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Abstract
New mathematical model equations for O^sub 2^ and CO^sub 2^ saturations of hemoglobin (S ^sub HbO^ ^sub 2^ and S ^sub HbCO^ ^sub 2^) are developed here from the equilibrium binding of O^sub 2^ and CO^sub 2^ with hemoglobin inside RBCs. They are in the form of an invertible Hill-type equation with the apparent Hill coefficients ^sub K^ ^sub HbO^ ^sub 2^ and K ^sub HbCO^ ^sub 2^ in the expressions for S ^sub HbO^ ^sub 2^ and S ^sub HbCO^ ^sub 2^ dependent on the levels of O^sub 2^ and CO^sub 2^ partial pressures (P^sub O^ ^sub 2^ and P ^sub CO^ ^sub 2^), pH, 2,3-DPG concentration, and temperature in blood. The invertibility of these new equations allows P^sub O^ ^sub 2^ and P ^sub CO^ ^sub 2^ to be computed efficiently from S ^sub HbO^ ^sub 2^ and S ^sub HbCO^ ^sub 2^ and vice-versa. The oxyhemoglobin (HbO^sub 2^) and carbamino-hemoglobin (HbCO^sub 2^) 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 O^sub 2^ and the amino group of hemoglobin is about 13.1% saturated by CO^sub 2^. The O^sub 2^ and CO^sub 2^ content in whole blood are also calculated here from the gas solubilities, hematocrits, and the new formulas for S ^sub HbO^ ^sub 2^ and S ^sub HbCO^ ^sub 2^. Because of the mathematical simplicity and invertibility, these new formulas can be conveniently used in the modeling of simultaneous transport and exchange of O^sub 2^ and CO^sub 2^ in the alveoli-blood and blood-tissue exchange systems.[PUBLICATION ABSTRACT]