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


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.


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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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