Issue 3 (197), article 5

DOI:https://doi.org/10.15407/kvt197.03.065

Cybernetics and Computer Engineering, 2019, 3(197), pp.

Aralova N.I., PhD (Engineering), Senior Researcher,
Senior Researcher of the Department of Controlled Processes Optimization
email: aralova@ukr.net

Aralova A.A., PhD (Phys and Math),
Researcher of the Department of Methods for Discrete Optimization,
Mathematical Modelling and Analyses of Complex Systems
email: aaaralova@gmail.com

Glushkov Institute of Cybernetics of National Academy of Sciences of Ukraine,
40, Acad.Glushkov av., 03187, Kyiv, Ukraine

MATHEMATICAL MODELS OF CONFLICT CONTROLLED PROCESSES UNDER FUNCTIONAL SELF-ORGANIZATION OF THE RESPIRATORY SYSTEM

Introduction. Modern human life imposes more stringent requirements for ability to adapt to increasingly complex conditions, such as unfavorable environmental conditions, potential danger, increased responsibility, extreme physical exertion and their combined effect. This leads to a decrease in exercise tolerance, unfavorable changes in hemodynamic parameters, and disorders in the functional activity of other body organs and tissues. The decisive role in the adaptation of the organism to physical and psycho-emotional stress belongs to the oxygen transport system. However, at present, the possibilities of instrumental methods are rather limited, moreover, they can only characterize the state of the body at the current moment, and not predict its reserve capabilities in case of disturbances in the internal and external environment, in the process of recovery and rehabilitation. Partially, this gap can be filled by mathematical models of the functional respiratory system, which allow to imitate disturbances of the internal and external environment of an organism in the dynamics of the respiratory cycle and, thus, predict possible controlling actions of the organs of self-regulation of the organism when adapting to these disturbances.

The purpose of the article is to build a mathematical model of a functional respiration system that simulates resolving a conflict situation between executive and managing bodies of self-regulation in the conflict for oxygen, which allows predicting the parameters of self-organization of the respiratory system under internal and external disturbances.

Results. A mathematical model of mass transfer and mass transfer of respiratory gases in the human body is presented in the form of a system of non-linear differential equations, which is a controlled dynamic system, the state of which is determined at each time point by oxygen and carbon dioxide stresses in each structural link of the respiratory system (alveoli, blood and tissues). The control (self-regulation) of the condition under permanent or at a given time interval of the current disturbance (high functional activity of certain groups of tissues) is carried out by the self-regulation organs — respiratory muscles that form the necessary level of ventilation to compensate for the resulting hypoxic states, cardiac muscle providing the minute blood volume, and smooth muscles, vessels, vasodilation and vasocostriction which contributes to the distribution of systemic blood flow through the organs and tissues. There are also passive mechanisms of self-regulation: the concentration of hemoglobin in the blood, myoglobin in skeletal and cardiac muscles, their ability to oxygenate, the concentration of buffer bases in the blood etc. It is assumed that the decision on the choice of the values of compensating influences is made by the decision center based on the information activity and degree of oxygen deficiency, excessive accumulation of carbon dioxide in all tissue regions of the body, is transmitted to the executive bodies of self-regulation, increases their functional activity, which ensures the implementation of the main function of respiration.

Conclusion The per-set mathematical model of the FRS allows the researcher to analyze the oxygen and carbon dioxide regimes of body in dynamics at various levels of functional load and under various environmental conditions; to form such regimes of the external respiration system, which contribute to an increase in the oxygen supply in the body and thereby increase the resource of the cardiac muscle during the regulation of hypoxic states that occur when the combined effects of hypobaric hypoxia and hypermetabolic hypoxia; predict the state of the body during various physical efforts and evaluate the effectiveness of the preparation process; plan and distribute heavy loads, taking into account the functionality of the individual and depending on the prevailing situations. The work presents the results of numerical experiments with a model for simulating internal (physical activity) and external (hypoxic hypoxia) disturbances on the human body.

Keywords: conflict-controlled processes, a functional system of respiration, functional self-organization of the respiratory system, adaptation to stress.

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Received 20.05.2019