New Hybrid 3D Analytical Linear Energy Transfer (LET) Calculation Algorithm Based on the Pre-Calculated Data from Monte Carlo (MC) Simulations

Abstract

The traditional 1D analytical LET model of the spot scanned proton therapy (SSPT) assumes a uniform LET distribution in the lateral direction for each depth, which will under-estimate the LET value in the low dose penumbra region and over-estimate the LET value in the high dose region compared with Monte Carlo (MC) simulations. We propose a fast and accurate hybrid 3D analytical LET calculation method based on the pre-calculated data from MC simulations. The method is analogous to the pencil beam algorithm to calculate the physical dose in proton therapy with the 3D LET calculation kernel generated by MC as follows: Step-1: Using a well-benchmarked MC code (Geant4) to generate LET distributions of single energy proton beams in water for all 97 energies and derive the dose-averaged LET (LETd) lateral profiles at various depths starting from the surface with 1mm depth interval increase until the depth with the 1% of the peak dose after the Bragg peak. Step-2: Using a customized “error function” to fit the aforementioned LET lateral profiles for every depth of every energy, and store the fitted coefficients as a lookup table. Step-3: During the dose/LET calculation, the stored fitted coefficients and the fitting function will be used to calculate the LETd values based on the spot energies and the water equivalence thickness (WET). The inhomogeneity is handled by taking WET into account in both beam and lateral directions. We then validated the improvement of our new method by comparing the calculated LET distributions with the results calculated from the MC and the previous 1D analytical LET model in twelve patients with different disease sites. Compared with the MC simulation results, the LETd calculation of our new method is systematically better than the traditional 1D model, with the average 3D gamma analysis results of all 12 patients with the threshold of 3% and 2mm increased from 94% to 98% in the region with dose >10% of the maixumum dose. The majority improvement comes from the more accurate LETd calculation in the low dose penumbra region (5%-20% of the prescription dose). In some cases, our new method only has less than 3% relatively difference compared with the MC simulation in the penumbra region, while the previous 1D model under-estimates the LETd value by about 20% to 50%. The calculation time of our new method is comparable to our previous 1D analytical LET calculation algorithm. Our new hybrid 3D analytical method (1) can calculate LETd in SSPT accurately and efficiently, (2) will be used for biological effects evaluation and LET-guided robust optimization in SSPT to improve the OAR protection, (3) is easily to be integrated by other analytical dose engine.