Issue 1 (203), article 4


Cybernetics and Computer Engineering, 2021, 1(203)

ARALOVA N.I.1, DSc (Engineering), Senior Researcher,
Senior Researcher of Optimization of Controlled Processes Department,
ORCID: 0000-0002-7246-2736,

KLYUCHKO O.M.2, PhD (Biology), Associate Professor,
Associate Professor, Faculty of Air Navigation,
ORCID: 0000-0003-4982 7490

MASHKIN V.I.1, PhD (Engineering), Senior Researcher,
Senior Researcher of Optimization of Controlled Processes Department,
ORCID: 0000-0002-4479-6498,

MASHKINA I.V.3, PhD (Engineering), Associate Professor
Associate Professor, Faculty of Information Technology and Management
ORCID: 0000-0002-0667-5749,

1V.M. Glushkov Institute of Cybernetics of National Academy of Sciences of Ukraine.
40, Acad.Glushkov av., Kyiv, 03680, Ukraine
2Electronics and Telecommunications National Aviation University,
1, Lubomyr Huzar av., Kyiv, 03058, Ukraine
3Borys Grinchenko Kyiv University,
18/2, Bulvarno-Kudriavska str., Kyiv, 04053 Ukraine, 04053


Introduction. The areas around industrial objects, and now in regions of military actions are characterized by a high content of pollutants. Qualitative spectrum of these pollutants is extremely broad and contains both inorganic and organic elements and compounds. In particular, environmental pollution is caused by hydrocarbons with wide range of chemical structures, the study of which is very important due to their harmful and toxic influences on living organisms. The methods, currently used in medicine, give only a “thin slice” of current pathological state of organism, but they cannot predict the long-term consequences of such lesions. That is why it seems appropriate to use mathematical models that simulate the movement of organic compounds in the respiratory and circulatory systems and thus to predict possible pathologies in organs and tissues caused by hypoxic states that occur when these organs and tissues are affected.

Purpose of the paper is to create a mathematical model of functional respiratory system, which simulates the influence of external environment on the parameters of self-organization of human respiratory system in the dynamics of respiratory cycle; and thus to predict hypoxic conditions during tissue damage by hydrocarbons.

Results. The mathematical model for respiratory gases transport and mass transfer in human organism is represented as a system of differential equations, which is a controlled dynamic system, and the states of which are determined by oxygen and carbon dioxide stresses in each structural link of the respiratory system (alveoli, blood, and tissues) at each moment of time. The model is supplemented by the equations of transport of the substances in each structural link as well as by the mathematical model of organism oxygen regimes regulation. The model includes seven groups of tissues – brain, heart, liver and gastrointestinal tissues, kidneys, muscle tissue etc. The algorithm of the work and iterative procedure of research with application of suggested complex are given.

Conclusion. The proposed mathematical model for studying of the transport of organic substances in human organism which consists of differential equations of respiratory gases transport and mass transfer in it, and for the transport of organic compounds is theoretical only for today. However, in the presence of appropriate array of experimental data, it will be able to monitor the state of functional respiratory system after the pathogenic organic compounds inquiry, which may be useful in choosing of strategies and tactics for the treatment of particular lesion.

Keywords: functional respiratory system, regulation of organism oxygen regimes, harmful organic substances, hypoxic state, mathematical model of respiratory system, transport of gases by blood, self-regulation of respiratory system.

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1. Isayenko V.M., Lisichenko G.V., Dudar T.V., Franchuk G.M. et al. Monitoring and methods of measuring the parameters of the environment. Kyiv: NAU-druck. 2009. 312 p. (In Ukrainian)

2. Franchuk G.M., Zaporozhets O.A., Arkhipova G.I. Urban ecology and technoecology. Kyiv: NAU-druck. 2011. 496 p. (In Ukrainian)

3. Franchuk G.M. Isayenko V.M. Ecology, aviation and space. Kyiv. NAU-druck. 2005. 456 p. (In Ukrainian)

4. Klyuchko O.M., Biletsky A.Ya. Computer recognition of chemical substances based on their electrophysiological characteristics. Biotechnologia Acta, 2019 (12). N 5. P. 5-28.

5. Klyuchko O.M. Information and computer technologies in biology and medicine. Kyiv: NAU-druck. 2008. 252 p. (In Ukrainian)

6. Onopchuk Yu.N. Homeostasis of functional respiratory system as a result of intersystem and system-medium informational interaction. Bioecomedicine. Uniform information space /Ed. by V.I. Gritsenko. Kiev. 2001. P. 59-84 (In Russian)

7. Onopchuk Yu.N. Homeostasis of the functional circulatory system as a result of intersystem and system-medium informational interaction. Bioecomedicine. Uniform information space / Ed. by V.I. Gritsenko. Kiev. 2001. P. 85-104 (In Russian)

8. Aralova N.I. Mathematical models of functional respiratory system for solving the applied problems in occupational medicine and sports. Saarbrucken: LAP LAMBERT Academic Publishing GmbH&Co, KG. 2019. 368 p.

9. Lyashko N.I., Onopchuk G.Yu. Pharmacological correction of organism states. Mathematical model and its analysis. Computer mathematics. 2005. N 1. P. 127-134 (In Russian)

10. Aralova N.I. Information Technologies of Decision Making Support for Rehabilitation of Sportsmen Engaged in Combat Sports DOI: 10.1615/J Automat Inf Scien.v48.i6.70. pages 68-78

11. Maslenikova L.D., Ivanov S.V., Fabulyak F.G. et al. Physical chemistry of polymers. Kyiv: NAU-druck. 2009. 312 p. (In Ukrainian)

12. Polynkievich K.B., Onopchuk Yu.N. Conflict situations during the regulation of the main function of organism respiratory system and mathematical models of their resolution.Cybernetics.1986. No. 3. P. 100-104 (In Russian)

13. Aralova A.A., Aralova N.I., Klyuchko O.M., Mashkin V.I., Mashkina I.V. Information system for the examination of organism adaptation characteristics of flight crews’ personnel. Electronics and control systems. 2018. 2. P. 106-113. DOI:

14. Klyuchko O.M., Aralova N.I., Aralova A.A. Electronic automated work places for biological investigations Biotechnologia Acta. V. 12. N 2. P. 5-26

15. Onopchuk Yu.N., Aralova N.I., Beloshitsky P.V., Podlivaev B. A., Mastucash Yu. I. Forecasting of wrestler’ state in the combat on the base of mathematic model of functional respiratory system. Computer mathematics. 2005. N 2. P. 69-79 (In Russian)

16. Aralova N.I., Shakhlina L.Ya.-G., Futornyi S.M., Kalytka S.V. Information Technologies for Substantiation of the Optimal Course of Interval Hypoxic Training in Practice of Sports Training of Highly Qualified Sportswomen. Journal of Automation and Information Sciences, V. 52. Iss 1, pp. 41-55 DOI:

Received 04.11.2020