Mathematical modeling of the hypothalamic-pituitary-adrenal system activity
Catherine
Lloyd
Auckland Bioengineering Institute, The University of Auckland
Model Status
This CellML model runs in PCEnv and OpenCell, but not in COR because the free variable (time) is dimensionless. The units are consistent throughout, and it runs to reproduce figure 5 from the paper. In order to reproduce figure 5, equation 7 was discarded and the variables were defined explicitly as described in the legend for figure 5. An equation was also added describing the SCN periodic input to PVN. The model must be run for roughly 1 day before it stabilizes.
Model Structure
ABSTRACT: Mathematical modeling has proven to be valuable in understanding of the complex biological systems dynamics. In the present report we have developed an initial model of the hypothalamic-pituitary-adrenal system self-regulatory activity. A four-dimensional non-linear differential equation model of the hormone secretion was formulated and used to analyze plasma cortisol levels in humans. The aim of this work was to explore in greater detail the role of this system in normal, homeostatic, conditions, since it is the first and unavoidable step in further understanding of the role of this complex neuroendocrine system in pathophysiological conditions. Neither the underlying mechanisms nor the physiological significance of this system are fully understood yet.
The 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.
endocrine
hpa axis
HPA axis
hypothalamus
cortisol
The University of Auckland
Auckland Bioengineering Institute
A Hypothalamic-Pituitary-Adrenal System Model: Figure 5
The University of Auckland, 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
$\mathrm{time}=\frac{\mathrm{tau}}{\mathrm{C\_0}}$
$A=\mathrm{C\_1}a\frac{d a}{d \mathrm{tau}}=\mathrm{KP}-(1+\mathrm{alpha}+\mathrm{beta})a+ag^{2}$
$G=\mathrm{C\_2}g\frac{d g}{d \mathrm{tau}}=1a+ag^{2}-L+\mathrm{gamma}g$
$\mathrm{C\_0}=\mathrm{k2}\mathrm{C\_1}=\sqrt{\frac{\mathrm{k2}}{\mathrm{k4}}}\mathrm{C\_2}=\sqrt{\frac{\mathrm{k2}}{\mathrm{k4}}}\mathrm{KP}=KPP=0.735+0.1563\sin \left(\frac{2\times 3.141592653\mathrm{time}}{24\times 3600}\right)+0.3127\left|\sin \left(\frac{3.141592653\mathrm{time}}{24\times 3600}\right)\right|$