Mathematical Model for the Investigation of Human Organism Functional Self-organisation
DOI:
https://doi.org/10.18372/1990-5548.68.16083Keywords:
functional respiratory system, controlled dynamic system, self-organization of respiratory system, operators of continuous interaction system, disturbing influence of environmentAbstract
Mathematical modeling of processes occurring in living organism is convenient and reliable tool for the understanding of mechanisms of human organism self-organization, interaction and inter-influence of its functional systems. The simulations of processes occurring in organism during various extreme perturbations at mathematical models allow us to study the parameters of self-organization in these perturbations at the level unavailable currently for modern invasive methods as well as to predict the organism steady state at given level of perturbing effects. The objects of study were the reactions of respiratory and blood circulatory systems, because these systems, according to the theory of adaptation by F. Meerson, are the most sensitive to the disturbing effects of environment. The paper provides a brief overview of mathematical models of respiratory and blood circulatory system; in the construction of these models rather complex mathematical apparatus was used and, accordingly, the implementation of which requires significant computational resources. The mathematical model of the functional respiratory system was proposed; it is based on the principle of the main function of respiratory system realization and takes into account conflict situations that occur in organism during this function fulfillment. This conflict happens between the governing and executive self-regulatory organism organs as well as between the different tissues groups in their fight for the oxygen. Mathematically, the model is a system of ordinary nonlinear differential equations that describe the transport and mass transfer of respiratory gases in all structural parts of respiratory system. The task of control of gases dynamics in organism was solved using the principle of Pontryagin maximum.
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