Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the role of the epithelium in a model of sodium exchange in renal
  tubules   In this study we present a mathematical model describing the transport of
sodium in a fluid circulating in a counter-current tubular architecture, which
constitutes a simplified model of Henle's loop in a kidney nephron. The model
explicitly takes into account the epithelial layer at the interface between the
tubular lumen and the surrounding interstitium. In a specific range of
parameters, we show that explicitly accounting for transport across the apical
and basolateral membranes of epithelial cells, instead of assuming a single
barrier, affects the axial concentration gradient , an essential determinant of
the urinary concentrating capacity. We present the solution related to the
stationary system, and we perform numerical simulations to understand the
physiological behaviour of the system. We prove that when time grows large, our
dynamic model converges towards the stationary system at an exponential rate.
In order to prove rigorously this global asymptotic stability result, we study
eigen-problems of an auxiliary linear operator and its dual.

24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn