Mixed integer programming with dose-volume constraints in intensity-modulated proton therapy

Background: In treatment planning for intensity-modulated proton therapy (IMPT), we aim to deliver the prescribed dose to the target yet minimize the dose to adjacent healthy tissue. Mixed-integer programming (MIP) has been applied in radiation therapy to generate treatment plans. However, MIP has not been used effectively for IMPT treatment planning with dose-volume constraints. In this study, we incorporated dose-volume constraints in an MIP model to generate treatment plans for IMPT. Methods: We created a new MIP model for IMPT with dose volume constraints. Two groups of IMPT treatment plans were generated for each of three patients by using MIP models for a total of six plans: one plan was derived with the Limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) method while the other plan was derived with our MIP model with dose-volume constraints. We then compared these two plans by dose-volume histogram (DVH) indices to evaluate the performance of the new MIP model with dose-volume constraints. In addition, we developed a model to more efficiently find the best balance between tumor coverage and normal tissue protection. Results: The MIP model with dose-volume constraints generates IMPT treatment plans with comparable target dose coverage, target dose homogeneity, and the maximum dose to organs at risk (OARs) compared to treatment plans from the conventional quadratic programming method without any tedious trial-and-error process. Some notable reduction in the mean doses of OARs is observed. Conclusions: The treatment plans from our MIP model with dose-volume constraints can meet all dose-volume constraints for OARs and targets without any tedious trial-and-error process. This model has the potential to automatically generate IMPT plans with consistent plan quality among different treatment planners and across institutions and better protection for important parallel OARs in an effective way.