Modelling Gonadotropin Regulation during the Menstrual Cycle in Women
Catherine
Lloyd
Auckland Bioengineering Institute, The University of Auckland
Model Status
This CellML model runs in OpenCell to recreate the pubslihed results. The model also runs in COR but due to the time unit being days the model is not ideal for simulation in COR (where the default unit of time is ms). The units have been checked and they are consistent. The LH system (eq 1a-1e) and the FSH system (eq 2a-2e) are both described in this CellML model. Parameter values have been taken from tables 1 and 2 in the original published paper. We were unable to represent the time delays in equations 1c and 2c.
Model Structure
Abstract: Increasing concerns that environmental contaminants may disrupt the endocrine system require development of mathematical tools to predict the potential for such compounds to significantly alter human endocrine function. The endocrine system is largely self-regulating, compensating for moderate changes in dietary phytoestrogens (e.g., in soy products) and normal variations in physiology. However, severe changes in dietary or oral exposures or in health status (e.g., anorexia) , can completely disrupt the menstrual cycle in women. Thus, risk assessment tools should account for normal regulation and its limits. We present a mathematical model for the synthesis and release of luteinizing hormone (LH) and follicle-stimulating hormone (FSH) in women as a function of estrogen, progesterone, and inhibin blood levels. The model reproduces the time courses of LH and FSH during the menstrual cycle and correctly predicts observed effects of administered estrogen and progesterone on LH and FSH during clinical studies. The model should be useful for predicting effects of hormonally active substances, both in the pharmaceutical sciences and in toxicology and risk assessment.
model diagram
Schematic diagram of the mathematical model of luteinizing hormone (LH) and follicle-stimulating hormone (FSH) synthesis and release. Solid arrows represent pathways of synthesis (syn), release into the blood (rel), and clearance from the blood (clear). Dashed arrows represent regulatory pathways, either positive (+) or negative (-), with feedback from estradiol (E2), progesterone (P4), and inhibin (Ih).
The original paper reference is cited below:
A model of gonadotropin regulation during the menstrual cycle in women: qualitative features Paul M. Schlosser and James F. Selgrade, 2000,
Environmental Health Perspectives, 108, 873-881. PubMed ID: 11035997
$\frac{d \mathrm{RP\_LH}}{d \mathrm{time}}=\mathrm{syn\_LH\_E2\_P4}-\mathrm{rel\_LH\_E2\_P4\_RP\_LH}\mathrm{syn\_LH\_E2\_P4}=\frac{\mathrm{V0\_LH}+\frac{\mathrm{V1\_LH}\mathrm{E2\_dE}^{h}}{\mathrm{Km\_LH}^{h}+\mathrm{E2\_dE}^{h}}}{1.0+\frac{\mathrm{P4\_dP}}{\mathrm{Ki\_LHP}}}\mathrm{rel\_LH\_E2\_P4\_RP\_LH}=\frac{\mathrm{kLH\_rel}(1.0+\mathrm{CLH\_P}\mathrm{P4})\mathrm{RP\_LH}}{1.0+\mathrm{CLH\_E}\mathrm{E2}}$
$\frac{d \mathrm{LH}}{d \mathrm{time}}=\frac{\mathrm{rel\_LH\_E2\_P4\_RP\_LH}}{\mathrm{v\_dis}}-\mathrm{clear\_LH}\mathrm{clear\_LH}=\mathrm{kLH\_cl}\mathrm{LH}$
$\frac{d \mathrm{RP\_FSH}}{d \mathrm{time}}=\mathrm{syn\_FSH\_Ih}-\mathrm{rel\_FSH\_E2\_P4\_RP\_FSH}\mathrm{syn\_FSH\_Ih}=\frac{\mathrm{V\_FSH}}{1.0+\frac{\mathrm{Ih\_dIh}}{\mathrm{Ki\_FSH\_Ih}}}\mathrm{rel\_FSH\_E2\_P4\_RP\_FSH}=\frac{\mathrm{kFSH\_rel}(1.0+\mathrm{CFSH\_P}\mathrm{P4})\mathrm{RP\_FSH}}{1.0+\mathrm{CFSH\_E}\mathrm{E2}^{2.0}}$
$\frac{d \mathrm{FSH}}{d \mathrm{time}}=\frac{\mathrm{rel\_FSH\_E2\_P4\_RP\_FSH}}{\mathrm{v\_dis}}-\mathrm{clear\_FSH}\mathrm{clear\_FSH}=\mathrm{kFSH\_cl}\mathrm{FSH}$
$\mathrm{E2}=300.0-\frac{240.0(\mathrm{time}+1.0)^{2.0}}{3.0+(\mathrm{time}+1.0)^{2.0}}+90.0e^{-\left(\frac{(\mathrm{time}-8.0)^{2.0}}{10.0}\right)}$
$\mathrm{E2\_dE}=300.0-\frac{240.0(\mathrm{time}+1.0-\mathrm{dE})^{2.0}}{3.0+(\mathrm{time}+1.0-\mathrm{dE})^{2.0}}+90.0e^{-\left(\frac{(\mathrm{time}-\mathrm{dE}+8.0)^{2.0}}{10.0}\right)}$
$\mathrm{P4}=52.0e^{-\left(\frac{(\mathrm{time}-7.0)^{2.0}}{18.0}\right)}$
$\mathrm{P4\_dP}=52.0e^{-\left(\frac{(\mathrm{time}-\mathrm{dP}+7.0)^{2.0}}{18.0}\right)}$
$\mathrm{Ih}=300.0+1330.0e^{-\left(\frac{(\mathrm{time}-7.0)^{2.0}}{19.0}\right)}$
$\mathrm{Ih\_dIh}=300.0+1330.0e^{-\left(\frac{(\mathrm{time}-7.0+\mathrm{dIh})^{2.0}}{19.0}\right)}$
endocrine
pituitary
hypothalamus
gonadotropin
Schlosser and Selgrade's 2000 mathematical model of gonadotropin regulation during the menstrual cycle in women.
hypothalamus
pituitary
The University of Auckland, Auckland Bioengineering Institute
2007-06-20T00:00:00+00:00
estradiol concentration at a time with a delay
E2_dE
2000-00-00 00:00
Catherine Lloyd
Catherine
Lloyd
May
Catherine Lloyd
keyword
2007-09-05T15:07:12+12:00
c.lloyd@auckland.ac.nz
inhibin
Ih
The University of Auckland
Auckland Bioengineering Institute
This is the CellML description of Schlosser and Selgrade's 2000 mathematical model of gonadotropin regulation during the menstrual cycle in women.
Paul
Schlosser
M
blood concentration of luteinizing hormone
LH
11035997
progesterone concentration at a time with a delay
P4_dP
inhibin concentration at a time with a delay
Ih_dIh
blood concentration of follicle-stimulating hormone
FSH
Catherine
Lloyd
May
estradiol
E2
A model of gonadotropin regulation during the menstrual cycle in women: qualitative features
108
873
881
The units are consistent and the model runs in PCEnv to give the published results - one note: to recreate all the published results will require different variants of the model (or CellML1.1 to import different initial conditions and parameter values) because the conditions for each result were different.
I've run the model in COR and in the process corrected all the units such that they are now consistent. I also altered a couple of the equations - in this case CellML could handle the time delays because they were fixed - and the model now runs in PCEnv to give the published results.
releasable pool of luteinizing hormone
RP_LH
Environmental Health Perspectives
progesterone
P4
releasable pool of follicle-stimulating hormone
RP_FSH
James
Selgrade
F