We give a scenario-based treatment plan optimization formulation that is equivalent to planning with geometric margins if the scenario doses are calculated using the static dose cloud approximation. If the scenario doses are instead calculated more accurately, then our formulation provides a novel robust planning method that overcomes many of the difficulties associated with previous scenario-based robust planning methods. In particular, our method protects only against uncertainties that can occur in practice, it gives a sharp dose fall-off outside high dose regions, and it avoids underdosage of the target in ``easy'' scenarios. The method shares the benefits of the previous scenario-based robust planning methods over geometric margins for applications where the static dose cloud approximation is inaccurate, such as irradiation with few fields and irradiation with ion beams. These properties are demonstrated on a suite of phantom cases planned for treatment with scanned proton beams subject to systematic setup uncertainty.

翻译：我们给出一种基于情景的治疗计划优化配方,如果使用静剂量云近似值来计算假设情景剂量,就相当于用几何边规划。如果假设情景剂量的计算更为准确,那么我们的配方就提供了一种新的稳健的规划方法,克服了以往基于情景的稳健规划方法带来的许多困难。特别是,我们的方法只能防止实际中可能出现的不确定因素,在高剂量区域之外会发生急性剂量下降,并避免在“塞塞”情景中发生目标误入。这种方法分享了先前基于情景的稳健规划方法对静剂量云近似值不准确的应用的几何边的惠益,例如对少数田地的辐照和对离子束的辐照。这些特性在计划用扫描质波束进行处理的一组幻象病例中展示,这些特性取决于系统设置的不确定性。