Numerical solution of the Boltzmann transport equation for photons and of some equations derived from the Fokker-Planck approximation for electrons. Application to radiotherapy

Abstract

This work is focused on the numerical resolution of the Boltzmann transport equation (BTE) for photons and of a certain type of degenerate parabolic equations which come from the Fokker‐Planck equation. BTE is solved in the three‐dimensional case by means of the so‐called “expansion in orders of scattering”, and the degenerate parabolic equation is solved with a finite difference method. MATLAB language programming has been employed to obtain the numerical results and graphics. The motivation of the thesis is the calculus of the absorbed dose of radiation during external radiotherapy cancer treatment. The first chapters gather medical‐biological and physical information, explaining the fundamentals of radiotherapy and the interaction phenomena between radiation and matter.