A Hypothalamic-Pituitary-Adrenal System Model
Catherine
Lloyd
Bioengineering Institute, University of Auckland
Model Structure
The hypothalamic pituitary adrenal (HPA) axis represents a neuroendocrine system which plays an essential role in maintaining body homeostasis in response to stress. These stresses can be physical (e.g. infection) or psychological (e.g. fear), and both activate the hypothalamus to secrete corticotropin releasing hormone (CRH). In turn, the presence of CRH in the circulation stimulates the pituitary to release adrenocorticotropic hormone (ACTH) into the blood, where it travels to the adrenal glands and induces the secretion of cortisol from the adrenal cortex. Cortisol has a negative feedback effect on the hypothalamus and pituitary such that the secretion of CRH and ACTH are inhibited.
The HPA system operates as a complex feedforward and feedback control system. There are three main pathways of activation for this system:
The internal biological clock, the hypothalamic supraiasmatic nucleus (SCN) with circadian oscillations in hormone levels;
Ultradian oscillations due to pulsatile patterns of HPA system hormone secretion and negative feedback loops; and
Stressful events (as described above) can also activate the HPA system and additional cortisol secretion occurs on top of the circadian and ultradian hormone oscillations.
Direct experimental assessment of complex biological systems is generally very difficult, and our understanding of these systems has been improved by the development of mathematical models. Several mathematical models describing the HPA system have been published (most recently by Gupta et al. (2007), and this model can be found in the CellML model repository along with other HPA models). The mathematical model described here in CellML (see figure below) is a four-dimensional non-linear differential equation model which can be used to analyse plasma cortisol levels in humans.
The complete original paper reference is cited below:
Mathematical modeling of the hypothalamic-pituitary-adrenal system activity., Smiljana Jelic, Zeljko Cupic, and Ljiljana Kolar-Anic, 2005, Mathematical Biosciences, 197, pp173-187. PubMed ID: 16112688
model diagram
A schematic diagram of the hypothalamic-pituitary-adrenal system. Corticotrophin-releasing hormone (CRH) and arginin-vasopressin (AVP) stimulate adrenocorticotropin (ACTH) secretion from the pituitary, followed by cortisol secretion from the adrenal cortex. GR represents a glucocorticoid receptor and MR denotes a mineralocorticoid receptor. + represents a postive feedback loop while - represents a negative feedback loop.
$\frac{d a}{d \mathrm{time}}=\mathrm{KP}-(1.0+\mathrm{alpha}+\mathrm{beta})a+ag^{2.0}$
$\frac{d g}{d \mathrm{time}}=1.0a+ag^{2.0}-L+\mathrm{gamma}g$
$\mathrm{alpha}=\frac{\mathrm{k3}}{\mathrm{k2}}\mathrm{beta}=\frac{\mathrm{k6}}{\mathrm{k2}}\mathrm{gamma}=\frac{\mathrm{k7}}{\mathrm{k2}}\mathrm{KP}=KPK=\left(\frac{\mathrm{k0}^{2.0}\mathrm{k4}}{\mathrm{k2}^{3.0}}\right)^{0.5}P=0.735+0.1563\sin \left(\frac{2.0\times 3.141592653\mathrm{time}}{24.0\times 3600.0}\right)+0.3127\left|\sin \left(\frac{3.141592653\mathrm{time}}{24.0\times 3600.0}\right)\right|L=\left(\frac{\mathrm{km}^{2.0}\mathrm{k4}}{\mathrm{k2}^{3.0}}\right)^{0.5}$
endocrine
hpa axis
HPA axis
hypothalamus
cortisol
The University of Auckland
The Bioengineering Institute
The University of Auckland, Bioengineering Institute
Catherine Lloyd
2005-00-00 00:00
Catherine
Lloyd
May
The model has now been checked in COR too. I've added a complicated pulse stimulus equation to the model - but I'm not sure it's working properly! Can PCEnv handle "sin"?
I've added initially values from the paper and have also made every varible (except time) dimensionless.
ACTH
adrenocorticotropic hormone
a
cortisol
o
2007-06-15T00:00:00+00:00
Mathematical modeling of the hypothalamic-pituitary-adrenal system activity
197
173
187
Catherine
Lloyd
May
Jelic et al's 2005 hypothalamic pituitary adrenal axis model.
hypothalamic pituitary adrenal axis
Ljiljana
Kolar-Anic
Zeljko
Cupic
16112688
This is the CellML description of Jelic et al's 2005 hypothalamic pituitary adrenal axis model.
2007-09-03T07:48:26+12:00
The model has now been checked in COR too. I've added a complicated pulse stimulus equation to the model - but I'm not sure it's working properly! Can PCEnv handle "sin"?
I've added initially values from the paper and have also made every varible (except time) dimensionless.
c.lloyd@auckland.ac.nz
Smiljana
Jelic
keyword
Mathematical Biosciences
Catherine Lloyd