Influence of multiple scattering and energy loss straggling on the absorbed dose distributions of therapeutic light ion beams: I. Analytical pencil beam model.

The lateral and longitudinal distributions of absorbed dose of broad and narrow light ion beams in water are investigated. An analytical algorithm based on the generalized Fermi-Eyges theory is developed and used to calculate the effects of multiple scattering and range straggling on the dose distribution of light ion beams in water. A first-order Gaussian multiple scattering and energy loss straggling approach is generally sufficiently accurate for describing the lateral and longitudinal spread of the Bragg peak and the associated energy deposition distribution of therapeutic light ion beams at ranges of clinical interest. Nuclear reactions are not taken into account in this study. The analytical algorithm given in the present study allows an accurate description of the radial spread and the range straggling of light ions traversing matter. A verification of this approach by comparing with experimental data, Monte Carlo methods and other analytical techniques will be presented in a forthcoming paper.