Analysis of capillary-tissue diffusion in multicapillary systems

Research output: Contribution to journalArticle

Abstract

The diffusive transport of a substance between a parallel capillary network and the surrounding tissue is investigated. The consumption/production rate of the substance in the tissue is assumed to be constant (zero-order chemical kinetics). The solution of the diffusion problem which describes the distribution of the substance in the tissue and along the capillary network is found in an analytical form. A rather general assumption regarding the symmetry of capillary network makes it possible to formulate a Neumann-type boundary-value problem in a rectangular domain. The solution of the diffusion problem in the rectangle allows the capillary-tissue fluxes to be expressed linearly in terms of the concentrations in the capillaries, and hence leads to ordinary differential equations for those concentrations. Several examples are considered with different network geometry and concurrent or countercurrent flow conditions. The solution makes it possible to investigate the effect of capillary interaction on mass transfer in various microcirculatory units.

Original languageEnglish (US)
Pages (from-to)187-211
Number of pages25
JournalMathematical Biosciences
Volume39
Issue number3-4
DOIs
StatePublished - 1978
Externally publishedYes

Fingerprint

Tissue
Diffusion Problem
countercurrent
mass transfer
Ordinary differential equations
Reaction kinetics
Boundary value problems
symmetry
Chemical Kinetics
Mass transfer
Mass Transfer
Fluxes
kinetics
geometry
Rectangle
Geometry
analysis
tissue
tissues
Concurrent

ASJC Scopus subject areas

  • Agricultural and Biological Sciences(all)
  • Ecology, Evolution, Behavior and Systematics

Cite this

Analysis of capillary-tissue diffusion in multicapillary systems. / Popel, Aleksander S.

In: Mathematical Biosciences, Vol. 39, No. 3-4, 1978, p. 187-211.

Research output: Contribution to journalArticle

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