A dynamic numerical method for models of renal tubules

We show that an explicit method for solving hyperbolic partial differential equations can be applied to a model of a renal tubule to obtain both dynamic and steady-state solutions. Appropriate implementation of this method eliminates numerical instability arising from reversal of intratubular flow d...

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Bibliographic Details
Published in:Bulletin of mathematical biology 1994-05, Vol.56 (3), p.547-565
Main Authors: Layton, H E, Pitman, E B
Format: Article
Language:English
Subjects:
Body Water - metabolism
Calculi
Cell Membrane Permeability
Computer Simulation
Diuresis
Kidney Tubules - physiology
Models, Biological
Rheology
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Summary:We show that an explicit method for solving hyperbolic partial differential equations can be applied to a model of a renal tubule to obtain both dynamic and steady-state solutions. Appropriate implementation of this method eliminates numerical instability arising from reversal of intratubular flow direction. To obtain second-order convergence in space and time, we employ the recently developed ENO (Essentially Non-Oscillatory) methodology. We present examples of computed flows and concentration profiles in representative model contexts. Finally, we indicate briefly how model tubules may be coupled to construct large-scale simulations of the renal counterflow system.
ISSN:0092-8240
1522-9602
DOI:10.1007/BF02460470