论文标题
减少肾脏肾脏钠交换模型
Reduction of a model for sodium exchanges in kidney nephron
论文作者
论文摘要
这项工作介绍了在肾脏肾单管结构中钠的运输的数学分析。肾单位由两个反电流小管建模。离子交换发生在小管与上皮之间的界面以及上皮和周围环境（间质）之间。从数学角度来看，该模型由5x5半线性双曲系统组成。在文献中，类似模型忽略了上皮层。在本文中，我们严格地表明，可以通过假设管腔和上皮之间的渗透率很大来获得此类模型。实际上，我们表明，当它们增长时，5x5系统的解决方案以某种方式将不存在上皮层的降低的3x3系统的解决方案收敛。该问题在具有初始数据和边界数据的有界的空间域上被否认。建立BV紧凑性引入初始层并仔细处理横向边界的存在。
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 5x5 semi-linear hyperbolic system. In the 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. Indeed we show that when these grow, solutions of the 5x5 system converge in a certain way to solutions of a reduced 3x3 system where no epithelial layer is present. The problem is dened on a bounded spacial domain with initial and boundary data. Establishing BV compactness forces to introduce initial layers and to handle carefully the presence of lateral boundaries.
