A simplified analytical random walk model for proton dose calculation

We propose an analytical random walk model for proton dose calculation in a laterally homogeneous medium. A formula for the spatial fluence distribution of primary protons is derived. The variance of the spatial distribution is in the form of a distance-squared law of the angular distribution. To improve the accuracy of dose calculation in the Bragg peak region, the energy spectrum of the protons is used. The accuracy is validated against Monte Carlo simulation in water phantoms with either air gaps or a slab of bone inserted. The algorithm accurately reflects the dose dependence on the depth of the bone and can deal with small-field dosimetry. We further applied the algorithm to patients' cases in the highly heterogeneous head and pelvis sites and used a gamma test to show the reasonable accuracy of the algorithm in these sites. Our algorithm is fast for clinical use. (paper)