Existence and uniqueness of solutions to a mathematical model of the urine concentrating mechanism


Journal Article

This paper establishes some results for the existence and uniqueness of solutions to a previously published mathematical model of the mammalian urine concentrating mechanism [H.E. Layton, Distribution of Henle's loops may enhance urine concentrating capability, Biophys. J. 49:1033-1040 (1986)]. In particular, the contraction mapping principle is used to show that for sufficiently small and sufficiently large values of a positive parameter β there exist unique solutions to the model, whether it be endowed with first-order kinetics or Michaelis-Menten kinetics. Large or small β corresponds to large or small rates of active transport of NaCl from the ascending limbs. The Schauder principle is used to show that there exist solutions to the model for physiologically reasonable reabsorption kinetics, including first-order and Michaelis-Menten kinetics for all values of β. © 1987.

Full Text

Duke Authors

Cited Authors

  • Layton, HE

Published Date

  • January 1, 1987

Published In

Volume / Issue

  • 84 / 2

Start / End Page

  • 197 - 210

International Standard Serial Number (ISSN)

  • 0025-5564

Digital Object Identifier (DOI)

  • 10.1016/0025-5564(87)90092-7

Citation Source

  • Scopus