Feedback-mediated dynamics in a model of coupled nephrons with compliant thick ascending limbs
| Autor: | Amy M. Wen, Harold E. Layton, Matthew Bowen, Anita T. Layton |
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| Rok vydání: | 2011 |
| Předmět: |
Statistics and Probability
Tubular fluid Kidney Models Biological Article General Biochemistry Genetics and Molecular Biology Control theory Rats Inbred SHR Negative feedback Animals Homeostasis Humans Computer Simulation Tubuloglomerular feedback Mathematics Feedback Physiological General Immunology and Microbiology urogenital system Applied Mathematics Hemodynamics Characteristic equation Nephrons General Medicine Delay differential equation Mechanics Rats Coupling (electronics) Nonlinear system Nonlinear Dynamics Flow (mathematics) Modeling and Simulation Loop of Henle General Agricultural and Biological Sciences Algorithms Compliance Glomerular Filtration Rate |
| Zdroj: | Mathematical Biosciences. 230:115-127 |
| ISSN: | 0025-5564 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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