/*
* A model for the control of testosterone secretion
*
* Model Status
*
* This CellML model runs in OpenCell and can reproduce one oscillation
* (which is true to the published results) but is unable to produce
* further oscillations. This is probably because there are time
* delays in the origianl model which as yet can not be described
* in CellML. The units have been checked and they are consistent
* with just small equivalencies in pico and nano grams per ml.
* The CellML model also runs in COR but the long duration of the
* simulation is not ideal for this tool.
*
* ValidateCellML verifies this model as valid CellML, although
* unit inconsistencies are detected.
*
* Model Structure
*
* ABSTRACT: We produce here a model to explain the control of
* testosterone secretion. In this model the hypothalamic secretion
* of the hormone LHRH (luteinizing hormone releasing hormone)
* is controlled by a combination of local testosterone concentration
* and of the local concentration of the pituitary hormone LH (luteinizing
* hormone). Since LHRH stimulates the release of LH, and LH in
* turn stimulates the release of testosterone, the three hormones
* constitute a three-component "feedback" network. We show how
* this model is able to account for the pulsatility of the release
* of these three hormones. Furthermore, the model is consistent
* with results obtained from a wide range of experimental manipulations
* of the system. For example, it accounts for the changes observed
* in hormone release patterns after castration. In particular,
* it follows that no "neural clock", or "neural pulse-generator",
* is required to force the system into pulsatile behaviour.
*
* model diagram
*
* [[Image file: cartwright_1986.png]]
*
* Schematic diagram of the mathematical model representing the
* luteinizing hormone releasing hormone (LHRH), luteinizing hormone
* (LH), and testosterone system. The model has three main components:
* the hypothalamus which secretes LHRH, the pituitary which responds
* to LHRH by secreting LH, and the 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:
*
* A model for the control of testosterone secretion, Mark Cartwright
* and Masud Husain, 1986, Journal of Theoretical Biology 123,
* 239-250. PubMed ID: 3306160
*/
import nsrunit;
unit conversion on;
unit minute=60 second^1;
unit pg_per_ml=1E-9 kilogram^1*meter^(-3);
unit ng_per_ml=1E-6 kilogram^1*meter^(-3);
unit ng_per_ml_min=1.6666667E-8 kilogram^1*meter^(-3)*second^(-1);
unit first_order_rate_constant=.01666667 second^(-1);
math main {
realDomain time minute;
time.min=0;
extern time.max;
extern time.delta;
real R(time) pg_per_ml;
when(time=time.min) R=0.0;
real L_ ng_per_ml;
L_=30.0;
real T_ ng_per_ml;
T_=8.0;
real dR first_order_rate_constant;
dR=0.10;
real rR ng_per_ml_min;
rR=0.1;
real H(time) dimensionless;
real x(time) dimensionless;
real L(time) ng_per_ml;
when(time=time.min) L=10.0;
real T(time) ng_per_ml;
when(time=time.min) T=12.0;
real dL first_order_rate_constant;
dL=0.015;
real rL first_order_rate_constant;
rL=5.0;
real dT first_order_rate_constant;
dT=0.023;
real rT first_order_rate_constant;
rT=0.01;
//
//
R:time=(rR*H-dR*R);
x=(2-(L/L_+T/T_));
H=(if (x<0) 0 else if (x=0) .5 else if (x>0) 1 else 0);
//
L:time=(rL*R-dL*L);
//
T:time=(rT*L-dT*T);
}