Modelling Whole Blood Oxygen Equilibrium: Comparison of Nine Different Models Fitted to Normal Human Data

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Abstract
The ability of nine different models, prominent in the literature, to meaningfully characterize the oxygen-hemoglobin equilibrium curve (OHEC) of normal individuals was examined. Previously reported data (N=33), obtained using the DCA-1 (Radiometer, Copenhagen), and new data (N=8), obtained using the Hemox-Analyzer (TCS, Southampton, PA), from blood samples of normal, non-smoking volunteers were used and these devices were found to give statistically similar results. The OHECs were digitized and fitted to the models using least-squares techniques developed in this laboratory. The “goodness-of-fit” was determined by the root-mean-squared (RMS) error, the number of parameters, and the parameter redundancy, i.e., correlation between the parameters. The best RMS error did not necessarily indicate the best model. Most literature models consist of ratios of similar-order polynomials. These showed considerable parameter redundancy which made the curve fitting difficult. The best fits gave RMS errors as low as 0.2% saturation. The Hill model gave a good characterization over the saturation range 20%–98% with RMS errors of about 0.6% saturation. On the other hand, good characterizations over the entire range were given by several other models. The relative advantages and disadvantages of each model have been compared as well as the difficulties in fitting several of the models. No single model is best under all circumstances. The best model depends upon the particular circumstances for which it is to be utilized.