The angular transition density describing the proton trajectory is based on Moliere's multiple scattering theory and Vavilov's theory of energy loss along the protons' path increment. These multiple scattering and energy loss distributions are sampled using equal probability spacing to optimize computational speed while maintaining calculational accuracy. Nuclear interactions are accounted for by using a simple exponential expression to describe the loss of protons along a given path increment and the fraction of the original energy retained by the proton is deposited locally.
Three levels of testing for the algorithm are provided: 1) Absolute dose comparisons with PTRAN Monte Carlo simulations in homogeneous water media, 2) Modeling of a fixed beam line including the scattering system and range modulator and comparisons with measured data in a homogeneous water phantom, and 3) Relative dose comparisons with the predictions of an equivalent pathlength method for a patient's anatomy described X-ray CT.
The dose qccuracy of this algorithm is shown to be within 5% throughout the range of a 200 MeV proton and it has an adequate spatial accuracy of 1 mm.