Estimation of doubly labeled water energy expenditure with confidence intervals

Bivariate regression is used to estimate energy expenditure from doubly labeled water data. Two straight lines are fitted to the logarithms of the enrichments of oxygen-18 and deuterium simultaneously as a bivariate regression, so that the correlations between the oxygen and deuterium regression coefficients can be estimated. Maximum likelihood methods are used to extend bivariate regression to unbalanced situations caused by missing observations and to include replicate laboratory determination from the same urine samples, even if one of the replicates is missing. Use of maximum likelihood allows the determination of a confidence interval for the energy expenditure based on the log likelihood surface rather than use of the propagation of variance methods for nonlinear transformations. The model is extended to include the subject's deviations from the two lines as a bivariate continuous-time first-order autoregression to allow for serial correlation in the observations. The analysis of data from two subjects, one without apparent serial correlation and one with serial correlation, is presented.     

Sensitivity of methods for calculating energy expenditure by use of doubly labeled water

Attempts to estimate human energy expenditure by use of doubly labeled water have produced three methods currently used for calculating carbon dioxide production from isotope disappearance data: 1) the two-point method, 2) the regression method, and 3) the integration method. An ideal data set was used to determine the error produced in the calculated energy expenditure for each method when specific variables were perturbed. The analysis indicates that some of the calculation methods are more susceptible to perturbations in certain variables than others. Results from an experiment on one adult human subject are used to illustrate the potential for error in actual data. Samples of second void urine, 24-h urine, and breath collected every other day for 21 days are used to calculate the average daily energy expenditure by three calculation methods. The difference between calculated energy expenditure and metabolizable energy on a weight-maintenance diet is used to estimate the error associated with the doubly labeled water method.     

Effect of bolus fluid intake on energy expenditure values as determined by the doubly labeled water method.

The doubly labeled water (DLW, 2H(2)18O) method is a highly accurate method for measuring energy expenditure (EE). A possible source of error is bolus fluid intake before body water sampling. If there is bolus fluid intake immediately before body water sampling, the saliva may reflect the ingested water disproportionately, because the ingested water may not have had time to mix fully with the body water pool. To ascertain the magnitude of this problem, EE was measured over a 5-day period by the DLW method. Six subjects were dosed with 2H2(18)O. After the reference salivas for the two-point determination were obtained, subjects drank water (700-1,000 ml), and serial saliva samples were collected for the next 3 h. Expressing the postbolus saliva enrichments as a percentage of the prebolus value, we found 1) a minimum in the saliva isotopic enrichments were reached at approximately 30 min with the minimum for 2H (95.48 +/- 0.43%) being significantly lower than the minimum for 18O (97.55 +/- 0.44, P less than 0.05) and 2) EE values calculated using the postbolus isotopic enrichments are appreciably higher (19.9 +/- 7.5%) than the prebolus reference values. In conclusion, it is not advisable to collect saliva samples for DLW measurements within approximately 1 h of bolus fluid intake.     

Use of the doubly labeled water method for measurement of energy expenditure, total body water, water intake, and metabolizable energy intake in humans and small animals

The basis of the doubly labeled water method is measurement of the differential rates of disappearance of two isotopes of water (H2 18O and either 2H2O or 3H2O, administered at the start of the study) from body water. Published studies indicate that, in its current forms, this technique can be used to provide accurate and reasonably precise information on carbon dioxide production, total body water, and water intake in free-living humans and many small animals. Total energy expenditure can be calculated from carbon dioxide production with little loss of precision. Metabolizable energy intake can also be predicted, as the sum of total energy expenditure plus an estimate for the change in body energy stores during the measurement, but this prediction is unlikely to be accurate and precise unless the subject is in approximate energy balance.     

Measurement of CO2 production by the doubly labeled water technique

Recent applications of the doubly labeled water technique to the study of human metabolism have employed multiple sampling of body water over protracted periods, rather than the more traditional method of taking only an initial and final sample for isotopic analysis. In addition fractional turnovers of the body pools have been estimated by fitting curves to the sequential log-converted isotope enrichment against time. By manipulation of data collected in the field in a study of metabolism of vespertilionid bats, it is shown the curve-fitting technique results in an accurate estimate of CO2 production only when the rate of CO2 production is constant. Biologically realistic nonsteady-state conditions result in errors in estimates of CO2 production of up to 30%. In conditions where CO2 production is known to be temporally variable, the more traditional two-sample method may provide a more accurate estimate of CO2 production.     

Comparison of different approaches for the calculation of energy expenditure using doubly labeled water in a small mammal

The doubly labeled water (DLW) method is an isotope-based technique for the estimation of the CO(2) production, and hence energy expenditure, of free-living animals and humans. Several methods are available for the calculation of CO(2) production from the isotope fluxes, depending on different assumptions about the behavior of isotopes during the elimination process. We used the DLW method to estimate the daily energy expenditures (DEE) of 55 field voles (Microtus agrestis) held in a captive facility at 8 degrees C. We calculated DEE using both plateau and intercept approaches for estimating the sizes of the isotope dilution spaces, three different assumptions about fractionation processes, and two ways of treating the different dilution spaces of the oxygen and hydrogen isotopes. We compared the resultant DEE estimates with metabolizable energy intake (MEI) measured during a 3-d feeding trial immediately before the DLW measurements, during which the animals were in energy balance. By making different assumptions about the apparent energy absorption efficiency, we generated a range of direct estimates of MEI. When we compared DEE and MEI, we found that the two-pool model formulations consistently underestimated energy demands by up to 29.8%, depending on the assumptions made in the reference calculation. However, while our data suggest that some correction for fractionation is necessary, with the present data we were unable to separate the two most common treatments of fractionation. These data strongly support the previous suggestion that for small mammals single-pool models provide more accurate estimates of energy demands than two-pool formulation of the DLW method.     

A rapid analytical technique for the determination of energy expenditure by the doubly labelled water method

The doubly labelled water method involves the administration of water enriched in 2H and 18O followed by determination of the turnover rates of these isotopes. Since 18O is eliminated from the body as both CO2 and water, while 2H leaves only as water, the difference between the two turnover rates provides a measure of CO2 production and hence energy expenditure. Isotopic analysis by conventional stable isotope ratio analysis (SIRA) is labour intensive and time consuming, as it requires off-line conversion of water samples to gases (H2 and CO2) followed by sequential analysis for each of the two isotopes using the mass spectrometer. Lack of suitable automated instrumentation with the ability to process large numbers of samples has prevented routine application of the method. We describe here an automated technique in which body water samples (urine, saliva, breath water or milk) are analysed simultaneously for 2H and 18O. The single bench system comprises two mass spectrometer analysers, one for measuring 2H from H2 gas, the other for measuring 18O from the water vapour (masses 18, 20). Both analysers share a common heated inlet system into which microlitre quantities of the body fluids are injected from an autosampler (102 samples). The water vapour flows both directly to one analyser for 18O measurement and into a uranium reduction furnace for conversion to H2, prior to 2H measurement by the second analyser. Both analysers also share vacuum and electronic components, enabling savings in both space and cost. In this paper we present results illustrating performance characteristics and procedures for routine application to human subjects.(ABSTRACT TRUNCATED AT 250 WORDS)     

Energy expenditure of elite female runners measured by respiratory chamber and doubly labeled water.

To determine whether female athletes have unusually low energy requirements as suggested by many food intake studies, energy expenditure (EE) and intake were assessed in nine elite distance runners [26 +/- 3 (SD) yr, 53 +/- 4 kg, 12 +/- 3% body fat, and 66 +/- 4 ml.kg-1.min-1 maximal O2 uptake]. Subjects were admitted to a metabolic ward for 40 h during which 24-h sedentary EE was measured in a respiratory chamber. Free-living EE was then assessed by the doubly labeled water method for the next 6 days while the women recorded all food intake, daily body weight, and training mileage (10 +/- 3 miles/day). Energy intakes estimated from free-living EE (2,826 +/- 312 kcal/day) and body weight changes (-84 +/- 71 g/day) averaged 221 +/- 550 kcal/day in excess of those calculated from food records (2,193 +/- 466 kcal/day). The energy cost of training (1,087 +/- 244 kcal/day) was calculated as the difference between free-living EE and 24-h EE in the respiratory chamber (1,681 +/- 84 kcal/day) corrected for the thermic effect of food of the extra energy intake. These data do not support the hypothesis that training as a distance runner results in metabolic adaptations that lower energy requirements in women.     

Use of the doubly labeled water technique in humans during heavy sustained exercise

We measured energy expenditure with the doubly labeled water technique during heavy sustained exercise in the Tour de France, a bicycle race lasting more than 3 wk. Four subjects were observed for consecutive intervals of 7, 8, and 7 days. Each interval started with an oral isotope dose to reach an excess isotope level of 200 ppm 18O and 130 ppm 2H. The biological half-lives of the isotopes were between 2.25 and 3.80 days. Energy expenditure was compared with simultaneous measurements of energy intake, and body mass and body composition did not change significantly. The doubly labeled water technique gave higher values for energy expenditure than the food record technique. The discrepancy showed a systematic increment from the first to the third interval, being 12.9 +/- 7.9, 21.4 +/- 9.8, and 35.3 +/- 4.4% of the energy expenditure calculated from dietary intake, respectively. Possible explanations for the discrepancy are discussed. The subjects reached an average daily metabolic rate of 3.4-3.9 or 4.3-5.3 times basal metabolic rate based on the food record technique and the doubly labeled water technique, respectively. Thus, when measured with the same technique, the energetic ceiling for performance in humans is comparable with that of animals like birds.     

Doubly labeled water measurement of human energy expenditure during strenuous exercise

The energy expenditures (EE) of 23 adult male Marines were measured during a strenuous 11-day cold-weather field exercise at 2,200- to 2,550-m elevation by both doubly labeled water (2H2 18O, DLW) and intake balance methods. The DLW EE calculations were corrected for changes in baseline isotopic abundances in a control group that did not receive 2H2 18O. Intake balance EE was estimated from the change in body energy stores and food intake. Body energy-store changes were calculated from anthropometric [-1,574 +/- 144 (SE) kcal/day] and isotope dilution (-1,872 +/- 293 kcal/day) measurements made before and after the field exercise. The subjects kept daily logbook records of ration consumption (3,132 +/- 165 kcal/day). Mean DLW EE (4,919 +/- 190 kcal/day) did not differ significantly from intake balance EE estimated from food intake and either anthropometric (4,705 +/- 181 kcal/day) or isotope dilution (5,004 +/- 240 kcal/day) estimates of the change in body energy stores. The DLW method can be used with at least the same degree of confidence as the intake balance method to measure the EE of active free-living humans.     

A review of seabird energetics using the doubly labeled water method

The doubly labeled water (DLW) method has been essential for understanding animal energetics of free-ranging individuals. The first published studies on free-ranging seabirds were conducted on penguins in the early 1980s. Since then, nearly 50 seabird species with representatives from each major taxonomic order have been studied using DLW. Although the basic methodology has not changed, there are at least nine different equations, varying with respect to assumptions on fractionation and the total body water pool, to estimate field metabolic rate (FMR) from isotopic water turnover. In this review, I show that FMR can vary by as much as 45% depending on the equation used to calculate CO₂ production in five albatross species. Energy budgets derived from DLW measurements are critical tools for understanding patterns of energy use and allocation in seabirds. However, they depend on accurate and representative measurements of FMR, so analyses that include greater partitioning of activity specific FMR yield more realistic cost estimates. I also show how the combined use of DLW and biologging methods can 1) provide greater clarity for explaining observed variation in FMR measurements within a species and 2) allow FMRs to be viewed in a wider physiological, behavioral, or ecological context. Finally, I update existing allometric equations with new FMR data. These updates reaffirm that albatrosses have the lowest at-sea FMRs per equivalent body mass and that individuals of other seabird orders have FMRs ranging between 1.39 and 2.24 times higher than albatrosses.     

Adaptation of the doubly labeled water method for subjects consuming isotopically enriched water

Gretebeck, Randall J., Dale A. Schoeller, Rick A. Socki,Janis Davis-Street, Everett K. Gibson, Leslie O. Schulz, and Helen W. Lane. Adaptation of the doubly labeled water methodfor subjects consuming isotopically enriched water. J. Appl. Physiol. 82(2): 563-570, 1997.The use ofdoubly labeled water (DLW) to measure energy expenditure is subject toerror if the background abundance of the oxygen and hydrogen isotopetracers changes during the test period. This study evaluated theaccuracy and precision of different methods by which such backgroundisotope changes can be corrected, including a modified method thatallows prediction of the baseline that would be achieved if subjectswere to consume water from a given source indefinitely. Subjects inthis study were eight women (4 test subjects and 4 control subjects)who consumed for 28 days water enriched to resemble drinking water aboard the United States space shuttle. Test subjects and control subjects were given a DLW dose on days1 and 15,respectively. The change to an enriched water source produced a bias inexpenditure calculations that exceeded 2.9 MJ/day (35%), relative tocalculations from intake-balance. The proposed correction based on thepredicted final abundance of ¹⁸Oand deuterium after equilibration to the new water source eliminated this bias, as did the traditional use of a control group. This newmodified correction method is advantageous under field conditions whensubject numbers are limited.

     

Validation of the doubly labeled water technique for measuring energy metabolism in starlings and sparrows

I have tested the idea that doubly labeled water (DLW) can accurately predict CO2 production in savannah sparrows, song sparrows, white-throated sparrows, starlings, and a single house sparrow by comparing DLW estimates with those obtained simultaneously by capturing expired CO2 in Ascarite. In addition I used the energy balance method to see if metabolic rates generated from DLW measurements accurately reflected the actual metabolic rates of these birds. I found close agreement in DLW and the gravimetric and energy balance methods, with DLW underestimating CO2 production on average by -3.5% in sparrows, and -7.1% in starlings. Similarly, the energy balance method indicated a -3.1% underestimate by DLW for sparrows and a -5.1% for starlings. The DLW method can yield reasonable estimates of CO2 production in a variety of passerine birds.     

Validation of the doubly labeled water method in rats during isolation and simulated weightlessness

Total energy expenditure (TEE) of rats during simulated microgravity is unknown. The doubly labeled water method (DLW) reliably measures TEE, but the results depend on the methods of calculation. These methods were validated and appraised by indirect calorimetry in eight rats during isolation (7 days) and simulated microgravity (10 days). There were no effects on CO(2) production in the method used to derive constant flux rates as in the regression models. r(CO(2)) estimates were dependent on the assumed fractionation processes, the derivation of constant flux rate methods, and the selected pool models. Use of respiratory or food quotients did not influence TEE estimations, which were similar during isolation and simulation. During either isolation with growth or simulation with a stabilized mass, the one-pool model of Speakman (Speakman JR. Doubly Labelled Water. Theory and Practice. London: Chapman and Hall, 1997) resulted in the more reliable validation (0.8 +/- 2.2 and 2.2 +/- 3.4% vs. calorimetry, respectively). However, during simulation, agreement was also observed with the single pool model of Lifson (Lifson N, Gordon GB, and McClintock R. J Appl Physiol 7: 704-710, 1955) (-2.5 +/- 2.5%), and two two-pool models [Schoeller (Schoeller DA. J Nutr 118: 1278-1289, 1988) (0.5 +/- 3.1%) and Speakman (Speakman, JR. Doubly Labelled Water. Theory and Practice. London: Chapman and Hall, 1997) (-1.9 +/- 2.7%)]. This latter finding seems linked to the stable body mass and to fractionation consideration close to the single-pool model of Speakman. During isolation or simulated microgravity, the other equations underestimated TEE by 10-20%.