Bifurcation Study of Blood Flow Control in the Kidney

Overview

Journal Math Biosci

Specialty Public Health

Date 2015 Mar 10

PMID 25747903

Citations 3

Authors

Ashlee N Ford Versypt

Elizabeth Makrides

Julia C Arciero

Laura Ellwein

Anita T Layton

Affiliations

Soon will be listed here.

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.

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Bifurcation study of blood flow control in the kidney.

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References

Cupples W, Novak P, Novak V, Salevsky F . Spontaneous blood pressure fluctuations and renal blood flow dynamics. Am J Physiol. 1996; 270(1 Pt 2):F82-9. DOI: 10.1152/ajprenal.1996.270.1.F82. View

Cupples W . Angiotensin II conditions the slow component of autoregulation of renal blood flow. Am J Physiol. 1993; 264(3 Pt 2):F515-22. DOI: 10.1152/ajprenal.1993.264.3.F515. View

Marsh D, Sosnovtseva O, Pavlov A, Yip K, Holstein-Rathlou N . Frequency encoding in renal blood flow regulation. Am J Physiol Regul Integr Comp Physiol. 2005; 288(5):R1160-7. DOI: 10.1152/ajpregu.00540.2004. View

Garg L, Mackie S, Tisher C . Effect of low potassium-diet on Na-K-ATPase in rat nephron segments. Pflugers Arch. 1982; 394(2):113-7. DOI: 10.1007/BF00582911. View

Ryu H, Layton A . Tubular fluid flow and distal NaCl delivery mediated by tubuloglomerular feedback in the rat kidney. J Math Biol. 2013; 68(4):1023-49. PMC: 3757103. DOI: 10.1007/s00285-013-0667-5. View

LEYSSAC P, Holstein-Rathlou N . Tubulo-glomerular feedback response: enhancement in adult spontaneously hypertensive rats and effects of anaesthetics. Pflugers Arch. 1989; 413(3):267-72. DOI: 10.1007/BF00583540. View

Holstein-Rathlou N . Synchronization of proximal intratubular pressure oscillations: evidence for interaction between nephrons. Pflugers Arch. 1987; 408(5):438-43. DOI: 10.1007/BF00585066. View

Layton H, Pitman E, Moore L . Instantaneous and steady-state gains in the tubuloglomerular feedback system. Am J Physiol. 1995; 268(1 Pt 2):F163-74. DOI: 10.1152/ajprenal.1995.268.1.F163. View

Ford Versypt A, Makrides E, Arciero J, Ellwein L, Layton A . Bifurcation study of blood flow control in the kidney. Math Biosci. 2015; 263:169-79. PMC: 4768488. DOI: 10.1016/j.mbs.2015.02.015. View

10.

Layton A, Bowen M, Wen A, Layton H . Feedback-mediated dynamics in a model of coupled nephrons with compliant thick ascending limbs. Math Biosci. 2011; 230(2):115-27. PMC: 3070299. DOI: 10.1016/j.mbs.2011.02.004. View

11.

Knepper M, Danielson R, Saidel G, Post R . Quantitative analysis of renal medullary anatomy in rats and rabbits. Kidney Int. 1977; 12(5):313-23. DOI: 10.1038/ki.1977.118. View

12.

Pfaller W . Structure function correlation on rat kidney. Quantitative correlation of structure and function in the normal and injured rat kidney. Adv Anat Embryol Cell Biol. 1982; 70:1-106. View

13.

Sgouralis I, Layton A . Theoretical assessment of renal autoregulatory mechanisms. Am J Physiol Renal Physiol. 2014; 306(11):F1357-71. PMC: 4042104. DOI: 10.1152/ajprenal.00649.2013. View

14.

Basar E, Weiss C . Time series analysis of spontaneous fluctuations of the flow in the perfused rat kidney. Pflugers Arch. 1970; 319(3):205-14. DOI: 10.1007/BF00586451. View

15.

Layton A, Moore L, Layton H . Multistability in tubuloglomerular feedback and spectral complexity in spontaneously hypertensive rats. Am J Physiol Renal Physiol. 2005; 291(1):F79-97. DOI: 10.1152/ajprenal.00048.2005. View

16.

Takabatake T, Ushiogi Y, Ohta K, Hattori N . Attenuation of enhanced tubuloglomerular feedback activity in SHR by renal denervation. Am J Physiol. 1990; 258(4 Pt 2):F980-5. DOI: 10.1152/ajprenal.1990.258.4.F980. View

17.

de Rouffignac C, Monnens L . Functional and morphologic maturation of superficial and juxtamedullary nephrons in the rat. J Physiol. 1976; 262(1):119-29. PMC: 1307633. DOI: 10.1113/jphysiol.1976.sp011588. View

18.

Holstein-Rathlou N, LEYSSAC P . TGF-mediated oscillations in the proximal intratubular pressure: differences between spontaneously hypertensive rats and Wistar-Kyoto rats. Acta Physiol Scand. 1986; 126(3):333-9. DOI: 10.1111/j.1748-1716.1986.tb07824.x. View

19.

Holstein-Rathlou N . A closed-loop analysis of the tubuloglomerular feedback mechanism. Am J Physiol. 1991; 261(5 Pt 2):F880-9. DOI: 10.1152/ajprenal.1991.261.5.F880. View

20.

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):564-92. DOI: 10.1016/j.mbs.2007.03.007. View