The overall goal of this work is to synthesize experimental data at the membrane and molecular level into predictive mathematical models of the mammalian kidney that are useful in understanding both its normal and diseased function. The general purpose of the research proposed in this application is to develop for the first time a mathematical model of the mammalian kidney that combines a realistic architecture, cellular and paracellular transport of water and solutes, and exchange of solutes and water between plasma and red blood cells. This development builds on simpler models, but requires the vector and parallel processing capabilities of supercomputers. Development of the supercomputer models will proceed in several stages: 1. Detailed models of proximal tubule, thick ascending limb, cortical collecting tubule, and collecting duct, which include both cellular and paracellular pathways and the following variables: Na+, K+, H+, NH4+, Cl-, HCO3-, HPO4-,H2PO42-, glucose, urea, hydrostatic pressure, electric potential, and volume flow will be incorporated into a central core model of a cortical nephron In this phase our primary mathematical aim will be to optimize the vector Fortran code. Physiologically this model will be used to analyze cortical micropuncture data, particularly with respect to Na and K handling. 2. A multinephron electrolyte central core model of the kidney with a distribution of lengths of loops of Henle but less detailed tubular models will be used to optimize parallel code. This model will be applied to understanding the possible role of osmolyte production in the inner medullary concentrating mechanism. It will also be used to simulate the transition of the kidney from diuresis to antidiuresis. 3. The multinephron model will evolve further by incorporation of the detailed tubular models, and the detailed medullary architecture of tubules and blood vessels. With progressively more detailed models it will be possible to simulate the effect on overall function of hypothesized target actions of drugs and hormones on membrane transport. 4. Exchange of solutes and water between red blood cells and plasma will be added to the model.
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