/*
 * Guyton Model: Electrolytes
 * 
 * Model Status
 * 
 * This CellML model has not been validated. The equations in this
 * file may contain errors and the output from the model may not
 * conform to the results from the MODSIM program. Due to the differences
 * between procedural code (in this case C-code) and declarative
 * languages (CellML), some aspects of the original model were
 * not able to be encapsulated by the CellML model (such as the
 * damping of variables). Work is underway to fix these omissions
 * and validate the CellML model. We also anticipate that many
 * of these problems will be fixed when the CellML 1.0 models are
 * combined in a CellML 1.1 format.
 * 
 * Model Structure
 * 
 * Arthur Guyton (1919-2003) was an American physiologist who became
 * famous for his 1950s experiments in which he studied the physiology
 * of cardiac output and its relationship with the peripheral circulation.
 * The results of these experiments challenged the conventional
 * wisdom that it was the heart itself that controlled cardiac
 * output. Instead Guyton demonstrated that it was the need of
 * the body tissues for oxygen which was the real regulator of
 * cardiac output. The "Guyton Curves" describe the relationship
 * between right atrial pressures and cardiac output, and they
 * form a foundation for understanding the physiology of circulation.
 * 
 * The Guyton model of fluid, electrolyte, and circulatory regulation
 * is an extensive mathematical model of human circulatory physiology,
 * capable of simulating a variety of experimental conditions,
 * and contains a number of linked subsystems relating to circulation
 * and its neuroendocrine control.
 * 
 * This is a CellML translation of the Guyton model of the regulation
 * of the circulatory system. The complete model consists of separate
 * modules each of which characterise a separate physiological
 * subsystems. The Circulation Dynamics is the primary system,
 * to which other modules/blocks are connected. The other modules
 * characterise the dynamics of the kidney, electrolytes and cell
 * water, thirst and drinking, hormone regulation, autonomic regulation,
 * cardiovascular system etc, and these feedback on the central
 * circulation model. The CellML code in these modules is based
 * on the C code from the programme C-MODSIM created by Dr Jean-Pierre
 * Montani.
 * 
 * This particular CellML model describes the extracellular and
 * intracellular fluid electrolytes and volumes.
 * 
 * model diagram
 * 
 * [[Image file: full_model.png]]
 * 
 * A systems analysis diagram for the full Guyton model describing
 * circulation regulation.
 * 
 * model diagram
 * 
 * [[Image file: electrolytes.png]]
 * 
 * A schematic diagram of the components and processes described
 * in the current CellML model.
 * 
 * There are several publications referring to the Guyton model.
 * One of these papers is cited below:
 * 
 * Circulation: Overall Regulation, A.C. Guyton, T.G. Coleman,
 * and H.J. Granger, 1972, Annual Review of Physiology , 34, 13-44.
 * PubMed ID: 4334846
 */

import nsrunit;
unit conversion on;
unit minute=60 second^1;
unit monovalent_mEq=.001 mole^1;
unit monovalent_mEq_per_minute=1.6666667E-5 second^(-1)*mole^1;
unit monovalent_mEq_per_litre=1 meter^(-3)*mole^1;
unit monovalent_mEq_per_litre_per_minute=.01666667 meter^(-3)*second^(-1)*mole^1;
unit litre2_per_monovalent_mEq_per_minute=1.6666667E-5 meter^6*second^(-1)*mole^(-1);
unit L_per_minute=1.6666667E-5 meter^3*second^(-1);

math main {
	realDomain time minute;
	time.min=0;
	extern time.max;
	extern time.delta;
	real AMK dimensionless;
	AMK=1.037;
	real TVD L_per_minute;
	TVD=0.000980838;
	real NOD monovalent_mEq_per_minute;
	NOD=0.0959449;
	real STH dimensionless;
	STH=0.977181;
	real KOD monovalent_mEq_per_minute;
	KOD=0.0804374;
	real VUD L_per_minute;
	VUD=0.000989;
	real VEC(time) litre;
	real CNA(time) monovalent_mEq_per_litre;
	real NID monovalent_mEq_per_minute;
	NID=0.1;
	real TRPL L_per_minute;
	TRPL=0;
	real NED monovalent_mEq_per_minute;
	real NAE(time) monovalent_mEq;
	when(time=time.min) NAE=2109.91;
	real AMK1 dimensionless;
	real ALCLK dimensionless;
	ALCLK=0.3;
	real CKE(time) monovalent_mEq_per_litre;
	real KE(time) monovalent_mEq;
	real KTOT(time) monovalent_mEq;
	when(time=time.min) KTOT=3622.54;
	real KID monovalent_mEq_per_minute;
	KID=0.08;
	real KTOTD monovalent_mEq_per_minute;
	real VIC(time) litre;
	when(time=time.min) VIC=25.0404;
	real CKI(time) monovalent_mEq_per_litre;
	real KI(time) monovalent_mEq;
	real VID(time) L_per_minute;
	real VIDML litre2_per_monovalent_mEq_per_minute;
	VIDML=0.01;
	real CCD(time) monovalent_mEq_per_litre;
	real VTW(time) litre;
	when(time=time.min) VTW=39.8952;

	// <component name="environment">

	// <component name="electrolytes">

	// <component name="extracellular_Na_concentration">
	NED=(NID*STH-NOD+TRPL*(142 monovalent_mEq_per_litre));
	NAE:time=NED;
	CNA=(NAE/VEC);

	// <component name="aldosterone_effect_on_cellular_K_distribution">
	AMK1=((AMK-1)*ALCLK+1);

	// <component name="extracellular_K_concentration">
	KTOTD=(KID-KOD);
	KTOT:time=KTOTD;
	KE=((KTOT-(3E3 monovalent_mEq))/(AMK1*9.3333));
	CKE=(KE/VEC);

	// <component name="intracellular_K_concentration">
	KI=(KTOT-KE);
	CKI=(KI/VIC);

	// <component name="intracellular_fluid_volume">
	CCD=(CKI-CNA);
	VID=(CCD*VIDML);
	VIC:time=VID;

	// <component name="total_body_water">
	VTW:time=(TVD-VUD);

	// <component name="extracellular_fluid_volume">
	VEC=(VTW-VIC);

	// <component name="parameter_values">
}