Fu Anqi, Ungun Barıș, Xing Lei, Boyd Stephen
Department of Electrical Engineering, Stanford University, 350 Serra Mall, Stanford, CA 94305, USA.
Department of Bioengineering, Stanford University, 443 Via Ortega, Stanford, CA 94305, USA.
Optim Eng. 2019 Mar;20(1):277-300. doi: 10.1007/s11081-018-9409-2. Epub 2018 Nov 22.
We present a method for handling dose constraints as part of a convex programming framework for inverse treatment planning. Our method uniformly handles mean dose, maximum dose, minimum dose, and dose-volume (i.e., percentile) constraints as part of a convex formulation. Since dose-volume constraints are non-convex, we replace them with a convex restriction. This restriction is, by definition, conservative; to mitigate its impact on the clinical objectives, we develop a two-pass planning algorithm that allows each dose-volume constraint to be met exactly on a second pass by the solver if its corresponding restriction is feasible on the first pass. In another variant, we add slack variables to each dose constraint to prevent the problem from becoming infeasible when the user specifies an incompatible set of constraints or when the constraints are made infeasible by our restriction. Finally, we introduce ConRad, a Python-embedded open-source software package for convex radiation treatment planning. ConRad implements the methods described above and allows users to construct and plan cases through a simple interface.
我们提出了一种方法，用于在逆治疗计划的凸规划框架中处理剂量约束。我们的方法将平均剂量、最大剂量、最小剂量和剂量体积（即百分位数）约束统一作为凸公式的一部分进行处理。由于剂量体积约束是非凸的，我们用一个凸限制来替代它们。根据定义，这个限制是保守的；为了减轻其对临床目标的影响，我们开发了一种两遍规划算法，如果相应的限制在第一遍可行，求解器可以在第二遍精确满足每个剂量体积约束。在另一种变体中，我们向每个剂量约束添加松弛变量，以防止当用户指定一组不兼容的约束时，或者当约束因我们的限制而变得不可行时，问题变得不可行。最后，我们引入了ConRad，这是一个用于凸放射治疗计划的嵌入Python的开源软件包。ConRad实现了上述方法，并允许用户通过一个简单的界面构建和规划病例。
