A model for flow through discontinuities in the tight junction of the endothelial intercellular cleft
| Autor: | Wen Wang, Kim H. Parker, C.G. Phillips |
|---|---|
| Rok vydání: | 1994 |
| Předmět: |
Pharmacology
Intercellular cleft Laplace transform General Mathematics General Neuroscience Immunology Geometry Conformal map Classification of discontinuities Models Biological General Biochemistry Genetics and Molecular Biology Domain (mathematical analysis) Capillary Permeability Discontinuity (linguistics) Matrix (mathematics) Intercellular Junctions Computational Theory and Mathematics Flow (mathematics) Animals Endothelium Vascular General Agricultural and Biological Sciences Mathematics General Environmental Science |
| Zdroj: | Bulletin of Mathematical Biology. 56:723-741 |
| ISSN: | 0092-8240 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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