Defining the Relationship of Oxygen Delivery and Consumption: Use of Biologic System Models

• Published in: The Journal of surgical research 1995-05, Vol.58 (5), p.503-508
• Main Authors: Lubarsky, David A., Smith, L.Richard, Sladen, Robert N., Mault, James R., Reed, R.Lawrence
• Format: Article
• Language: English
• Subjects: Animals; Biological and medical sciences; Biological Availability; Blood gas. Hemoglobin. Myoglobin. Hemotissulary gas exchange. Acid-base balance; Dose-Response Relationship, Drug; Fundamental and applied biological sciences. Psychology; Kinetics; Models, Biological; Oxygen - blood; Oxygen Consumption; Rabbits; Vertebrates: respiratory system
• ISSN: 0022-4804; 1095-8673
• DOI: 10.1006/jsre.1995.1079

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 D o 2 . V o 2 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 ( r 2 = 0.88, 0.91, and 0.92). However, there were significant differences in maximum predicted V o 2 ( V o 2max )—6.8, 9.9, 7.2 ml O 2·kg -1·min-1( P < 0.0002)—and a wide range in the model-specific parameters for individual rabbits (critical D o 2 6.5-11.8 ml O 2·kg -1·min -1, K m 4.2-11.4 ml O 2·kg -1·min -1, and k 0.12-0.23 ml O -1 2·kg*middot;min). In the curvilinear models, average and population parameters were not significantly different. However, in the piecewise linear model, population critical D o 2 (10.9 ml O 2·kg -1·min -1) was 30% more than the average critical D o 2 (8.4 ml O 2·kg -1·min -1) for the nine rabbits ( P < 0.005). V 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 V o 2max predicted by the MM model. The difference in the average versus population critical D o 2 in the piecewise linear model meant that population modeling was inaccurate because it yielded a critical D o 2 higher than that demonstrated by eight of nine individual rabbits. Despite the high r 2 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 D o 2 / V o 2 relationship given its advantages with regard to V o 2max prediction and population modeling.