上皮细胞在肾小管钠交换模型中的作用
On the role of the epithelium in a model of sodium exchange in renal tubules
摘要：
在这项研究中，我们提出了一个数学模型，描述了在一个逆流的管状结构，这构成了一个简化的模型，在肾脏肾单位的亨利氏袢循环的流体中的钠的运输。该模型明确考虑到在管腔和周围的上皮细胞之间的界面上的上皮层。在一个特定的参数范围内，我们表明，明确占跨上皮细胞的顶膜和基底膜的运输，而不是假设一个单一的障碍，影响轴向浓度梯度，尿浓缩能力的一个重要决定因素。我们提出的解决方案相关的固定系统，我们进行数值模拟，以了解系统的生理行为。我们证明，当时间变大，我们的动态模型收敛到平稳系统的指数速度。为了严格证明这个全局渐近稳定性结果，我们研究了辅助线性算子及其对偶算子的特征值问题。
英文摘要：
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.
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