Minimum-monitor-unit optimization via a stochastic coordinate descent method

Area of Science:

• Medical Physics
• Radiation Oncology
• Computational Optimization

Background:

• Proton radiotherapy (RT) planning involves optimizing deliverable proton spots under minimum monitor-unit (MMU) constraints.
• The MMU optimization problem is mathematically challenging due to strong nonconvexity, particularly with large MMU thresholds.
• Efficient intensity-modulated proton therapy (IMPT) and proton arc delivery (ARC) rely on effective MMU optimization.

Purpose of the Study:

• To develop a novel optimization algorithm capable of effectively solving the MMU problem in proton radiotherapy.
• To address the mathematical challenges posed by the nonconvexity of MMU optimization with large MMU thresholds.

Main Methods:

• A new algorithm based on the stochastic coordinate decent (SCD) method was developed.
• The approach involves decoupling dose-volume-histogram (DVH) planning constraints, localizing non-zero spots using SCD, and solving convex subproblems via projected gradient descent.
• The SCD method was validated against the alternating direction method of multipliers (ADMM) for IMPT and ARC.

Main Results:

• The SCD method demonstrated superior plan quality compared to ADMM, evidenced by improved conformal index (CI) values in both IMPT and ARC.
• SCD successfully handled the nonconvexity associated with large MMU thresholds, a limitation for ADMM.
• For a lung case, SCD improved CI from 0.56 to 0.69 (IMPT) and 0.28 to 0.80 (ARC), with ARC achieving better quality than IMPT under SCD, unlike with ADMM.

Conclusions:

• The developed SCD-based MMU optimization method effectively addresses the nonconvexity of large MMU thresholds, a significant advancement over current techniques.
• This unique algorithm offers a solution for efficient IMPT, proton ARC, and other particle RT applications requiring large MMU thresholds.
• The SCD method enables improved treatment plan quality and optimization flexibility in advanced proton radiotherapy delivery.