  This work deals with a mathematical analysis of sodium's transport in a
tubular architecture of a kidney nephron. The nephron is modelled by two
counter-current tubules. Ionic exchange occurs at the interface between the
tubules and the epithelium and between the epithelium and the surrounding
environment (interstitium). From a mathematical point of view, this model
consists of a 5x5 semi-linear hyperbolic system. In the literature similar
models neglect the epithelial layers. In this paper, we show rigorously that
such models may be obtained by assuming that the permeabilities between lumen
and epithelium are large. Indeed we show that when these grow, solutions of the
5x5 system converge in a certain way to solutions of a reduced 3x3 system where
no epithelial layer is present. The problem is dened on a bounded spacial
domain with initial and boundary data. Establishing BV compactness forces to
introduce initial layers and to handle carefully the presence of lateral
boundaries.
