A MATHEMATICAL-MODEL OF THE HEMOGLOBIN OXYGEN DISSOCIATION CURVE OF HUMAN BLOOD AND OF THE OXYGEN PARTIAL-PRESSURE AS A FUNCTION OF TEMPERATURE (REPRINTED FROM CLINICAL-CHEMISTRY, VOL 30, PG 1646, 1984)

A mathematical model is described giving the Oxygen saturation fractio n (s) as a function of the oxygen partial pressure (p): y - y0 = x - x 0 + 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 t he base excess of the blood and c(DPG) is the concentration of 2,3-dip hosphoglycerate in the erythrocytes. The Hill slope, n = dy/dx, is giv en by n = 1 + h . k . {1 - tanh2[k . (x - x0)]}. n attains a maximum o f 2.87 for x = x0, and n --> 1 for x --> +/- is-proportional-to. The m odel gives a very good fit to the Severinghaus standard oxygen dissoci ation curve and the parameters may easily be fitted to other oxygen di ssociation curves as well. Applications of the model are described inc luding the solution of the inverse function (p as a function of s) by a Newton-Raphson iteration method. The p(O2)-temperature coefficient i s given by dlnp/dT = [A . alpha . p + c(Hb) . n . s . (1 - s) . B]/[al pha . P + c(Hb) . n . s . (1 - s)], where A = -dlnalpha/dT almost-equa l-to 0.012 K-1; B = (partial derivative lnp/partial derivative T)s = 0 .073 K-1 for y = y0; alpha = the solubility coefficient Of 02 in blood = 0.0105 mmol . L-1 . kPa-1 at 37-degrees-C; c(Hb) = 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 c(Hb) into account.