Bifurcation study of blood flow control in the kidney

Mathematical Biosciences
Ashlee N Ford VersyptAnita T Layton

Abstract

Renal blood flow is maintained within a narrow window by a set of intrinsic autoregulatory mechanisms. Here, a mathematical model of renal hemodynamics control in the rat kidney is used to understand the interactions between two major renal autoregulatory mechanisms: the myogenic response and tubuloglomerular feedback. A bifurcation analysis of the model equations is performed to assess the effects of the delay and sensitivity of the feedback system and the time constants governing the response of vessel diameter and smooth muscle tone. The results of the bifurcation analysis are verified using numerical simulations of the full nonlinear model. Both the analytical and numerical results predict the generation of limit cycle oscillations under certain physiologically relevant conditions, as observed in vivo.

References

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Oct 6, 2005·American Journal of Physiology. Renal Physiology·Anita T LaytonHarold E Layton
May 15, 2007·Mathematical Biosciences·Paula Budu-GrajdeanuHarold E Layton
Aug 30, 2008·American Journal of Physiology. Heart and Circulatory Physiology·Brian E CarlsonTimothy W Secomb
Feb 12, 2009·Bulletin of Mathematical Biology·Anita T LaytonHarold E Layton
Oct 12, 2010·Mathematical Biosciences·Anita T Layton
Feb 19, 2011·Mathematical Biosciences·Anita T LaytonHarold E Layton
Apr 29, 2011·Mathematical Medicine and Biology : a Journal of the IMA·J C Arciero, T W Secomb
Jan 18, 2013·American Journal of Physiology. Renal Physiology·Lai-Jing GuoHui-Fang Bao
Mar 27, 2013·Journal of Mathematical Biology·Hwayeon Ryu, Anita T Layton
Mar 14, 2014·American Journal of Physiology. Renal Physiology·Ioannis Sgouralis, Anita T Layton

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Citations

Mar 15, 2016·Mathematical Biosciences·Runjing Liu, Anita T Layton

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