1. Oscillations In A Simple Model Of Tubuloglomerular Feedback
- Author
-
E. B. Pitman and Harold E. Layton
- Subjects
Steady state ,urogenital system ,Quantitative Biology::Tissues and Organs ,Mechanics ,Juxtaglomerular apparatus ,Nephron ,Feedback loop ,medicine.anatomical_structure ,Control theory ,medicine ,Macula densa ,Hyperbolic partial differential equation ,Bifurcation ,Tubuloglomerular feedback ,Mathematics - Abstract
The tubuloglomerular feedback (TGF) system regulates the fluid and solute load in each nephron of the mammalian kidney. In this report, we obtain a necessary condition for sustained oscillations in a simple mathematical model for the TGF loop. This model consists of a hyperbolic partial differential equation representing the chloride concentration in the thick ascending limb and an empirical function describing the feedback response of the juxtaglomerular apparatus. A bifurcation analysis shows that critical parameters are the time delay, the slope of the empirical feedback relation at the steady state, and the steady-state space derivative of the chloride concentration at the macula densa.
- Published
- 2005