Blood oxygen content is a non-linear function of blood PO2. We base this calculation on the sigmoidal Hill equation.

 

  S = An / 1 + An

                                                                                                                       

(1) where S is the fractional saturation, n is an exponent which we'll call the Hill constant.

  A = P / P50                                                                                                  

 

(2) where P is the PO2 and P50 is the PO2  that produces a saturation of 1/2 or 50%. Using the work of Severinghaus, P50 is adjusted for the effects of temperature, pH, PCO2 and POC (not shown here).

 

Hill, A.V. The possible effects of the aggregation of the molecules of haemoglobin on its dissociation curves. J.Physiol. 40:iv-vii, 1910.  http://jp.physoc.org/cgi/reprint/40/Suppl/i

 

This equation is invertible.

 

  P = P50 * (S / 1 - S)^1/n                                                                              

 

(3) The benchmark data set is

Dill, D.B., H.T. Edwards, M. Florkin and R.W. Campbell. Properties of dog blood. J.Biol.Chem. 95:143-152, 1932.  http://www.jbc.org/cgi/reprint/95/1/143