基于空间不确定性集合的鲁棒放射治疗规划
Robust Radiotherapy Planning with Spatially Based Uncertainty Sets
AI总结：
针对放射治疗计划中的不确定性，提出基于空间的不确定性集合的鲁棒优化方法，实现个性化参数与紧凑重构，并通过行生成及松弛方案求解，在模拟和真实数据上验证了其鲁棒性与性能优势。
摘要：
放射治疗计划是一个具有挑战性的大规模优化问题，其受到不确定性的困扰。遵循鲁棒优化方法，我们提出了一种新颖的、基于空间的不确定性集合，用于放射治疗计划的鲁棒建模，从而产生对生物条件的意外变化具有免疫力的解决方案。我们提出的不确定性集合真实地捕捉了利用近期成像进展观察到的生物放射敏感性模式，而其参数可以针对个体患者进行个性化设置。我们利用该集合的结构，为鲁棒模型设计了一种紧凑的重构形式。我们开发了一种行生成方案来解决鲁棒模型的真实大规模实例。该方法随后被扩展为一种基于松弛的方案，用于强制执行具有挑战性但临床上重要的剂量-体积基数约束。我们算法的计算性能以及计算出的治疗计划的质量和鲁棒性，在模拟和真实成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，这些例子表明，空间鲁棒模型在名义场景下几乎达到与名义模型相同的性能，而在其他情况下，空间模型优于名义模型和箱式不确定性模型。
英文摘要：
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.
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