Implementation of a robust optimisation genetic algorithm for HDR prostate brachytherapy including all major uncertainties

Abstract

Abstract Introduction In high-dose-rate prostate brachytherapy, uncertainties cause a deviation from the nominal treatment plan, leading to a possible failure of clinical objectives in the delivered scenario. Robust optimisation has the potential to maximise the probability that these objectives are met during treatment. Method A computationally efficient probabilistic robust optimisation algorithm was developed and evaluated comprehensively on one patient by comparing it to the treatment-planning-systems (TPS) optimised plan. Three objective functions were maximised within a genetic algorithm (NSGA-ii), each an approximation for robustness against uncertainty for three clinical objectives: the minimum dose to the hottest 90% of the prostate target, \({\text{D}}_{90}^{\text{P}}\), and the maximum doses to the urethra, \({\text{D}}_{0.01 \text{c}\text{c}}^{\text{U}}\), and the rectum, \({\text{D}}_{0.1 \text{c}\text{c}}^{\text{R}}\). The approximations are derived from a probabilistic robust evaluation algorithm incorporating 14 major planning and treatment uncertainties. The robustness of a plan was quantified as a pass-rate from 500 probabilistic uncertainty scenarios for \({\text{D}}_{90}^{\text{P}}, {\text{D}}_{0.01 \text{c}\text{c}}^{\text{U}}\), and\({\text{D}}_{0.1 \text{c}\text{c}}^{\text{R}}\). Two hundred robust-optimised plans are generated that are the best trade-off between the three-competing DVH metric pass-rates. Results The robust-optimised plans on average (mean) increased in overall robustness by 58.5 ± 3.0% (SD: 7.1%, min: 34.1%, max: 67.7%) compared to the TPS-optimised plan. The robustness increase for the \({\text{D}}_{90}^{\text{P}}\) pass-rate was 31.2 ± 2.2% (SD: 15.6%, min: -5.1%, max: 46.7%), for the \({\text{D}}_{0.01 \text{c}\text{c}}^{\text{U}}\) pass-rate, the increase was 48.2 ± 2.6% (SD: 11.9%, min: 26.9%, max: 67.7%), and for the \({\text{D}}_{0.1 \text{c}\text{c}}^{\text{R}}\) pass-rate, the change was 0.0 ± 1.1% (SD: 0.72%, min: -2.6%, max: 0.4%). Conclusion The robust optimisation algorithm was demonstrated to produce more robust plans than the TPS, in an increased probability of target coverage and organs-at-risk sparing within a clinically reasonable time.