A mathematical model for the deficiency-excess mechanism of yin-yang in five viscera.

To raise traditional medicine to a higher level of scientific research, a mathematical model has been proposed using symbolic notations and operators to describe several disease symptoms generally recognized in traditional medicine. Even though this model to a certain degree offers a mathematical approach to identify the relationships between yin-yang and the five viscera, it is not an efficient means of explaining the pathology in traditional medicine due to its use of superfluous notations and definitions. In this paper, we introduce two concise operators, a self-development operator and an action operator: the former describes the effect of a viscus in the unbalanced state on other viscera: the latter explains the engendering and restraining relationships between the two viscera. These tools are useful to elucidate the interactions among the states of the five viscera based on yin-yang and the five elements theory. Our mathematical model with these two operators facilitates description for the scheme of deficiency-excess of yin-yang in the five viscera. Accordingly, we have mathematically refined the existing results and shown clinical applications as well.