Modelling whole blood oxygen equilibrium: comparison of nine different models fitted to normal human data.

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.

Diabetic oxygen-hemoglobin equilibrium curves evaluated by nonlinear regression of the Hill equation.

The oxygen-hemoglobin equilibrium curves ( OHECs ) were measured on whole blood samples from 131 individuals (33 normal and 26 diabetic adults and 30 normal and 42 diabetic juveniles) using a Radiometer Dissociation Curve Analyzer (DCA-1). All measurements were made in the morning following an overnight fast and without exogenous insulin. The saturation versus Po2 data were fitted to the Hill equation using a previously described nonlinear regression algorithm to yield the parameters describing the position (P50) and shape (n) of each OHEC . It was found that the Hill model could be used to describe OHECs of both normal and diabetic subjects. A small (approximately 10%) but significant decrease in P50 was found for the diabetic juveniles compared to normal juveniles. There appeared to be no change in P50 with diabetes in adults. However, in these diabetic subjects, the P50 had been increased by the somewhat elevated levels of 2,3-DPG. No difference in n was found between either group of diabetics and their corresponding group of normals but n was approximately 5% lower in juveniles than in adults. The ability of blood to release oxygen to tissue may be transiently impaired in diabetic juveniles because of the left shift of their OHECs .

Characterization of oxygen-hemoglobin equilibrium curves using nonlinear regression of the Hill equation: parameter values for normal human adults.

Measurements of oxygen concentration versus PO2 in blood from 33 normal adults were fitted, using a special nonlinear regression analysis, to the Hill equation to obtain the parameters describing the position (P50) and shape (n) of each oxygen-hemoglobin equilibrium curve (OHEC). Data between 20% and 97% saturation were described well by this empirical two-parameter model. The mean (+/- SD) P50 and n were found to be 26.2 (+/- 0.8) torr and 2.50 (+/- 0.07), respectively, in good agreement with previously published values. Some normal individuals, however, deviated markedly from the averages indicating that the published values cannot be applied to everyone.