Development of Mathematical Formulae for O<sub>2</sub> and CO<sub>2</sub> Dissociation Curves in the Blood

Singh, Murari; Sharan, Maithili; Aminataei, A.

doi:10.1093/imammb/6.1.25

Cited by 13 publications

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“…20,51,54 Oxygen's binding to hemoglobin (Hb) is affected directly by carbon dioxide (CO 2 ) levels, pH, temperature, and 2,3-diphosphoglycerate (2,3-DPG) levels, and affected indirectly therefore by bicarbonate ( ) buffering, metabolism and tissue acidification, renal acid and base handling, and the hemoglobin mediated nonlinear O 2 -CO 2 interactions. 26,37,44,63 A decrease in pH or an increase in CO 2 partial pressure (P CO 2 ) in the systemic capillaries reduces the affinity of Hb for O 2 (the Bohr effect) and enhances the delivery of O 2 to tissue. A decrease in pH or an increase in O 2 partial pressure (P CO 2 ) in the pulmonary capillaries reduces the affinity of Hb for CO 2 and enhances the removal of CO 2 from blood into alveoli (Haldane effect).…”

Section: Introductionmentioning

confidence: 99%

Simultaneous Blood–Tissue Exchange of Oxygen, Carbon Dioxide, Bicarbonate, and Hydrogen Ion

Dash

Bassingthwaighte

2006

Ann Biomed Eng

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A detailed nonlinear four-region (red blood cell, plasma, interstitial fluid, and parenchymal cell) axially distributed convection-diffusion-permeation-reaction-binding computational model is developed to study the simultaneous transport and exchange of oxygen (O 2 ) and carbon dioxide (CO 2 ) in the blood-tissue exchange system of the heart. Since the pH variation in blood and tissue influences the transport and exchange of O 2 and CO 2 (Bohr and Haldane effects), and since most CO 2 is transported as (bicarbonate) via the CO 2 hydration (buffering) reaction, the transport and exchange of and H + are also simulated along with that of O 2 and CO 2 . Furthermore, the model accounts for the competitive nonlinear binding of O 2 and CO 2 with the hemoglobin inside the red blood cells (nonlinear O 2 -CO 2 interactions, Bohr and Haldane effects), and myoglobin-facilitated transport of O 2 inside the parenchymal cells. The consumption of O 2 through cytochrome-c oxidase reaction inside the parenchymal cells is based on MichaelisMenten kinetics. The corresponding production of CO 2 is determined by respiratory quotient (RQ), depending on the relative consumption of carbohydrate, protein, and fat. The model gives a physiologically realistic description of O 2 transport and metabolism in the microcirculation of the heart. Furthermore, because model solutions for tracer transients and steady states can be computed highly efficiently, this model may be the preferred vehicle for routine data analysis where repetitive solutions and parameter optimization are required, as is the case in PET imaging for estimating myocardial O 2 consumption.

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Section: Introductionmentioning

confidence: 99%

Simultaneous Blood–Tissue Exchange of Oxygen, Carbon Dioxide, Bicarbonate, and Hydrogen Ion

Dash

Bassingthwaighte

2006

Ann Biomed Eng

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“…Hill et al 14,15,16 and Salathe et al 31 have computed the concentration of HbCO 2 during O 2 and CO 2 exchange through mathematical modeling by accounting for the physical and biochemical processes including the acid-base balance. Later, Singh et al 38 , extending their earlier work, 36 developed mathematical formulas for nonstandard HbO 2 and HbCO 2 dissociation curves from the equilibrium binding of O 2 and CO 2 with Hb inside RBCs; these were similar to Hill's equation but included the effects of P O 2 , P CO 2 and pH. However, the effects of 2,3-DPG and temperature were not established.…”

Section: Carboxyhemoglobinmentioning

confidence: 99%

“…2,16,28,31,38 Hemoglobin, Hb, consists of four hemeamino chains, two α and two β chains; each contains a heme group, Hm, which binds to an O 2 molecule and has a terminal amino group, −NH 2 , which can bind to a CO 2 molecule to form an ionizable carbamino terminus, −NHCOOH. We consider the α and β chains to be identical in their binding with CO 2 .…”

Section: Governing Biochemical Reactionsmentioning

confidence: 99%

Blood HbO2 and HbCO2 Dissociation Curves at Varied O2, CO2, pH, 2,3-DPG and Temperature Levels

Dash

Bassingthwaighte

2004

Ann Biomed Eng

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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.

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“…The variable Hill constant model and the modified Hill equation were presented by Sharan et al 14 and Sharan & Singh 13 , respectively. All the variables in these equations have also been defined in the nomenclature section of this paper, and can also be found in the appropriate papers.…”

Section: Mathematical Model Oxygen Transport Simulationmentioning

confidence: 99%

An Oxygen Transport Model of Human Bone Marrow for Hemolytic Sickle Cell Anemia

Islam

Kumar²

2010

J Chem Engg

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Development of Mathematical Formulae for O₂ and CO₂ Dissociation Curves in the Blood

Cited by 13 publications

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Simultaneous Blood–Tissue Exchange of Oxygen, Carbon Dioxide, Bicarbonate, and Hydrogen Ion

Simultaneous Blood–Tissue Exchange of Oxygen, Carbon Dioxide, Bicarbonate, and Hydrogen Ion

Blood HbO2 and HbCO2 Dissociation Curves at Varied O2, CO2, pH, 2,3-DPG and Temperature Levels

An Oxygen Transport Model of Human Bone Marrow for Hemolytic Sickle Cell Anemia

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Development of Mathematical Formulae for O2 and CO2 Dissociation Curves in the Blood

Cited by 13 publications

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Simultaneous Blood–Tissue Exchange of Oxygen, Carbon Dioxide, Bicarbonate, and Hydrogen Ion

Simultaneous Blood–Tissue Exchange of Oxygen, Carbon Dioxide, Bicarbonate, and Hydrogen Ion

Blood HbO2 and HbCO2 Dissociation Curves at Varied O2, CO2, pH, 2,3-DPG and Temperature Levels

An Oxygen Transport Model of Human Bone Marrow for Hemolytic Sickle Cell Anemia

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Development of Mathematical Formulae for O₂ and CO₂ Dissociation Curves in the Blood