Revised equations for calculating CO₂ production from doubly labeled water in humans

The Schoeller model for calculating rate of CO₂ production (r(CO₂)) from doubly labeled water (DLW) relies on the assumption that deuterium and oxygen-18 overestimate body water by 4 and 1%, respectively. However, the deuterium-to-oxygen-18 dilution space ratio (DSR) varies considerably, and it is unknown whether this is due to analytical or biological sources. From 161 published values in adult humans, we derived a mean DSR of 1.0427 ± 0.0218. Propagation of error suggests that analytical uncertainty accounts for 20- 50% of the observed variation in the DSR, whereas reliability testing in vivo and in vitro demonstrate that 70-100% of observed interindividual variation in the DSR can be attributed to analytical uncertainty. The discrepancy between propagated error and experimental reliability suggest that it is unwise to rely on propagation of error when evaluating sources of error in DLW. The new constant of 1.0427 was used to revise existing equations for calculating r(CO₂) from DLW. Compared with the existing equation, the revised equation improved the accuracy (-0.38 vs. + 10.3%) and the precision (9.3 vs 10.7%) of r(CO₂) calculations in previously published validation studies. We conclude that 1) variation in the oxygen-18-to-deuterium DSR is primarily influenced by analytical noise and warrants use of a fixed ratio, 2) existing equations should be revised because the original DSR may have been underestimated, and 3) the modified equations improve the accuracy and precision of r(CO₂) calculated from DLW.