Modelling fluctuation phenomena in the plasma cortisol secretion system in normal man
Catherine
Lloyd
Auckland Bioengineering Institute, The University of Auckland
Model Status
This CellML model runs in OpenCell and COR, and the units are consistent. The model is an accurate representation of the published model (equations 1a-1c), and runs to recreate the published results (figure 4). Parameter values were taken from the legend of figure 4.
Model Structure
ABSTRACT: A system of three non-linear differential equations with exponential feedback terms is proposed to model the self-regulating cortisol secretion system and explain the fluctuation patterns observed in clinical data. It is shown that the model exhibits bifurcation and chaos patterns for a certain range of parametric values. This helps us to explain clinical observations and characterize different dynamic behaviors of the self-regulative system.
The original paper reference is cited below:
Modelling fluctuation phenomena in the plasma cortisol secretion system in normal man, Yongwimon Lenbury and Pariwatana Pacheenburawana, 1991, BioSystems
, 26, 117-125. PubMed ID: 1668715
model diagram
Schematic diagram of the self-regulatory system for corticol secretion. CRH represents corticotropin-releasing hormone, ACTH is adrenocorticotropic hormone, and F represents cortisol. The red lines represent positive feedback pathways, while the blue lines represent negative feedback loops.
cortisol
endocrine
keyword
The University of Auckland, Auckland Bioengineering Institute
Catherine
Lloyd
May
1991-00-00 00:00
Modelling fluctuation phenomena in the plasma cortisol secretion system in normal man
26
117
125
Pariwatana
Pacheenburawana
Catherine Lloyd
BioSystems
cortisol
z
CRH
corticotropin releasing hormone
x
ACTH
adrenocorticotropic hormone
y
I've checked the model in COR and I've made all the units (except time) dimensionless to be true to the paper. I've also replaced the stimulus equation with a cosine function. This is the original stimulus. The equation I'd included in the previous model was taken from a theoretical study. I think the CellML model can recreate the original model's results. I can't be 100% sure though as the figures published in the paper are based on altering the model in a matrix form... and I can't set those initial conditions because they're not mentioned in the core model.
1668715
Catherine Lloyd
I've checked the model in COR and I've made all the units (except time) dimensionless to be true to the paper. I've also replaced the stimulus equation with a cosine function. This is the original stimulus. The equation I'd included in the previous model was taken from a theoretical study. I think the CellML model can recreate the original model's results. I can't be 100% sure though as the figures published in the paper are based on altering the model in a matrix form... and I can't set those initial conditions because they're not mentioned in the core model.
2007-09-03T08:45:42+12:00
This is the CellML description of Lenbury and Pacheenburawana's 1991 mathematical model of plasma cortisol secretion fluctuations.
c.lloyd@auckland.ac.nz
Yongwimon
Lenbury
The University of Auckland
Auckland Bioengineering Institute
Lenbury and Pacheenburawana's 1991 mathematical model of plasma cortisol secretion fluctuations.
cortisol
2007-06-18T00:00:00+00:00
Catherine
Lloyd
May
$\frac{d x}{d \mathrm{time}}=\mathrm{alpha}e^{a(1-z^{2})+b(1-y^{2})}+D\cos (\mathrm{omega}\mathrm{time})-\mathrm{alpha}x$
$\frac{d y}{d \mathrm{time}}=\mathrm{beta}xe^{b(1-z^{2})}-\mathrm{beta}y$
$\frac{d z}{d \mathrm{time}}=\mathrm{gamma}y-\mathrm{gamma}z$