肾单位钠交换模型的简化
Reduction of a model for sodium exchanges in kidney nephron
摘要：
本工作涉及一个肾脏肾单位的管状结构中的钠的运输的数学分析。肾单位由两个逆流小管模拟。离子交换发生在小管和上皮之间以及上皮和周围环境（上皮）之间的界面处。从数学的角度来看，该模型由5x5半线性双曲系统组成。在文献中，类似的模型忽略了上皮层。在本文中，我们严格地表明，这样的模型可以通过假设管腔和上皮之间的渗透性是大的。事实上，我们表明，当这些增长，5x5系统的解决方案收敛在一定的方式，以减少3x3系统的解决方案，其中没有上皮层存在。该问题是在一个有界的空间区域上的初始和边界数据。建立BV紧凑性迫使引入初始层并小心处理横向边界的存在。
英文摘要：
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.
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