Bifurcation study of blood flow control in the kidney.
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.
School of Chemical Engineering, Oklahoma State University, Stillwater, OK 74078, USA.
Ashlee N
AN
Ford Versypt
Division of Applied Mathematics, Brown University, Providence, RI 02912, USA. Electronic address: elizabeth_makrides@brown.edu.
Elizabeth
E
Makrides
Department of Mathematical Sciences, Indiana University-Purdue University Indianapolis, Indianapolis, IN 46202, USA.
Julia C
JC
Arciero
Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA 23284, USA.
Laura
L
Ellwein
Department of Mathematics, Duke University, Durham, NC 27708, USA.
Anita T
AT
Layton
D006801:Humans; D008962:Models, Theoretical; D012079:Renal Circulation / Q000502:physiology*
Bifurcation analysis; Delay differential equation; Myogenic response; Renal hemodynamics; Tubuloglomerular feedback