Heuristics for integrated optimization of catheter positioning and dwell time distribution in prostate HDR brachytherapy

High dose-rate (HDR) brachytherapy is one kind of radiotherapy used to treat different forms of cancer, such as prostate cancer. When this treatment is used for prostate cancer, a radioactive source is moved through catheters implanted into the prostate. For each patient, a treatment plan is constructed. This plan determines for example catheter positions and dwell time distribution, that is, where to the radioactive source should stop and for how long. Mathematical optimization methods have been used to find dwell time distributions of high quality; however few optimization approaches that concern catheter positioning have been studied. In this article we present an integrated model that optimizes catheter positioning and dwell time distribution simultaneously. Our results show that integrating the catheter positioning yields a large reduction of the dwell time distribution objective value (15-94 %) and slight improvements in clinical quality measures. Since the presented model is computationally demanding to solve, we also present three heuristics: a tabu search, a variable neighbourhood search and a genetic algorithm. Of these, variable neighbourhood search is the best, and out-performs a state-of-the-art optimization software (CPLEX) and the two other heuristics.