European Journal of Applied Physiology

, Volume 116, Issue 1, pp 97–113

Simple accurate mathematical models of blood HbO2 and HbCO2 dissociation curves at varied physiological conditions: evaluation and comparison with other models

Original Article

Abstract

Purpose

Equations for blood oxyhemoglobin (HbO2) and carbaminohemoglobin (HbCO2) dissociation curves that incorporate nonlinear biochemical interactions of oxygen and carbon dioxide with hemoglobin (Hb), covering a wide range of physiological conditions, are crucial for a number of practical applications. These include the development of physiologically-based computational models of alveolar-blood and blood-tissue O2–CO2 transport, exchange, and metabolism, and the analysis of clinical and in vitro data.

Methods and results

To this end, we have revisited, simplified, and extended our previous models of blood HbO2 and HbCO2 dissociation curves (Dash and Bassingthwaighte, Ann Biomed Eng 38:1683–1701, 2010), validated wherever possible by available experimental data, so that the models now accurately fit the low HbO2 saturation (\(S_{{{\text{HbO}}_{ 2} }}\)) range over a wide range of values of \(P_{{{\text{CO}}_{ 2} }}\), pH, 2,3-DPG, and temperature. Our new equations incorporate a novel \(P_{{{\text{O}}_{ 2} }}\)-dependent variable cooperativity hypothesis for the binding of O2 to Hb, and a new equation for P50 of O2 that provides accurate shifts in the HbO2 and HbCO2 dissociation curves over a wide range of physiological conditions. The accuracy and efficiency of these equations in computing \(P_{{{\text{O}}_{ 2} }}\) and \(P_{{{\text{CO}}_{ 2} }}\) from the \(S_{{{\text{HbO}}_{ 2} }}\) and \(S_{{{\text{HbCO}}_{ 2} }}\) levels using simple iterative numerical schemes that give rapid convergence is a significant advantage over alternative \(S_{{{\text{HbO}}_{ 2} }}\) and \(S_{{{\text{HbCO}}_{ 2} }}\) models.

Conclusion

The new \(S_{{{\text{HbO}}_{ 2} }}\) and \(S_{{{\text{HbCO}}_{ 2} }}\) models have significant computational modeling implications as they provide high accuracy under non-physiological conditions, such as ischemia and reperfusion, extremes in gas concentrations, high altitudes, and extreme temperatures.

Keywords

O2 and CO2 binding to hemoglobin O2 and CO2 saturation of hemoglobin Oxyhemoglobin and carbaminohemoglobin dissociation curves Nonlinear O2–CO2 interactions Bohr and Haldane effects Mathematical modeling 

Abbreviations

\(\alpha_{{{\text{O}}_{ 2} }}\)

Solubility of oxygen in water

\(\alpha_{{{\text{CO}}_{ 2} }}\)

Solubility of carbon dioxide in water

[O2]

Concentration of free oxygen

[CO2]

Concentration of free carbon dioxide

[H+]

Concentration of hydrogen ions (protons)

[DPG]

Concentration of 2,3-diphosphoglycerate (2,3-DPG)

T

Temperature

pH

−log10([H+])

\(P_{{{\text{O}}_{ 2} }}\)

Partial pressure of oxygen

\(P_{{{\text{CO}}_{ 2} }}\)

Partial pressure of carbon dioxide

P50

Partial pressure of oxygen for 50 % HbO2 saturation

Hb

Hemoglobin

HbO2

Oxyhemoglobin

HbCO2

Carbaminohemoglobin

\(K_{{{\text{HbO}}_{ 2} }}\)

Apparent equilibrium constant for the binding of oxygen to hemoglobin

\(K_{{{\text{HbCO}}_{ 2} }}\)

Apparent equilibrium constant for the binding of carbon dioxide to hemoglobin

\(S_{{{\text{HbO}}_{ 2} }}\)

Saturation of hemoglobin with oxygen

\(S_{{{\text{HbCO}}_{ 2} }}\)

Saturation of hemoglobin with carbon dioxide

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of Physiology, Biotechnology and Bioengineering CenterMedical College of WisconsinMilwaukeeUSA
  2. 2.Department of Anaesthesia and Pain MedicineRoyal Perth HospitalPerthAustralia
  3. 3.Department of BioengineeringUniversity of WashingtonSeattleUSA

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