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Math Model of the Passage of a Diffusible Indicator Throughout Microcirculation Based on a Stochastic Description of Diffusion and Flow

  • V. V. Kislukhin
  • E. V. Kislukhina
Chapter

Abstract

Aim: (1) To develop a math model of the passage of any indicator through microcirculation; (2) To use Goresky transform of the dilution curves for the estimation of the permeability of a capillary wall. Method: The passage of an indicator throughout any tissue is formed by next events: (1) be in intravascular space, (2) be in extravascular space, (3) a microvessel is closed, (4) a microvessel is open, and also (5) a particle, being in open microvessel, experiences a variation of velocity. We assume that named events are stochastic. Result: (a) Distribution of the time to pass microcirculation by any indicator is given by a compound Poisson distribution; (b) The permeability of tissue-capillary barrier can be obtained by Goresky transform.

References

  1. 1.
    C.A. Goresky, A linear method for determining liver sinusoidal and extravascular volumes. Am. J. Physiol. 204, 626–640 (1963)Google Scholar
  2. 2.
    K. Zierler, Indicator dilution methods for measuring blood flow, volume, and other properties of biological systems: a brief history and memoir. Ann. Biomed. Eng. 28(8), 836–848 (2000)CrossRefGoogle Scholar
  3. 3.
    W. Feller, An Introduction to Probability Theory and Its Applications. Volume II (Wiley, New York, 1966)Google Scholar
  4. 4.
    Y.C. Fung, Stochastic flow in capillary blood vessels. Microvasc. Res. 5(1), 34–48 (1973)CrossRefGoogle Scholar
  5. 5.
    W.S. Kendal, A stochastic model for the self-similar heterogeneity of regional organ blood flow. Proc. Natl. Acad. Sci. U. S. A. 98(3), 837–841 (2001)MathSciNetCrossRefGoogle Scholar
  6. 6.
    J.H. Matis, H.D. Tolley, On the stochastic modeling of tracer kinetics. Fed. Proc. 39(1), 104–109 (1980)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • V. V. Kislukhin
    • 1
  • E. V. Kislukhina
    • 2
  1. 1.MedisonicMoscowRussia
  2. 2.Sklifosovsky Institute for Emergency MedicineMoscowRussia

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