A mathematical model of the hemoglobin-oxygen dissociation curve of human blood and of the oxygen partial pressure as a function of temperature.

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Abstract
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 X tanh [k X (x - x0)], where y = kn[s/(1-s)] and x = ln(p/kPa). The parameters are: y0 = 1.875; x0 = 1.946 + a + b; h = 3.5 + a; k = 0.5343; b = 0.055 X [T/(K - 310.15)]; a = 1.04 X (7.4 - pH) + 0.005 X Cbase/(mmol/L) + 0.07 X [[CDPG/(mmol/L)] - 5], where Cbase is the base excess of the blood and CDPG is the concentration of 2,3-diphosphoglycerate in the erythrocytes. The Hill slope, n = dy/dx, is given by n = 1 + h X k X [1 - tanh2[k X (x - x0)]]. n attains a maximum of 2.87 for x = x0, and n----1 for x----+/- infinity. 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 po2-temperature coefficient is given by dlnp/dT = [A X alpha X p + CHb X n X S X (1 - s) X B]/[alpha X p + CHB X n X s X (1 - s)], where A = -dln alpha/dT approximately equal to 0.012 K-1; B = (lnp/T)s = 0.073 K-1 for y = y0; alpha = the solubility coefficient of O2 in blood = 0.0105 mmol X L-1 X kPa-1 at 37 degrees C; CHb = concentration of hemoglobin iron in the blood. Approximate equations currently in use do not take the variations of the po2-temperature coefficient with p50 and CHb into account.

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