The model of high-order multidimensional tree with tristate applied to the digitalization of Yin-Yang theory of Traditional Chinese Medicine

To approach the digital reciprocal expression with undamaged information about the topology of the high-order multidimensional tree with sequenced nodes(HMTSN) and to build method for calculating the characteristic discrepancy of state-space between HMTSN, this paper applies mapping and matrix theory to seek for the potential applicability in biomedical field, especially in Traditional Chinese Medicine (TCM). [Methods] 1. Applying n-dimensional spatial vector representation, as well as set and mapping theory, this research mappings HMTSN to a characterized square matrix (CSM) based on a customer-set protocol; 2. Calculating the differences in value between the elements from two different square matrices being mapped from corresponding tree spatial status, the result obtains the difference between two multidimensional structures with multi-state.[Results] 1. With a special case with {-1,0, +1} in effective nodes, HMTSN can be used to describe the characteristics of multidimensional structure in Yin-Yang differentiation of TCM(DIFF) with tristate; 2. The customer-set protocol is satisfied to reciprocally and fully express the characterized of HMTSN with CSM through mapping from HMTSN model to a matrix; 3. The square root of the matrix trace (SRMT) calculated from two CSM, which is the matrix product made by the difference between square matrices (DSM) multiplied by the transpose of DSM, may reflect the structural difference in value between HMTSN. HMTSN with tristate and SRMT may express the Yin-Yang DIFF and have potential benefit for its transmission study. [Conclusions] The matrixing for the model of HMTSN and its algorithm, as a special case of tristate with Yin, Balance and Yang, being as a method of the DIFF and a potential algorithm for DIFF transmission in TCM with the core of Yin and Yang, may offer a creative metrizable method for TCM theory.