/*
 * 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;

	// <component name="environment">

	// <component name="R">
	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);

	// <component name="L">
	L:time=(rL*R-dL*L);

	// <component name="T">
	T:time=(rT*L-dT*T);
}