/*
 * Guyton Model: Capillary Dynamics
 * 
 * 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 the the movement of fluid
 * and protein through the capillary membrane. It also calculates
 * the volumes of fluid in the free fluid space of the interstitium
 * and in the gel fluid space. It calculates the pressures in both
 * of these fluids as well as the so-called solid tissue pressure
 * caused by the compression of solid elements against other portions
 * of the interstitium. In addition, the quantities of proteins
 * and their concentrations in both the free fluid and the gel
 * fluid are calculated. And, finally, the flow of both fluid and
 * proteins in the lymph system are computed, as well as the overall
 * body protein balance.
 * 
 * model diagram
 * 
 * [[Image file: full_model.png]]
 * 
 * A systems analysis diagram for the full Guyton model describing
 * circulation regulation.
 * 
 * model diagram
 * 
 * [[Image file: capillary_dynamics.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;
// Warning: unit conversion turned off due to unit errors in 2 equation(s)
unit conversion off;
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 per_mmHg=.00750064 kilogram^(-1)*meter^1*second^2;
unit mmHg_L=.133322 kilogram^1*meter^2*second^(-2);
unit per_mmHg2=5.6259564E-5 kilogram^(-2)*meter^2*second^4;
unit mmHg3=2.369766E6 kilogram^3*meter^(-3)*second^(-6);
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 mL=1E-6 meter^3;
unit gram_per_L=1 kilogram^1*meter^(-3);
unit L_mmHg_per_gram=133.322 meter^2*second^(-2);
unit L2_mmHg_per_gram2=133.322 kilogram^(-1)*meter^5*second^(-2);
unit mmHg_minute_per_L=7999320 kilogram^1*meter^(-4)*second^(-1);
unit gram_per_minute=1.6666667E-5 kilogram^1*second^(-1);
unit mL_per_L=.001  dimensionless;
unit mL_per_L_per_mmHg=7.5006376E-6 kilogram^(-1)*meter^1*second^2;
unit mL_per_L_per_minute=1.6666667E-5 second^(-1);
unit mL_per_minute_per_mmHg=1.2501063E-10 kilogram^(-1)*meter^4*second^1;
unit L_mL_per_minute_per_mmHg=1.2501063E-13 kilogram^(-1)*meter^7*second^1;
unit L_per_mL=1E3  dimensionless;
unit mL_per_minute=1.6666667E-8 meter^3*second^(-1);
unit L_per_minute_per_mmHg=1.2501063E-7 kilogram^(-1)*meter^4*second^1;
unit mmHg_per_mL=1.33322E8 kilogram^1*meter^(-4)*second^(-2);

math main {
	realDomain time minute;
	time.min=0;
	extern time.max;
	extern time.delta;
	real VEC litre;
	VEC=14.8548;
	real PPD gram_per_minute;
	PPD=4.4805e-06;
	real RVS mmHg_minute_per_L;
	RVS=2.77751;
	real DFP L_per_minute;
	DFP=-4.078e-07;
	real VPF litre;
	VPF=0.0123238;
	real BFN L_per_minute;
	BFN=2.79521;
	real PVS mmHg_;
	PVS=3.71612;
	real PC mmHg_;
	real PGH(time) mmHg_;
	real PTC(time) mmHg_;
	real PPC(time) mmHg_;
	real VTCPL L_per_minute;
	real VTC(time) L_per_minute;
	real CFC L_per_minute_per_mmHg;
	CFC=0.01167;
	real VTL(time) L_per_minute;
	real VP(time) litre;
	when(time=time.min) VP=3.00449;
	real TRPL L_per_minute;
	TRPL=0;
	real VPD(time) L_per_minute;
	real PRP(time) gram;
	when(time=time.min) PRP=216.243;
	real CPP(time) gram_per_L;
	real DLP(time) gram_per_minute;
	real CPR gram_per_L;
	CPR=40;
	real LPPR gram_per_minute;
	LPPR=0.03;
	real LPDE dimensionless;
	LPDE=8;
	real LPK L_per_minute;
	LPK=2.728e-14;
	real CPPD(time) gram_per_L;
	real PCR mmHg_;
	PCR=15;
	real CPK L_per_minute_per_mmHg;
	CPK=0.000253;
//	Var below replaced by constant in model eqns to satisfy unit correction
//	real PCE dimensionless;
//	PCE=1;
	real PRCD mmHg_;
	real CPI(time) gram_per_L;
	real DPC(time) gram_per_minute;
	real DPL(time) gram_per_minute;
	real DPP(time) gram_per_minute;
	real VTS(time) litre;
	real VTS1(time) litre;
	real TSSLML dimensionless;
	TSSLML=0.15;
	real TSSLTC per_minute;
	TSSLTC=0.005;
	real VTS2(time) litre;
	when(time=time.min) VTS2=0.0;
	real TSP(time) gram;
	when(time=time.min) TSP=279.945;
	real DPI(time) gram_per_minute;
	real PTCPR(time) mmHg_;
	real PTT(time) mmHg_;
	real CHY(time) gram_per_L;
	real HYL gram;
	HYL=60;
	real CMPTSS dimensionless;
	CMPTSS=2;
	real PGHF L_mmHg_per_gram;
	PGHF=-2;
	real POSHYL(time) mmHg_;
	real GCOPF per_mmHg;
	GCOPF=0.8092;
	real VTSF litre;
	VTSF=6;
	real PIF(time) mmHg_;
	real PTS(time) mmHg_;
	real PLDF mmHg_;
	PLDF=4.2;
	real PLD1(time) mmHg_;
	real PLD(time) mmHg_;
	real VG(time) litre;
	real VIF(time) litre;

	// <component name="environment">

	// <component name="capillary_dynamics">

	// <component name="capillary_membrane_dynamics">

	// <component name="capillary_pressure">
	PC=(RVS*1.7*BFN+PVS);

	// <component name="rate_of_fluid_out_of_capillaries">
	VTC=((PC-PPC-PGH+PTC)*CFC+VTCPL);

	// <component name="plasma_volume_and_protein">

	// <component name="plasma_volume">
	VPD=(VTL-VTC-DFP+TRPL);
	VP:time=VPD;

	// <component name="plasma_protein_concentration">
	CPP=(PRP/VP);

	// <component name="protein_destruction_and_formation">
	CPPD=(if ((CPP-CPR)<(0 gram_per_L)) (0 gram_per_L) else CPP-CPR);
	DLP=(LPPR-CPPD^LPDE*LPK);

	// <component name="plasma_leakage">
	PRCD=(if ((PC-PCR)<(0 mmHg_)) (0 mmHg_) else PC-PCR);
	VTCPL=((PRCD*CPK)^1);

	// <component name="protein_influx_into_interstitium">
	DPC=(VTCPL*CPP+(CPP-CPI)*(.00104 L_per_minute));

	// <component name="total_plasma_protein">
	DPP=(DLP+DPL-DPC-PPD+TRPL*(72 gram_per_L));
	PRP:time=DPP;

	// <component name="plasma_colloid_osmotic_pressure">
	PPC=((.28 L_mmHg_per_gram)*CPP+(.0019 L2_mmHg_per_gram2)*CPP^2);

	// <component name="systemic_tissue_fluid_volume_and_protein">

	// <component name="total_systemic_fluid_volume">
	VTS=(VEC-VP-VPF);

	// <component name="interstitial_fluid_volume">
	VTS2:time=(((VTS-(12 litre))*TSSLML-VTS2)*TSSLTC);
	VTS1=(VTS-VTS2);

	// <component name="total_interstitial_protein">
	DPI=(DPC-DPL);
	TSP:time=DPI;

	// <component name="interstitial_protein_concentration">
	CPI=(TSP/VTS);

	// <component name="interstitial_colloid_osmotic_pressure">
	PTCPR=((.28 L_mmHg_per_gram)*CPI+(.0019 L2_mmHg_per_gram2)*CPI^2);

	// <component name="lymph_protein_flow">
	DPL=(CPI*VTL);

	// <component name="tissue_gel_and_fluid_and_lymph_flow">

	// <component name="hydrostatic_pressure_of_tissue_gel">
	CHY=((HYL/VTS/5)^CMPTSS);
	PGH=(CHY*PGHF+PTT);

	// <component name="total_osmotic_pressure_of_tissue_gel">
	POSHYL=(CHY*(2 L_mmHg_per_gram));
	PTC=(POSHYL*PTCPR*GCOPF);

	// <component name="total_tissue_pressure">
	PTT=(((VTS1-VTSF)/VTSF)^2*(1 mmHg_));

	// <component name="interstial_free_fluid_pressure">
	PIF=(PGH-POSHYL);

	// <component name="interstitial_solid_tissue_pressure">
	PTS=(PTT-PIF);

	// <component name="lymph_flow">
	PLD1=(PIF+PLDF-PTT);
	PLD=(if (PLD1>(7 mmHg_)) (7 mmHg_) else PLD1);
	VTL=(if (PLD<(0 mmHg_)) (0 L_per_minute) else PLD*(.02 L_per_minute_per_mmHg));

	// <component name="interstitial_gel_volume">
	VG=(if (VTS<=(0 litre)) (0 litre) else if ((VTS>(0 litre)) and (VTS<=(12 litre))) (0 litre)+(11.4-0)*(VTS-(0 litre))/(12-0) else if ((VTS>(12 litre)) and (VTS<=(15 litre))) (11.4 litre)+(14-11.4)*(VTS-(12 litre))/(15-12) else if ((VTS>(15 litre)) and (VTS<=(18 litre))) (14 litre)+(16-14)*(VTS-(15 litre))/(18-15) else if ((VTS>(18 litre)) and (VTS<=(21 litre))) (16 litre)+(17.3-16)*(VTS-(18 litre))/(21-18) else if ((VTS>(21 litre)) and (VTS<=(24 litre))) (17.3 litre)+(18-17.3)*(VTS-(21 litre))/(24-21) else (18 litre));

	// <component name="interstitial_free_fluid_volume">
	VIF=(VTS-VG);

	// <component name="parameter_values">
}