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7978639 
Journal Article 
A mathematical model of the hemoglobin-oxygen dissociation curve of human blood and of the oxygen partial pressure as a function of temperature 
Siggaard-Andersen, O; Wimberley, PD; Gothgen, I; Siggaard-Andersen, M 
1984 
Yes 
Clinical Chemistry
ISSN: 0009-9147
EISSN: 1530-8561 
AMER ASSOC CLINICAL CHEMISTRY 
WASHINGTON 
30 
10 
1646-1651 
English 
6478594 
WOS:A1984TM30400011 
A mathematical model is described giving the oxygen saturation fraction (s) as a function of the oxygen partial pressure (p): y - y0 = x - x0 + h . tanh [k.(x - x0)], where y = In[s/(1 - s)] and x = In(p/kPa). The parameters are: y0 = 1.875; x0 = 1.946 + a + b; h = 3.5 + a; k = 0.5343; b = 0.055 . [T/(K - 310.15)]; a = 1.04.(7.4 - pH) + 0.005 . c(base)/(mmol/L) + 0.07 . {[c(DPG)/(mmol/L)] - 5}, where c(base) is the base excess of the blood and c(DPG) is the concentration of 2,3-diphosphoglycerate in the erythrocytes. The Hill slope, n = dy/dx, is given by n = 1 + h . k . {1 - tanh2[k . (x - x0)]}. n attains a maximum of 2.87 for x = x0, and n → 1 for x → ± ∞. The model gives a very good fit to the Severinghaus standard oxygen dissociation curve and the parameters may easily be fitted to other oxygen dissociation curves as well. Applications of the model are described including the solution of the inverse function (p as a function of s) by a Newton-Raphson iteration method. The p(O2)-temperature coefficient is given by dinp/dT = [A . α . p + c(Hb) . n . s . (1 - s) . B]/[α . p + c(Hb) . n . s . (1 - s)], where A = -dlnα/dT ≃ 0.012 K-1; B = (δlnp/δT)(s) = 0.073 K-1 for y = y0; α = the solubility coefficient of O2 in blood = 0.0105 mmol . L-1 . kPa1- at 37°C; c(Hb) = concentration of hemoglobin iron in the blood. Approximate equations currently in use do not take the variations of the p(O2)-temperature coefficient with p50 and c(Hb) into account. 
blood and hemopoietic system; mathematical model; nonbiological model; oxygen dissociation curve; priority journal; temperature