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

In: Trends in Biomathematics: Modeling, Optimization and Computational Problems

Author

Listed:
  • V. V. Kislukhin

    (Medisonic)

  • E. V. Kislukhina

    (Sklifosovsky Institute for Emergency Medicine)

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.

Suggested Citation

  • V. V. Kislukhin & E. V. Kislukhina, 2018. "Math Model of the Passage of a Diffusible Indicator Throughout Microcirculation Based on a Stochastic Description of Diffusion and Flow," Springer Books, in: Rubem P. Mondaini (ed.), Trends in Biomathematics: Modeling, Optimization and Computational Problems, pages 365-373, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-91092-5_25
    DOI: 10.1007/978-3-319-91092-5_25
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