Analytical approach to heterogeneity correction factor calculation for brachytherapy.

In brachytherapy treatment planning, the effects of tissue and applicator heterogeneities are commonly neglected due to lack of accurate, general, and fast three-dimensional (3D) dose-computational algorithms. A novel approach, based on analytical calculation of scattered photon fluxes inside and around a disk-shaped heterogeneity, has been developed for use in the three-dimensional scatter-subtraction algorithm. Specifically, our model predicts the central-ray dose distribution for a collimated photon isotropic source or brachytherapy "minibeam" in the presence of a slab of heterogeneous material. The model accounts for the lateral dimensions, location, composition, density, and thickness of the heterogeneity using precalculated scatter-to-primary ratios (SPRs) for the corresponding homogeneous problem. The model is applicable to the entire brachytherapy energy range (25 to 662 keV) and to a broad range of materials having atomic numbers of 13 to 82, densities of 2.7 g.cm-3 (Al) to 21.45 g.cm-3 (Pt) and thicknesses up to 1 mean free path. For this range of heterogeneous materials, the heterogeneity correction factors (HCFs) vary from 0.09 to 0.75. The model underestimates HCF when multiple scattering prevails and overestimates HCF when absorption dominates. However, the analytic model agrees with Monte Carlo photon transport (MCPT) benchmark calculations within 1.8% to 10% for 125I, 169Yb, 192Ir, and 137Cs for a wide variety of materials, with the exception of Ag. For 125I shielded by Ag, where the mean discrepancy can exceed 25%, the error is due to K-edge characteristic x rays originating within the heterogeneity. The proposed approach provides reductions in CPU time required of 5 x 10(4)-10(5) and 100 in comparison with direct MCPT simulation and 1D numerical integration, respectively. The limitations of model applicability, as determined by the physical properties of heterogeneity material and accuracy required, are also discussed.