Presenter(s)
N. Shinde1, Y. Zhu2, H. Shen3, and H. Gao4; 1University of Texas Southwestern Medical Center, Dallas, TX, 2Harbin Insititute of Technology, Harbin, China, 3University of Michigan-Shanghai Jiao Tong University Joint Institute, Shanghai Jiao Tong University, Shanghai, China, 4Department of Radiation Oncology, University of Texas Southwestern Medical Center, Dallas, TX
Purpose/Objective(s): Beam angle optimization (BAO) plays a pivotal role in radiation therapy (RT) treatment planning, especially in proton therapy, where minor changes in beam orientation can significantly influence plan quality. BAO can be formulated as a mixed-integer programming (MIP) problem and is computationally challenging (NP-hard) due to the combinatorial explosion of the search space. Traditional optimization techniques often struggle with scalability and computational burden. In this study, we propose QC-BAO, a quantum-inspired optimization framework designed to efficiently solve the MIP formulation of BAO.
Materials/Methods: The BAO problem is formulated as an MIP model that includes binary decision variables for beam angle selection and continuous variables for proton spot intensity optimization. The proposed QC-BAO framework integrates iterative convex relaxation with an alternating direction method of multipliers (ADMM) scheme. A quantum-inspired optimization strategy is employed to address the binary decision subproblem, while classical optimization methods are used to optimize the continuous spot intensity variables.
Results: Computational evaluations were performed on clinical cases to compare QC-BAO with institute-standard (IS) beam configurations and two heuristic approaches: GS-BAO and AG-BAO [1]. QC-BAO achieved superior or comparable treatment plan quality relative to clinical and heuristic methods. Specifically, QC-BAO consistently improved the conformity index (CI) for target coverage while reducing both mean and maximum doses to organs-at-risk (OARs). For example, in the lung case, QC-BAO obtained a CI of 0.89, compared to 0.89 (IS), 0.76 (GS-BAO), and 0.86 (AG-BAO), while reducing the mean lung dose to 2.78 Gy versus 3.36 Gy (IS), 4.80 Gy (GS-BAO), and 3.03 Gy (AG-BAO). Furthermore, QC-BAO yielded the lowest objective function values across all evaluated cases.
Conclusion: The findings highlight the promise of quantum-inspired optimization techniques for improving BAO in proton therapy. QC-BAO enhances both plan quality and optimization performance, supporting the potential clinical adoption of quantum-accelerated methodologies in RT treatment 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 Table 1: Comparison of objective function values and runtimes. The best (lowest) objective values are highlighted in bold.| Test case | Quantity | IS | GS-BAO | AG-BAO | Classical MIP | QC-BAO |
| HN | Time (secs) | 40.73 | 289.35 | 8035.57 | 159.13 | 149.2±1.31 |
| Obj fn val | 4.42 | 3.94 | 3.44 | 3.93 | 3.39±0.08 | |
| Abdomen | Time (secs) | 57.00 | 533.77 | 9610.17 | 484.69 | 656.89±6.58 |
| Obj fn val | 0.33 | 0.16 | 0.14 | 0.20 | 0.14±0.01 | |
| Lung | Time (secs) | 140.98 | 599.48 | 14657.95 | 349.07 | 620.74±2.11 |
| Obj fn val | 7.50 | 12.53 | 7.22 | 7.60 | 6.81±0.14 |