TH‐A‐116‐06: Near‐Global Beam Angle Optimization for Intensity Modulated Proton Therapy

Abstract

Purpose: To solve the beam angle optimization (BAO) problem of IMPT to provable near‐global optimality. Global BAO, the selection of a given small number of beams from a large set of candidate beams, remains computationally hard due to the large scale and combinatorial nature of the problem. Exhaustive search is computationally prohibited. Stochastic optimization and local search have been used but confidence in global optimality cannot be established. Methods: We use a fast projection solver for the multi‐criteria robust IMPT optimization. Equally spaced 36 beams are optimized initially to generate a global optimal solution. The 36‐beam plan is then reduced to a 3‐beam plan by iteratively removing the beam with least average intensity and re‐optimizing subjected to 3% relaxation on the best objective value. The true optimal 3‐beam plan is also found by exhaustive search as a benchmark. Results: We apply the method to a chordoma case and an orbital rhabdomyosarcoma case. The optimal 3‐beam plan is only 3–5% worse than the optimal 36‐beam plan in terms of the objective value. The 3‐beam plan efficiently reduced from the 36‐beam optimal plan is almost as good as the optimal 3‐beam plan. There exist a large number of nearly optimal 3‐beam combinations. For these two cases our method finds near‐global optimal plan using 3 beams in a time scale of minutes. Exhaustive search would take on the order of days. Conclusion: We find that IMPT plans using 3 or 4 beams are only marginally improved by adding more beams. By exploiting the high degeneracy of the solution space, we present an efficient column reducing framework for global IMPT BAO. It first finds an optimal many‐beam plan and then uses the column reducing approach to produce a plan with a small number of beams at a user‐selected tolerance from the global optimal plan. This work was supported in part by NCI Grant P01 CA21239 Proton Radiation Therapy Research and NCI Grant R01 CA103904‐01A1 Multi‐criteria IMRT Optimization.