### 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 language | English (US) |
---|---|

Pages (from-to) | 187-211 |

Number of pages | 25 |

Journal | Mathematical Biosciences |

Volume | 39 |

Issue number | 3-4 |

DOIs | |

State | Published - 1978 |

Externally published | Yes |

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### 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.

Research output: Contribution to journal › Article

*Mathematical Biosciences*, vol. 39, no. 3-4, pp. 187-211. https://doi.org/10.1016/0025-5564(78)90053-6

}

TY - JOUR

T1 - Analysis of capillary-tissue diffusion in multicapillary systems

AU - Popel, Aleksander S

PY - 1978

Y1 - 1978

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0017978787&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0017978787&partnerID=8YFLogxK

U2 - 10.1016/0025-5564(78)90053-6

DO - 10.1016/0025-5564(78)90053-6

M3 - Article

AN - SCOPUS:0017978787

VL - 39

SP - 187

EP - 211

JO - Mathematical Biosciences

JF - Mathematical Biosciences

SN - 0025-5564

IS - 3-4

ER -