Abstract
A model of countercurrent exchange has been developed to simulate transport of salt, urea and water among vasa recta and descending limbs of the loop of Henle in the inner medulla. These vessels are abstracted as three concentric cylinders: the inne one represents descending vasa recta, the middle one represents ascending vasa recta and the outer one represents descending limbs. The capillary plexus, which connects the ascending and descending vasa recta, is modeled as a series of well-mixe compartments. Multicomponent transport equations for the sytem are derived from steady state mass balances and simple passive flux relations. The resulting set of nonlinear equations are solved numerically by an iterative Gauss-Seidel algorithm with under-relaxation. Simulations yield the salt and urea concentrations as well as volume flow rates in all tubes and compartments. The simulations indicate that solute concentrations can increase monotonically toward the papillae even if all transport processes within the exchanger are passive and source fluxes decrease monotonically toward the papillae.
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Literature
Kriz, W. 1967. “Der Architektonische und funktionelle Aufbau der Ratteniere”Z. Zellforsch.,82, 495–535.
— and A. F. Lever. 1969. “Renal Countercurrent Mechanisms: Structure and Function.”Am. Heart J.,78, 101–118.
Jacquez, J. A., B. Carnahan and P. Abbrecht. 1967. “A Model of the Renal Cortex and Medulla.”Math. Biosci.,1, 227–261.
Morgan, T. and R. W. Berliner. 1968. “Permeability of the Loop of Henle, Vasa Recta, and Collecting Duct to Water, Urea and Sodium.”Am. J. Physiol.,215, 108–115.
Palatt, P. J. and G. M. Saidel. 1973. “An Analysis of Countercurrent Exchange with Emphasis on Renal Function.”Bull. Math. Biol.,35, 275–286.
—— and M. Macklin. 1970. “Transport Processes in the Renal Cortex.”J. Theor. Biol.,29, 251–274.
Smith, H. W.. 1951.The Kidney, its Structure and Function in Health and Disease. New York: Oxford University Press.
Sperber, I.. 1944. “Studies on the Mammalian Kidney.”Zool. Bidray. Uppsala.,22, 249–435.
Tarica, R. R., E. Koushanpour and W. F. Stevens. 1969. “Mathematical Simulation of Renal Function.”A.I.Ch.E. Symp. 64a, Washington, D.C., Nov 16–20.
Thurau, K. 1964. “Renal Hemodynamics.”Am. J. Med.,36, 698–719.
Ullrich, K. J., G. Rumrich and G. Fuchs. 1964. “Wasserpermeabilität and transtubulärer Wasserfluss corticaler Nephronabschnitte bei verschiedenen Diuresezuständen.”Pflügers Archiv.,280, 99–119.
—, K. Kramer and J. W. Boylan. 1962. “Countercurrent system in the mammalian kidney.” InHeart, Kidney and Electrolytes (Ed. C. K. Friedberg) New York: Grune & Stratton.
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Palatt, P.J., Saidel, G.M. Countercurrent exchange in the inner renal medulla: Vasa recta-descending limb system. Bltn Mathcal Biology 35, 431–447 (1973). https://doi.org/10.1007/BF02575187
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DOI: https://doi.org/10.1007/BF02575187