ADVANCE Fellows Award: Mathematical Modeling of Renal Physiology

尿液浓缩机制(UCM)使哺乳动物有能力产生高渗尿，定位于肾髓质。在外髓，UCM是由粗大的升支的主动氯化钠运输驱动的，再加上肾单位和血管的逆流流动结构；在内髓，UCM的基本原理仍有待确定。为了更好地了解哺乳动物的UCM，PI试图开发一个高度详细的、基于区域的大鼠肾脏皮质和髓质数学模型的动态公式。“基于区域”的建模方法代表了解剖学研究中揭示的肾单位和血管的放射状组织，并捕捉到了髓结构之间的优先相互作用。该模型将纳入和评估以前没有包括在模型中的实验结果，包括最近免疫标记实验的含义。为了研究UCM与肾小管上皮细胞反馈机制之间的相互作用，PI将建立近端小管上皮细胞的动态转运模型，并将该模型纳入到一个转化生长因子框架中。由此得到的模型可能为研究饮食盐摄入量对肾小球滤过率的矛盾影响以及细胞外液容量或钠转运调节紊乱的疾病的发病机制提供完整的见解。此外，使用上述模型，PI将生成过滤后的溶质分布的动画，并开发供实验者使用的用户友好的建模程序包。该项目的总体目标是使用分析和计算数学来更好地了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，尽管被动机制经常在生理学教科书中被用来解释哺乳动物产生浓缩尿液的原因，但它在计算机模拟中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，这些模型可能会为以下问题提供深入的见解：挑战公认的浓缩机制概念的意外实验发现会产生什么影响？管球反馈系统(调节液体进入肾单位的速率)在调节健康和高血压大鼠的钠排泄方面扮演什么角色？尤其是，为什么糖尿病患者和实验性糖尿病大鼠的肾脏血流量与饮食盐成反比，而相反的效果是预期的？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。将开发的拟议建模包应该会鼓励实验者使用建模技术，以更好地理解现在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意义。

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.