论文标题
剂量 - 体积直方图的分析概率建模
Analytical probabilistic modeling of dose-volume histograms
论文作者
论文摘要
放射疗法对剂量和计划质量指标（如剂量 - 体积直方图（DVHS））的不确定性传播的执行和准备不确定性敏感。量化和减轻此类不确定性的当前方法取决于明确计算的错误场景，因此受到基本不确定性模型的统计不确定性和局限性。在这里，我们提出了一种替代，分析方法，以近似DVH点的概率分布的矩，并评估其在患者数据上的准确性。我们使用分析概率建模（APM）根据剂量的概率分布来得出单个DVH点的这些矩。此外，我们使用计算的矩对DVH点（此处正常或beta分布）的不同概率分布进行参数化计算百分位/$α$ -DVHS。然后，通过假设遵循从APM获得的多元正态分布，在30和单分数场景中对三个患者病例进行评估。将结果与采样基准进行比较。对采样基准的新概率模型的评估证明了其在完美的假设和现实条件下的良好一致性下的正确性。大约在所有计算的预期DVH点及其标准偏差中，有90％在1％的体积范围内与抽样的经验对应物相吻合，用于分馏和单个分数处理。 $α$ -DVHS在假设Beta时与经验百分位数达成更好的一致性，而不是正态分布：虽然在这两种情况下，概率都显示出较大的本地偏差（最高$ \ pm $ 0.2），而相应的$α$ -DVH仅显示出小偏差（最高$ \ $ \ $ \ $ \ $ \ $ \ $ \ pm $ pm $ $ $ $ $ $ $ $ pm $ $ $ $ $ $ $ $ $ $ pm $ $ $ $ $ $ pm $ $ $ $ $ $ $ $ $ pm $ $ $ $ $ $ $ $ $ $ pm $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ dVH均可达到2％的beta分配）。先前由不同作者发表的模型产生了$α$ -DVHS的实质性偏差。
Radiotherapy is sensitive to executional and preparational uncertainties that propagate to uncertainty in dose and plan quality indicators like dose-volume histograms (DVHs). Current approaches to quantify and mitigate such uncertainties rely on explicitly computed error scenarios and are thus subject to statistical uncertainty and limitations regarding the underlying uncertainty model. Here we present an alternative, analytical method to approximate moments of the probability distribution of DVH-points and evaluate its accuracy on patient data. We use analytical probabilistic modeling (APM) to derive those moments for individual DVH-points based on the probability distribution over dose. Further we use the computed moments to parameterize distinct probability distributions over DVH-points (here normal or beta distributions) to compute percentiles/$α$-DVHs. The model is then evaluated on three patient cases in 30- and single-fraction scenarios by assuming the dose to follow a multivariate normal distribution obtained from APM. The results are compared to a sampling benchmark. The evaluation of the new probabilistic model against the sampling benchmark proves its correctness under perfect assumptions as well as good agreement in realistic conditions. Ca. 90% of all computed expected DVH-points and their standard deviations agree within 1% volume with their empirical counterpart from sampling, for both fractionated and single fraction treatments. $α$-DVHs achieve better agreement with empirical percentiles when assuming a beta instead of a normal distribution: While in both cases probabilities show large local deviations (up to $\pm$0.2), the respective $α$-DVH only showed small deviations (up to $\pm$5% volume for a normal, and up to 2% for a beta distribution). A previously published model by different authors yielded substantially deviating $α$-DVHs.
