Evaluating the accuracy of a three-term pencil beam algorithm in heterogeneous media

The goal of this work was to evaluate the accuracy of our in-house analytical dose calculation code against MCNPX data in heterogeneous phantoms. The analytical model utilizes a pencil beam model based on Fermi-Eyges theory to account for multiple Coulomb scattering and a least-squares fit to Monte Carlo data to account for nonelastic nuclear interactions as well as any remaining, uncharacterized scatter (the 'nuclear halo'). The model characterized dose accurately (up to 1% of maximum dose in broad fields (4 × 4 cm² and 10 × 10 cm²) and up to 0.01% in a narrow field (0.1 × 0.1 cm²) fit to MCNPX data). The accuracy of the model was benchmarked in three types of stylized phantoms: (1) homogeneous, (2) laterally infinite slab heterogeneities, and (3) laterally finite slab heterogeneities. Results from homogeneous phantoms and laterally infinite slab heterogeneities showed high levels of accuracy (>98% of points within 2% or 0.1 cm distance-to-agreement (DTA)). However, because range straggling and secondary particle production were not included in our model, central-axis dose differences of 2-4% were observed in laterally infinite slab heterogeneities when compared to Monte Carlo dose. In the presence of laterally finite slab heterogeneities, the analytical model resulted in lower pass rates (>96% of points within 2% or 0.1 cm DTA), which was attributed to the use of the central-axis approximation.