INDICATOR TRANSIT TIME CONSIDERED AS GAMMA VARIATE
INDICATOR TRANSIT TIME CONSIDERED AS GAMMA VARIATE
复制标题
DOI：
10.1161/01.res.14.6.502
复制
发表时间：
1964-01-01
影响因子：
20.1
通讯作者：
MCINTOSH, HD
中科院分区：
文献类型：
--
作者：
THOMPSON, HK;WHALEN, RE;MCINTOSH, HD
在再循环峰值出现之前的指示剂稀释曲线与称为“伽马变量”的随机变量类的频率分布曲线具有惊人的相似性。“这种分布曲线的数学表达式导致指示剂浓度作为时间函数的可能数学表示[图像]，其中C（t）=注射后时间t的指示剂浓度; AT =出现时间; [alpha]，[beta] =分布参数; K是比例常数。在数字计算机的帮助下，对70例患者和2例正常人的114条染料曲线分别应用矩和最小二乘法拟合方程。对于所有曲线，可以找到[alpha]和[beta]的值，这些值提供了极好的拟合。通过组内相关系数（R）比较C（t）的观察值和计算值。通过最小二乘法（0.9805 < R < 0.9996）获得的拟合比通过不太精细的矩法（0.9332 < R < 0.9990）获得的拟合更接近。由于前一方程中的曲线族成员与实验曲线之间的对应关系非常密切，因此出于实际目的，可以认为指示剂渡越时间在数学上表现得像伽马变量。伽马变量具有众所周知的和方便的数学性质。预计指示剂浓度作为时间函数的分析表达式的可用性将有助于动脉指示剂稀释曲线的理论分析、正常和异常曲线的表征以及使用高速计算机处理实验曲线。
Indicator dilution curves before the onset of the recirculation peak bear a striking resemblance to the frequency distribution curves of the class of random variables called "gamma variates." The mathematical expression for such distribution curves leads to a possible mathematical representation for indicator concentration as a function of time [image] where C(t) = indicator concentration at time, t, after injection; AT = appearance time; [alpha],[beta] = parameters of distribution; and K is a proportionality constant. With the help of a digital computer, the methods of moments and least squares were applied to each of 114 dye curves from 70 patients and 2 normals to fit the equation to the experimental curves. For all the curves, values for [alpha] and [beta] could be found which provided excellent fits. Observed and computed values for C(t) were compared by means of intraclass correlation coefficients ( R ). Closer fits were obtained by least squares (0.9805 < R < 0.9996) than by the less elaborate method of moments (0.9332 < R < 0.9990). Because of the very close correspondence between members of the family of curves in the former equation and experimental curves, indicator transit time may be considered, for practical purposes, to behave mathematically like a gamma variate. The gamma variates have well-known and convenient mathematical properties. It is anticipated that the availability of an analytical expression for indicator concentration as a function of time will facilitate theoretical analysis of arterial indicator dilution curves, characterization of normal and abnormal curves, and handling of experimental curves using high-speed computers.