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)
O. Siggaardandersen et al., 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), Scandinavian journal of clinical & laboratory investigation, 53, 1993, pp. 10000032-10000037
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.