Liu Jiulong, Zhu Ya-Nan, Zhang Xiaoqun, Gao Hao
LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China.
Department of Radiation Oncology, University of Kansas Medical Center, Kansas City, USA.
Med Phys. 2025 Jul;52(7):e17929. doi: 10.1002/mp.17929. Epub 2025 Jun 8.
The treatment uncertainties such as patient positioning can significantly affect the accuracy of proton radiation therapy (RT). Robust optimization can account for these uncertainties during treatment planning, for which the minimax approach optimizes the worst-case plan quality.
This work will develop an efficient minimax robust optimization algorithm for improving plan quality and computational efficiency.
The proposed method reformulates the minimax problem so that it can be conveniently solved by the first-order operator-splitting algorithm (OS). That is, the reformulated problem is split into several subproblems, which either admit a closed-form solution or can be efficiently solved as a linear system.
The proposed method OS was demonstrated with improved plan quality, robustness, and computational efficiency, compared to robust optimization via stochastic programming (SP) and current minimax robust method via minimax stochastic programming (MSP). For example, in a prostate case, compared to MSP and SP, OS decreased the max target dose from 140% and 121% to 118%, and the mean femoral head dose from 28.6% and 26.3% to 24.8%. In terms of robustness, OS reduced the robustness variance (RV) of the target from 56.07 and 0.30 to 0.04. Compared to MSP, OS decreased the computational time from 16.4 min to 1.7 min.
A novel operator-splitting minimax robust optimization is proposed with improved plan quality and computational efficiency, compared to conventional minimax robust optimization method MSP and probabilistic robust optimization method SP.
诸如患者体位等治疗不确定性会显著影响质子放射治疗（RT）的准确性。稳健优化可在治疗计划期间考虑这些不确定性，其中极小极大方法可优化最坏情况的计划质量。
本研究将开发一种高效的极小极大稳健优化算法，以提高计划质量和计算效率。
所提出的方法对极小极大问题进行了重新表述，以便能够通过一阶算子分裂算法（OS）方便地求解。也就是说，重新表述后的问题被分解为几个子问题，这些子问题要么有闭式解，要么可以作为线性系统有效求解。
与通过随机规划（SP）的稳健优化和通过极小极大随机规划（MSP）的当前极小极大稳健方法相比，所提出的OS方法在计划质量、稳健性和计算效率方面均有改进。例如，在一个前列腺病例中，与MSP和SP相比，OS将最大靶剂量从140%和121%降至118%，将股骨头平均剂量从28.6%和26.3%降至24.8%。在稳健性方面，OS将靶区的稳健性方差（RV）从56.07和0.30降至0.04。与MSP相比，OS将计算时间从16.4分钟降至1.7分钟。
与传统的极小极大稳健优化方法MSP和概率稳健优化方法SP相比，提出了一种具有改进的计划质量和计算效率的新型算子分裂极小极大稳健优化方法。
