Modern understanding of hypertonic urine formation is organized around the countercurrent hypothesis. Experimental evidence supports the countercurrent idea, as do solutions of many mathematical models that incorporate a number of simplifying assumptions. Isomorphic models have failed, however, to predict the interstitial concentrations of NaCl and urea that are found in common laboratory animals. A feature common to all simulations solved thus far is that they use only a single independent spatial variable. Anatomical studies suggest a three dimensional ordering of tubules and blood vessels in the renal medulla. The major long term goal of this project is to solve a system of differential equations that describe flows of NaCl, urea, and water in renal medullary structures that are organized in the three dimensional arrangement suggested by anatomists. The hypothesis to be tested is that the three dimensional ordering is essential to achieve experimentally observed hypertonicity. The system of equations is a nonlinear two-point boundary value problem that will be solved with numerical methods that have been adapted to solve this specific problem, and that include quasilinearization, automatic evaluation of partial derivatives, and invariant embedding.

Agency
National Institute of Health (NIH)
Institute
National Institute of Diabetes and Digestive and Kidney Diseases (NIDDK)
Type
Research Project (R01)
Project #
5R01DK033729-05
Application #
3232138
Study Section
Physiology Study Section (PHY)
Project Start
1984-07-01
Project End
1990-06-30
Budget Start
1988-07-01
Budget End
1989-06-30
Support Year
5
Fiscal Year
1988
Total Cost
Indirect Cost
Name
University of Southern California
Department
Type
Schools of Medicine
DUNS #
041544081
City
Los Angeles
State
CA
Country
United States
Zip Code
90033
Thomas, S R; Wexler, A S (1995) Inner medullary external osmotic driving force in a 3-D model of the renal concentrating mechanism. Am J Physiol 269:F159-71
Holstein-Rathlou, N H; Marsh, D J (1994) Renal blood flow regulation and arterial pressure fluctuations: a case study in nonlinear dynamics. Physiol Rev 74:637-81
Wexler, A S; Kalaba, R E; Marsh, D J (1991) Three-dimensional anatomy and renal concentrating mechanism. I. Modeling results. Am J Physiol 260:F368-83
Marsh, D J; Yip, K P; Kallskog, O et al. (1991) Oscillations and more complex dynamics in tubuloglomerular feedback. Kidney Int Suppl 32:S94-7
Wexler, A S; Kalaba, R E; Marsh, D J (1991) Three-dimensional anatomy and renal concentrating mechanism. II. Sensitivity results. Am J Physiol 260:F384-94
Holstein-Rathlou, N H; Wagner, A J; Marsh, D J (1991) Tubuloglomerular feedback dynamics and renal blood flow autoregulation in rats. Am J Physiol 260:F53-68
Holstein-Rathlou, N H; Wagner, A J; Marsh, D J (1991) Dynamics of renal blood flow autoregulation in rats. Kidney Int Suppl 32:S98-101
Holstein-Rathlou, N H; Marsh, D J (1990) A dynamic model of the tubuloglomerular feedback mechanism. Am J Physiol 258:F1448-59
Cupples, W A; Wexler, A S; Marsh, D J (1990) Model of TGF-proximal tubule interactions in renal autoregulation. Am J Physiol 259:F715-26
Wexler, A S; Kalaba, R E; Marsh, D J (1987) Passive, one-dimensional countercurrent models do not simulate hypertonic urine formation. Am J Physiol 253:F1020-30