Skip to main content
SpringerLink
Log in

Mathematical modeling of blood circulation system and its practical application

  • Control in Biological Systems and Medicine
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

The human blood circulation system is represented by a nonlinear oscillation system for computer-aided digital modeling in real time scale. A parametric identification problem is formulated and its numerical solution algorithm is designed. A computer-aided blood circulation modeling and identification system is designed. The new approaches to construct real control systems for artificial and auxiliary blood circulation elements are based on neurocomputer technologies.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Shumakov, V.I., Novosel’tsev, V.N., Shtengol’d, E.Sh., and Sakharov, M.P., Modelirovanie fiziologicheskikh sistem organizma (Modeling of Physiological Systems of an Organism), Moscow: Meditsina, 1971.

    Google Scholar 

  2. Shumakov, V.I., Zimin, N.K., Itkin, G.P., and Osadchii, L.I., Iskus stvennoe serdtse (Artificial Heart), Leningrad: Nauka, 1988.

    Google Scholar 

  3. Shumakov, V.I. and Tolpekin, V.E., Vspomogatel’noe krovoobrashchenie (Auxiliary Blood Circulation), Moscow: Meditsina, 1980.

    Google Scholar 

  4. Itkin, G.P., Artificial Heart: Control Principles, in Akhytin, B.M., Nefedov, V.M., and Sakharov, M.P., et al., Inzhenernaya fiziologiya i modelirovanie sistem organizma (Engineering Physiology and Modeling of Systems of an Organism), Novosibirsk: Nauka, 1987.

    Google Scholar 

  5. Itkin, G.P., Design and Investigation of Control Systems for Artificial Hearts by Mathematical Modeling, Cand. Sci. Dissertation, Moscow, 1974.

  6. Gus’kov, I.A. and Zatyuryukin, A.B., Iskusstvennoe serdtse kak faktor podderzhaniya gomeostaza organizma: gomeostaz na raznykh urovnyakh organizatsii biosistem (Artificial Heart for Maintaining the Homeostasis of an Organism: Homeostasis at Different levels of Organization of Biosystems), Novosibirsk: Nauka, 1991.

    Google Scholar 

  7. Novosel’tsev, V.N., Teoriya upravleniya i biosistemy (Control Theory and Biosystems), Moscow: Nauka, 1978.

    Google Scholar 

  8. Shumakov, V.N. and Itkin, G.P., Control of Heart Assist Devices, in Control Aspect of Biomedical Engineering, London: Pergamon, 1987, pp. 91–121.

    Google Scholar 

  9. Solodyannikov, Yu.V., Elementy matematicheskogo modelirovaniya i identifikatsii sistemy krovoobrashcheniya (Elements of Mathematical Modeling and Identification of Blood Circulation System), Samara: Samar. Univ., 1994.

    Google Scholar 

  10. Guyton, A.C., Coleman, T.G., Cowley, A.W., Jr., et al., A Systems Analysis Approach to Understanding Long-Range Arterial Blood Pressure Control and Hypertension, Circulation Res., 1974, vol. 35, pp. 237–255.

    Google Scholar 

  11. Neimark, Yu.I., Metod tochechnykh otobrazhenii v teorii nelineinykh kolebanii (The Point Mapping Method in Nonlinear Oscillation Theory), Moscow: Nauka, 1972.

    Google Scholar 

  12. Teoreticheskoe issledovanie fiziologicheskikh sistem. Matematicheskoe modelirovanie (Theoretical Investigation of Physiological Systems: Mathematical Modeling), Amosov, N.M., Ed., Kiev: Naukova Dumka, 1977.

    Google Scholar 

  13. Galushkin, A.I., Teoriya neironnykh setei. Kh. 1 (Neural Network Theory, vol. 1), Moscow: IPRZhR, 2000.

    Google Scholar 

  14. Guyton, A., Cardiac Output and Its Regulation, Philadelphia: Saunders, 1963. Translated under the title Minutnyi ob”em serdtsa i ego regulyatsiya, Moscow: Meditsina, 1969.

    Google Scholar 

  15. Möller, D., Popović, D., and Thiele, G., Modelling, Simulation and Parameter-Estimation of the Human Cardiovascular System, Braunsweig: Vieweg, 1983.

    Google Scholar 

  16. Sadovnichii, V.A., Aleksandrov, V.V., Aleksandrova, T.B., et al., Mathematical Modeling of Physiological Systems and Dynamic Adaptation of Sensor Zero-Gravity Conflict, Fundament. Prikl. Mat., 1997, vol. 3, no. 1, pp. 129–147.

    Google Scholar 

  17. Novosel’tsev, V.N., Sakharov, M.P., Dartau, L.A., and Klimov, A.I., Modeling of Baroreceptor Relations in an Organism and Their Normalization in Artificial Blood Circulation, Vest. Akad. Med. Nauk, 1973, no. 3, pp. 53–56.

  18. Rastrigin, L.A., Adaptatsiya slozhnykh sistem (Adaptation of Complicated Systems), Riga: Zinatne, 1981.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Povolzhskaya State Academy of Telecommunication and Information, Samara, Russia

    A. P. Proshin & Yu. V. Solodyannikov

Authors
  1. A. P. Proshin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yu. V. Solodyannikov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text © A.P. Proshin, Yu.V. Solodyannikov, 2006, published in Avtomatika i Telemekhanika, 2006, No. 2, pp. 174–188.

This work was supported by “Samara-Dialog” Inc.

This paper was recommended for publication by V.N. Novosel’tsev, a member of the Editorial Board

Rights and permissions

Reprints and permissions

About this article

Cite this article

Proshin, A.P., Solodyannikov, Y.V. Mathematical modeling of blood circulation system and its practical application. Autom Remote Control 67, 329–341 (2006). https://doi.org/10.1134/S000511790602010X

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S000511790602010X

PACS number

Search

Navigation