A model for flow through discontinuities in the tight junction of the endothelial intercellular cleft

A mathematical model for steady flow through a discontinuity in the tight junction of an endothelial intercellular cleft is presented. Subject to plausible assumptions the problem of calculating the flow in the cleft, in either the presence or the absence of a fibre matrix, reduces to the solution o...

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Bibliographic Details
Published inBulletin of mathematical biology Vol. 56; no. 4; pp. 723 - 741
Main Authors Phillips, C. G., Parker, K. H., Wang, W.
Format Journal Article
LanguageEnglish
Published Heidelberg Springer 01.07.1994
Subjects
Animals
Biological and medical sciences
Capillary Permeability
Endothelium, Vascular - physiology
Fundamental and applied biological sciences. Psychology
General aspects
Intercellular Junctions - physiology
Mathematics
Mathematics in biology. Statistical analysis. Models. Metrology. Data processing in biology (general aspects)
Models, Biological
Flux
Discontinuity
Tight junction
Mathematical model
Modeling
Endothelium
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Summary:A mathematical model for steady flow through a discontinuity in the tight junction of an endothelial intercellular cleft is presented. Subject to plausible assumptions the problem of calculating the flow in the cleft, in either the presence or the absence of a fibre matrix, reduces to the solution of Laplace's equation in a two-dimensional domain. For an idealized geometry representing a discontinuity between two semi-infinite tight junction regions, a general analytic solution is found by means of conformal mappings. The model geometry, unlike those assumed in previous studies, allows the tight junction regions to be out of alignment with each other, and even to overlap, modelling flow through a tortuous, rather than a direct, pathway. Useful asymptotic approximations for the flow rate are derived when the discontinuity is either very small or very large. For small discontinuities, the predicted flow rate is much greater than a naïve estimate based on uniform parallel flow through the discontinuity. For the special case where the tight junction regions are aligned with each other, comparison of our results with those of an approximate treatment due to Tsay et al. [Chem. Engng Commun. 82, 67-102 (1989)] shows generally very close agreement.
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ISSN:0092-8240
1522-9602
DOI:10.1007/BF02460718