ADVANCE Fellows Award: Mathematical Modeling of Renal Physiology

Duke University, Durham NC

Investigators

Abstract

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 underlying principles 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 physiology textbooks as an explanation for the production of a concentrated urine in mammals, it does not produce a satisfactory concentration gradient in computer simulations. Through the development of a series of mathematical models, the PI seeks to 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 rate of 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.