The Renal Countercurrent Mechanism

  • Frank C. Hoppensteadt
  • Charles S. Peskin
Part of the Texts in Applied Mathematics book series (TAM, volume 10)


The function of the kidney is to regulate the composition of the blood plasma. The plasma is the part of the blood that remains when the cells have been removed. We shall consider only the regulation of the Na + content of the blood plasma, but the reader should keep in mind that the kidney is actually regulating the concentrations of many other substances at the same time.


Blood Plasma Proximal Tubule Interstitial Fluid Volume Rate Distal Tubule 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Annotated References

For students who want to learn more about the physiology of the kidney, the following two texts should be useful (the first is elementary and the second is advanced)

  1. Sullivan, L.P., and Grantham, J.J.: Physiology of the Kidney ( 2nd edition ). Lea Febiger, Philadelphia, 1982.Google Scholar
  2. Koushanpour, E. and Kriz, W.: Renal Physiology: Principles, Strucutre, and Function ( 2nd edition ). Springer-Verlag, New York, NY, 1986.Google Scholar

The discussion of the juxtaglomerular apparatus in this Chapter is strongly influenced by the work of Thurau

  1. Thurau, K. and Mason, J.: Intrarenal function of the juxtaglomerular apparatus. In: Kidney and Urinary Tract Physiology (Thurau, K., ed.). M.T.P. International Review of Science, Physiology Series 1, Volume 6. University Park Press, Baltimore, MD, 1974, 357 - 390.Google Scholar

There is a considerable body of mathematical work concerning the kidney. This literature is reviewed in the following papers

  1. Knepper, M.A., and Rector, F.C., Jr.: Urinary concnetrationa nd dilution. In: The Kidney ( 4th edition ) Volume 1, ( Brenner, B.M. and Rector, F.C., Jr., eds.) Harcourt Brace Javanovich, Philadelphia, PA, 1991, 445 - 482.Google Scholar
  2. Roy, D.R., Layton, H.E., and Jamison, R.L.: Countercurrent mechanism and its regulation. In: The Kidney: Physiology and Pathophysiology (2nd edition) (Seldin, D.W. and Giebish, G., eds.) Raven Press, New York, NY, in press.Google Scholar

Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • Frank C. Hoppensteadt
    • 1
  • Charles S. Peskin
    • 2
  1. 1.College of Natural ScienceMichigan State UniversityEast LansingUSA
  2. 2.Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA

Personalised recommendations