Tubuloglomerular Feedback

  • Anita T. Layton
  • Aurélie Edwards
Part of the Lecture Notes on Mathematical Modelling in the Life Sciences book series (LMML)


Tubuloglomerular feedback (TGF) contributes to hemodynamics control by adjusting the single nephron glomerular filtration rate according to the chloride concentration sensed downstream. To analyze the TGF system, which is a negative feedback loop, we first formulate model equations consisting of a partial differential equation that describes solute conservation along the thick ascending limb, and a delay equation that describes the feedback response. Depending on model parameters, in particular the feedback delay and gain, the model may predict limit-cycle oscillations or a time-independent steady state, following a transient perturbation. We analyze the dynamic behaviors of the TGF model by linearizing the model equations and deriving a characteristic equation. Numerical simulations can also be conducted to assist in the interpretation of the analysis.


Bifurcation Curve Afferent Arteriole Thick Ascending Limb Tubular Fluid Good Initial Guess 
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  1. Layton, A.T., Moore, L.C., Layton, H.E.: Multistable dynamics mediated by tubuloglomerular feedback in a model of coupled nephrons. Bull. Math. Biol. 71, 515–555 (2009)CrossRefzbMATHMathSciNetGoogle Scholar
  2. Pitman, E.B., Zaritski, R.M., Kesseler, K.J., Moore, L.C., Layton, H.E.: Feedback-mediated dynamics in two coupled nephrons. Bull. Math. Biol. 66(6), 1463–1492 (2004)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Anita T. Layton
    • 1
  • Aurélie Edwards
    • 2
  1. 1.Department of MathematicsDuke UniversityDurhamUSA
  2. 2.Centre de Recherche des Cordeliers ERL 8228, UMRS 1138 Equipe 3ParisFrance

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