Hypothalamic regulation of pituitary secretion of luteinizing hormone. II. Feedback control of gonadotropin secretion
Catherine
Lloyd
Auckland Bioengineering Institute, The University of Auckland
Model Status
This model is valid CellML and runs in PCEnv, OpenCell and COR. The units have been checked and are consistent. The model itself runs to reproduce published results within a margin of error, which was judged to be acceptable, as the model authors explicitly state that the figures reproduced in the paper are only representative of the actual results.
Model Structure
ABSTRACT: A general mathematical model describing the biochemical interactions of the hormones luteinizing hormone releasing hormone (LHRH), luteinizing hormone (LH) and testosterone (T) in the male is presented. The model structure consists of a negative feedback system of three ordinary differential equations, in which the qualitative behavior is either a stable constant equilibrium solution or oscillatory solutions. A specific realization of the model is used to describe the experimental observations of pulsatile hormone release, its experimental suppression, the onset of puberty, the effects of castration, and several other qualitative and quantitative results. This model is presented as a first step in understanding the physicochemical interactions of the hypothalamic-pituitary-gonadal axis.
model diagram
Schematic diagram of the mathematical model representing the male hypothalamic-pituitary-gonadal system. The model has three main components: the hypothalamus which secretes luteinizing hormone releasing hormone (LHRH), the pituitary which responds to LHRH by secreting luteinizing hormone (LH), and the gonads (or testes) which, in responds to LH, secrete testosterone. Finally, LH and testosterone feedback on the hypothalamus to regulate LHRH secretion.
The original paper reference is cited below:
Hypothalamic regulation of pituitary secretion of luteinizing hormone. II. Feedback control of gonadotropin secretion, William R. Smith, 1980,
Bulletin of Mathematical Biology, 42, 57-78. PubMed ID: 6986927
R
LHRH
luteinizing hormone releasing hormone
L
LH
luteinizing hormone
T
testosterone
testis
testosterone
luteinizing hormone
endocrine
hypothalamus
pituitary
I've added initial values and have checked and corrected the units such that they are now consistent.
The University of Auckland, Auckland Bioengineering Institute
6986927
2007-07-18T00:00:00+00:00
keyword
2007-09-06T09:34:21+12:00
This model runs in PCEnv to replicate the published results. The units have been checked and are consistent.
c.lloyd@auckland.ac.nz
Catherine
Lloyd
May
1980-00-00 00:00
Catherine
Lloyd
May
Bulletin of Mathematical Biology
This is a CellML description of Smith's 1980 mathematical model for the hypothalamic regulation of pituitary secretion of luteinizing hormone - feedback control of gonadotropin secretion.
William
Smith
R
Catherine Lloyd
Hypothalamic regulation of pituitary secretion of luteinizing hormone. II. Feedback control of gonadotropin secretion
42
57
78
Catherine Lloyd
Smith's 1980 mathematical model for the hypothalamic regulation of pituitary secretion of luteinizing hormone - feedback control of gonadotropin secretion.
The University of Auckland
Auckland Bioengineering Institute
$\frac{d R}{d \mathrm{time}}=(c-hT)(1-H)-\mathrm{b1}Rx=T-\frac{c}{h}H=\begin{cases}1 & \text{if $x> 0$}\\ 0 & \text{otherwise}\end{cases}$
$\frac{d L}{d \mathrm{time}}=\mathrm{g1}R-\mathrm{b2}L$
$\frac{d T}{d \mathrm{time}}=\mathrm{g2}L-\mathrm{b3}T$