significance of the improvement in Gamma index analysis passing rates over the 1D analytical model was determined using the Wilcoxon rank-sum test. Results: The passing rate of 3D Gamma analysis comparing LET_d distributions from the hybrid 3D method and the 1D method to MC simulations was significantly improved from 94.0% ± 2.5% to 98.0% ± 1.0% (P = 0.0003). The typical time to calculate dose and LET_d simultaneously using an Intel Xeon E5-2680 2.50 GHz workstation was approximately 2.5 min. Conclusions: Our new method significantly improved the LET_d calculation accuracy compared to the 1D method while maintaining significantly shorter calculation time even comparing with the GPU-based fast MC code.