Semi-empirical formulation of multiple scattering for Gaussian beam model of heavy charged particles stopping in tissue-like matter

TL;DR

This paper introduces a simple, semi-empirical model for multiple scattering of heavy charged particles in tissue, improving dose calculation accuracy and efficiency in radiotherapy by approximating scattering behavior with a linear formula.

Contribution

It presents a new linear formula for scattering power based on empirical RMS displacement data, simplifying calculations for ions stopping in water and tissue.

Findings

Model agrees with measurements within 2% or 0.02 cm RMS displacement.

Derived scattering power is inversely proportional to residual range.

Simplifies and accelerates numerical path integral calculations in heterogeneous tissues.

Abstract

Dose calculation for radiotherapy with protons and heavier ions deals with a large volume of path integrals involving a scattering power of body tissue. This work provides a simple model for such demanding applications. There is an approximate linearity between RMS end-point displacement and range of incident particles in water, empirically found in measurements and detailed calculations. This fact was translated into a simple linear formula, from which the scattering power that is only inversely proportional to residual range was derived. The simplicity enabled analytical formulation for ions stopping in water, which was designed to be equivalent with the extended Highland model and agreed with measurements within 2% or 0.02 cm in RMS displacement. The simplicity will also improve the efficiency of numerical path integrals in the presence of heterogeneity.