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Mathematical Description of Systemic and Micro Circulations

In: Trends in Biomathematics: Modeling Cells, Flows, Epidemics, and the Environment

Author

Listed:
  • V. V. Kislukhin

    (Medisonic)

  • E. V. Kislukhina

    (Sklifosovsky Institute for Emergency Medicine)

Abstract

Aim of the presentation is to reveal (a) that two complications: post dialysis urea rebound and the bends are related to a phenomenon of a separation of blood volume (BV) into active (ACV) and slow (SCV) circulating volumes; (b) that Laser-Doppler flowmeter (LDF) could be a means to predict named complications. A separation of BV takes place if the time for indicator to mix within cardiovascular system (CVS) requires 5 min or more. Method: CVS is an oriented closed graph with three types of edges: (a) heart chambers, (b) transport vessels, arteries and venues, (c) microvessels, with random blood flow. Result: The delay in mixing of indicator (thus rebound or bends) could happen if within some tissues appear “swamp” type blood areas. The use of LDF gives quantity estimation of such state of microcirculation.

Suggested Citation

  • V. V. Kislukhin & E. V. Kislukhina, 2020. "Mathematical Description of Systemic and Micro Circulations," Springer Books, in: Rubem P. Mondaini (ed.), Trends in Biomathematics: Modeling Cells, Flows, Epidemics, and the Environment, pages 161-168, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-46306-9_12
    DOI: 10.1007/978-3-030-46306-9_12
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