Experimental evaluation of a spatial resampling technique to improve the accuracy of pencil-beam dose calculation in proton therapy

Abstract

In proton therapy, pencil-beam algorithms (PBAs) are the most widely used dose calculation methods. However, the PB calculations that employ one-dimensional density scaling neglect the effects of lateral density heterogeneity on the dose distributions, whereas some particles included in such pencil beams could overextend beyond the interface of the density heterogeneity. We have simplified a pencil-beam redefinition algorithm (PBRA), which was proposed for electron therapy, by a spatial resampling technique toward an application for proton therapy. The purpose of this study is to evaluate the calculation results of the spatial resampling technique in terms of lateral density heterogeneity by comparison with the dose distributions that were measured in heterogeneous slab phantoms. The pencil beams are characterized for multiple residual-range (i.e., proton energy) bins. To simplify the PBRA, the given pencil beams are resampled on one or two transport planes, in which smaller sub-beams that are parallel to each other are generated. We addressed the problem of lateral density heterogeneity comparing the calculation results to the dose distributions measured at different depths in heterogeneous slab phantoms using a two-dimensional detector. Two heterogeneity slab phantoms, namely, phantoms A and B, were designed for the measurements and calculations. In phantom A, the heterogeneity slab was placed close to the surface. On the other hand, in phantom B, it was placed close to the Bragg peak in the mono-energetic proton beam. In measurements, lateral dose profiles showed a dose reduction and increment in the vicinity of x = 0 mm in both phantoms at depths z = 142 and 161 mm due to lateral particle disequilibrium. In phantom B, these dose reduction∕increment effects were higher∕lower, respectively, than those in phantom A. This is because a longer distance from the surface to the heterogeneous slab increases the strength of proton scattering. Sub-beams, which were generated from the resampling plane, formed a detouring∕overextending path that was different from that of elemental pencil beams. Therefore, when the spatial resampling was implemented at the surface and immediately upstream of the lateral heterogeneity, the calculation could predict these dose reduction∕increment effects. Without the resampling procedure, these dose reduction∕increment effects could not be predicted in both phantoms owing to the blurring of the pencil beam. We found that the PBA with the spatial resampling technique predicted the dose reduction∕increment at the dose profiles in both phantoms when the sampling plane was defined immediately upstream of the heterogeneous slab. We have demonstrated the implementation of a spatial resampling technique for pencil-beam calculation to address the problem of lateral density heterogeneity. While further validation is required for clinical use, this study suggests that the spatial resampling technique can make a significant contribution to proton therapy.