论文标题
关于上皮在肾小管中钠交换模型中的作用
On the role of the epithelium in a model of sodium exchange in renal tubules
论文作者
论文摘要
在这项研究中，我们提出了一个数学模型，该模型描述了逆流管结构中流体循环中钠的运输，该结构构成了肾脏肾脏中Henle循环的简化模型。该模型明确考虑了管状管腔和周围间质之间的界面处的上皮层。在特定的参数范围内，我们表明，明确考虑上皮细胞的顶端和基底外侧膜的转运，而不是假设单个屏障会影响轴向浓度梯度，这是尿浓度能力的必要决定因素。我们提供与固定系统相关的解决方案，并执行数值模拟以了解系统的生理行为。我们证明，随着时间的变化，我们的动态模型以指数速率收敛到固定系统。为了严格证明这种全球渐近稳定性结果，我们研究了辅助线性算子及其双重的特征问题。
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.
