Validation of an equation for energy expenditure that does not require the respiratory quotient

BACKGROUND: Energy expenditure (EE) calculated from respirometric indirect calorimetry is most accurate when based on oxygen consumption (VO(2)), carbon dioxide production (VCO(2)) and estimated protein metabolism (PM). EE has a substantial dependence of ~7% on the respiratory quotient (RQ, VCO(2)/VO(2)) and a lesser dependence on PM, yet many studies have instead estimated EE from VO(2) only while PM has often been ignored, thus reducing accuracy. In 1949 Weir proposed a method to accurately calculate EE without using RQ, which also adjusts for estimated PM based on dietary composition. This RQ(-) method utilizes the calorimeter airflow rate (FR), the change in fractional O(2) concentration (ΔFO(2)) and the dietary protein fraction. The RQ(-) method has not previously been empirically validated against the standard RQ(+) method using both VO(2) and RQ. Our aim was to do that. METHODS: VO(2) and VCO(2) were measured repeatedly in 8 mice fed a high protein diet (HPD) during exposure to different temperatures (n = 168 measurements of 24h gas exchange). The HPD-adjusted RQ(+) equation was: EE [kcal/time] = VO(2) [L/time]×(3.853+1.081RQ) while the corresponding RQ(-) equation was: EE = 4.934×FR×ΔFO(2). Agreement was analyzed using the ratios of the RQ(-) to RQ(+) methods along with regression and Bland-Altman agreement analyses. We also evaluated the standard equation using the dietary food quotient (FQ) of 0.91 as a proxy for RQ (FQ(+) method). RESULTS: Ratio analysis revealed that the mean error of the RQ(-) method was only 0.11 ± 0.042% while the maximum error was only 0.21%. Error using the FQ(+) method was 4 -and 10-fold greater, respectively. Bland-Altman analysis demonstrated that the RQ(-) method very slightly overestimates EE as RQ decreases. Theoretically, this error can be eliminated completely by imposing an incurrent fractional oxygen concentration at a value only slightly greater than the atmospheric level. CONCLUSIONS: The Weir ‘RQ-free’ method for calculating EE is a highly valid alternative to the ‘gold standard’ method that requires RQ. The RQ(-) approach permits reduced cost and complexity in studies focused on EE and provides a way to rescue EE measurement in studies compromised by faulty CO(2) measurements. Practitioners of respirometry should consider adjusting EE calculations for estimated protein metabolism based on dietary composition.