Mathematical Model for Analyzing Five Flavor Compatibility-transformation Theory in Tangye Jingfatu / 中国实验方剂学杂志

ABSTRACT

Objective:<italic>Auxiliary Verse on Drugs and</italic> <italic>methods</italic> <italic>for Zang-Fu Organs （Fuxingjue Wuzangyongyao Fayao）</italic> written by TAO Hong-jing from the Liang dynasty covered many contents from<italic> </italic>a missing prescription book<italic> Classic of Decoction （Tangye Jingfa）</italic>， including a map revealing the compatibility principle of Chinese herbs， namely the Tangye Jingfatu. Represented by a centrosymmetric pentagon， the map describes a unique theoretical system for deficiency-excess syndrome differentiation of five Zang organs （liver， heart， spleen， lung and kidney） and the tonification-purgation and compatibility theory of five flavors （pungent， salt， sweet， sour and bitter）. Each Zang organ fixedly corresponds to one "property" flavor （purgation）， one "function" flavor （tonification） and one "transformation" flavor （harmonization） resulting from the combination of the former two. For example， the liver can be purged by sour， tonified by pungent， and moderated by sweet transformed by the combination of sour with pungent. The heart can be purged by bitter， tonified by salt， and astringed by sour transformed by the combination of bitter with salt. The spleen can be purged by pungent， tonified by sweet， and dried by bitter transformed by the interaction between pungent and sweet. The lung can be purged by salt， tonified by sour， and dispersed by pungent transformed by the combination of salt with sour. The kidney can be purged by sweet， tonified by bitter， and moistened by salt transformed by the combination of sweet with bitter. This study selected appropriate mathematical tools to analyze the fixed relationship between "property" flavor， "function" flavor and "transformation" flavor among the five Zang organs in “Tangye Jingfatu” and establish a mathematical model revealing the compatibility-transformation relationship among five flavors. Method:Based on the group representation of five elements （wood， fire， earth， metal， and water）， the correlations of "property" flavor， "function" flavor， and "transformation" flavor with five elements’ generation-restriction were deduced based on matrix calculation and group theory. The three-dimensional calculation method for vector product was expanded for establishing the mathematical operator of five flavors' compatibility-transformation. Result:<bold>and</bold> Conclusion:There is a mapping relationship of the purging， tonifying， and harmonizing functions represented by the "property" flavor， "function" flavor， and "transformation" flavor of the five zang organs in the "Tangye Jingfatu" with the five elements' generation-restriction. The established mathematical operator contributes to explaining the fixed collocations of five flavor transformation. Based on such algorithm， the tonifying and purging characteristics of five flavors in 10 representative classic prescriptions have been clearly expounded.