Purpose: The delivery efficiency of spot-scanning fixed-beam (IMPT) or arc (ARC) therapy is primarily subject to the minimum monitor-unit (MMU) constraint, which requires proton spots to be at least the MMU threshold in order to be deliverable. Large MMU threshold can proportionally increase the beam current and therefore accelerate the dose delivery. However, treatment planning with large MMU constraint is highly challenging, owing to the nonconvexity of the MMU constraint. This work aims to develop a new optimization algorithm that is effective in solving IMPT or ARC with large MMU threshold, for efficient proton therapy.
Methods: The new method is primarily based on so-called stochastic coordinate decent (SCD) method, with three major steps: (1) to decouple the determination of active sets for dose-volume-histogram (DVH) planning constraints from the MMU problem via iterative convex relaxation method; (2) to handle the nonconvexity of the MMU constraint via SCD to localize the index set of nonzero spots; (3) to solve convex subproblems projected to this convex set of nonzero spots via projected gradient descent method.
Results: The new method SCD was validated in comparison to alternating direction method of multipliers (ADMM) for IMPT and ARC optimization problems. SCD provided better plan quality than ADMM, e.g., improving conformity index (CI) from 0.56 to 0.69 for IMPT, from 0.28 to 0.80 for ARC. Moreover, SCD successfully handled the nonconvexity from large MMU threshold that ADMM failed to handle, in the sense that (1) the plan quality from ARC was worse than IMPT, when ADMM was used; (2) in contrast, with SCD, ARC achieved better plan quality than IMPT, which is compatible with more optimization degrees of freedom from ARC compared to IMPT.
Conclusion: A new MMU optimization method via SCD is developed for rapid spot-scanning fixed-beam or arc therapy.
Funding Support, Disclosures, and Conflict of Interest: This research is partially supported by the NIH Grant No. R37CA250921 and a KUCC physicist-scientist recruiting grant.