Clark V H, Chen Y, Wilkens J, Alaly J R, Zakaryan K, Deasy J O
Department of Radiation Oncology, Washington University School of Medicine, and the Siteman Cancer Center, Saint Louis, MO, USA.
Linear Algebra Appl. 2008 Mar 1;428(5-6):1345-1364. doi: 10.1016/j.laa.2007.07.026.
Treatment planning for intensity modulated radiation therapy (IMRT) is challenging due to both the size of the computational problems (thousands of variables and constraints) and the multi-objective, imprecise nature of the goals. We apply hierarchical programming to IMRT treatment planning. In this formulation, treatment planning goals/objectives are ordered in an absolute hierarchy, and the problem is solved from the top-down such that more important goals are optimized in turn. After each objective is optimized, that objective function is converted into a constraint when optimizing lower-priority objectives. We also demonstrate the usefulness of a linear/quadratic formulation, including the use of mean-tail-dose (mean dose to the hottest fraction of a given structure), to facilitate computational efficiency. In contrast to the conventional use of dose-volume constraints (no more than x% volume of a structure should receive more than y dose), the mean-tail-dose formulation ensures convex feasibility spaces and convex objective functions. To widen the search space without seriously degrading higher priority goals, we allowed higher priority constraints to relax or 'slip' a clinically negligible amount during lower priority iterations. This method was developed and tuned for external beam prostate planning and subsequently tested using a suite of 10 patient datasets. In all cases, good dose distributions were generated without individual plan parameter adjustments. It was found that allowance for a small amount of 'slip,' especially in target dose homogeneity, often resulted in improved normal tissue dose burdens. Compared to the conventional IMRT treatment planning objective function formulation using a weighted linear sum of terms representing very different dosimetric goals, this method: (1) is completely automatic, requiring no user intervention, (2) ensures high-priority planning goals are not seriously degraded by lower-priority goals, and (3) ensures that lower priority, yet still important, normal tissue goals are separately pushed as far as possible without seriously impacting higher priority goals.
由于计算问题的规模（数千个变量和约束条件）以及目标的多目标、不精确性质，调强放射治疗（IMRT）的治疗计划具有挑战性。我们将分层规划应用于IMRT治疗计划。在这种公式化方法中，治疗计划目标按绝对层次结构排序，问题从顶部向下解决，以便依次优化更重要的目标。在每个目标优化之后，在优化较低优先级目标时，该目标函数被转换为一个约束条件。我们还展示了线性/二次公式化方法的实用性，包括使用平均尾剂量（给定结构最热部分的平均剂量），以提高计算效率。与传统的剂量体积约束（一个结构的体积不超过x%应接受超过y剂量）的使用不同，平均尾剂量公式确保了凸可行空间和凸目标函数。为了在不严重降低较高优先级目标的情况下扩大搜索空间，我们允许较高优先级的约束在较低优先级迭代期间放宽或“滑动”临床上可忽略的量。该方法是针对外照射前列腺计划开发和调整的，随后使用一组10个患者数据集进行了测试。在所有情况下，无需调整单个计划参数即可生成良好的剂量分布。结果发现，允许少量的“滑动”，特别是在靶区剂量均匀性方面，通常会导致正常组织剂量负担的改善。与使用代表非常不同剂量学目标的项的加权线性和的传统IMRT治疗计划目标函数公式相比，该方法：（1）完全自动，无需用户干预；（2）确保高优先级计划目标不会因低优先级目标而严重降低；（3）确保低优先级但仍然重要的正常组织目标在不严重影响高优先级目标的情况下尽可能分别推进。
