A kernel‐based algorithm for the spectral fluence of clinical proton beams to calculate dose‐averaged LET and other dosimetric quantities of interest

PURPOSE: To introduce a new analytical methodology to calculate quantities of interest in particle radiotherapy inside the treatment planning system. Models are proposed to calculate dose-averaged LET (LETd) in proton radiotherapy. METHODS AND MATERIAL: A kernel-based approach for the spectral fluence of particles is developed by means of analytical functions depending on depth and lateral position. These functions are obtained by fitting them to data calculated with Monte Carlo (MC) simulations using Geant4 in liquid water for energies from 50 MeV to 250 MeV. Contributions of primary, secondary protons and alpha particles are modeled separately. Lateral profiles and spectra are modeled as Gaussian functions to be convolved with the fluence coming from the nozzle. LETd is obtained by integrating the stopping power curves from the PSTAR and ASTAR databases weighted by the spectrum at each position. The fast MC code MCsquare is employed to benchmark the results. RESULTS: Considering the nine energies simulated, fits for the functions modeling the fluence in-depth provide an average R(2) equal to 0.998, 0.995 and 0.986 for each one of the particles considered. Fits for the Gaussian lateral functions yield average R(2) of 0.997, 0.982 and 0.993, respectively. Similarly, the Gaussian functions fitted to the computed spectra lead to average R(2) of 0.995, 0.938 and 0.902. LETd calculation in water shows mean differences of -0.007 +/- 0.008 keV/mum with respect to MCsquare if only protons are considered and 0.022 +/- 0.007 keV/mum including alpha particles. In a prostate case, mean difference for all voxels with dose greater than 5% of prescribed dose is 0.28 +/- 0.23 keV/mum. CONCLUSION: This new spectral fluence-based methodology allows for simultaneous calculations of quantities of interest in proton radiotherapy such as dose, LETd or microdosimetric quantities. The method also enables the inclusion of more particles by following an analogous process.