Romeijn H Edwin, Dempsey James F, Li Jonathan G
Department of Industrial and Systems Engineering, University of Florida, Gainesville, Florida 32611-6595, USA.
Phys Med Biol. 2004 May 21;49(10):1991-2013. doi: 10.1088/0031-9155/49/10/011.
Models for finding treatment plans for intensity modulated radiation therapy are usually based on a number of structure-based treatment plan evaluation criteria, which are often conflicting. Rather than formulating a model that a priori quantifies the trade-offs between these criteria, we consider a multi-criteria optimization approach that aims at finding the so-called undominated treatment plans. We present a unifying framework for studying multi-criteria optimization problems for treatment planning that establishes conditions under which treatment plan evaluation criteria can be transformed into convex criteria while preserving the set of undominated treatment plans. Such transformations are identified for many of the criteria that have been proposed to date, establishing equivalences between these criteria. In addition, it is shown that the use of a nonconvex criterion can often be avoided by transformation to an equivalent convex criterion. In particular, we show that models employing criteria such as tumour control probability, normal tissue complication probability, probability of uncomplicated tumour control, as well as sigmoidal transformations of (generalized) equivalent uniform dose are equivalent to models formulated in terms of separable voxel-based criteria that penalize dose in individual voxels.
用于强度调制放射治疗治疗计划的模型通常基于一些基于结构的治疗计划评估标准，而这些标准往往相互冲突。我们没有制定一个先验量化这些标准之间权衡的模型，而是考虑一种多标准优化方法，旨在找到所谓的非支配治疗计划。我们提出了一个统一框架，用于研究治疗计划的多标准优化问题，该框架建立了在保持非支配治疗计划集的同时，将治疗计划评估标准转化为凸标准的条件。对于迄今为止提出的许多标准，都确定了这样的转换，从而建立了这些标准之间的等效关系。此外，研究表明，通过转换为等效的凸标准，通常可以避免使用非凸标准。特别是，我们表明，采用诸如肿瘤控制概率、正常组织并发症概率、无并发症肿瘤控制概率以及（广义）等效均匀剂量的S形转换等标准的模型，等同于根据基于体素的可分离标准制定的模型，这些标准对各个体素中的剂量进行惩罚。
