Two-dimensional scatter integration method for brachytherapy dose calculations in 3D geometry

In brachytherapy clinical practice, applicator shielding and tissue heterogeneities are usually not explicitly taken into account. None of the existing dose computational methods are able to reconcile accurate dose calculation in complex three-dimensional (3D) geometries with high efficiency and simplicity. We propose a new model that performs two-dimensional integration of the scattered dose component. The model calculates the effective primary dose at the point of interest and estimates the scatter dose as a superposition of the scatter contributions from pyramid-shaped minibeams. The approach generalizes a previous scatter subtraction model designed to calculate the dose for axial points in simple cylindrically symmetric geometry by dividing the scattering volume into spatial regions coaxial with the source-to-measurement point direction. To allow for azimuthal variation of the primary dose, these minibeams were divided into equally spaced azimuthally distributed pyramidal volumes. The model uses precalculated scatter-to-primary ratios (SPRs) for collimated isotropic sources. Effective primary dose, which includes the radiation scattered in the source capsule, is used to achieve independence from the source structure. For realistic models of the ¹⁹²Ir HDR and PDR sources, the algorithm agrees with Monte Carlo within 2.5% and for the ¹²⁵I type 6702 seed within 6%. The 2D scatter integration (2DSI) model has the potential to estimate the dose behind high-density heterogeneities both accurately and efficiently. The algorithm is much faster than Monte Carlo methods and predicts the dose around sources with different γ-ray energies and differently shaped capsules with high accuracy.