Comparative dosimetric analysis of concave versus convex surface curvatures in external beam radiotherapy: a Monte Carlo investigation revealing opposing geometric effects

This study explores the opposing dosimetric behavior of concave geometries and establishes a framework for understanding the effects of surface curvature in radiotherapy. We hypothesized that concave surfaces would produce inverse dosimetric perturbations compared with convex geometries, with important implications for treatment planning accuracy. Using validated GATE Monte Carlo simulations with phase-space data from PRIMO for a Varian Clinac 2100C accelerator, we examined concave hemispherical cavities of 2 cm depth with radii ranging from 5 to 20 cm in water phantoms. Electron beams of 6, 9, and 12 MeV, as well as 6 MV photon beams, were studied across multiple field sizes. Comparisons with our previous convex surface data enabled quantification of geometric asymmetry through a novel Geometric Perturbation Factor (GPF). The results showed that concave surfaces produced effects opposite to convex geometries: R50 decreased linearly with curvature (R50 = -5.37<i>ρ</i>, -9.58<i>ρ</i>, -14.23<i>ρ</i>for 6, 9, and 12 MeV, respectively), in contrast to the increases observed for convex surfaces. Notably, concave perturbations were 15-17 times stronger than convex effects for identical curvatures, and surface doses increased by up to 15% for concave compared with decreases for convex geometries. Photon beams exhibited minimal sensitivity (≤3% variation) for both geometries. This comparative analysis highlights a fundamental asymmetry in radiotherapy dose perturbations, showing that concave surfaces induce significantly stronger and opposing effects relative to convex geometries. These findings underscore the need for geometry-specific correction factors in treatment planning systems, particularly for electron beam therapy where geometric effects are most pronounced.