Mixed Integer Programming for Radiotherapy Optimization

0120145兰格在美国每年大约有120万新的癌症病例，大约一半的人接受放射治疗。外部射束治疗将来自患者体外的高能射束的集合引导向肿瘤。使用适形放射治疗的广泛方法，波束被定位在多个角度，每个角度的形状与肿瘤相匹配。最新的技术，调强放射治疗（IMRT），将整个射束分解成更细的射束，实际上，每一个射束都可以被分配一个单独的强度。放射治疗规划问题是选择一组射束/子射束，并将强度分配给它们，以将肿瘤剂量推高到附近健康组织允许的容限。即使是与耐受性限制一致的肿瘤剂量的微小增加，每年也可以改善数千人的生命。该研究的目标是开发适合放射治疗的计算方法，该方法可以在24-48小时内计算出可证明的可行计划，以确定剂量的体积分布，肿瘤学家通常将组织结构的不规则几何形状建模为大量嵌入离散点的联合。假设输送到点的剂量可以近似为射束强度的线性，则治疗计划优化的任务可以建模为具有对应于这些强度的变量和限制每个组织点处的剂量的约束的混合整数规划（MIP）。剂量体积的约束，这需要一个指定的分数，每个正常器官的体积接收剂量低于其阈值的损害，强制执行收集点的约束，为每个组织在一个多选择组与替代品划定与二进制variables.The研究将开发和测试两个贡献，以使计算效率的解决方案，以找到通用MIP方法的放射治疗计划问题。其目的是提供满足规定的约束条件的解决方案，其目标值位于最优值周围的可证明范围内。其中第一个将加强LP松弛MIP配方的多选择（剂量-体积）的约束，通过构建和添加新的有效的不等式。第二个将采用列生成的方法来处理大规模的调强放射治疗配方。代替对IMRT射束内的每个子射束的强度进行建模，子射束强度的整个图案将被表示为单个列并根据需要生成。

0120145LangerThere are approximately 1.2 million new cases of cancer each year in the US and about half undergo treatment with radiation therapy. External beam treatment directs a collection of high energy beams from outside the patient's body towards the tumor. Using the widespread method of conformal radiotherapy, beams are positioned at multiple angles, each shaped to match the tumor. The newest technique, intensity modulated radiotherapy (IMRT), breaks down whole beams into finer beamlets, each of which can, in effect, be assigned a separate intensity. The radiation therapy planning problem is to choose a set of beams/beamlets and assign intensities to them to push tumor dose as high as the tolerances of nearby healthy tissue will allow. Even small increments in tumor dose consistent with tolerance constraints can improve thousands of lives per year. The objective of the proposed research is to develop computational methods tailored to radiation therapy that can compute feasible plans provably within a specified percent of the best possible within the 24-48 hours available for treatment planning.To determine volume distributions of dose, oncologists typically model the irregular geometry of tissue structures as the union of a large number of embedded discrete points. Given that the dose delivered to a point can be approximated as linear in the beam intensities, the task of treatment planning optimization can be modeled as mixed-integer program (MIP) with variables corresponding to those intensities, and constraints limiting the dose at each of the tissue points. Dose-volume constraints, which require a specified fraction of each normal organ volume receive a dose below its threshold for damage, are enforced by collecting point constraints for each tissue in a multiple-choice group with alternatives delineated with binary variables.The research will develop and test two contributions to generic MIP methodology in order to enable computationally efficient solutions to be be found for the radiotherapy planning problem. The aim is to provide solutions that satisfy prescribed constraints with an objective value that lies within a provable bound around the optimum. The first of these will strengthen LP relaxations of MIP formulations for the multiple-choice (dose--volume) constraints by constructing and adding new valid inequalities. The second will adapt a column-generation approach to deal with the massive IMRT formulations. Instead of modeling the intensity of each beamlet within an IMRT beam, whole patterns of beamlet intensities will be represented as single columns and generated as required.