Feedback-mediated dynamics in a model of a compliant thick ascending limb |
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| Authors: | Anita T. Layton |
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| Affiliation: | 1. Department of Bioengineering, University of Utah, USA;2. Nora Eccles Harrison Cardiovascular Research and Training Institute, University of Utah, USA;3. Department of Biology, University of Utah, USA;4. Department of Cardiology, University of Washington, USA;1. Division of Nephrology, Department of Medicine, University of California, San Francisco, California, USA;2. Department of Experimental and Clinical Medical Sciences, University of Udine, Udine, Italy;1. Department of Urology, China Medical University Hospital, Taichung, Taiwan;2. School of Medicine, China Medical University, Taichung, Taiwan;3. Department of Urology, An-Nan Hospital, Tainan, Taiwan;1. University of California, Merced, School of Natural Sciences, Applied Mathematics Unit, Merced, CA 95343, United States;2. Duke University, Department of Mathematics, Durham, NC 27708, United States;3. Furman University, Department of Mathematics, Greenville, SC 29613, United States;4. Tulane University, Department of Mathematics, New Orleans, LA 70118, United States;1. Department of Mathematics, Florida Institute of Technology, Melbourne, FL 32901, USA;2. Department of Mathematics, University of California, Davis, CA 95616, USA;3. Department of Mathematics, University of Utah, Salt Lake City, UT 84112, USA;4. Department of Bioengineering, University of Utah, Salt Lake City, UT 84112, USA;1. Center for Brain Injury & Repair, Department of Neurosurgery, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA, USA;2. Department of Bioengineering, School of Engineering & Applied Science, University of Pennsylvania, Philadelphia, PA, USA;3. Center for Neurotrauma, Neurodegeneration & Restoration, Corporal Michael J. Crescenz Veterans Affairs Medical Center, Philadelphia, PA, 19104, USA;4. Axonova Medical, LLC, Philadelphia, PA, USA;5. Dartmouth-Hitchcock Medical Center, Division of Plastic Surgery, Dartmouth College, Lebanon, NH, USA |
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| Abstract: | 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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