title: Simple accurate mathematical models of blood HbO2 and HbCO2 dissociation curves at varied physiological conditions: evaluation and comparison with other models.
abstract: OBJECTIVE
  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.
  
  
  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 (SHbO2) range over a wide range of values of PCO2, pH, 2,3-DPG, and temperature. Our new equations incorporate a novel PO2-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 PO2 and PCO2 from the SHbO2 and SHbCO2 levels using simple iterative numerical schemes that give rapid convergence is a significant advantage over alternative SHbO2 and SHbCO2 models.
  
  
  CONCLUSIONS
  The new SHbO2 and SHbCO2 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.
authors: Department of Physiology, Biotechnology and Bioengineering Center, Medical College of Wisconsin, 8701 Watertown Plank Road, Milwaukee, WI, 53226, USA. rdash@mcw.edu.
authors: Ranjan K
authors: RK
authors: Dash
authors: Department of Anaesthesia and Pain Medicine, Royal Perth Hospital, Perth, WA, Australia. ben@korman.com.au.
authors: Ben
authors: B
authors: Korman
authors: Department of Bioengineering, University of Washington, Box 355061, N210G North Foege Bldg, Seattle, WA, 9895-5061, USA. jbb2@u.washington.edu.
authors: James B
authors: JB
authors: Bassingthwaighte
mesh_terms: D002245:Carbon Dioxide / Q000097:blood*; D006441:Hemoglobin A / Q000031:analogs & derivatives / Q000378:metabolism; D006454:Hemoglobins / Q000378:metabolism*; D006801:Humans; D006863:Hydrogen-Ion Concentration; D008954:Models, Biological; D010100:Oxygen / Q000097:blood*; D010108:Oxyhemoglobins / Q000378:metabolism*; D013696:Temperature
chemical_list: D006454:Hemoglobins; D010108:Oxyhemoglobins; D002245:Carbon Dioxide; C022017:hemoglobin A, carbamylated; D006441:Hemoglobin A; D010100:Oxygen
keywords: Bohr and Haldane effects; Mathematical modeling; Nonlinear O2–CO2 interactions; O2 and CO2 binding to hemoglobin; O2 and CO2 saturation of hemoglobin; Oxyhemoglobin and carbaminohemoglobin dissociation curves