9216614 Tewarson The investigator and his collaborators develop realistic and comprehensive mathematical models, and the necessary computational algorithms, to understand the concentrating mechanism of the mammalian kidney. Their immediate goal is to find out how the inner part of the kidney (inner medulla) concentrates urine. The role of loops of varying lengths and their parallel operation are studied. Presently available experimental data, as well as new data, as it becomes available, are utilized to calibrate and exercise the models. Current algorithms for solving the stiff multipoint boundary value differential equations for serial computers are adapted for the parallel supercomputers. New algorithms based on split system solvers are developed for parallel computation. Mammals maintain the volume and composition of their body fluids within very narrow limits. A basic mechanism for this purpose is the kidney -- which can produce urine that is either more or less concentrated than plasma or other body fluids. The kidney consists of a large number of distinct functional units called nephrons, operating in parallel. The human kidney contains roughly one million nephrons. A lengthwise cross-section of the kidney reveals two distinct parts: the cortex and the medulla. In view of differing physiological characteristics of the tubules, the medulla is subdivided into the outer and the inner parts. Mathematical models have been responsible for many of the basic ideas leading to our understanding of the urinary concentrating mechanism. These models --- using experimentally available parameters --- have established that the outer medulla uses the active mode (metabolic pumps) for concentration but no model has been able to generate any significant concentration in the inner medulla. How the inner medulla concentrates urine is still one of the major unsolved problems in renal physiology. Hypotheses continue to be proposed to answer this question. Mathematical models are essential in the testing of such alternate hypotheses. Realistic and comprehensive models involve the solution of thousands of equations. Therefore, it is essential that the solution algorithms for the algebraic equations not only run fast and but also minimize computer storage. Since the nephrons operate in parallel, algorithms and computers that are able to utilize this physiological property are eminently suitable for kidney modeling. The goal of this interdisciplinary project is to develop efficient methods for parallel computers to understand the concentrating mechanism of the mammalian kidney. The use of these methods in several other important physiological modeling applications will also be investigated. The project increases our fundamental understanding of basic and essential physiological functions, develops software and algorithms that can be used in other physiological studies, and may have significant diagnostic implications. ***
