A Quantum-Inspired Approach to Beam Angle Optimization
Abstract
Purpose
Beam angle optimization (BAO) is a critical component of radiation therapy (RT) treatment planning, particularly for proton therapy, where small variations in beam configuration can substantially affect plan quality. BAO is naturally formulated as a mixed-integer programming (MIP) problem and is NP-hard due to its exponentially growing search space. Conventional optimization methods often face scalability and computational efficiency limitations. This work introduces QC-BAO, a quantum-inspired framework for efficiently solving the MIP formulation of BAO.
Methods
The proposed approach models BAO as an MIP problem, incorporating binary variables for beam angle selection and continuous variables for optimizing spot intensities for proton therapy. The proposed approach employs iterative convex relaxation and alternating direction method of multipliers, utilizing quantum-inspired method to solve the binary decision component while integrating classical optimization techniques for continuous spot intensity decisions.
Results
Computational experiments were conducted on clinical test cases to evaluate QC-BAO’s performance against institute-standard (IS) angles and a heuristic approaches [1], GS-BAO and AG-BAO. QC-BAO demonstrated improved treatment plan quality over clinical, GS-BAO and AG-BAO-selected angles. QC-BAO consistently increased the conformity index (CI) for target coverage while reducing mean and maximum doses to organs-at-risk (OAR). For instance, in lung case, QC-BAO achieved a CI of 0.89, compared to 0.89 (IS), 0.76 (GS-BAO) and 0.86 (AG-BAO), while lowering the mean lung dose to 2.78 Gy from 3.36 Gy (IS), 4.80 Gy (GS-BAO) and 3.03 Gy (AG-BAO). Additionally, QC-BAO produced the lowest objective function values across all cases.
Conclusion
These results demonstrate the potential of quantum-inspired optimization to enhance BAO by improving plan quality and optimization performance, supporting future clinical translation of quantum-accelerated methods in RT planning. References: [1] Shen H, Zhang G, Lin Y, Rotondo RL, Long Y, Gao H. Beam angle optimization for proton therapy via group‐sparsity based angle generation method. Medical Physics. 2023;50(6):3258-3273. doi:https://doi.org/10.1002/mp.16392