The doubly labelled water (DLW) method is widely used to determine energy expenditure. In this work, we demonstrate the addition of the third stable isotope, 17O, to turn it into triply labelled water (TLW), using the three isotopes measurement of optical spectrometry. We performed TLW (2H, 18O and17O) measurements for the analysis of the CO2 production (rCO2) of mice on different diets for the first time. Triply highly enriched water was injected into mice, and the isotope enrichments of the distilled blood samples of one initial and two finals were measured by an off-axis integrated cavity output spectroscopy instrument. We evaluated the impact of different calculation protocols and the values of evaporative water loss fraction. We found that the dilution space and turnover rates of 17O and 18O were equal for the same mice group, and that values of rCO2 calculated based on 18O–2H, or on 17O–2H agreed very well. This increases the reliability and redundancy of the measurements and it lowers the uncertainty in the calculated rCO2 to 3% when taking the average of two DLW methods. However, the TLW method overestimated the rCO2 compared to the indirect calorimetry measurements that we also performed, much more for the mice on a high-fat diet than for low-fat. We hypothesize an extra loss or exchange mechanism with a high fractionation for 2H to explain this difference.

The stable isotopes of water are extensively used as tracers in many fields of research. For this use, it is essential to know the isotope fractionation factors connected to various processes, the most important of which being phase changes. Many experimental studies have been performed on phase change fractionation over the last decades. Whereas liquid-vapour fractionation measurements are relatively straightforward, vapour-solid and liquid-solid fractionation measurements are more complicated, as maintaining equilibrium conditions when a solid is involved is difficult. In this work, we determine the ice-liquid isotope fractionation factors in an indirect way, by applying the Van't Hoff equation. This equation describes the relationship of the fractionation factors with isotope-dependent temperature changes. We apply it to the recently experimentally determined isotope dependences of the triple point temperature of water [Faghihi V, Peruzzi A, Aerts-Bijma AT, et al. Accurate experimental determination of the isotope effects on the triple point temperature of water. I. Dependence on the H abundance. Metrologia. 2015;52:819-826; Faghihi V, Kozicki M, Aerts-Bijma AT, et al. Accurate experimental determination of the isotope effects on the triple point temperature of water. II. Combined dependence on theO and O abundances. Metrologia. 2015;52:827-834]. This results in new values for theH (deuterium) and O fractionation factors for the liquid-solid phase change of water, which agree well with existing, direct experimental data [Lehmann M, Siegenthaler U. Equilibrium oxygen- and hydrogen-isotope fractionation between ice and water. J Glaciol. 1991;37:23-26]. ForH, the uncertainty is improved by a factor of 3, whereas for O the uncertainty is similar. Our final results are α (H/H) = 1.02093(13), and α (O/O) = 1.002909(25), where the latter is the weighted average of the previous experimental study and this work.

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