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Mathematical Biosciences and Engineering

2005, Volume 2, Issue 1: 97-109. doi: 10.3934/mbe.2005.2.97
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The Effect of Different Forms for the Delay in A Model of the Nephron

  • 1.
    Department of Mathematics and Statistics, Surrey University, Guildford, Surrey, UK GU2 7SW
  • Received: 01 August 2004 Accepted: 29 June 2018 Published: 01 November 2004

  • MSC : 92C99,37N25,34K60.

  • We investigate how the dynamics of a mathematical model of a nephron depend on the precise form of the delay in the tubuloglomerular feedback loop. Although qualitative behavioral similarities emerge for different orders of delay, we find that significant quantitative differences occur. Without more knowledge of the form of the delay, this places restrictions on how reasonable it is to expect close quantitative agreement between the mathematical model and experimental data.

    Citation: Anne C. Skeldon, Ian Purvey. The Effect of Different Forms for the Delay in A Model of the Nephron[J]. Mathematical Biosciences and Engineering, 2005, 2(1): 97-109. doi: 10.3934/mbe.2005.2.97

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  • We investigate how the dynamics of a mathematical model of a nephron depend on the precise form of the delay in the tubuloglomerular feedback loop. Although qualitative behavioral similarities emerge for different orders of delay, we find that significant quantitative differences occur. Without more knowledge of the form of the delay, this places restrictions on how reasonable it is to expect close quantitative agreement between the mathematical model and experimental data.


  • This article has been cited by:

    1. Aline Duarte, Eva Löcherbach, Guilherme Ost, Stability, convergence to equilibrium and simulation of non-linear Hawkes processes with memory kernels given by the sum of Erlang kernels, 2019, 23, 1262-3318, 770, 10.1051/ps/2019005
    2. Susanne Ditlevsen, Eva Löcherbach, Multi-class oscillating systems of interacting neurons, 2017, 127, 03044149, 1840, 10.1016/j.spa.2016.09.013
    3. Anita T. Layton, Leon C. Moore, Harold E. Layton, Multistable Dynamics Mediated by Tubuloglomerular Feedback in a Model of Coupled Nephrons, 2009, 71, 0092-8240, 515, 10.1007/s11538-008-9370-x
    4. Jerry J. Batzel, Franz Kappel, Time delay in physiological systems: Analyzing and modeling its impact, 2011, 234, 00255564, 61, 10.1016/j.mbs.2011.08.006
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  • © 2005 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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