总量统计矩标准相似度数学模型的建立及应用研究

Establishment of the mathematic model of total quantum statistical moment standard similarity for application to medical theoretical research

在原总量统计矩分析法的基础上阐明并建立总量统计矩标准相似度法,阐明在医药基础理论研究中的应用。运用统计矩原理与正态分布概率密度函数性质建立数学模型,并以补阳还五汤三成分三方法的药物动力学、不同溶度参数溶剂获取补阳还五汤水煎样品液的指纹图谱为例验证所创的数学模型。建立了总量统计矩标准相似度数学模型,包括4个参数①总量统计矩标准相似度,即两标准正态概率分布曲线下重叠的面积;②总差异DT,即与两标准正态曲线交点的累积分布概率之差的绝对值相等的标准正态分布曲线累积概率的对称可信限;③总差异度1-Ss,即总差异可信限对应的正态累积概率;④总差异把握度(1-β)α与⑤总肯定把握度β(1-α),即是在检测水准α作出否定与肯定正确的概率。以此法分析补阳还五汤三成分三方法的药物动力学的标准相似度介于0.385 2～0.987 5,其药物动力学行为各异;不同溶度参数溶剂获取补阳还五汤水煎样品液的指纹图谱的相似度介于0.684 2～0.999 2,不同溶剂提取成分的构成比不同。统计矩相似度可用来刻画样本的相似特征,对任一总量统计矩标准相似度作出肯定或否定不源于同一整体结论时可用把握度来定量衡量结论正确的概率;该法能实现宏观与微观相结合分析,是重要的基础医药理论多因素相似性方法。

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 Buvanghanwu-decoction extract The established model consists of four mainly parameters： ①total 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 DT;④ total variable probability （1-β）α and @ stable confident probability β（1-α）： the correct probability to make positive and negative conclusions under confident coefficient a. 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 0.385 2 - 0.987 5 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 0.684 2 - 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.