A MODEL FOR FLOW-THROUGH DISCONTINUITIES IN THE TIGHT JUNCTION OF THEENDOTHELIAL INTERCELLULAR CLEFT

A mathematical model for steady flow through a discontinuity in the ti ght junction of an endothelial intercellular cleft is presented. Subje ct to plausible assumptions the problem of calculating the flow in the cleft, in either the presence or the absence of a fibre matrix, reduc es to the solution of Laplace's equation in a two-dimensional domain. For an idealized geometry representing a discontinuity between two sem i-infinite tight junction regions, a general analytic solution is foun d by means of conformal mappings. The model geometry, unlike those ass umed in previous studies, allows the tight junction regions to be out of alignment with each other, and even to overlap, modelling flow thro ugh a tortuous, rather than a direct, pathway. Useful asymptotic appro ximations for the flow rate are derived when the discontinuity is eith er very small or very large. For small discontinuities, the predicted flow rate is much greater than a naive estimate based on uniform paral lel flow through the discontinuity. For the special case where the tig ht junction regions are aligned with each other, comparison of our res ults with those of an approximate treatment due to Tsay et al. [Chem. Engng Commun. 82, 67-102 (1989)] shows generally very close agreement.