A test problem for kidney models

Mejia, Raymond; Stephenson, John L.; LeVeque, R

doi:10.1016/0025-5564(80)90126-1

Cited by 8 publications

(1 citation statement)

References 6 publications

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“…In the interest of enhanced numerical accuracy, we have specified uniform channel area for 0<x<L. As in previous work (Weinstein & Stephenson, 1979), the model equations were cast as a spatially centered finite difference scheme and all variables determined simultaneously using Newton's method. This method has been carefully tested, particularly on large kidney models (Mejia, Stephenson & LeVeque, 1980). It has been found to be efficient and accurate, giving the same results as other tested boundary value problem solvers.…”

Section: (X)= A2~) G Tx)mentioning

confidence: 82%

Models of coupled salt and water transport across leaky epithelia

Weinstein

Stephenson

1981

J. Membrain Biol.

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A general formulation is presented for the verification of isotonic transport and for the assignment of a degree of osmotic coupling in any epithelial model. In particular, it is shown that the concentration of the transported fluid in the presence of exactly equal bathing media is, in general, not a sufficient calculation by which to decide the issue of isotonicity of transport. Within this framework, two epithelial models are considered: (1) A nonelectrolyte compartment model of the lateral intercellular space is presented along with its linearization about the condition of zero flux. This latter approximate model is shown to be useful in the estimation of deviation from isotonicity, intraepithelial solute polarization effects, and the capacity to transport water against a gradient. In the case of uphill water transport, some limitations of a model of fixed geometry are indicated and the advantage of modeling a compliant interspace is suggested. (2) A comprehensive model of cell and channel is described which includes the major electrolytes and the possible presence of intraepithelial gradients. The general approach to verification of isotonicity is illustrated for this numerical model. In addition, the insights about parameter dependence gained from the linear compartment model are shown to be applicable to understanding this large simulation.

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Section: (X)= A2~) G Tx)mentioning

confidence: 82%

Models of coupled salt and water transport across leaky epithelia

Weinstein

Stephenson

1981

J. Membrain Biol.

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Urinary Concentration and Dilution: Models

Stephenson

1992

Comprehensive Physiology

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The sections in this article are: Whole‐Body Water and Solute Balance Osmolal Clearance Effect on Plasma Osmolality of Urine Flow of a Given Osmolality Hypertonic Urine Implies a Hypotonic Tubular Reabsorbate and Vice Versa Free Water Clearance Antidiuretic Hormone Controls Water Excretion Functional Implications of Renal Architecture Production of Hyperosmotic Urine Is Related to the Loop of Henle Significance of the S‐Shaped Configuration of the Mammalian Nephron for the Concentration of Urine New Functional Features Introduced by the S‐Shaped Configuration A Short History of Models of the Renal Counterflow System Active Water Transport Concentration by Differential Permeabilities and Counterflow Concentration by Multiplication of a “Single Effect” along the Loop of Henle Active Salt Transport out of the AHL Is the Probable Single Effect Experimental Predictions of the Kuhn Models Problems with the Kuhn Models Vasa Recta Models Nephrovascular Models Equations for the Renal Medulla Differential Equations Integrated Mass Balance Equations Generalized Multiplication Rule Nephrovascular Coupling Transmural Fluxes Analytical Solution of the Differential Equations Solutions for Single Flow Tubes Analytical Solutions of Multitube Counterflow Problems Solutions for Central Core Model Externally Driven Central Core Multiplier Multiplication in Inner and Outer Medullae Non‐Zero Diffusion Coefficient Solution of Time‐Dependent Equations Numerical Solution of the Differential Equations Method of Lines Shooting Method Quasilinearization Finite Difference Methods Results of Computer Simulation Origin of Inner Medullary Concentration Gradient Role of Collecting Duct Role of Vasa Recta Transition from Diuresis to Antidiuresis Free‐Energy Balance in Renal Counterflow Systems Summary and Future Directions

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On the use of Simpson's rule in renal models

Tewarson

1981

Mathematical Biosciences

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A test problem for kidney models

Cited by 8 publications

References 6 publications

Models of coupled salt and water transport across leaky epithelia

Models of coupled salt and water transport across leaky epithelia

Urinary Concentration and Dilution: Models

On the use of Simpson's rule in renal models

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