To determine the most appropriate mathematical description of the relationship between oxygen consumption and oxygen delivery, we compared the statistical validity of a piecewise linear model to two different biologic system models-Michaelis-Menten (MM) kinetics (used for enzyme systems) and the exponential dose-response relationship (used to describe drug administration and induced response). Nine rabbits underwent five incremental steps of normovolemic hemodilution to progressively decrease Ḋ(O2). V̇(O2) was measured concurrently by a metabolic gas monitor. All three models (piecewise linear, Michaelis-Menten, and exponential) provided a very close population curve fit to the data points (r2 = 0.88, 0.91, and 0.92). However, there were significant differences in maximum predicted V̇(O2) (V̇(O(2max)))-6.8, 9.9, 7.2 ml O2 · kg-1 · min-1 (P < 0.0002)-and a wide range in the model-specific parameters for individual rabbits (critical Ḋ(O2) 6.5-11.8 ml O2 · kg-1 · min-1, K(m) 4.2-11.4 ml O2 · kg- 1 · min-1, and k 0.12-0.23 ml O2/-1 · kg · min). In the curvilinear models, average and population parameters were not significantly different. However, in the piecewise linear model, population critical Ḋ(O2) (10.9 ml O2 · kg-1 · min-1) was 30% more than the average critical Ḋ(O2) (8.4 ml O2 · kg-1 · min-1) for the nine rabbits (P < 0.005). V̇(O(2max)) values predicted by the piecewise linear and exponential dose- response model were more consistent with those in previous publications than was the higher V̇(O(2max)) predicted by the MM model. The difference in the average versus population critical Ḋ(O2) in the piecewise linear model meant that population modeling was inaccurate because it yielded a critical Ḋ(O2) higher than that demonstrated by eight of nine individual rabbits. Despite the high r2 values for all three models and the historical use of the piecewise linear model, we consider the exponential dose-response model the most appropriate description of the Ḋ(O2)/V̇(O2) relationship given its advantages with regard to V̇(O(2max)) prediction and population modeling.
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