Numerical methods for three-dimensional models of the urine concentrating mechanism

Wexler, Anthony S.; Marsh, Donald J.

doi:10.1016/0096-3003(91)90082-x

Cited by 9 publications

(3 citation statements)

References 21 publications

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“…This equation and the following two boundary conditions reflect the turn of the loop: An alternative is to combine like tubules into common structures. This approach has been suggested in [9] and has been used subsequently in several articles [2,4,[10][11][12][13][14]. The procedure to produce the combined structure is described in the next section with the help of a simple example.…”

Section: These Equations Reflect the Local Conservation Of Mass The mentioning

confidence: 99%

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A mathematical modeling technique for renal counterflow systems

Lory¹

1993

Applied Mathematics Letters

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Realistic and comprehensive mathematical models of the renal concentrating mechanism lead to large Systems of nonlinear differential equations. Their complexity can be considerably reduced by combining like tubules into common structures. Then the different lengths of the combined tubules have to be modeled by the shunt flow technique. The present paper investigates the validity of this methodology.

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Section: These Equations Reflect the Local Conservation Of Mass The mentioning

confidence: 99%

“…In this section, a recent kidney model [13,14] This means that a population of 40 loops is present. In [14] ascending vasa recta and interstitial capillary nodes play the role of the interstitial space.…”

Section: A Realistic Problemmentioning

confidence: 99%

A mathematical modeling technique for renal counterflow systems

Lory¹

1993

Applied Mathematics Letters

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“…These models have usually been formulated as steady-state boundary value problems (BVP's) involving ordinary differential equations (ODE's) expressing solute and water conservation in one space dimension corresponding to the cortico-medullary axis [1]. Since the nephron has a number of distinct tubules with different membrane transport properties, the equation set of urine concentrating mechanism for several constituents is a high order system [9]. Therefore, the steady-state model consists of a high order system of coupled and nonlinear ODEs [10].…”

Section: Introductionmentioning

confidence: 99%

An Efficient Numerical Method and Parametric Study for Electrolyte Transport in the Renal Medulla

Saadatmand¹,

Abdekhodaie²,

Pishvaie³

et al. 2014

JBiSE

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Mathematical models of the mamalian urine concentrating mechanism consist of a large system of coupled, nonlinear and stiff equations. An efficient numerical orthogonal collocation method was employed to solve the steady-state formulation of urine concentrating mechanism. This method was used to solve the stiff and high order equations of electrolyte transport in a central core, single nephron model of the renal outer medulla. The presented results were in good agreement with implicit finite difference method's results, but this new method was faster and more stable. Due to the greater stability and larger convergence domain of collocation method over Newton's method, a parametric study on concentrated urine was investigated. The results showed that this model was sensitive to non-ideal countercurrent exchange between medulla interstitium and vasa recta. Although distal tubule lies in the cortex interstitium, it affects on the inflow to the collecting duct. This study showed that the effect of changing membrane transport properties of distal tubule wall on properties of outflow from the outer medulla collecting duct was considerable.

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Mathematical Models of the Mammalian Urine Concentrating Mechanism

Layton¹

2002

Membrane Transport and Renal Physiology

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Numerical methods for three-dimensional models of the urine concentrating mechanism

Cited by 9 publications

References 21 publications

A mathematical modeling technique for renal counterflow systems

A mathematical modeling technique for renal counterflow systems

An Efficient Numerical Method and Parametric Study for Electrolyte Transport in the Renal Medulla

Mathematical Models of the Mammalian Urine Concentrating Mechanism

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