Analytical depth-dose curves in radiotherapy with hadrons

Abstract

Hadrons are increasingly used in external-beam radiotherapy owing mainly to their characteristic Bragg-peak depth-dose curves, which are suitable to treat deep-seated tumors. An analytical approach to this distribution, rather than relying on measured or numerically calculated data, offers several advantages. This report aims to provide an analytical model for proton (1H+) and alpha particle (4He2+) beams traversing liquid water, as surrogate of human tissue. The model is based on the following premises: (i) the particle energy loss is described beyond the continuous-slowing-down approximation following Bethe–Bloch function, (ii) the range-energy dependency follows a power-law relationship, (iii) the particle fluence decreases linearly with depth due to nonelastic nuclear interactions and (iv) the range straggling distribution can be approximated by a Gaussian.