Brachytherapy scatter dose calculation in heterogeneous media: I. A microbeam ray-tracing method for the single-scatter contribution

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Abstract
In this work, we propose a framework for calculating brachytherapy dose distributions in heterogeneous media. The approach taken includes analytical calculation of the primary dose, and separately treats contributions of the once-scatter photons and multiple-scatter photons to the total scatter dose. This paper focuses on the evaluation of the once-scatter dose, which is based on a micro-beam ray-tracing model developed by the authors that incorporates an accurate description of the physical scattering of photons (Compton and Rayleigh scattering) with considerable flexibility in accommodating diverse geometries in a heterogeneous medium. The accuracy of the ray-tracing model has been verified by comparing model-calculated once-scatter doses with corresponding Monte Carlo results. For a 22 keV, 27 keV and 300 keV point source in water containing a disc-shaped heterogeneity of whitlockite, stainless steel or lead, our calculated results for once-scatter doses are in excellent agreement with corresponding Monte Carlo results over a wide range of heterogeneity dimensions and positions. Our investigation also explores the differences between physical scattering and isotropic scattering in evaluating the once-scatter dose, and thus enables the domain of applicability of the latter to be assessed. An appropriate method for evaluating the multiple-scatter dose, which together with the micro-beam method described here provides a means to calculate the total dose, is the subject of a companion paper.

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