Robust optimization of catheter positions and dwell times for HDR prostate brachytherapy

HDR prostate brachytherapy plans are sensitive to catheter placement uncertainty, as discrepancies between planned and delivered catheter positions can degrade target coverage and increase organ at risk dose. Current inverse planning methods optimize dwell times for a fixed implant geometry and do not account for geometric uncertainty during planning. Existing robust optimization approaches for HDR brachytherapy are similarly limited to dwell time optimization, and no framework has jointly optimized catheter configurations and dwell times while explicitly incorporating catheter insertion uncertainty.

To develop an analytical inverse planning method for prostate HDR brachytherapy that improves robustness to catheter placement uncertainty while maintaining nominal target coverage and organ at risk constraints.

Overall, 32 previously treated prostate HDR cases were retrospectively analyzed. Dose was modeled with a TG-43U1 influence matrix. A candidate catheter set was generated by adding four translated trajectories per clinical catheter at $\pm 5\mathrm{mm}$ in the anterior posterior and lateral directions, with dwell positions cropped to remain within the loading structure. Dwell times and catheter selection were optimized using a dose fidelity term with a group minimax concave penalty (gMCP) to enforce catheter level sparsity, and a surface restricted dose gradient penalty (SDGP) applied to organ at risk surface voxels. Four strategies were compared: clinical planning, dose fidelity+SDGP, dose fidelity+gMCP, and dose fidelity+gMCP+SDGP. Hyperparameters remained fixed for all patients, respectively. All nominal plans were normalized to PTV $V_{100\%}=95\%$ . Robustness was evaluated using 1000 Monte Carlo trials per patient per uncertainty level with independent Gaussian catheter displacements in $x,y,z$ and $\sigma \in \{0,0.5,1.0,1.5,2.0,2.5,3.0\}\mathrm{mm}$ . Endpoints included PTV $V_{100\%}$ , bladder and rectum $V_{75\%}$ , urethra $V_{125\%}$ , and the clinical acceptability rate of the intersection of these metrics, using NRG-GU009 HDR boost criteria.

Overall, the combined approach was comparable or an improvement to clinical positions alone. At $\sigma =1.5\mathrm{mm}$ , the complete approach with dose fidelity+gMCP+SDGP improved perturbed target coverage, with mean PTV $V_{100\%}=92.0\%\pm 1.1\%$ versus $89.5\%\pm 1.2\%$ for clinical planning and $89.8\%\pm 0.9\%$ for dose fidelity+gMCP. The corresponding acceptability rate was $77.7\%$ for dose fidelity+gMCP+SDGP versus $50.0\%$ for clinical planning.

Coupling gMCP based catheter selection with an organ surface dose gradient penalty improved robustness of prostate HDR brachytherapy plans to independent catheter placement uncertainty, with comparable nominal plan quality after normalization.