He Fu-yuan, Deng Kai-wen, Huang Sheng, Liu Wen-long, Shi Ji-lian
Department of Pharmaceutics, Hunan University of Chinese Medicine, Changsha 410208, China.
The First Affinity Hospital, Hunan University of Chinese Medicine, Changsha 410007, China.
Yao Xue Xue Bao. 2013 Sep;48(9):1453-8.
The paper aims to elucidate and establish a new mathematic model: the total quantum statistical moment standard similarity (TQSMSS) on the base of the original total quantum statistical moment model and to illustrate the application of the model to medical theoretical research. The model was established combined with the statistical moment principle and the normal distribution probability density function properties, then validated and illustrated by the pharmacokinetics of three ingredients in Buyanghuanwu decoction and of three data analytical method for them, and by analysis of chromatographic fingerprint for various extracts with different solubility parameter solvents dissolving the Buyanghanwu-decoction extract. The established model consists of four mainly parameters: (1) total quantum statistical moment similarity as ST, an overlapped area by two normal distribution probability density curves in conversion of the two TQSM parameters; (2) total variability as DT, a confidence limit of standard normal accumulation probability which is equal to the absolute difference value between the two normal accumulation probabilities within integration of their curve nodical; (3) total variable probability as 1-Ss, standard normal distribution probability within interval of D(T); (4) total variable probability (1-beta)alpha and (5) stable confident probability beta(1-alpha): the correct probability to make positive and negative conclusions under confident coefficient alpha. With the model, we had analyzed the TQSMS similarities of pharmacokinetics of three ingredients in Buyanghuanwu decoction and of three data analytical methods for them were at range of 0.3852-0.9875 that illuminated different pharmacokinetic behaviors of each other; and the TQSMS similarities (ST) of chromatographic fingerprint for various extracts with different solubility parameter solvents dissolving Buyanghuanwu-decoction-extract were at range of 0.6842-0.999 2 that showed different constituents with various solvent extracts. The TQSMSS can characterize the sample similarity, by which we can quantitate the correct probability with the test of power under to make positive and negative conclusions no matter the samples come from same population under confident coefficient a or not, by which we can realize an analysis at both macroscopic and microcosmic levels, as an important similar analytical method for medical theoretical research.
本文旨在基于原有的总量子统计矩模型，阐明并建立一种新的数学模型：总量子统计矩标准相似度（TQSMSS），并说明该模型在医学理论研究中的应用。该模型结合统计矩原理和正态分布概率密度函数性质建立，然后通过补阳还五汤中三味药的药代动力学及其三种数据分析方法进行验证和说明，并通过用不同溶解度参数溶剂溶解补阳还五汤提取物得到的各种提取物的色谱指纹图谱分析进行验证和说明。所建立的模型主要由四个参数组成：（1）总量子统计矩相似度ST，为两个TQSM参数转换时两条正态分布概率密度曲线的重叠面积；（2）总变异度DT，为标准正态累积概率的置信限，等于其曲线节点积分范围内两个正态累积概率的绝对差值；（3）总变异概率1-Ss，为D(T)区间内的标准正态分布概率；（4）总变异概率(1-β)α和（5）稳定置信概率β(1-α)：在置信系数α下做出正负结论的正确概率。利用该模型，我们分析了补阳还五汤中三味药的药代动力学及其三种数据分析方法的TQSMS相似度在0.3852 - 0.9875范围内，这表明它们各自具有不同的药代动力学行为；用不同溶解度参数溶剂溶解补阳还五汤提取物得到的各种提取物的色谱指纹图谱的TQSMS相似度（ST）在0.6842 - 0.9992范围内，这表明不同溶剂提取物具有不同的成分。TQSMSS可以表征样品相似度，通过它我们可以在置信系数α下，无论样品是否来自同一总体，通过功效检验定量做出正负结论的正确概率，通过它我们可以实现宏观和微观层面的分析，作为医学理论研究的一种重要的相似性分析方法。
