Issue 3 (193), article 4


Kibern. vyčisl. teh., 2018, Issue 3 (193), pp.

Shakhlina L.Ya.-G.1, DSc. (Medicine), Professor,
Professor of Sport Medicine cafedra

Aralova N.I.2, PhD. (Engineering),Senior Researcher,
Senior Researcher of Dept. of Optimization of Controlled Processes

1 National University of Physical Education and Sport of Ukraine
Fiscultury Street, 1, Kiev, 03150, Ukraine

2 Institute of Cybernetics of National Academy of Science of Ukraine, Acad.Glushkov av., 40, Kiev, 03187, Ukraine


Introduction. In the modern sports of higher achievements, the issues of training and competitive activity of athletes using the hypoxic factor in natural-mountain conditions or with artificial hypoxic training with the use of pressure chambers or hypoxicators continue to attract great interest among specialists in the field of physiology, medicine, sports pedagogy. The influence of reproductive hormones on the functional breathing system responsible for the aerobic capacity of the female body remains insufficiently studied. There are no scientifically substantiated programs for training athletes, mainly developing the quality of endurance, in conditions of hypoxic hypoxia, taking into account the phases of the menstrual cycle.

The purpose of the article is to determine the reaction of the functional breathing system and to reveal the degree of tissue hypoxia in athletes when inhaled hypoxic gas mixture with 11% oxygen in different phases of the menstrual cycle.

Results. On the mathematical model of the functional breathing system, based on physiological examination data, an imitation of a hypoxic mixture with athletes was performed with athletes of 11% oxygen in different phases of the menstrual cycle. The partial pressures and voltages of oxygen in alveolar air, arterial and mixed venous blood, heart, brain and skeletal muscle tissues were calculated. Numerical experiments were also performed with the replacement of the real values of the minute volume of respiration and the minute volume of blood in the corresponding phases of MC for adaptation processes in other phases of the cycle.

Conclusions. The results of the prediction on the mathematical model of the respiratory system of the athlete’s reactions to the inhalation of hypoxic mixtures testify to the specificity of functional self-regulation and, consequently, the adaptive capabilities to the hypoxia of the female body during cyclic changes in the hormonal status in different phases of the menstrual cycle. The results of preliminary studies show that under hypoxic conditions, as a result of inhalation of a gas mixture with 11% oxygen without a compenetration increase in pulmonary ventilation and systemic circulation, the oxygen tension in the body tissues may be below the critical level and with different degrees of expression in different phases of the MC, which is confirmed by the presented results of calculation on a mathematical model of oxygen tension in the studied tissues.

The obtained results testify to the need for further study of the individual reactions of the organism of athletes in conditions of hypoxia for the scientific substantiation of sports training for women taking into account the biological characteristics of their organism.

Keywords: mathematical model of the functional breathing system, training process of athletes, interval hypoxic training, phases of the menstrual cycle, functional self-organization of the organism

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Received 04.05.2018

Issue 2 (188), article 3


Kibern. vyčisl. teh., 2017, Issue 2 (188), pp.

Aralova N.I., senior researcher of department of optimization of controlled processes
Institute of cybernetics of National Academy of Science of Ukraine,
Acad. Glushkov ave., 40, Kiev, 03680 GSP, Ukraine


Introduction. Under conditions of the physical exertion and human presence on the altitude, the oxygen deficiency in tissues occurs. For a theoretical study of the role of various mechanisms in the regulation of the respiratory system, the use of the mathematical model for the transport of respiratory gases in the body was proposed.

Purpose. Researches of the role of hypoxia, hypercapnia and hypometabolism in external and internal disturbances, based on the mathematical model of the respiratory system.

Results. On the mathematical model of respiratory gas transport in the dynamics of the respiratory cycle, as control parameters, pulmonary ventilation, minute blood volume and local blood flow, as well as self-regulation mechanisms — respiratory muscles, cardiac muscle and smooth muscle vessels — were used. It resolved the conflict situation that arises between the managers and the executive tissues in the fight for oxygen. An analysis of the results of numerical experiments in simulating hypoxia and hypoxic hypoxia and their comparison with experimental data was made.

Conclusion. The proposed approach can be useful in assessing the role of hypoxia, hypercapnia and hypometabolism in the disturbances of the internal and external environment in the process of human vital activity under extreme conditions and leads to the formulation of new tasks in the physiology of sports, work and leisure.

Keywords: Mathematical model of respiratory gas transport, load hypoxia, hypoxic hypoxia, regulation of the respiratory system, disturbing effects, oxygen deficiency.

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Recieved 29.03.2017

Issue 182, article 5


Kibern. vyčisl. teh., 2015, Issue 182, pp.

Aralova N.I.

V.M. Glushkov Institute of Cybernetics of the National Academy of Sciences
of Ukraine (Kiev)


Introduction. In addition to experimental studies in recent years the methods of mathematical modeling of individual functional systems and the whole organism in certain situations are widely used, the results of which complement the system of experimental data and allow to make a more complete assessment of the functional state of the organism.
Purpose. To explore on a mathematical model of the respiratory system the functional mechanisms of adaptation of the respiratory system to the conditions of mountain meteorological factors for persons performing heavy exercise in a hypobaric hypoxia.
Results. The model, that describes transport and mass exchange of respiratory gases in the respiratory tract, the alveolar space, blood and tissues with use of ordinary nonlinear differential equations, for the mathematical analysis of the adaptive capacity of the organism hypoxia of various etiologies is used. The regulation is based on a compromise resolution of conflicts arising between the tissues and organs in the struggle for oxygen in a deficit. On the basis of this model, the models of short time and medium adaptation persons performing heavy physical activity in a midlands are created. Results of simulation experiment are presented.
Conclusion. The article presents a mathematical model of short-term and medium term adaptation FRS for rescuers and the results of the numerical analysis of this model. On this basis, the practical recommendations for the selection of the persons, that are exposed to the combined effects of hypobaric hypoxia and the hypermetabolic hypoxia, are given.
Keywords: short-term adaptation, medium term adaptation, respiration system, hypobaric hypoxia, hypermetabolic hypoxia, reliability, mathematical model of respiratory system.

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  1. Onopchuk Yu.N. Homeostasis function of the respiratory system as a result of in-system and system-environment interaction // Bioekomedicine. Unified Information Space — Kiev — 2001. — P.59–81(in Russian)
  2. Onopchuk Y.N., Beloshitsky P.V. Aralova N.I. On the question of reliability of functional systems // Cybernetics and computing tehnics. 1999. — Vol. 122. — P. 72–89 (in Russian)
  3. Polinkevich K.B., Onopchuk Y.N. Conflicts in the regulation of the main function of the respiratory system of the body, and mathematical models of their solution // Cybernetics. — 1986. — № 3. — P. 100–104.
  4. Bіloshitsky P.V. Klyuchko O.M., Onopchuk Y.N. Research results of the problems of adaptation by Ukrainian scientists on Elbrus // Vіsn. NAU. — 2008. — № 1. — P. 102–108.
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Received 07.09.2015