Guaranteed Epsilon-Optimal Treatment Plans with Minimum Number of Beams for Stereotactic Body Radiation Therapy
H Yarmand*, D Craft, Massachusetts General Hospital, Boston, MATH-A-116-8 Thursday 8:00AM - 9:55AM Room: 116
Purpose: To efficiently find quality-guaranteed treatment plans with the minimum number of beams for stereotactic body radiation therapy (SBRT).
Methods: We formulate the beam angle optimization problem (BAO) as a mixed integer programming problem (MIP) whose solution gives the optimal beam orientation as well as optimal beam intensity. We first allow use of all candidate beams and find the ⁽⁽ideal plan⁾⁾ with the objective of minimizing dose to organs at risk (OARs) while keeping the dose to the tumor and other structures in specified ranges. Then we resolve the MIP with the objective of minimizing the number of beams while remaining in a predetermined epsilon-optimality of the ideal plan with respect to the dose to OARs. Since the treatment plan optimization is a multicriteria optimization problem, the planner can navigate the ideal dose distribution Pareto surface and select a plan of desired target coverage versus OARs sparing, and then use the proposed technique to reduce the number of beams while guaranteeing epsilon-optimality. To reduce the computation time, we use a family of heuristic cuts, known as ⁽⁽neighbor cuts⁾⁾ while preserving epsilon-optimality. For the numerical experiments a liver case with 34 and a lung case with 36 coplanar beams were considered.
Results: The ideal plan uses an impractically large number of beams. The proposed technique reduced the number of beams to the range of practical application (5 to 9 beams) while remaining in the epsilon-optimal range of 1% to 5% optimality gap. Adding the neighbor cuts reduced the computation time considerably.
Conclusion: The proposed method can be integrated into a general algorithm for fast navigation of the ideal dose distribution Pareto surface and finding the treatment plan with the minimum number of beams, which corresponds to the delivery time, in epsilon-optimality range of the desired ideal plan.
Funding Support, Disclosures, and Conflict of Interest: The project was supported by the Federal Share of program income earned by Massachusetts General Hospital on C06 CA059267, Proton Therapy Research and Treatment Center and also partially by RaySearch laboratories.