Optimization of Catheter Position and Dwell Time in Prostate HDR Brachytherapy using HIPO and Linear Programming

Abstract

In this work the problem of determination of the optimal catheter position and source loading in HDR prostate brachytherapy is modeled as a Mixed Integer Linear Programming (MILP) problem and solved by ILOG CPLEX. The results are compared to those of HIPO, a state of the art inverse treatment plan optimization algorithm. Given that MILP is guaranteed to find the global optimum, it provides the baseline for the evaluation of HIPO solutions. The quality of 12 clinical HDR brachytherapy implants for prostate utilizing HIPO, for dwell time optimization only, has been compared to alternative plans with Linear Programming (LP). All common dose-volume indices for the prostate and the organs at risk have been considered. Our results demonstrate that in the case of dwell time optimization, HIPO delivers high quality plans and the differences to the LP solutions are statistically insignificant (p > 0.05) for all indices examined. In the case of combined catheter position and dwell time optimization, the results for 3 clinical cases have been compared. MILP was able to deliver the optimal solution only for one simple case and upper- lower bounds for the rest. The plans produced by HIPO were clinically acceptable, close and clinically equivalent to the global optimum or the upper bounds delivered by MILP for all 3 cases.