ADVANCE Fellows Award: Mathematical Modeling of Renal Physiology

尿浓缩机制（UCM），使哺乳动物产生高渗尿的能力，位于肾髓质。在外髓，UCM是由来自粗的上行肢体的主动NaCl运输驱动的，再加上肾单位和血管的逆流配置;在内髓，UCM的基本原理仍有待确定。为了更好地理解哺乳动物UCM，PI寻求开发一个高度详细的基于区域的大鼠肾皮质和髓质数学模型的动态公式。"基于区域“的建模方法代表了肾单位和血管的放射状组织，如解剖研究所揭示的，并捕获了髓质结构之间的优先相互作用。该模型将纳入和评估以前未包括在模型中的实验结果，包括最近的免疫标记实验的影响。为了研究UCM和肾小管肾小球反馈（TGF）机制之间的相互作用，PI将开发一个近端小管的动态上皮转运模型，并将该模型纳入TGF框架。由此产生的模型可能提供对疾病发病机制的综合见解，其中膳食盐摄入对肾小球滤过率有矛盾的影响，并且其中细胞外液量或钠转运的调节紊乱。此外，使用上述模型，PI将生成过滤溶质分布的动画，并开发用户-这个项目的总体目标是使用分析和计算数学来更好地理解传统生理学中一个长期存在的谜团：哺乳动物产生浓缩尿液的机制。事实上，尽管生理学教科书中经常给出被动机制作为哺乳动物产生浓缩尿液的解释，但在计算机模拟中它并没有产生令人满意的浓度梯度。通过开发一系列数学模型，PI寻求评估某些建模假设的有效性。此外，模型可以提供洞察力的问题，如：什么是意想不到的实验结果，挑战公认的概念的集中机制的影响？在健康和高血压大鼠中，肾小管肾小球反馈系统（调节液体进入肾单位的速率，肾单位是肾脏的功能单位）在调节钠排泄中的作用是什么？特别是，为什么在糖尿病患者和实验性糖尿病大鼠中，肾血流量与膳食盐呈反比，而预期会产生相反的效果？该项目的另一个目标是传播建模方法和结果，部分是通过计算机可视化技术的应用，拟开发的建模软件包应鼓励实验人员使用建模技术，以更好地了解目前通过计算机辅助显微解剖和转基因动物技术出现的许多新实验数据的重要性。

The urine concentrating mechanism (UCM), which gives mammals the capability to produce hypertonic urine, is localized in the renal medulla. In the outer medulla, the UCM is driven by active NaCl transport from thick ascending limbs, coupled with a countercurrent flow configuration of nephrons and vessels; in the inner medulla, the underlyingprinciples of the UCM remain to be determined. To better understand the mammalian UCM, the PI seeks to develop a dynamic formulation of a highly-detailed region-based mathematical model of the renal cortex and medulla of the rat kidney. The ``region-based'' modeling approach represents radial organization of nephrons and vessels, as revealed in anatomic studies, and captures the preferential interactions among medullary structures. The model will incorporate and evaluate experimental findings not previously included in models, including the implications of recent immunolabeling experiments. To investigate the interactions between UCM and tubuloglomerular feedback (TGF) mechanism, the PI will develop a dynamic epithelial transport model of the proximal tubule, and incorporate that model into a TGF framework.The resulting model may provide integrated insight into pathogenesis of diseases in which dietary salt intake has a paradoxical effect on glomerular filtration rate, and in which extracellular fluid volume or the regulation of sodium transport are deranged.In addition, using the above models, the PI will generate animations of distributions of filtered solutes and develop user-friendly modeling packages for use by experimentalists.The overall objective of this project is to use analysis and computational mathematics to gain a better understanding of a long-standing mystery in traditional physiology: the mechanism by which mammals produce concentrated urine.Indeed, although the passive mechanism is frequently given in physiologytextbooks as an explanation for the production of a concentrated urinein mammals, it does not produce a satisfactory concentration gradient in computer simulations. Through the development of a series of mathematical models, the PI seeksto assess the validity of certain modeling assumptions. Moreover, the models may provide insights into questions such as: What are the impacts of unexpected experimental findings that challenge accepted notions of the concentrating mechanism?What is the role of the tubuloglomerular feedback system (which regulates the rateof fluid entry into the nephrons, which are functional units of the kidney)in the regulation of sodium excretion in both healthy and hypertensive rats?In particular, why does renal blood flow vary inversely with dietary salt in both diabetic patients and rats with experimental diabetes, when the opposite effect is expected?Another objective of this project is to disseminate modeling methodologies and results, in part through the applications of computer visualization techniques.The proposed modeling packages to be developed should encourage experimentalists to use modeling techniques to gain a better understanding of the significance of much new experimental data now emerging through techniques involving computer-assisted micro-anatomy and transgenic animals.