Erratum to: Blood HbO2 and HbCO2 dissociation curves at varied O2, CO2, pH, 2,3-DPG and temperature levels

Abstract

New mathematical model equations for O(2) and CO(2) saturations of hemoglobin (S(HbO)(2) and S(HbCO)(2) are developed here from the equilibrium binding of O(2) and CO(2) with hemoglobin inside RBCs. They are in the form of an invertible Hill-type equation with the apparent Hill coefficients KHbO(2) and KHbCO(2) in the expressions for SHbO(2) and SHbCO(2) dependent on the levels of O(2) and CO(2) partial pressures (P(O)(2) and P(CO)(2)), pH, 2,3-DPG concentration, and temperature in blood. The invertibility of these new equations allows PO(2) and PCO(2) to be computed efficiently from S(HbO)(2) and S(HbCO)(2) and vice versa. The oxyhemoglobin (HbO(2)) and carbamino-hemoglobin (HbCO(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(2) and the amino group of hemoglobin is about 13.1% saturated by CO(2). The O(2) and CO(2) content in whole blood are also calculated here from the gas solubilities, hematocrits, and the new formulas for S(HbO)(2) and S(HbCO)(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(2) and CO(2) in the alveoli-blood and blood-tissue exchange systems.

Figure 1

The plot of oxygen P₅₀ (pH_rbc, P_CO2, [DPG]_rbc, T) with one of the variables varying and the other three fixed at their standard physiological values. The P₅₀’s computed from Buerk and Bridges’ model are shown by solid points, from our best-fit polynomial (11) are shown by solid lines, and from Kelman’s empirical equation (12) are shown by dashed lines.

Figure 2

The exponents for Eq. (9); the plots of n₁(pH_{rb c}), n₂(P_CO2), n₃([DPG]_rbc) and n₄(T) with the other three variables fixed at their standard physiological values. These are computed from Eqs. (16a)–(16d) using the estimated value of $K_4^{″}$ and n₀ and the best-fit polynomial (11) for oxygen P₅₀.

Figure 3

The comparison of the HbO₂ dissociation curves computed from our model, Kelman model, and Buerk and Bridges model for different values of pH_rbc with P_CO2, [DPG]_rbc and T fixed at their standard physiological values.

Figure 4

The quantitative behavior of the HbO₂ dissociation curves at various physiological conditions (i.e., with varying levels of pH_rbc, P_CO2, [DPG]_rbc and T) as computed from Eqs. (7a), (8a), (9), (15), and (16a)–(16d).

Figure 5

The quantitative behavior of the HbCO₂ dissociation curves at various physiological conditions (i.e., with varying levels of pH_rbc, P_O2 [DPG]_rbc and T) as computed from Eqs. (7b), (8b), (9), (15), and (16a)–(16d).

Figure 6

Total CO₂ content of whole blood ([CO₂]_bl, mL CO₂ per 100 mL blood) as a function of P_CO2 at various physiological conditions (i.e., with varying levels of pH_rbc, P_O2, [DPG]_rbc, T and Hct) as computed through Eqs. (A.2) and (A.3).