Implementation of pencil kernel and depth penetration algorithms for treatment planning of proton beams

The implementation of two algorithms for calculating dose distributions for radiation therapy treatment planning of intermediate energy proton beams i s described. A pencil kernel algorithm and a depth penetration algorithm ha ve been incorporated into a commercial three-dimensional treatment planning system (Helax-TMS, Helax AB, Sweden) to allow conformal planning technique s using irregularly shaped fields, proton range modulation, range modificat ion and dose calculation for non-coplanar beams. The pencil kernel algorith m is developed from the Fermi-Eyges formalism and Moliere multiple-scatteri ng theory with range straggling corrections applied. The depth penetration algorithm is based on the energy loss in the continuous slowing down approx imation with simple correction factors applied to the beam penumbra region and has been implemented for fast, interactive treatment planning. Modellin g of the effects of air gaps and range modifying device thickness and posit ion are implicit to both algorithms. Measured and calculated dose values ar e compared for a therapeutic proton beam in both homogeneous and heterogene ous phantoms of varying complexity. Both algorithms model the beam penumbra as a function of depth in a homogeneous phantom with acceptable accuracy. Results show that the pencil kernel algorithm is required for modelling the dose perturbation effects from scattering in heterogeneous media.