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

V. V. Kislukhin and E. V. Kislukhina
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V. V. Kislukhin: Medisonic
E. V. Kislukhina: Sklifosovsky Institute for Emergency Medicine

A chapter in Trends in Biomathematics: Modeling, Optimization and Computational Problems, 2018, pp 365-373 from Springer

Abstract: 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.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-91092-5_25

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DOI: 10.1007/978-3-319-91092-5_25

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