A linear programming model for optimizing HDR brachytherapy dose distributions with respect to mean dose in the DVH-tail

Purpose: Recent research has shown that the optimization model hitherto used in high-dose-rate (HDR) brachytherapy corresponds weakly to the dosimetric indices used to evaluate the quality of a dose distribution. Although alternative models that explicitly include such dosimetric indices have been presented, the inclusion of the dosimetric indices explicitly yields intractable models. The purpose of this paper is to develop a model for optimizing dosimetric indices that is easier to solve than those proposed earlier. Methods: In this paper, the authors present an alternative approach for optimizing dose distributions for HDR brachytherapy where dosimetric indices are taken into account through surrogates based on the conditional value-at-risk concept. This yields a linear optimization model that is easy to solve, and has the advantage that the constraints are easy to interpret and modify to obtain satisfactory dose distributions. Results: The authors show by experimental comparisons, carried out retrospectively for a set of prostate cancer patients, that their proposed model corresponds well with constraining dosimetric indices. All modifications of the parameters in the authors' model yield the expected result. The dose distributions generated are also comparable to those generated by the standard model with respect to the dosimetric indices that are used for evaluating quality. Conclusions: The authors' new model is a viable surrogate to optimizing dosimetric indices and quickly and easily yields high quality dose distributions. (C) 2013 American Association of Physicists in Medicine.