/*
 * Blood HbO2 and HbCO2 Dissociation Curves at Varies O2, CO2,
 * pH, 2,3-DPG and Temperature Levels
 * 
 * Model Status
 * 
 * This particular CellML description of the Dash-Bassingthwaighte
 * model is a reduced version of the complete model. It requires
 * extensive curation as it currently cannot be solved in either
 * OpenCell or COR. Since this model was translated the authors
 * have published an updated, corrected model (corrected and republished
 * in: Ann Biomed Eng. 2010 Apr;38(4):1683-701). We intend to use
 * this new model as the basis for the next translation.
 * 
 * Model Structure
 * 
 * ABSTRACT: New mathematical model equations for O2 and CO2 saturations
 * of hemoglobin (S(HbO2) and S(HbCO2)) are developed here from
 * the equilibrium binding of O2 and CO2 with hemoglobin inside
 * RBCs. They are in the form of an invertible Hill-type equation
 * with the apparent Hill coefficients K(HbO2) and K(HbCO2) in
 * the expressions for S(HbO2) and S(HbCO2) dependent on the levels
 * of O2 and CO2 partial pressures (P(O2) and P(CO2), pH, 2,3-DPG
 * concentration, and temperature in blood. The invertibility of
 * these new equations allows P(O2) and P(CO2) to be computed efficiently
 * from S(HbO2) and S(Hbco2) and vice-versa. The oxyhemoglobin
 * (HbO2) and carbamino-hemoglobin (HbCO2) dissociation curves
 * computed from these equations are in good agreement with the
 * published experimental and theoretical curves in the literature.
 * The model solutions describe that, at standard physiological
 * conditions, the hemoglobin is about 97.2% saturated by O2 and
 * the amino group of hemoglobin is about 13.1% saturated by CO2.
 * The O2 and CO2 content in whole blood are also calculated here
 * from the gas solubilities, hematocrits, and the new formulas
 * for S(HbO2) and S(HbCO2). Because of the mathematical simplicity
 * and invertibility, these new formulas can be conveniently used
 * in the modeling of simultaneous transport and exchange of O2
 * and CO2 in the alveoli-blood and blood-tissue exchange systems.
 * 
 * The original paper reference is cited below:
 * 
 * Blood HbO2 and HbCO2 dissociation curves at varied O2, CO2,
 * pH, 2,3-DPG and temperature levels, Ranjan K. Dash and James
 * B. Bassingthwaighte, 2004, Annals of Biomedical Engineering,
 * 32, 1676-1693. PubMed ID: 15682524
 */

import nsrunit;
// Warning: unit conversion turned off due to unit errors in 1 equation(s)
unit conversion off;
//Warning:  the unit 'celsius' is not well defined.
//  It may mean 'distance from 0 degrees C' in some contexts,  and 'distance in C degrees' in others.
//  We assume this model meant the latter, and have converted the unit to the equivalent but better-defined 'kelvin' instead.
// unit kelvin predefined
unit mmHg=1.3332237E2 kilogram^1*meter^(-1)*second^(-2);
// unit molar predefined
unit per_molar=.001 meter^3*mole^(-1);
// unit nanomolar predefined
// unit micromolar predefined
// unit millimolar predefined
unit ml_ml=1  dimensionless;
unit M_mmHg=7.5006168 kilogram^(-1)*meter^(-2)*second^2*mole^1;
unit M_mmHg_ml_ml=7.5006168 kilogram^(-1)*meter^(-2)*second^2*mole^1;
unit pH = fundamental;
unit celsius_1=1 kelvin^(-1);
unit celsius_2=1 kelvin^(-2);

math main {
	real SHbO2 dimensionless;
	real KHbO2 per_molar;
	real O2 molar;
	real SHbCO2 dimensionless;
	real KHbCO2 per_molar;
	real CO2 molar;
	real Hrbc molar;
	real K2 per_molar;
	K2=29.5;
	real K2_ molar;
	K2_=1E-6;
	real K3 per_molar;
	K3=25.1;
	real K3_ molar;
	K3_=1E-6;
	real K4 per_molar;
	real K5_ molar;
	K5_=2.63E-8;
	real K6_ molar;
	K6_=1.91E-8;
	real O2_S micromolar;
	O2_S=146.0;
	real H_S nanomolar;
	H_S=57.5;
	real n1 dimensionless;
	n1=1.06;
	real n2 dimensionless;
	n2=0.12;
	real CO2_S millimolar;
	CO2_S=1.31;
	real K4_ per_molar;
	K4_=202123.0;
	real n0 dimensionless;
	n0=1.7;
	real alpha_O2 M_mmHg;
	real PO2 mmHg;
	PO2=100.0;
	real alpha_CO2 M_mmHg;
	real PCO2 mmHg;
	PCO2=40.0;
	real Wpl ml_ml;
	Wpl=0.94;
	real T kelvin;
	T=37.0;
	real Rrbc dimensionless;
	Rrbc=0.69;
	real Hpl molar;
	real pHpl pH;
	pHpl=7.24;

	// <component name="SHbO2">
	SHbO2=(KHbO2*O2/(1+KHbO2*O2));

	// <component name="SHbCO2">
	SHbCO2=(KHbCO2*CO2/(1+KHbCO2*CO2));

	// <component name="KHbO2">
	KHbO2=(K4*(K3*CO2*(1+K3_/Hrbc)+(1+Hrbc/K6_))/(K2*CO2*(1+K2_/Hrbc)+(1+Hrbc/K5_)));

	// <component name="KHbCO2">
	KHbCO2=((K2*(1+K2_/Hrbc)+K3*K4*(1+K3_/Hrbc)*O2)/(1+Hrbc/K5_+K4*(1+Hrbc/K6_)*O2));

	// <component name="K4">
	K4=(K4_*(O2/O2_S)^n0*(Hrbc/H_S)^((-1)*n1)*(CO2/CO2_S)^((-1)*n2));

	// <component name="O2">
	O2=(alpha_O2*PO2);

	// <component name="CO2">
	CO2=(alpha_CO2*PCO2);

	// <component name="alpha_O2">
	alpha_O2=((1.37-(.0137 celsius_1)*(T-(37 kelvin))+(5.8E-4 celsius_2)*(T-(37 kelvin))^2)*((1E-6 M_mmHg_ml_ml)/Wpl));

	// <component name="alpha_CO2">
	alpha_CO2=((3.07-(.057 celsius_1)*(T-(37 kelvin))+(.002 celsius_2)*(T-(37 kelvin))^2)*((9.999999999999999E-6 M_mmHg_ml_ml)/Wpl));

	// <component name="model_parameters">
	Hpl=((10 molar)^((-1)*pHpl));
	Hrbc=(Hpl/Rrbc);
}