Bi-objective optimization of catheter positions for high-dose-rate prostate brachytherapy

Bi-objective simultaneous optimization of catheter positions and dwell times for high-dose-rate (HDR) prostate brachytherapy, based directly on dose-volume indices, has shown promising results. However, optimization with the state-of-the-art evolutionary algorithm MO-RV-GOMEA so far required several hours of runtime, and resulting catheter positions were not always clinically feasible. The aim of this study is to extend the optimization model and apply GPU parallelization to achieve clinically acceptable computation times. The resulting optimization procedure is compared with a previously introduced method based solely on geometric criteria, the adapted Centroidal Voronoi Tessellations (CVT) algorithm.

Bi-objective simultaneous optimization was performed with a GPU-parallelized version of MO-RV-GOMEA. This optimization of catheter positions and dwell times was retrospectively applied to the data of 26 patients previously treated with HDR prostate brachytherapy for 8-16 catheters (steps of 2). Optimization of catheter positions using CVT was performed in seconds, after which optimization of only the dwell times using MO-RV-GOMEA was performed in 1 min.

Simultaneous optimization of catheter positions and dwell times using MO-RV-GOMEA was performed in 5 min. For 16 down to 8 catheters (steps of 2), MO-RV-GOMEA found plans satisfying the planning-aims for 20, 20, 18, 14, and 11 out of the 26 patients, respectively. CVT achieved this for 19, 17, 13, 9, and 2 patients, respectively. The P-value for the difference between MO-RV-GOMEA and CVT was 0.023 for 16 catheters, 0.005 for 14 catheters, and <0.001 for 12, 10, and 8 catheters.

With bi-objective simultaneous optimization on a GPU, high-quality catheter positions can now be obtained within 5 min, which is clinically acceptable, but slower than CVT. For 16 catheters, the difference between MO-RV-GOMEA and CVT is clinically irrelevant. For 14 catheters and less, MO-RV-GOMEA outperforms CVT in finding plans satisfying all planning-aims.