Modelling the Hypothalamic Control of Growth Hormone Secretion
Catherine
Lloyd
Auckland Bioengineering Institute, The University of Auckland
Model Status
This particular CellML model describes the pituitary model of the published article. The units have been checked and are consistent and the model runs in both OpenCell and COR to replicate the published results (as shown in figure 3B of the paper).
Model Structure
Abstract: Here, we construct a mathematical model of the hypothalamic systems that control the secretion of growth hormone (GH). The work extends a recent model of the pituitary GH system, adding representations of the hypothalamic GH-releasing hormone (GHRH) and somatostatin neurones, each modelled as a single synchronised unit. An unpatterned stochastic input drives the GHRH neurones generating pulses of GHRH release that trigger GH pulses. Delayed feedback from GH results in increased somatostatin release, which inhibits both GH secretion and GHRH release, producing an overall pattern of 3-h pulses of GH secretion that is very similar to the secretory profile observed in male rats. Rather than directly stimulating somatostatin release, GH feedback triggers a priming effect, increasing releasable stores of somatostatin. Varying this priming effect to reduce the effect of GH can reproduce the less pulsatile form of GH release observed in the female rat. The model behaviour is tested by comparison with experimental observations with a range of different experimental protocols involving GHRH injections and somatostatin and GH infusion.
The complete original paper reference is cited below:
Modelling the hypothalamic control of growth hormone secretion, D. J. MacGregor and G. Leng, 2005, Journal of Neuroendocrinology, volume 17, 788-803. PubMed ID: 16280026
model diagram
A schematic diagram of the different components and connections in the growth hormone secretory system. Somatostatin (SOM) inhibits the secretion of both growth hormone-releasing hormone (GHRH) and growth hormone (GH). After a delay, GH feeds back to prime the pool of releasable somatostatin, resulting in the bulk release of somatostatin, which in turn allows further GHRH release and and another burst of GH.
$\frac{d r}{d \mathrm{time}}=\mathrm{Ir}-\mathrm{k6}r\mathrm{Ir}=\begin{cases}0.0 & \text{if $(\mathrm{time}\ge 0.0)\land (\mathrm{time}\le 90.0)$}\\ 10.0 & \text{if $(\mathrm{time}\ge 91.0)\land (\mathrm{time}\le 92.0)$}\\ 0.0 & \text{if $(\mathrm{time}\ge 93.0)\land (\mathrm{time}\le 113.0)$}\\ 10.0 & \text{if $(\mathrm{time}\ge 114.0)\land (\mathrm{time}\le 115.0)$}\\ 0.0 & \text{if $(\mathrm{time}\ge 116.0)\land (\mathrm{time}\le 136.0)$}\\ 10.0 & \text{if $(\mathrm{time}\ge 137.0)\land (\mathrm{time}\le 138.0)$}\\ 0.0 & \text{if $(\mathrm{time}\ge 139.0)\land (\mathrm{time}\le 159.0)$}\\ 10.0 & \text{if $(\mathrm{time}\ge 160.0)\land (\mathrm{time}\le 161.0)$}\\ 0.0 & \text{if $(\mathrm{time}\ge 162.0)\land (\mathrm{time}\le 252.0)$}\\ 10.0 & \text{if $(\mathrm{time}\ge 253.0)\land (\mathrm{time}\le 254.0)$}\\ 0.0 & \text{if $(\mathrm{time}\ge 255.0)\land (\mathrm{time}\le 275.0)$}\\ 10.0 & \text{if $(\mathrm{time}\ge 276.0)\land (\mathrm{time}\le 277.0)$}\\ 0.0 & \text{if $(\mathrm{time}\ge 278.0)\land (\mathrm{time}\le 298.0)$}\\ 10.0 & \text{if $(\mathrm{time}\ge 299.0)\land (\mathrm{time}\le 300.0)$}\\ 0.0 & \text{if $(\mathrm{time}\ge 301.0)\land (\mathrm{time}\le 321.0)$}\\ 10.0 & \text{if $(\mathrm{time}\ge 322.0)\land (\mathrm{time}\le 323.0)$}\\ 0.0 & \text{otherwise}\end{cases}$
$\frac{d s}{d \mathrm{time}}=\mathrm{Is}-\mathrm{k7}s$
$\frac{d f}{d \mathrm{time}}=-(\mathrm{k1}(r+c)f)+(\mathrm{k2}+\mathrm{k3}\mathrm{phi\_b\_s})(1.0-f)\mathrm{phi\_b\_s}=\frac{1.0}{1.0+e^{\frac{-(\lg (1.0s)-\mathrm{sb})}{\mathrm{delta\_b}}}}$
$\frac{d h}{d \mathrm{time}}=\mathrm{j1}((\mathrm{k4}+\mathrm{k5}(1.0-\mathrm{phi\_r\_s}))(r+c)f-\mathrm{k8}h)\mathrm{phi\_r\_s}=\frac{1.0}{1.0+e^{\frac{-(\lg (1.0s)-\mathrm{sr})}{\mathrm{delta\_r}}}}$
$\mathrm{Is}=\begin{cases}10.0 & \text{if $(\mathrm{time}> 0.0)\land (\mathrm{time}\le 90.0)$}\\ 0.0 & \text{if $(\mathrm{time}> 90.0)\land (\mathrm{time}\le 180.0)$}\\ 10.0 & \text{if $(\mathrm{time}> 180.0)\land (\mathrm{time}\le 270.0)$}\\ 0.0 & \text{if $(\mathrm{time}> 270.0)\land (\mathrm{time}\le 360.0)$}\\ 0.0 & \text{otherwise}\end{cases}$
endocrine
somatostatin
hypothalamus
growth hormone releasing hormone
growth hormone
Modelling the hypothalamic control of growth hormone secretion: pituitary model only
The University of Auckland, Auckland Bioengineering Institute
The University of Auckland
Auckland Bioengineering Institute
Journal of Neuroendocrinology
The model runs in PCEnv to replicate the results in the published paper. In particular the initial conditions have been set to the same as those which generate the results for figure 3B in the published paper.
2005-00-00 00:00
Catherine
Lloyd
May
keyword
density of free GHRH receptors
f
MacGregor and Leng's 2005 mathematical model of hypothalamic control of growth hormone secretion.
hypothalamus
GH
growth hormone
h
GHRH
growth hormone releasing hormone
r
endogenous somatostatin
s
16280026
c.lloyd@auckland.ac.nz
Modelling the hypothalamic control of growth hormone secretion.
17
788
803
2007-09-04T15:13:18+12:00
Catherine Lloyd
D
MacGregor
J
Checked the model in COR and made all the units consistent. I also reduced the model back to its foundation form (the pituitary part only), and added two complex piecewise equations to simulate the injection of the hormones.
G
Leng
Catherine
Lloyd
May
Catherine Lloyd
This is the CellML description of MacGregor and Leng's 2005 mathematical model of hypothalamic control of growth hormone secretion.
2007-05-28T00:00:00+00:00