Penalty weight tuning in high dose rate brachytherapy using multi-objective Bayesian optimization

Treatment plan optimization in high dose rate brachytherapy often requires manual fine-tuning of penalty weights for each objective, which can be time-consuming and dependent on the planner's experience. To automate this process, this study used a multi-criteria approach called multi-objective Bayesian optimization with q-noisy expected hypervolume improvement as its acquisition function (MOBO-qNEHVI). The treatment plans of 13 prostate cancer patients were retrospectively imported to a research treatment planning system, RapidBrachyMTPS, where fast mixed integer optimization (FMIO) performs dwell time optimization given a set of penalty weights to deliver 15 Gy to the target volume. MOBO-qNEHVI was used to find patient-specific Pareto optimal penalty weight vectors that yield clinically acceptable dose volume histogram metrics. The relationship between the number of MOBO-qNEHVI iterations and the number of clinically acceptable plans per patient (acceptance rate) was investigated. The performance time was obtained for various parameter configurations. MOBO-qNEHVI found clinically acceptable treatment plans for all patients. With increasing the number of MOBO-qNEHVI iterations, the acceptance rate grew logarithmically while the performance time grew exponentially. Fixing the penalty weight of the tumour volume to maximum value, adding the target dose as a parameter, initiating MOBO-qNEHVI with 25 parallel sampling of FMIO, and running 6 MOBO-qNEHVI iterations found solutions that delivered 15 Gy to the hottest 95% of the clinical target volume while respecting the dose constraints to the organs at risk. The average acceptance rate for each patient was 89.74% ± 8.11%, and performance time was 66.6 ± 12.6 s. The initiation took 22.47 ± 7.57 s, and each iteration took 7.35 ± 2.45 s to find one Pareto solution. MOBO-qNEHVI combined with FMIO can automatically explore the trade-offs between treatment plan objectives in a patient specific manner within a minute. This approach can reduce the dependency of plan quality on planner's experience and reduce dose to the organs at risk.