A numerical method for renal models that represent tubules with abrupt changes in membrane properties.

Journal Article (Journal Article)

The urine concentrating mechanism of mammals and birds depends on a counterflow configuration of thousands of nearly parallel tubules in the medulla of the kidney. Along the course of a renal tubule, cell type may change abruptly, resulting in abrupt changes in the physical characteristics and transmural transport properties of the tubule. A mathematical model that faithfully represents these abrupt changes will have jump discontinuities in model parameters. Without proper treatment, such discontinuities may cause unrealistic transmural fluxes and introduce suboptimal spatial convergence in the numerical solution to the model equations. In this study, we show how to treat discontinuous parameters in the context of a previously developed numerical method that is based on the semi-Lagrangian semi-implicit method and Newton's method. The numerical solutions have physically plausible fluxes at the discontinuities and the solutions converge at second order, as is appropriate for the method.

Full Text

Duke Authors

Cited Authors

  • Layton, AT; Layton, HE

Published Date

  • December 2002

Published In

Volume / Issue

  • 45 / 6

Start / End Page

  • 549 - 567

PubMed ID

  • 12439590

Electronic International Standard Serial Number (EISSN)

  • 1432-1416

International Standard Serial Number (ISSN)

  • 0303-6812

Digital Object Identifier (DOI)

  • 10.1007/s00285-002-0166-6


  • eng