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Effective Heuristic Cuts for Beam Angle Optimization in Radiation Therapy

H Yarmand

H Yarmand*, D Craft, Massachusetts General Hospital, Boston, MA

MO-A-137-3 Monday 8:00AM - 9:55AM Room: 137

Purpose: To improve the solution efficiency (i.e., reducing computation time while obtaining high-quality treatment plans) for the beam angle optimization problem (BAO) in radiation therapy treatment planning.

Methods: We formulate BAO as a mixed integer programming problem (MIP) whose solution gives the optimal beam orientation as well as optimal beam intensity map. We then incorporate a family of heuristic cuts into the resultant MIP based on the observation that the number of candidate beams is usually much larger than the number of beams used in the treatment plan, and therefore, it is less likely that adjacent beams are simultaneously used in the optimal treatment plan. The proposed cuts, referred to as ⁽⁽neighbor cuts⁾⁾, force the optimization system to choose one or a few beams from any set of adjacent beams. As a result, the search space and the computation time are reduced considerably. The neighbor cuts can be added to any MIP formulation for BAO including the cases of coplanar/noncoplanar beams for intensity modulated radiation therapy (IMRT) and stereotactic body radiation therapy (SBRT). For the numerical experiments a liver case (both IMRT and SBRT) with 34 and a head and neck case (only IMRT) with 36 coplanar beams were considered. Each beam was divided into 109-144 beamlets of size 1*1 cm².

Results: We first solved the corresponding MIP without the neighbor cuts and recorded the optimal solution and the computation time. Then we incorporated the neighbor cuts into the MIP and resolved it. Our results show that incorporating the neighbor cuts into the MIP reduces the computation time considerably and results in solutions with negligible optimality gaps.

Conclusion: This research incorporates the observation that optimal beam configurations are typically a sparse set of well-spaced beams to improve the efficiency of the solution technique drastically.

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.

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