2020/01/21 by Marta Marulli, Marulli, Marta, Aurélie Edwards +5
Economics, Econometrics and Finance · Mathematics · Medicine · #Analysis of PDEs (math.AP) #Chronic Kidney Disease and Diabetes #FOS: Mathematics #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.AP
paper · pdf · doi:10.48550/arxiv.2001.07400
arxiv created 2020/01/21 · openalex publication_date 2020/01/21 · arxiv updated 2020/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.