# Issue 4 (202), article 4

Cybernetics and Computer Engineering, 2020, 4(202)

ANTOMONOV M.Y., DSc (Biology), Professor,
Chief Researcher, the Department of Epidemiological Research and Medical Informatics,
e-mail: antomonov@gmail.com

A.M. Marzeev Institute of Public Health of National Academy of Medical Sciences of Ukraine, 50, Popudrenko str., 02660, Kyiv, Ukraine

IMITATION OF COMPENSATOR AND ADAPTIVE PROCESSES IN BIOSYSTEMS

Introduction. The functioning efficiency of any biosystem (BS), regardless of its hierarchy level, depends on its adapt ability to changes in the environment or its state. Adaptive processes are implemented at the molecular, subcellular, cellular, tissue, organ, systemic and organismal levels. This adaptation can occur with the help of various mechanisms, has different dynamic characteristics, be accompanied by different energy costs and be more or less efficient. In this regard, it is expedient to identify as accurately as possible the type of adaptive process and assess its stressfulness for BS. In our opinion, such a classification can be carried out by formal markers of adaptive processes (by graphs) using mathematical methods of their description.

The purpose of the paper is to develop a formalized classification of adaptive processes types based on mathematical modeling of their dynamics.

Methods: structural and functional modeling using the approaches and mathematical apparatus of the theory of automatic control, using differential equations, probabilistic approaches and graphical analysis.

Results. The structurally functional model of the adaptive process is presented as three connected subsystems. The output process of the first subsystem is described by an exponential function with a constraint, of the second — a logistic (S-shaped) function, of the third — their difference, i.e. unimodal curve.The operation of such a system is considered for different ratios of the parameters of the transfer functions of the subsystems (conversion factors and time constants). It is proposed to use the output function of this system as an identifier of various types of adaptive reactions: adaptation, compensation, reparative regeneration and a pathological process. Criteria for definition of such a distinction are proposed using integral and dynamic characteristics of mathematical models.

Conclusions. The proposed three-block diagram of the adaptive process makes it possible to perform its mathematical description in the simplest and most adequate form. Based on the paradigm of one-to-one correspondence of the structure and function of the adaptive process, it is possible to calculate the parameters of the subsystems involved in organizing the systemic response in response to external influences using the actually recorded graphs of thees adaptive processes: their conversion coefficients and time conctant. The systemic representation of the biosystem work gives us the probabilistically represent the participation process of the constituent subsystems when an external influence changes (evolutionary transformations). The developed criterion system allows, according to the graphs of the dynamics of the output function of a real biomedical research, to determine the type of adaptive process, that is, to correlate it with specific biological mechanisms and to assess the degree of its “pathology” for the biosystem.

Keywords: information technology, system approach, structural and functional modeling, approaches to the theory of automatic control, differential equations, probabilistic methods, graphic analysis.

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