MATHEMATICAL MODELS OF HUMAN RESPIRATORY AND BLOOD CIRCULATORY SYSTEMS N. I. Aralova, O. M. Klyuchko , V. I. Mashkin, I. V. Mashkina, P. A. Radziejowski , M. P. Radziejowski

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ISSN 2410-7751 (Print)
ISSN 2410-776X (Online)

Biotechnologia Acta Т. 15, No. 1, 2022
P. 23-42. Bibliography 125, Engl.
UDC: 519.8.612.007
https://doi.org/10.15407/biotech15.01.023

MATHEMATICAL MODELS OF HUMAN RESPIRATORY AND BLOOD CIRCULATORY SYSTEMS

N. I. Aralova ¹, O. M. Klyuchko ², V. I. Mashkin¹, I. V. Mashkina ³, P. A. Radziejowski ⁴, M. P. Radziejowski ⁵

¹V. M. Glushkov Institute of Cybernetics of the National Academy of Sciences of Ukraine, Kyiv
²National Aviation University Kyiv, Ukraine
³Boris Grinhenko Kiyv University, Ukraine
⁴Kazimiera Milanowska College of Education and Therapy , Poznan, Poland
⁵Czestochowa University of Technology, Czestochowa, Poland

Aim. To analyze modern approaches to mathematical modeling of human respiratory and blood circulatory systems.

Methods. Comprehensive review of scientific literature sources extracted from domestic and international resources databases.

Results. Historical information and modern data concerning mathematical modeling of human functional respiratory and blood circulatory systems were summarized and analyzed in present ¬review; current trends in approaches to the construction of these models were revealed.

Conclusions. Currently, two main approaches to the mathematical modeling of respiratory and blood circulatory systems exist. One of them is the construction of models of the mechanics of respiration and blood circulation. They are based on the models of mechanics of solid deformable body, thermomechanics, hydromechanics, and continuum mechanics. This approach uses complex mathematical apparatus, including Navier-Stokes equation, which makes it possible to obtain a number of theoretical results, but it is hardly usable for real problems solutions at present time. The second approach is based on the model of F. Grodins, who represented the process of breathing as a controlled dynamic system, described by ordinary differential equations, in which the process control is carried out according to the feedback principle. There is a significant number of modifications of this model, which made it possible to simulate various disturbing influences, such as physical activity, hypoxia and hyperemia, and to predict parameters characterizing functional respiratory system under these disturbing influences.

Key words: mathematical model of respiratory system, mathematical model of blood circulatory system, hypoxic state, theoretical analysis.

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