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

Maryam Saadatmand, Mohammad J. Abdekhodaie, Mahmoud R. Pishvaie, Fathollah Farhadi

Department of Chemical and Petroleum Engineering, Sharif University of Technology, Tehran, Iran.

DOI: 10.4236/jbise.2014.79068                

Abstract

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.

Keywords

Urine Concentrating Mechanism, Central Core Model, Electrolyte Transport, Orthogonal Collocation, Parametric Study

Conflicts of Interest

The authors declare no conflicts of interest.

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