/*
 * Guyton Model: red_cells_and_viscosity
 * 
 * Model Status
 * 
 * This CellML model has been validated. 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). This may effect the transient behaviour
 * of the model, however the steady-state behaviour would remain
 * the same. The equations in this file and the steady-state output
 * from the model conform to the results from the MODSIM program.
 * 
 * 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 how the red blood cell
 * volume is considered to be controlled by two principal factors
 * that control the production of erythropoietin: (1) the arterial
 * blood oxygen saturation (OSA) and renal function as determined
 * by renal blood flow (RFN), and (2) the fraction (REK) of the
 * renal mass that is functional.
 * 
 * model diagram
 * 
 * [[Image file: full_model.png]]
 * 
 * A systems analysis diagram for the full Guyton model describing
 * circulation regulation.
 * 
 * model diagram
 * 
 * [[Image file: red_cells.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 per_minute=.01666667 second^(-1);
//Warning:  unit mmHg_ renamed from mmHg, as the latter is predefined in JSim with different fundamental units.
unit mmHg_=133.322 kilogram^1*meter^(-1)*second^(-2);
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);
unit L_per_minute_per_mmHg=1.2501063E-7 kilogram^(-1)*meter^4*second^1;

math main {
	realDomain time minute;
	time.min=0;
	extern time.max;
	extern time.delta;
	real VP litre;
	VP=3.00449;
	real VRC(time) litre;
	when(time=time.min) VRC=2.00439;
	real HM(time) dimensionless;
	real HM1(time) dimensionless;
	real VB(time) litre;
	real VIE(time) dimensionless;
	real HMK dimensionless;
	HMK=90;
	real HKM dimensionless;
	HKM=0.53333;
	real VIM(time) dimensionless;
	real VIB(time) dimensionless;
	real HM7(time) mmHg_;
	real PO2AMB mmHg_;
	PO2AMB=150;
	real HM6 mmHg_;
	HM6=1850;
	real PO2AM1 mmHg_;
	real HM3(time) mmHg_;
	real HM4 mmHg_;
	real HM5(time) mmHg_;
	real RC1(time) L_per_minute;
	real HM8 L_per_minute_per_mmHg;
	HM8=4.714e-08;
	real REK dimensionless;
	REK=1;
	real RC2(time) L_per_minute;
	real RKC per_minute;
	RKC=5.8e-06;
	real TRRBC L_per_minute;
	TRRBC=0;
	real RCD(time) L_per_minute;

	// <component name="environment">

	// <component name="red_cells_and_viscosity">

	// <component name="blood_viscosity_calculations">

	// <component name="hematocrit_fraction">
	VB=(VP+VRC);
	HM1=(VRC/VB);
	HM=(100*HM1);

	// <component name="viscosity_due_to_RBCs">
	VIE=(HM/((HMK-HM)*HKM));

	// <component name="blood_viscosity">
	VIB=(VIE+1.5);
	VIM=(.3333*VIB);

	// <component name="RBC_formation_and_destruction">

	// <component name="oxygen_stimulation">
	PO2AM1=(if (PO2AMB>(80 mmHg_)) (80 mmHg_) else PO2AMB);
	HM3=((PO2AM1-(40 mmHg_))*HM);
	HM4=(PO2AMB-(40 mmHg_));
	HM5=(if ((HM3+HM4)<(0 mmHg_)) (0 mmHg_) else HM3+HM4);
	HM7=(HM6-HM5);

	// <component name="RBC_production">
	RC1=(if ((HM7*HM8*REK+(5E-6 L_per_minute))<(0 L_per_minute)) (0 L_per_minute) else HM7*HM8*REK+(5E-6 L_per_minute));

	// <component name="RBC_destruction">
	RC2=(VRC*RKC*VIM);

	// <component name="RBC_volume">
	RCD=(RC1-RC2+TRRBC);
	VRC:time=RCD;

	// <component name="parameter_values">
}