The Effect of Different Forms for the Delay in A Model of the Nephron

2005, Volume 2, Issue 1: 97-109. doi: 10.3934/mbe.2005.2.97

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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.
- mathematical model,
- nephron,
- delay,
- nonlinear dynamics.
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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Abstract

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.
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