Radiotherapy treatment planning is a challenging large-scale optimization problem plagued by uncertainty. Following the robust optimization methodology, we propose a novel, spatially based uncertainty set for robust modeling of radiotherapy planning, producing solutions that are immune to unexpected changes in biological conditions. Our proposed uncertainty set realistically captures biological radiosensitivity patterns that are observed using recent advances in imaging, while its parameters can be personalized for individual patients. We exploit the structure of this set to devise a compact reformulation of the robust model. We develop a row-generation scheme to solve real, large-scale instances of the robust model. This method is then extended to a relaxation-based scheme for enforcing challenging, yet clinically important, dose-volume cardinality constraints. The computational performance of our algorithms, as well as the quality and robustness of the computed treatment plans, are demonstrated on simulated and real imaging data. Based on accepted performance measures, such as minimal target dose and homogeneity, these examples demonstrate that the spatially robust model achieves almost the same performance as the nominal model in the nominal scenario, and otherwise, the spatial model outperforms both the nominal and the box-uncertainty models.

翻译：放射治疗规划是一个充满不确定性的大规模优化难题。遵循鲁棒优化方法论，我们提出了一种新颖的、基于空间的不确定性集，用于放射治疗规划的鲁棒建模，从而产生能够抵御生物条件意外变化的解决方案。我们提出的不确定性集真实地捕捉了通过近期影像学进展观测到的生物放射敏感性模式，同时其参数可根据个体患者进行个性化设定。我们利用该集合的结构，设计出鲁棒模型的紧凑重构形式。我们开发了一种行生成方案来求解鲁棒模型的实际大规模实例。该方法随后被扩展为一种基于松弛的方案，以强制执行具有挑战性但在临床上至关重要的剂量-体积基数约束。我们算法的计算性能，以及所计算治疗计划的质量和鲁棒性，均在模拟和真实影像数据上得到了验证。基于公认的性能指标，如最小靶区剂量和均匀性，这些示例表明，在标称场景下，空间鲁棒模型的性能几乎与标称模型相同；而在其他情况下，空间模型的表现优于标称模型和盒式不确定性模型。