Reduction of a model for sodium exchanges in kidney nephron
| Autor: | Marta Marulli, Nicolas Vauchelet, Vuk Milisic |
|---|---|
| Přispěvatelé: | Mathématiques Appliquées Paris 5 (MAP5 - UMR 8145), Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Statistics and Probability
Reduction (recursion theory) 030232 urology & nephrology boundary layers 01 natural sciences Domain (mathematical analysis) Combinatorics Hyperbolic systems 03 medical and health sciences 0302 clinical medicine Mathematics - Analysis of PDEs Boundary data FOS: Mathematics [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] 0101 mathematics Physics Applied Mathematics General Engineering Order (ring theory) Computer Science Applications characteristics method relaxation limit 010101 applied mathematics Compact space ionic exchanges Bounded function Analysis of PDEs (math.AP) |
| Zdroj: | Networks and Heterogeneous Media Networks and Heterogeneous Media, AIMS-American Institute of Mathematical Sciences, 2020, ⟨10.3934/nhm.2021020⟩ |
| ISSN: | 1556-1801 |
| DOI: | 10.3934/nhm.2021020⟩ |
| Popis: | 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 5\begin{document}$ \times $\end{document}5 semi-linear hyperbolic system. In literature similar models neglect the epithelial layers. In this paper, we show rigorously that such models may be obtained by assuming that the permeabilities between lumen and epithelium are large. We show that when these permeabilities grow, solutions of the 5\begin{document}$ \times $\end{document}5 system converge to those of a reduced 3\begin{document}$ \times $\end{document}3 system without epithelial layers. The problem is defined on a bounded spacial domain with initial and boundary data. In order to show convergence, we use \begin{document}$ {{{\rm{BV}}}} $\end{document} compactness, which leads to introduce initial layers and to handle carefully the presence of lateral boundaries. We then discretize both 5\begin{document}$ \times $\end{document}5 and 3\begin{document}$ \times $\end{document}3 systems, and show numerically the same asymptotic result, for a fixed meshsize. |
| Databáze: | OpenAIRE |
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