Brachytherapy scatter dose calculation in heterogeneous media: II. Empirical formulation for the multiple-scatter contribution.

The presence of heterogeneous media can produce significant perturbations of dose distribution in brachytherapy. In a companion paper, we proposed a dose decomposition approach for dose calculation in a heterogeneous medium, which separately treats dose contributions from primary, once-scattered and multiple-scattered photons. The companion paper also describes and verifies a micro-beam ray-tracing method for evaluating the once-scatter dose. This paper deals with the calculation of the multiple-scatter dose. We present two empirical formulations for evaluating the heterogeneity correction factor for a 27 keV point source in a water sphere containing a disc-shaped heterogeneity. The empirical formulations are based on nonlinear curve fitting of the Monte Carlo multiple-scatter dose estimates calculated for the heterogeneous system. Extensive benchmark comparisons show that these formulations provide results for the multiple-scatter dose that agree within 10% (and mostly within 5%) with corresponding Monte Carlo dose estimates. Combining them with the algorithms for primary and once-scatter dose calculation described in the companion paper yields results for the total dose of equivalent accuracy. The empirical formulations are expressed in simple mathematical forms which involve a separation of the geometry and position variables of the heterogeneous system. Such representation provides a good tool to investigate the heterogeneity-induced perturbation of a multiple-scatter dose at low photon energy.