Low Daniel A, Dempsey James F
Department of Radiation Oncology, Washington University School of Medicine, St. Louis, Missouri 63110, USA.
Med Phys. 2003 Sep;30(9):2455-64. doi: 10.1118/1.1598711.
The gamma tool was developed to quantitatively compare dose distributions, either measured or calculated. Before computing gamma, the dose and distance scales of the two distributions, referred to as evaluated and reference, are renormalized by dose and distance criteria, respectively. The renormalization allows the dose distribution comparison to be conducted simultaneously along dose and distance axes. The gamma quantity, calculated independently for each reference point, is the minimum distance in the renormalized multidimensional space between the evaluated distribution and the reference point. The gamma quantity degenerates to the dose-difference and distance-to-agreement tests in shallow and very steep dose gradient regions, respectively. Since being introduced, the gamma quantity has been used by investigators to evaluate dose calculation algorithms, and compare dosimetry measurements. This manuscript examines the gamma distribution behavior in two dimensions and evaluates the gamma distribution in the presence of data noise. Noise in the evaluated distribution causes the gamma distribution to be underestimated relative to the no-noise, condition. Noise in the reference distribution adds noise in the gamma distribution in proportion to the normalized dose noise. In typical clinical use, the fraction of points that exceed 3% and 3 mm can be extensive, so we typically use 5% and 2-3 mm in clinical evaluations. For clinical cases, the calculation time is typically 5 minutes for a 1 x 1 mm2 interpolated resolution on an 800 MHz Pentium 4 for a 14.1 x 15.2 cm2 radiographic film.
伽马工具是为定量比较测量或计算得到的剂量分布而开发的。在计算伽马值之前，将两个分布（分别称为评估分布和参考分布）的剂量和距离尺度按剂量和距离标准进行重新归一化。这种重新归一化使得能够沿剂量轴和距离轴同时进行剂量分布比较。针对每个参考点独立计算的伽马值，是评估分布与参考点在重新归一化多维空间中的最小距离。在浅剂量梯度区域和非常陡峭的剂量梯度区域，伽马值分别退化为剂量差异和距离一致性测试。自引入以来，研究人员一直使用伽马值来评估剂量计算算法以及比较剂量测定测量结果。本手稿研究二维情况下的伽马分布行为，并评估存在数据噪声时的伽马分布。评估分布中的噪声会导致伽马分布相对于无噪声情况被低估。参考分布中的噪声会按归一化剂量噪声的比例在伽马分布中增加噪声。在典型的临床应用中，超过３％和３毫米的点的比例可能很大，所以我们在临床评估中通常使用５％和２至３毫米。对于临床病例，在一台８００兆赫奔腾４处理器上，对于一张１４.１×１５.２平方厘米的射线照相胶片，若插值分辨率为１×１平方毫米，计算时间通常为５分钟。
