Abstract
On the basis of the experiments of A. M. Walkeret al. (Am. J. Physiol.,134, 580–595, 1941), it is postulated that the fraction of glomerular filtrate reabsorbed up to a given point in the proximal tubule is independent of the rate of filtration. This, combined with the assumption that the proximal tubule is uniform from glomerular to distal end, implies that the volume of flow per unit of time past a given point in the proximal tubule decreases exponentially as a function of distance from the glomerulus. From this it is deduced that the rate of reabsorption of Na+ is proportional to the rate of formation of glomerular filtrate—a result established in clearance experiments. The analogy between a nephron and a catalytic flow reactor is indicated, and it is noted that, in both systems, reaction velocity can depend on the rate of flow.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature
Berliner, R. W. 1950. “Renal Excretion of Water, Sodium, Chloride, Potassium, Calcium and Magnesium.”Amer. J. Med.,9, 541–555.
Bergmann, F., and S. Dikstein. 1959. “The Theory of the Transfer Through the Walls of Biological Tubes of a Solute in a Moving Fluid.”J. Physiol. (London),145, 14–21.
Burgen, A. S. V. 1956. “A Theoretical Treatment of Glucose Reabsorption in the Kidney.”Canad. J. Biochem. Physiol.,34, 466–474.
Dole, V. P. 1943. “Back Diffusion of Urea in the Mammalian Kidney.”Amer. J. Physiol.,138, 504–513.
Gottschalk, C. W., and M. Mylle. 1959. “Micropuncture Study of the Mammalian Urinary Concentrating Mechanism: Evidence for the Countercurrent Hypothesis.”Amer. J. Physiol.,196, 927–936.
Hargitay, B., and W. Kuhn. 1951. “Das Multiplikationsprinzip als Grundlage der Harnkonzentrierung in der Niere.”Z. Electr. u. Angew. Physik Chemie.,55, 539–558.
Jakob, M. 1949.Heat Transfer. Vol. I. New York: J. Wiley & Sons, Inc.
Kuhn, W., and A. Ramel. 1959. “Activer Salztransport als Möglicher (und Wahrscheinlicher) Einzeleffekt bei der Harnkonzentrierung in der Niere.”Helvet. Chim. Acta,42, 628–660.
Lassiter, W. E., C. W. Gottschalk, and M. Mylle. 1961. “Micropuncture Study of Net Transtubular Water Movement of Water and Urea in Nondiuretic Mammalian Kidney.”Amer. J. Physiol.,200, 1139–1146.
Mudge, G. H., J. Foulks, and A. Gilman. 1949. “Effect of Urea Diuresis on Renal Excretion of Electrolytes.”Amer. J. Physiol.,58, 218–230.
Olson, R. W., R. W. Schuler, and J. M. Smith. 1950. “Oxidation of Sulfur Dioxide. Effect of Diffusion.”Chem. Eng. Progr.,46, 614–624.
Rhodin, J. 1958. “Anatomy of Kidney Tubules.” inInternational Review of Cytology, VII, G. H. Bourne and J. F. Danielli, eds.,7, 485–534. New York: Academic Press, Inc.
Robinson, J. R. 1954.Reflections on Renal Function. Oxford: Blackwell Scientific Publications.
Schmidt-Nielsen, Bodil. 1958. “Urea Excretion in Mammals.”Physiol. Rev.,38, 139–168.
Selkurt, E. E. 1954. “Sodium Excretion by the Mammalian Kidney.”Physiol. Rev.,34, 287–333.
Sherwood, T. K., and R. L. Pigford. 1952.Absorption and Extraction. New York: McGraw-Hill Book Co., Inc.
Smith, H. W. 1951.The Kidney. New York: Oxford University Press.
Smith, J. M. 1956.Chemical Engineering Kinetics. New York: McGraw-Hill Book Co., Inc.
Solomon, A. K. 1959. “Ion and Water Transport in Single Proximal Tubules of the Necturus Kidney.” InMethods of Isotopic Tracers Applied to the Study of Active Ion Transport. J. Coursaget, ed. London: Pergamon Press.
Sperber, I. 1944. “Studies on the Mammalian Kidney.”Zoologiska Bidrag. Uppsala.,22, 249–435.
Stoker, J. J. 1950.Nonlinear Vibrations. New York: Interscience Publishers, Inc.
Ullrich, K. J. 1960. “Function of the Collecting Ducts.”Circulation,21, 869–874.
Walker, A. M., P. A. Bott, J. Oliver, and M. C. MacDowell. 1941. “The Collection and Analysis of Fluid From Single Nephrons of the Mammalian Kidney.”Amer. J. Physiol.,134, 580–595.
Wesson, L. G., Jr. 1954a. “Renal Function and Velocity Effect.”J. Appl. Physiol.,6, 727–730.
— 1954b. “A Theoretical Analysis of Urea Excretion by The Mammalian Kidney.”Amer. J. Physiol.,179, 364–371.
— 1957. “Glomerular and Tubular Factors in the Renal Excretion of Sodium Chloride.”Medicine,36, 281–396.
Wesson, L. G., Jr., and W. P. Anslow, Jr. 1955. “Relationship of Changes in Glomerular Filtration, Plasma Chloride and Bicarbonate Concentrations, and Urinary Osmotic Load to Renal Excretion of Chloride.”Amer. J. Physiol.,180, 237–248.
Wirz, H., B. Hargitay, and W. Kuhn. 1951. “Lokalisation des Konzentrierungsprozesses in der Niere durch direkte Kyroskopie.”Helvet. Physiol. et Pharmacol. Acta,9, 196–207.
Wirz, H. 1956. “Der Osmotische Drück in den Corticalen Tubuli der Rattenniere.”Helv. Physiol. Acta,14, 353–362.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kelman, R.B. A theoretical note on exponential flow in the proximal part of the mammalian nephron. Bulletin of Mathematical Biophysics 24, 303–317 (1962). https://doi.org/10.1007/BF02477961
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02477961