Robust optimization for HDR prostate brachytherapy applied to organ reconstruction uncertainty

Purpose. Recently, we introduced a bi-objective optimization approach based on dose-volume indices to automatically create clinically good HDR prostate brachytherapy plans. To calculate dose-volume indices, a reconstruction algorithm is used to determine the 3D organ shape from 2D contours, inevitably containing settings that influence the result. We augment the optimization approach to quickly find plans that are robust to differences in 3D reconstruction. Methods. Studied reconstruction settings were: interpolation between delineated organ contours, overlap between contours, and organ shape at the top and bottom contour. Two options for each setting yields 8 possible 3D organ reconstructions per patient, over which the robust model defines minimax optimization. For the original model, settings were based on our treatment planning system. Both models were tested on data of 26 patients and compared by re-evaluating selected optimized plans both in the original model (1 organ reconstruction, the difference determines the cost), and in the robust model (8 organ reconstructions, the difference determines the benefit). Results. Robust optimization increased the run time from 3 to 6 min. The median cost for robust optimization as observed in the original model was -0.25% in the dose-volume indices with a range of [-0.01%, -1.03%]. The median benefit of robust optimization as observed in the robust model was 0.93% with a range of [0.19%, 4.16%]. For 4 patients, selected plans that appeared good when optimized in the original model, violated the clinical protocol with more than 1% when considering different settings. This was not the case for robustly optimized plans. Conclusions. Plans of high quality, irrespective of 3D organ reconstruction settings, can be obtained using our robust optimization approach. With its limited effect on total runtime, our approach therefore offers a way to account for dosimetry uncertainties that result from choices in organ reconstruction settings that is viable in clinical practice.