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Open Access Research

The passage of a diffusible indicator through a microvascular system

Victor V Kislukhin

Author Affiliations

Transonic System, Inc, 34 Dutch Mill Road, Ithaca, N.Y, 14850, USA

Theoretical Biology and Medical Modelling 2013, 10:10  doi:10.1186/1742-4682-10-10

Published: 13 February 2013

Abstract

The aim. (1) To develop a mathematical model of the passage of a diffusible indicator through microcirculation based on a stochastic description of diffusion and flow; (2) To use Goresky transform of the dilution curves of the diffusible indicators for the estimation of the permeability of a tissue-capillary barrier.

The method. We assume that there are two causes for flow to be stochastic: (a) All microvessels are divided between open and closed microvessels. There exists random exchange between the two groups. (b) The flow through open microvessels is also random. We assume that each diffusing tracer has a probability to leave the intravascular space, and has a probability to return. We also assume that all considered processes are stationary (stability of microcirculation).

Conclusion. (a) The distribution of the time to pass microcirculation by diffusing indicator is given by a compound Poisson distribution; (b) The permeability of tissue-capillary barrier can be obtained from the means, delay, and dispersions of the dilutions of intravascular and diffusing traces.

Keywords:
Mathematical model; Microcirculation; Permeability; Poisson distribution