Shinde Nimita, Zhu Ya-Nan, Shen Haozheng, Gao Hao
Department of Radiation Oncology, University of Kansas Medical Center, USA.
University of Michigan-Shanghai Jiao Tong University Joint Institute, Shanghai Jiao Tong University, Shanghai, China.
ArXiv. 2025 Apr 10:arXiv:2504.07844v1.
Beam angle optimization (BAO) is a critical component of radiation therapy (RT) treatment planning, where small changes in beam configuration can significantly impact treatment quality, especially for proton RT. Mathematically, BAO is a mixed integer programming (MIP) problem, which is NP-hard due to its exponential growing search space. Traditional optimization techniques often struggle with computational efficiency, necessitating the development of novel approaches.
This study introduces QC-BAO, a hybrid quantum-classical approach that leverages quantum computing to solve the MIP formulation of BAO.
The proposed approach, QC-BAO, 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 a hybrid quantum-classical framework, utilizing quantum computing to solve the binary decision component while integrating classical optimization techniques, including iterative convex relaxation and the alternating direction method of multipliers.
Computational experiments were conducted on clinical test cases to evaluate QC-BAO's performance against clinically verified angles and a heuristic approach, GS-BAO. QC-BAO demonstrated improved treatment plan quality over both clinical and GS-BAO-selected angles. The method consistently increased the conformity index (CI) for target coverage while reducing mean and maximum doses to organs-at-risk (OAR). For instance, in the lung case, QC-BAO achieved a CI of 0.89, compared to 0.85 (clinical) and 0.76 (GS-BAO), while lowering the mean lung dose to 2.85 Gy from 3.36 Gy (clinical) and 4.80 Gy (GS-BAO). Additionally, QC-BAO produced the lowest objective function value, confirming its superior optimization capability.
The findings highlight the potential of quantum computing to enhance the solution to BAO problem by demonstrated improvement in plan quality using the proposed method, QC-BAO. This study paves the way for future clinical implementation of quantum-accelerated optimization in RT.
射束角度优化（BAO）是放射治疗（RT）治疗计划的关键组成部分，其中射束配置的微小变化会显著影响治疗质量，尤其是对于质子放疗。从数学角度来看，BAO是一个混合整数规划（MIP）问题，由于其搜索空间呈指数增长，所以是NP难问题。传统优化技术在计算效率方面常常面临困难，因此需要开发新的方法。
本研究引入了QC-BAO，这是一种利用量子计算来解决BAO的MIP公式的混合量子-经典方法。
所提出的方法QC-BAO将BAO建模为一个MIP问题，为射束角度选择引入二元变量，并为质子治疗的光斑强度优化引入连续变量。该方法采用混合量子-经典框架，利用量子计算来解决二元决策部分，同时整合经典优化技术，包括迭代凸松弛和乘子交替方向法。
在临床测试案例上进行了计算实验，以评估QC-BAO相对于经临床验证的角度和一种启发式方法GS-BAO的性能。QC-BAO在治疗计划质量方面优于临床角度和GS-BAO选择的角度。该方法持续提高了靶区覆盖的适形指数（CI），同时降低了危及器官（OAR）的平均剂量和最大剂量。例如，在肺部案例中，QC-BAO实现的CI为0.89，而临床角度为0.85，GS-BAO为0.76，同时将肺部平均剂量从3.36 Gy（临床）和4.80 Gy（GS-BAO）降至2.85 Gy。此外，QC-BAO产生的目标函数值最低，证实了其卓越的优化能力。
研究结果突出了量子计算通过所提出方法QC-BAO在计划质量上的显著提升，增强解决BAO问题的潜力。本研究为未来量子加速优化在放疗中的临床应用铺平了道路。
