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Renal countercurrent system: Role of collecting duct convergence and pelvic urea predicted from a mathematical model

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Abstract

A differential equation model of the renal countercurrent system has been developed and physiological data from nephron segments were incorporated together with recently suggested urea recycling from renal pelvis to inner medulla and, particularly, an exponential reduction in the number of collecting tubules towards the renal papilla. The role of these features for the countercurrent concentrating mechanism has been studied by simulation runs. The computations, using the multiple shooting method, provide predictions about concentration profiles for salt and urea in tubes (nephron segments) and in the central core along the entire medullary countercurrent system. The results indicate that this model, without active salt or urea transport in the inner medulla, yields concentration gradients along the medullary axis compatible with those measured in the tissue.

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Authors and Affiliations

  1. Institut für Mathematik, Technische Universität München, D-8000, München, Federal Republic of Germany

    Peter Lory & Albert Gilg

  2. Physiologisches Institut, Universität München, D-8000, München, Federal Republic of Germany

    Michael Horster

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  1. Peter Lory
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  2. Albert Gilg
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  3. Michael Horster
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Additional information

A portion of this study has been presented at the Oberwolfach Conference on Mathematical Biology, November 1981

Part of the work was carried out while one of the authors (P. L.) was visiting at the State University of New York at Stony Brook. It was supported by the Science Committee of NATO via the DAAD

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Lory, P., Gilg, A. & Horster, M. Renal countercurrent system: Role of collecting duct convergence and pelvic urea predicted from a mathematical model. J. Math. Biology 16, 281–304 (1983). https://doi.org/10.1007/BF00276508

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