/*
 * A mathematical model of the regulation system of the secretion
 * of glucocorticoids
 * 
 * Model Status
 * 
 * This CellML model is known to run in OpenCell and COR and can
 * recreate the published results. The units have been checked
 * and are consistent.
 * 
 * Model Structure
 * 
 * ABSTRACT: We propose a mathematical model for the regulation
 * system of the secretion of glucocorticoids and determined the
 * coefficients in the system of ordinary differential equations.
 * Some results are calculated which agree with the experimental
 * results.
 * 
 * The original paper reference is cited below:
 * 
 * A mathematical model of the regulation system of the secretion
 * of glucocorticoids, Liu Bingzheng, Zhao Zhenye and Chen Liansong,
 * 1990, Journal of Biological Physics, volume 17, issue 4, 221-233.
 * 
 * model diagram
 * 
 * [[Image file: bingzheng_1990.png]]
 * 
 * The HPA axis model has three compartments, namely the hypothalamus,
 * pituitary and adrenals. Neural signals trigger CRF secretion
 * by the hypothalamus. In turn, this signals to the pituitary
 * to release ACTH which stimulates the adrenal gland to release
 * cortisol. Cortisol acts on the hypothalamus and the pituitary
 * to have a negative feedback effect on the release of CRH and
 * ACTH respectively.
 */

import nsrunit;
unit conversion on;
unit ng_ml=1E-6 kilogram^1*meter^(-3);
unit pg_ml=1E-9 kilogram^1*meter^(-3);
unit microg_dl=1E-5 kilogram^1*meter^(-3);
unit dl_microg=1E5 kilogram^(-1)*meter^3;
unit minute=60 second^1;
unit first_order_rate_constant=.01666667 second^(-1);
unit ng_ml_min=1.6666667E-8 kilogram^1*meter^(-3)*second^(-1);
unit pg_ml_min=1.6666667E-11 kilogram^1*meter^(-3)*second^(-1);
unit microg_dl_min=1.6666667E-7 kilogram^1*meter^(-3)*second^(-1);
unit mg_min=1.6666667E-8 kilogram^1*second^(-1);

math main {
	realDomain time minute;
	time.min=0;
	extern time.max;
	extern time.delta;
	real X1(time) ng_ml;
	when(time=time.min) X1=10.0;
	real a0 ng_ml_min;
	a0=0.0014;
	real a1 ng_ml_min;
	a1=0.000517;
	real a2 dl_microg;
	a2=0.0164;
	real b1 first_order_rate_constant;
	b1=0.0598;
	real X3(time) microg_dl;
	when(time=time.min) X3=0.0;
	real X2(time) pg_ml;
	when(time=time.min) X2=0.0;
	real a3 pg_ml_min;
	a3=1.38;
	real a4 first_order_rate_constant;
	a4=0.60;
	real a5 dl_microg;
	a5=0.00498;
	real b2 first_order_rate_constant;
	b2=0.053;
	real a6 microg_dl_min;
	a6=0.0084;
	real a7 first_order_rate_constant;
	a7=0.0081;
	real b3 first_order_rate_constant;
	b3=0.0138;

	// <component name="environment">

	// <component name="X1">
	X1:time=(a0+a1/(1+a2*X3)-b1*X1);

	// <component name="X2">
	X2:time=((a3+a4*X1)/(1+a5*X3)-b2*X2);

	// <component name="X3">
	X3:time=(a6+a7*X2-b3*X3);
}