Two-dimensional pencil beam scaling: an improved proton dose algorithm for heterogeneous media

New dose delivery techniques with proton beams, such as beam spot scanning or raster scanning, require fast and accurate dose algorithms which can be applied for treatment plan optimization in clinically acceptable timescales. The clinically required accuracy is particularly difficult to achieve for the irradiation of complex, heterogeneous regions of the patient's anatomy. Currently applied fast pencil beam dose calculations based on the standard inhomogeneity correction of pathlength scaling often cannot provide the accuracy required for clinically acceptable dose distributions. This could be achieved with sophisticated Monte Carlo simulations which are still unacceptably time consuming for use as dose engines in optimization calculations. We therefore present a new algorithm for proton dose calculations which aims to resolve the inherent problem between calculation speed and required clinical accuracy. First, a detailed derivation of the new concept, which is based on an additional scaling of the lateral proton fluence is provided. Then, the newly devised two-dimensional (2D) scaling method is tested for various geometries of different phantom materials. These include standard biological tissues such as bone, muscle and fat as well as air. A detailed comparison of the new 2D pencil beam scaling with the current standard pencil beam approach and Monte Carlo simulations, performed with GEANT, is presented. It was found that the new concept proposed allows calculation of absorbed dose with an accuracy almost equal to that achievable with Monte Carlo simulations while requiring only modestly increased calculation times in comparison to the standard pencil beam approach. It is believed that this new proton dose algorithm has the potential to significantly improve the treatment planning outcome for many clinical cases encountered in highly conformal proton therapy.