A 3D photon superposition/convolution algorithm and its foundation on results of Monte Carlo calculations

Based on previous publications on a triple Gaussian analytical pencil beam model and on Monte Carlo calculations using Monte Carlo codes GEANT-Fluka, versions 95, 98, 2002, and BEAMnrc/EGSnrc, a three-dimensional (3D) superposition/convolution algorithm for photon beams (6 MV, 18 MV) is presented. Tissue heterogeneity is taken into account by electron density information of CT images. A clinical beam consists of a superposition of divergent pencil beams. A slab-geometry was used as a phantom model to test computed results by measurements. An essential result is the existence of further dose build-up and build-down effects in the domain of density discontinuities. These effects have increasing magnitude for field sizes ≤5.5 cm2 and densities ≤0.25 g cm-3, in particular with regard to field sizes considered in stereotaxy. They could be confirmed by measurements (mean standard deviation 2%). A practical impact is the dose distribution at transitions from bone to soft tissue, lung or cavities