A delay-differential equation model of the feedback-controlled hypothalamus-pituitary-adrenal axis in humans
Catherine
Lloyd
Auckland Bioengineering Institute, The University of Auckland
Model Status
This CellML model runs in OpenCell but it does not replicate the published results (paramteter values for delta1 2 and 3 have been taken from the legend of figure 3 in the published paper, and initial conditions for x, y and z have been taken from the grpahs in figure 3). The inability of the CellML model to replicate the published results is most likely to be due to the lack of time delays in the CellML model (which currently can not be described). The units are all dimensionless and are therefore consistent, however expressing time as "dimensionless" means that the model cannot be run in COR.
Model Structure
ABSTRACT: The present work develops and analyses a model system of delay-differential equations which describes the core dynamics of the stress-responsive hypothalamus-pituitary-adrenal axis. This neuroendocrine ensemble exhibits prominent pulsatile secretory patterns governed by nonlinear and time-delayed feedforward and feedback signal interchanges. Formulation and subsequent bifurcation analysis of the model provide a qualitative and mathematical frame work for a better understanding of the delayed responsive mechanisms as well as the dynamic variations in different pathological situations.
model diagram
Schematic diagram of the hypothalamus-pituitary-adrenal (HPA) axis. Stimulatory and inhibitory paths are indicated by the arrows and + or - signs respectively. CRH represents corticotropin-releasing hormone and ACTH represents corticotropin.
The original paper reference is cited below:
A delay-differential equation model of the feedback-controlled hypothalamus-pituitary-adrenal axis in humans, Yongwimon Lenbury and Pornsarp Pornsawad, 2005,
Mathematical Medicine and Biology, 22, 15-33. PubMed ID: 15716298
It should be noted that in its current form, the CellML description of the this model is unable to perfectly capture the simulation results of the published model, this is due to the time delays which are difficult to describe in the CellML code.
x
CRH
corticotropin-releasing hormone
$\frac{d x}{d \mathrm{time}}=\mathrm{delta1}e^{\mathrm{beta}(1.0-y^{2.0})}-\mathrm{delta1}x$
y
ACTH
corticotropin
$\frac{d y}{d \mathrm{time}}=\mathrm{delta2}xe^{\mathrm{beta}(1.0-z^{2.0})}-\mathrm{delta2}y$
z
cortisol
$\frac{d z}{d \mathrm{time}}=\mathrm{delta3}y-\mathrm{delta3}z$
cortisol
endocrine
adrenal cortex
HPA axis
hypothalamus
hpa axis
anterior pituitary
The University of Auckland
Auckland Bioengineering Institute
This is a CellML description of Lenbury and Pornsawad's 2005 delay-differential equation model of the feedback-controlled hypothalamus-pituitary-adrenal axis in humans.
The University of Auckland, Auckland Bioengineering Institute
2007-07-13T00:00:00+00:00
c.lloyd@auckland.ac.nz
keyword
Pornsarp
Pornsawad
2005-03
Catherine Lloyd
Yongwimon
Lenbury
Mathematical Medicine and Biology
A delay-differential equation model of the feedback-controlled hypothalamus-pituitary-adrenal axis in humans
22
15
33
Lenbury and Pornsawad's 2005 delay-differential equation model of the feedback-controlled hypothalamus-pituitary-adrenal axis in humans.
Catherine
Lloyd
May
15716298