A dynamic numerical method for models of renal tubules

Layton, Harold E.; Pitman, E. Bruce

doi:10.1007/bf02460470

Cited by 26 publications

(6 citation statements)

References 25 publications

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“…(7) was advanced in time using a numerical method that is second order in space and time. Numerical solutions to the solute conservation equation (3) were computed by means of a spatially second-order ENO method applied in conjunction with Heun’s method to obtain a method that was second-order in both space and time [24, 25]. A time step of Δ t = 1/320 s was applied on a spatial grid of 1280 subintervals, which yielded a space step of Δ x = L 0 /1280 = 2/1280 cm.…”

Section: Mathematical Modelmentioning

confidence: 99%

Feedback-mediated dynamics in a model of coupled nephrons with compliant thick ascending limbs

Bowen

Wen

Layton

2011

Mathematical Biosciences

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The tubuloglomerular feedback (TGF) system in the kidney, a key regulator of glomerular filtration rate, has been shown in physiologic experiments in rats to mediate oscillations in thick ascending limb (TAL) tubular fluid pressure, flow, and NaCl concentration. In spontaneously hypertensive rats, TGF-mediated flow oscillations may be highly irregular. We conducted a bifurcation analysis of a mathematical model of nephrons that are coupled through their TGF systems; the TALs of these nephrons are assumed to have compliant tubular walls. A characteristic equation was derived for a model of two coupled nephrons. Analysis of that characteristic equation has revealed a number of parameter regions having the potential for differing stable dynamic states. Numerical solutions of the full equations for two model nephrons exhibit a variety of behaviors in these regions. Also, model results suggest that the stability of the TGF system is reduced by the compliance of TAL walls and by internephron coupling; as a result, the likelihood of the emergence of sustained oscillations in tubular fluid pressure and flow is increased. Based on information provided by the characteristic equation, we identified parameters with which the model predicts irregular tubular flow oscillations that exhibit a degree of complexity that may help explain the emergence of irregular oscillations in spontaneously hypertensive rats.

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Section: Mathematical Modelmentioning

confidence: 99%

Feedback-mediated dynamics in a model of coupled nephrons with compliant thick ascending limbs

Bowen

Wen

Layton

2011

Mathematical Biosciences

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“…Numerical solutions to the solute conservation equation (3) were found as previously described [16, 17]: a spatially second-order ENO method was used in conjunction with Heun’s method to obtain a method that was second-order in both space and time. A time step of Δ t = 1/320 s was applied on a spatial grid of 1280 subintervals, which yielded a space step of Δ x = L 0 /1280 = 2/1280 cm.…”

Section: Mathematical Modelmentioning

confidence: 99%

Feedback-mediated dynamics in a model of a compliant thick ascending limb

Layton

2010

Mathematical Biosciences

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The tubuloglomerular feedback (TGF) system in the kidney, which is a key regulator of filtration rate, has been shown in physiologic experiments in rats to mediate oscillations in tubular fluid pressure and flow, and in NaCl concentration in the tubular fluid of the thick ascending limb (TAL). In this study, we developed a mathematical model of the TGF system that represents NaCl transport along a TAL with compliant walls. The model was used to investigate the dynamic behaviors of the TGF system. A bifurcation analysis of the TGF model equations was performed by deriving and finding roots of the characteristic equation, which arises from a linearization of the model equations. Numerical simulations of the full model equations were conducted to assist in the interpretation of the bifurcation analysis. These techniques revealed a complex parameter region that allows a variety of qualitatively different model solutions: a regime having one stable, time-independent steady-state solution; regimes having one stable oscillatory solution only; and regimes having multiple possible stable oscillatory solutions. Model results suggest that the compliance of the TAL walls increases the tendency of the model TGF system to oscillate.

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“…When there is no electromotive force, we can safely drop the electrodiffusive terms in modeling the renal tubule (40). To examine whether similar simplification was acceptable in our case, solutions of the model equations with or without electrodiffusion were compared.…”

Section: Comparison Between Calculations With and Without Electrodiffusive Termsmentioning

confidence: 99%

A numerical model of the renal distal tubule

Chang¹,

Fujita

1999

American Journal of Physiology-Renal Physiology

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A numerical model of the rat distal tubule was developed to simulate water and solute transport in this nephron segment. This model incorporates the following: 1) Na-Cl cotransporter, K-Cl cotransporter, Na channel, K channel, and Cl channel in the luminal membrane; 2) Na-K-ATPase, K channel, and Cl channel in the basolateral membrane; and 3) conductances for Na, K, and Cl in the paracellular pathway. Transport rates were calculated using kinetic equations. Axial heterogeneity was represented by partitioning the model into two subsegments with different sets of model parameters. Model equations derived from the principles of mass conservation and electrical neutrality were solved numerically. Values of the model parameters were adjusted to minimize a penalty function that was devised to quantify the difference between model predictions and experimental results. The developed model could simulate the water and solute transport of the distal tubule in the normal state, as well as in conditions including thiazide or amiloride application and various levels of sodium load and tubular flow rate.

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A dynamic numerical method for models of renal tubules

Cited by 26 publications

References 25 publications

Feedback-mediated dynamics in a model of coupled nephrons with compliant thick ascending limbs

Feedback-mediated dynamics in a model of coupled nephrons with compliant thick ascending limbs

Feedback-mediated dynamics in a model of a compliant thick ascending limb

A numerical model of the renal distal tubule

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