Differential-pencil-beam dose calculations for charged particles.

The use of a convolution or differential-pencil-beam (DPB) algorithm has been studied for charged-particle dose calculations as a means of more accurately modeling the effects of multiple scattering. Such effects are not reflected in current charged-particle dose calculations since these calculations rely on depth-dose data measured in homogeneous water-equivalent phantoms and use ray-tracing techniques to calculate the water-equivalent pathlength from patient CT data. In this study, isodose plots were generated from three-dimensional dose calculations using Monte Carlo, DPB, and standard ray-tracing methods for a 4-cm modulated 150-MeV proton beam incident on both homogenous and heterogeneous phantoms. To simulate therapy conditions with charged particles, these studies included cases where compensating boluses were introduced to modify the particle range across the treatment field. Results indicate that multiple-scattering effects, including increased penumbral width as a function of beam penetration and the "smearing" of isodose distributions downstream from complex heterogeneities, are well modeled by the DPB algorithm. The DPB algoirthm may also be used to obtain more useful estimates of the dose uncertainty in regions near the end of the beam's range downstream from complex heterogeneities than can be derived from standard ray-tracing calculations.