Analytical probabilistic treatment planning

我们提出了一项为期三年的研究计划，延长了我们在放射治疗计划分析概率建模(APM)方面的联合工作。在当前的临床实践中，放射治疗计划并没有明确地建模不确定的来源，如分数间和分数内的运动、患者的固定和描绘错误。在通过图像制导尽可能地减少几何不确定性之后，仅用标准化的边际配方隐含地解释了不确定性。由于概念限制和运行时间问题，用于量化和最小化患者特定不确定性的数学方法从未在临床上得到广泛应用。通用边缘方法损害了个别患者的放射治疗质量。统一的边缘可能会导致不必要的健康组织暴露，边缘概念并不能防止肿瘤内的“冷点”。我们希望弥合这一不充分的临床不确定性建模的差距，并将APM发展成一个计算研究框架，用于质子和碳离子的概率放射治疗计划。APM允许对强度调制剂量分布(原则上是所有高阶矩)的期望值和(协方差)的封闭形式计算。这种封闭的代数形式为不确定性量化和最小化提供了核心优势1。所有数值模拟的质量都可以直接控制和评估；APM不受算法不确定性的影响，例如统计波动2。APM明确地结合了分割放射治疗中不确定性的复杂相关模型以及随机和系统不确定性的非平凡剂量学相互作用3。APM允许对现有的和新的概率目标4进行封闭形式的定义、区分，从而有效地优化。APM的输出是一个高斯概率密度，它使得不确定性能够在相关计算之间传播。在拟议的研究中，我们追求两个目标：1.利用通过治疗规划问题的解析公式实现的计算复杂性的降低，以实现有效的健壮的碳离子治疗规划，包括相关生物模型中的不确定性。使不确定性能够以封闭形式传播到综合治疗计划质量指标中。这将为临床医生提供与他们的决策直接相关的数量上的误差条，并随后通过直接指定概率治疗计划特征来实现反向计划。通过考虑模拟和实际提供的治疗计划之间的潜在差异，我们希望帮助减少放射治疗过程中的局部失败和正常组织并发症。

We propose a three year research program extending our joint work regarding analytical probabilistic modeling (APM) for radiation therapy treatment planning.In current clinical practice, radiation therapy treatment planning does not explicitly model sources of uncertainty such as inter- and intrafractional motion, patient immobilization, and delineation errors. After geometric uncertainties have been reduced as far as possible through image guidance, uncertainties are only implicitly accounted for with standardized margin recipes. Mathematical approaches for patient specific uncertainty quantification and minimization have never found broad clinical application due to conceptual limitations and run time issues. Generic margin approaches compromise the quality of radiation treatments for individual patients. A uniform margin may cause unnecessary exposure of healthy tissue and the margin concept does not prevent "cold spots" within the tumor.We want to close this gap of inadequate clinical uncertainty modeling and develop APM into a computational research framework for probabilistic radiation therapy treatment planning for protons and carbon ions.APM enables the closed form computation of the expectation value and the (co-)variance of intensity-modulated dose distributions (and in principle all higher-order moments). This closed algebraic form provides central advantages for uncertainty quantification and minimization.1. The quality of all numerical simulations can be directly controlled and evaluated; APM is not compromised by algorithmic uncertainties, e.g. statistical fluctuations2. APM explicitly incorporates complex correlation models of the uncertainties and the non-trivial dosimetric interplay of random and systematic uncertainties in fractionated radiation therapy3. APM allows for the closed form definition, differentiation, and thence efficient optimization of existing and novel probabilistic objectives4. The output of APM is a Gaussian probability density which enables the propagation of uncertainty between related computationsWith the proposed research we pursue two goals:1. Exploit the reduction in computational complexity achieved through the analytical formulation of the treatment planning problem, to enable efficient robust planning of carbon ion treatments including uncertainties in the associated biological models.2. Enable closed-form propagation of uncertainty into composite treatment plan quality indicators. This will provide clinicians with error bars on quantities directly relevant for their decision and subsequently enable inverse planning through direct specification of probabilistic treatment plan features.Through accounting for potential discrepancies between the simulated and the actually delivered treatment plan we want to help reduce both local failure and normal tissue complication during radiation therapy.