On the solution of equations for renal counterflow models

Tewarson, R. P.; Stephenson, John L.; García, María Isabel Ávalos; Zhang, Y.

doi:10.1016/0010-4825(85)90012-5

Cited by 19 publications

(3 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…If we consider tube j to be divided into n slices, then the spacecentered finite difference equations between nodes k-1 and k are where i represents flows of volume, NaCl, urea, glucose, or lactate. Thus the fluxes J i j are evaluated at the middle of the interval ["midpoint method" (38)], on the assumption that concentrations in the middle of the interval are the arithmetic average of the concentrations at k-1 and k.…”

Section: Numerical Solutionmentioning

confidence: 99%

Inner medullary lactate production and urine-concentrating mechanism: a flat medullary model

Hervy

Thomas

2003

American Journal of Physiology-Renal Physiology

View full text Add to dashboard Cite

We used a mathematical model to explore the possibility that metabolic production of net osmoles in the renal inner medulla (IM) may participate in the urine-concentrating mechanism. Anaerobic glycolysis (AG) is an important source of energy for cells of the IM, because this region of the kidney is hypoxic. AG is also a source of net osmoles, because it splits each glucose into two lactate molecules, which are not metabolized within the IM. Furthermore, these sugars exert their full osmotic effect across the epithelia of the thin descending limb of Henle's loop and the collecting duct, so they are apt to fulfill the external osmole role previously attributed to interstitial urea (whose role is compromised by the high urea permeability of long descending limbs). The present simulations show that physiological levels of IM glycolytic lactate production could suffice to significantly amplify the IM accumulation of NaCl. The model predicts that for this to be effective, IM lactate recycling must be efficient, which requires high lactate permeability of descending vasa recta and reduced IM blood flow during antidiuresis, two conditions that are probably fulfilled under normal circumstances. The simulations also suggest that the resulting IM osmotic gradient is virtually insensitive to the urea permeability of long descending limbs, thus lifting a longstanding paradox, and that this high urea permeability may serve for independent regulation of urea balance.

show abstract

Section: Numerical Solutionmentioning

confidence: 99%

Inner medullary lactate production and urine-concentrating mechanism: a flat medullary model

Hervy

Thomas

2003

American Journal of Physiology-Renal Physiology

View full text Add to dashboard Cite

show abstract

“…In the most numerical methods, Newton-based methods [2] [13] [14] and quasilinearization in conjunction with a Newton-type solver [4] [15] have been used to solve the steady-state model of urine concentrating mechanism. However, these methods have difficulties with numerical instability which arises from reversal intratubular flow relative to the assumed steady-state direction [16].…”

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

View full text Add to dashboard Cite

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.

show abstract

“…The method is based on splines as trial funetions for these concentrations and on collocation of the central-core equations (23). Once these trial funetions are given, the tubule equations and boundary conditions form a sequence of initial-value problems (each in the corresponding direction of flow).…”

mentioning

confidence: 99%

The kidney model as an inverse problem

Breinbauer¹,

Lory

1991

Applied Mathematics and Computation

View full text Add to dashboard Cite

The mammalian kidney is modeled by a multipoint boundary-value problem for a System of nonlinear ordinary differential equations. A corresponding inverse problem is presented, which allows the rigorous judgement of the potential of the given modeling technique. For its numerical Solution a discretization is proposed, which is tailor-made for kidney models. It leads to a nonlinear-programming problem with nonlinear equality and inequality constraints. The suggested methods are applied to current research problems in renal physiology.

show abstract

On the solution of equations for renal counterflow models

Cited by 19 publications

References 34 publications

Inner medullary lactate production and urine-concentrating mechanism: a flat medullary model

Inner medullary lactate production and urine-concentrating mechanism: a flat medullary model

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

The kidney model as an inverse problem

Contact Info

Product

Resources

About