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

Mathematical Biosciences

Volumn 228, Issue 2, 2010, Pages 185-194

  Layton, Anita T ^a  

^a DUKE UNIVERSITY   (United States)

Author keywords

Delay differential equation; Negative feedback loop; Non linear dynamics; Renal hemodynamic control

Indexed keywords

BIFURCATION ANALYSIS; CHARACTERISTIC EQUATION; COMPLEX PARAMETER; COMPLIANT WALLS; DELAY DIFFERENTIAL EQUATIONS; DYNAMIC BEHAVIORS; FILTRATION RATES; FINDING ROOTS; FLUID PRESSURES; FULL MODEL; KEY REGULATORS; MODEL EQUATIONS; MODEL RESULTS; MODEL SOLUTION; NACL CONCENTRATION; NEGATIVE FEEDBACK LOOP; NON-LINEAR DYNAMICS; NUMERICAL SIMULATION; OSCILLATORY SOLUTIONS; RENAL HEMODYNAMIC CONTROL; STEADY STATE SOLUTION;

BIFURCATION (MATHEMATICS); COMPUTER SIMULATION; DIFFERENTIAL EQUATIONS; FEEDBACK; HYDRODYNAMICS; SODIUM CHLORIDE;

MATHEMATICAL MODELS;

BIFURCATION; FLUID FLOW; FLUID PRESSURE; LIMB; NUMERICAL MODEL; PHYSIOLOGY; RODENT; SODIUM CHLORIDE;

ARTICLE; CONCENTRATION (PARAMETERS); CONTROLLED STUDY; EXPERIMENTAL RAT; FEEDBACK SYSTEM; HENLE LOOP; IN VIVO STUDY; INTERMETHOD COMPARISON; KIDNEY BLOOD FLOW; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; MICHAELIS MENTEN KINETICS; NEGATIVE FEEDBACK; NONHUMAN; NONLINEAR SYSTEM; OSCILLATION; PREDICTION; PROCESS DEVELOPMENT; QUALITATIVE ANALYSIS; SENSITIVITY ANALYSIS; STEADY STATE;

ALGORITHMS; ANIMALS; CHLORIDES; COMPLIANCE; COMPUTER SIMULATION; FEEDBACK, PHYSIOLOGICAL; HYDRODYNAMICS; LOOP OF HENLE; MODELS, BIOLOGICAL; NONLINEAR DYNAMICS; PRESSURE; RATS; SODIUM CHLORIDE;

RATTUS;

EID: 78649450981     PISSN: 00255564     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mbs.2010.10.002     Document Type: Article

References (24)

1. Eaton D., Pooler J. Vander's Renal Physiology 2004, McGraw-Hill Medical, New York. sixth ed.
2. Han J., Thompson K., Chou C., Knepper M. Experimental tests of three-dimensional model of urinary concentrating mechanism. J. Am. Soc. Nephrol. 1992, 2:1677.
3. Layton H., Pitman E., Moore L. Bifurcation analysis of TGF-mediated oscillations in SNGFR. Am. J. Physiol. (Renal Fluid Electrolyte Physiol) 1991, 261:F904.
4. Layton H., Pitman E., Moore L. Instantaneous and steady-state gains in the tubuloglomerular feedback system. Am. J. Physiol. Renal Physiol. 1995, 268:F163.
5. Layton A., Moore L., Layton H. Multistability in tubuloglomerular feedback and spectral complexity in spontaneously hypertensive rats. Am. J. Physiol. Renal Physiol. 2006, 291:F79.
6. Budu-Grajdeanu P., Moore L., Layton H. Effect of tubular inhomogeneities on filter properties of thick ascending limb of Henle's loop. Math. Biosci. 2007, 209(2):564.
7. Layton A., Moore L., Layton H. Multistable dynamics mediated by tubuloglomerular feedback in a model of coupled nephrons. Bull. Math. Biol. 2009, 71:515.
8. Holstein-Rathlou N., Marsh D. A dynamic model of the tubuloglomerular feedback mechanism. Am. J. Physiol. (Renal Fluid Electrolyte Physiol 27) 1990, 258:F1448.
9. Sakai T., Craig D., Wexler A., Marsh D. Fluid waves in renal tubules. Biophys. J. 1986, 50:805.
10. Young D., Marsh D. Pulse wave propagation in rat renal tubules: implications for GFR autoregulation. Am. J. Physiol. (Renal Fluid Electrolyte Physiol 9) 1981, 240:F446.
11. Layton H., Pitman E., Knepper M. A dynamic numerical method for models of the urine concentrating mechanism. SIAM J. Appl. Math. 1995, 55(5):1390.
12. Angell S., Pruthi R., Shortliffe L. The urodynamic relationship of renal pelvic bladder presures and urinary flow rate in rats with congenital vesicoureteral reflux. J. Urology 1998, 160:150.
13. Gottschalk C. A comparable study of renal interstitial pressure. Am. J. Physiol. 1952, 169:180.
14. Gottschalk C., Mylle M. Micropuncture study of pressures in proximal and distal tubules and peritubular capillaries of the rat kidney during osmotic diuresis. Am. J. Physiol. 1957, 189:323.
15. Layton A., Layton H. A region-based model framework for the rat urine concentrating mechanism. Bull. Math. Biol. 2003, 65(5):859.
16. Layton H., Pitman E. A dynamic numerical method for models of renal tubules. Bull. Math. Biol. 1994, 56(3):547.
17. Layton H., Pitman E., Moore L. Spectral properties of the tubuloglomerular feedback system. Am. J. Physiol. (Renal Fluid Electrolyte Physiol 42) 1997, 273:F635.
18. Pitman E., Layton H., Moore L. Dynamic flow in the nephron: filtered delay in the TGF pathway. Contemp. Math. 1993, 114:317.
19. Leyssac P., Baumbach L. An oscillating intratubular pressure response to alterations in Henle loop flow in the rat kidney. Acta Physiol. Scand. 1983, 117:415.
20. Hartman P. On local homeomorphisms of euclidean spaces. Bol. Soc. Math. Mexicana 1960, 5:220.
21. Layton H. Mathematical models of the mammalian urine concentrating mechanism. The IMA Volumes in Mathematics and Its Applications 2002, vol. 129:233. Springer, New York. L. HE, W. AM (Eds.).
22. Layton A., Moore L., Layton H. Waveform distortion in TGF-mediated limit-cycle oscillations: Effects of TAL flow. FASEB J. 2009, 23:804.1.
23. Layton H., Pitman E., Moore L. Limit-cycle oscillations and tubuloglomerular feedback regulation of distal sodium delivery. Am. J. Physiol. Renal Physiol. 2000, 278:F287.
24. Lai W., Rubin D., Krempl E. Introduction to Continuum Mechanics 1993, Pergamon LTD, Oxford UK. third ed.