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 (VO2), carbon dioxide production (VCO2) and estimated protein metabolism (PM). EE has a substantial dependence of similar to 7% on the respiratory quotient (RQ, VCO2/VO2) and a lesser dependence on PM, yet many studies have instead estimated EE from VO2 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 (Delta FO2) and the dietary protein fraction. The RQ(-) method has not previously been empirically validated against the standard RQ(+) method using both VO2 and RQ. Our aim was to do that. Methods VO2 and VCO2 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] = VO2 [L/time] x(3.853+1.081RQ) while the corresponding RQ(-) equation was: EE = 4.934xFRx Delta FO2. 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 CO2 measurements. Practitioners of respirometry should consider adjusting EE calculations for estimated protein metabolism based on dietary composition.