Department of Radiation Oncology, University of Florida College of Medicine, Gainesville, Florida, 32610, USA.
Department of Radiation Oncology, Washington University School of Medicine, St. Louis, Missouri, 63110, USA.
Med Phys. 2017 Jun;44(6):2096-2114. doi: 10.1002/mp.12250. Epub 2017 May 18.
Most VMAT algorithms compute the dose on discretized apertures with small angular separations for practical reasons. However, machines deliver the VMAT dose with a continuously moving MLC and gantry and a continuously changing dose rate. The computed dose can deviate from the delivered dose, especially if no, or loose, MLC movement constraints are applied for the VMAT optimization. The goal of this paper is to establish a simplified mathematical model to analyze the discrepancy between the VMAT plan calculation dose and the delivered dose and to provide a reasonable solution for clinical implementation.
A simplified metric is first introduced to describe the discrepancy between doses computed with discretized apertures and a continuous delivery model. The delivery fluences were formed separately for six different leaf movement scenarios. The formula was then rewritten in a more general form. The correlation between discretized and continuous fluence is summarized using this general form. The Fourier analysis for the impacts from three separate factors - dose kernel width, aperture width, aperture distance - to the dose discrepancy is also presented in order to provide insight into the dose discrepancy caused by under-sampling in the frequency domain. Finally, a weighting-based interpolation (WBI) algorithm, which can improve the aperture interpolation efficiency, is proposed. The associated evaluation methods and criteria for the proposed algorithm are also given.
The comparisons between the WBI algorithm and the equal angular interpolation (EAI) method suggested that the proposed algorithm has a great advantage with regard to aperture number efficiency. To achieve a 90% gamma passing rate using the dose computed with apertures generated with 0.5° EAI, with the initial optimization apertures as the standard for the comparison, the WBI needs only 66% and 54% of the aperture numbers that the EAI method needs for a 2° and a 4° angular separation of the VMAT optimization, respectively. The results also suggested that the weighted dose error index value, Θ, can be used as a stopping criterion for an interpolation algorithm, e.g., WBI or EAI, or as an indicator for sampling level evaluations. The phantom results indicate that the gamma passing rate decreases with increasing depth, from the phantom surface to the iso center, for the plans computed with under-sampled apertures. No obvious variation trends were observed for the plans computed with well-sampled apertures.
The mathematical analysis suggests that the dose discrepancies due to under-sampling are strongly correlated with the aperture width, the distance between apertures, and the width of the dose kernel. The WBI algorithm proves to be an efficient aperture interpolation strategy and is useful for dose computation of VMAT plans.
出于实际原因，大多数 VMAT 算法会在离散孔径上计算剂量，这些孔径的角度间隔很小。然而，机器使用连续移动的叶片和机架以及不断变化的剂量率来输送 VMAT 剂量。计算出的剂量可能与输送的剂量有偏差，尤其是如果在 VMAT 优化中没有应用或仅应用了宽松的叶片运动限制。本文的目的是建立一个简化的数学模型来分析 VMAT 计划计算剂量与输送剂量之间的差异，并为临床实施提供合理的解决方案。
首先引入一种简化的度量标准来描述离散孔径计算剂量与连续输送模型之间的差异。为六个不同的叶片运动场景分别形成输送通量。然后将公式重写为更一般的形式。使用该通用形式总结离散和连续通量之间的相关性。还呈现了剂量核宽度、孔径宽度和孔径距离这三个单独因素对剂量差异的傅里叶分析，以便深入了解在频率域中由于欠采样引起的剂量差异。最后，提出了一种基于加权的插值（WBI）算法，可以提高孔径插值效率。还给出了建议算法的相关评估方法和标准。
WBI 算法与等角插值（EAI）方法的比较表明，该算法在孔径数量效率方面具有很大的优势。为了实现使用以 0.5°EAI 生成的孔径计算剂量的 90%伽马通过率，以初始优化孔径作为比较的标准，WBI 分别仅需要 EAI 方法的 66%和 54%的孔径数量，用于 2°和 4°VMAT 优化的角分离。结果还表明，加权剂量误差指数值Θ可作为插值算法（例如 WBI 或 EAI）的停止标准，或作为采样水平评估的指标。体模结果表明，对于使用欠采样孔径计算的计划，从体模表面到等中心，剂量伽马通过率随深度的增加而降低。对于使用采样良好的孔径计算的计划，没有观察到明显的变化趋势。
数学分析表明，由于欠采样引起的剂量差异与孔径宽度、孔径之间的距离以及剂量核的宽度密切相关。WBI 算法被证明是一种有效的孔径插值策略，可用于 VMAT 计划的剂量计算。
