Some mathematical and technical issues in the measurement and interpretation of open-circuit indirect calorimetry in small animals

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Abstract
Indirect calorimetry is increasingly used to investigate why compounds or genetic manipulations affect body weight or composition in small animals. This review introduces the principles of indirect (primarily open-circuit) calorimetry and explains some common misunderstandings. It is not widely understood that in open-circuit systems in which carbon dioxide (CO2) is not removed from the air leaving the respiratory chamber, measurement of airflow out of the chamber and its oxygen (O2) content paradoxically allows a more reliable estimate of energy expenditure (EE) than of O2 consumption. If the CO2 content of the exiting air is also measured, both O2 consumption and CO2 production, and hence respiratory quotient (RQ), can be calculated. Respiratory quotient coupled with nitrogen excretion allows the calculation of the relative combustion of the macronutrients only if measurements are over a period where interconversions of macronutrients that alter their pool sizes can be ignored. Changes in rates of O2 consumption and CO2 production are not instantly reflected in changes in the concentrations of O2 and CO2 in the air leaving the respiratory chamber. Consequently, unless air-flow is high and chamber size is small, or rates of change of O2 and CO2 concentrations are included in the calculations, maxima and minima are underestimated and will appear later than their real times. It is widely appreciated that bigger animals with more body tissue will expend more energy than smaller animals. A major issue is how to compare animals correcting for such differences in body size. Comparison of the EE or O2 consumption per gram body weight of lean and obese animals is misleading because tissues vary in their energy requirements or in how they influence EE in other ways. Moreover, the contribution of fat to EE is lower than that of lean tissue. Use of metabolic mass for normalisation, based on interspecific scaling exponents (0.75 or 0.66), is similarly flawed. It is best to use analysis of covariance to determine the relationship of EE to body mass or fat-free mass within each group, and then test whether this relationship differs between groups.