Abstract
Finite difference equations describing salt and water movement in a model of the mammalian kidney have been solved numerically by an extension of the Newton-Raphson method used for the medullary counterflow system. The method permits both steady-state and transient solutions. It has been possible to simulate behavior of the whole kidney as a function of hydrostatic pressures in renal artery, vein, and pelvis; protein and other solute concentrations in arterial blood; and phenomenological equations describing transport of solute and water across nephron and capillary walls. With the model it has been possible to compute concentrations, flows, and hydrostatic pressures in the various nephron segments and in cortical and medullary capillaries and interstitium. In a general way, calculations on the model have met intuitive expectations. In addition, they have reemphasized the critical dependence of renal function on the hydraulic and solute permeabilities of glomerular, postglomerular, and medullary capillaries. These studies provide additional support for our thesis that the functional unit of the kidney is not the single nephron, but a nephrovascular unit consisting of a group of nephrons and their tightly coupled vasculature.
Full text
PDF
Images in this article
Selected References
These references are in PubMed. This may not be the complete list of references from this article.
- Kokko J. P., Rector F. C., Jr Countercurrent multiplication system without active transport in inner medulla. Kidney Int. 1972 Oct;2(4):214–223. doi: 10.1038/ki.1972.97. [DOI] [PubMed] [Google Scholar]
- Stephenson J. L. Concentrating engines and the kidney. I. Central core model of the renal medulla. Biophys J. 1973 Jun;13(6):512–545. doi: 10.1016/S0006-3495(73)86005-9. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Stephenson J. L. Concentrating engines and the kidney. II. Multisolute central core systems. Biophys J. 1973 Jun;13(6):546–567. doi: 10.1016/S0006-3495(73)86006-0. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Stephenson J. L. Concentration of urine in a central core model of the renal counterflow system. Kidney Int. 1972 Aug;2(2):85–94. doi: 10.1038/ki.1972.75. [DOI] [PubMed] [Google Scholar]
- Stephenson J. L., Tewarson R. P., Mejia R. Quantitative analysis of mass and energy balance in non-ideal models of the renal counterflow system. Proc Natl Acad Sci U S A. 1974 May;71(5):1618–1622. doi: 10.1073/pnas.71.5.1618. [DOI] [PMC free article] [PubMed] [Google Scholar]