Benchmarking analytical calculations of proton doses in heterogeneous matter

A proton dose computational algorithm, performing an analytical superposition of infinitely narrow proton beamlets (ASPB) is introduced. The algorithm uses the standard pencil beam technique of laterally distributing the central axis broad beam doses according to the Moliere scattering theory extended to slablike varying density media. The purpose of this study was to determine the accuracy of our computational tool by comparing it with experimental and Monte Carlo (MC) simulation data as benchmarks. In the tests, parallel wide beams of protons were scattered in water phantoms containing embedded air and bone materials with simple geometrical forms and spatial dimensions of a few centimeters. For homogeneous water and bone phantoms, the proton doses we calculated with the ASPB algorithm were found very comparable to experimental and MC data. For layered bone slab inhomogeneity in water, the comparison between our analytical calculation and the MC simulation showed reasonable agreement, even when the inhomogeneity was placed at the Bragg peak depth. There also was reasonable agreement for the parallelepiped bone block inhomogeneity placed at various depths, except for cases in which the bone was located in the region of the Bragg peak, when discrepancies were as large as more than 10%. When the inhomogeneity was in the form of abutting air-bone slabs, discrepancies of as much as 8% occurred in the lateral dose profiles on the air cavity side of the phantom. Additionally, the analytical depth-dose calculations disagreed with the MC calculations within 3% of the Bragg peak dose, at the entry and midway depths in the phantom. The distal depth-dose 20%-80% fall-off widths and ranges calculated with our algorithm and the MC simulation were generally within 0.1 cm of agreement. The analytical lateral-dose profile calculations showed smaller (by less than 0.1 cm) 20%-80% penumbra widths and shorter fall-off tails than did those calculated by the MC simulations. Overall, this work validates the usefulness of our ASPB algorithm as a reasonably fast and accurate tool for quality assurance in planning wide beam proton therapy treatment of clinical sites either composed of homogeneous materials or containing laterally extended inhomogeneities that are comparable in density and located away from the Bragg peak depths.