## Abstract

The doubly labeled water method for measuring total energy expenditure is subject to error from natural variations in the background ^{2}H and ^{18}O in body water. There is disagreement as to whether the variations in background abundances of the two stable isotopes covary and what relative doses of^{2}H and ^{18}O minimize the impact of variation on the precision of the method. We have performed two studies to investigate the amount and covariance of the background variations. These were a study of urine collected weekly from eight subjects who remained in the Madison, WI locale for 6 wk and frequent urine samples from 14 subjects during round-trip travel to a locale ≥500 miles from Madison, WI. Background variation in excess of analytical error was detected in six of the eight nontravelers, and covariance was demonstrated in four subjects. Background variation was detected in all 14 travelers, and covariance was demonstrated in 11 subjects. The median slopes of the regression lines of δ^{2}H vs. δ^{18}O were 6 and 7, respectively. Modeling indicated that^{2}H and ^{18}O doses yielding a 6:1 ratio of final enrichments should minimize this error introduced to the doubly labeled water method.

- stable isotope
- energy metabolism
- isotope fractionation

the doubly labeled water (DLW) method was developed by Nathan Lifson in the late 1940s primarily as a means of measuring energy expenditure in free-living animals. His experiments demonstrated that ^{18}O in body water was in isotopic equilibrium with the oxygen in respiratory CO_{2} (3, 12). Thus, after a loading dose of ^{2}H_{2}
^{18}O, the elimination of^{2}H from the body is a measure of water flux, whereas the elimination of ^{18}O is a measure of both water and CO_{2} flux. The difference between these two elimination rates allows for measurement of CO_{2} production (2,12), which can then be related to total energy expenditure (TEE) through standard indirect calorimetry equations.

One of the assumptions of the method is that the natural abundances of these stable isotopes entering the body are constant and thus that body water will return to the exact predose abundances after elimination of the ^{2}H_{2}
^{18}O loading dose. In actuality, this is not the case. The natural abundance of these isotopes in the body varies with the source and amount of water and food consumed, as well as with changes in the proportions of oxygen and hydrogen lost through CO_{2}, fractionated water, and nonfractionated water (8). The problem with assuming that the isotopic abundance is constant occurs when the baseline enrichment changes during the experiment. Increases or decreases in isotope abundances can occur when water intake varies or when there is a change in water source. In measuring the isotopic enrichment to determine the elimination rates, the absolute concentration of each isotope is not measured; it is the enrichment above predose baseline that is measured. If the natural abundance were to change, it could result in an overestimation or underestimation of the actual isotopic enrichment remaining in the body, which would result in a miscalculation of CO_{2} production and TEE.

Natural abundance shifts introduce error into calculations of the method. The impact of these baseline variations on the accuracy and precision of the method depends on the length of the study and the amount of dose administered (6, 11). As the size of the organism under study increases, so does the size of the water pool, and thus a higher dose is needed to enrich the pool. Therefore, the option to minimize these baseline fluctuations by giving a large dose of the isotope is not applicable in humans, and the impact of baseline variations becomes significant. It is possible, however, to minimize any error in baseline fluctuations if the relationship between the two isotopes in vivo is covariant. When the relationship is covariant, any shifts or changes in natural abundance will be in the same direction and magnitude for both isotopes, such that these errors will be partially canceled when the difference between the two elimination rates is calculated. This cancellation is maximal when the subjects are dosed in such a way that the enrichment ratio is equal to the slope of the covariant relationships of the two isotopes in vivo.

It has been assumed that the relationship between ^{2}H and^{18}O is covariant because of their known covariance in the environment, as depicted by the meteoric water line. Several studies have found that the relationship (6, 8, 14) between^{2}H and ^{18}O is covariant; however, the most recent human study has not (4). Because the majority of applications of the DLW method are currently in humans, our goal was to reinvestigate the relationship between ^{2}H and^{18}O to clearly determine it. Specifically, we believe that the relationship between ^{2}H and ^{18}O is covariant, with a slope that reflects the natural variations in meteoric water. Furthermore, the covariant relationship, if found, will have significant impact on the cost of the method, because it will allow a smaller dose of ^{2}H_{2}
^{18}O to be administered while error in the method is still minimized in humans.

## EXPERIMENTAL METHODS

#### Subjects.

Subjects were recruited from University of Wisconsin-Madison staff and students by local advertising. Subjects ranged from 18 to 50 yr of age. There were 3 males and 5 females for the nontravelers' study and 8 males and 6 females for the travelers' study. Subjects were excluded if they had a metabolic disease such as diabetes mellitus or thyroid dysfunction. Subjects participating in the first study were allowed to participate in the second, and they could participate multiple times provided each set of samples was from a different trip.

#### Protocol 1.

In the first part of this study, we recruited adult subjects to obtain urine samples from once a week for 6 wk. Samples were collected from the first void in the morning and placed in 5-ml cryogenic vials (Corning, Corning, NY) that were provided for each individual. Each sample was collected for 6 wk on the same day of each week so that each specimen was collected at weeklong intervals. Samples were stored at 4°C until analyzed.

#### Protocol 2.

For the second part of this study, we recruited subjects who were traveling ≥500 miles from Madison. Given that body water turns over ∼5–10% per day, entry criteria included the requirement that subjects must have left Madison for ≥3 days and traveled to a location with a change in water >10‰ in ^{2}H (13). Urine was collected from 3 days before the date of departure, during each day of travel, and for 1–2 wk upon return to Madison to monitor the turnover rate between water supplies.

#### Sample isotope analysis.

Urine specimens were obtained (5 ml) and treated with 200 mg of dry carbon black, filtered through 0.45-μm filters, and divided for isotope analysis. Deuterium abundance was measured by isotope ratio mass spectrometry (Delta Plus, Finnigan MAT, Bremen, Germany). An 0.8-μl aliquot of urine was automatically injected into a quartz tube packed with chromium metal powder (Fisher Scientific Chemical, Itaska, IL), and the hydrogen was admitted to a dual inlet for isotope analysis (7). Each mass spectrometric analysis included duplicate injections of the sample with independent isotope ratio analysis. Data were adjusted for H by a mathematical correction. Data were corrected for memory between sequential injections. Results were corrected to the standard mean ocean water (SMOW) scale using high (+679‰) and low (−49‰) secondary standards.

The ^{18}O-to-^{16}O isotope ratio analysis was performed on the Delta-S Isotope Ratio Mass Spectrometer (Finnigan MAT). Urine samples (1 ml) were isotopically equilibrated with 1 ml of CO_{2} in a 3-ml red cap Vacutainer (Becton-Dickinson, Franklin Lakes, NJ) at 25°C for a minimum of 48 h before sampling took place. The CO_{2} was introduced into a helium stream, chromatographed on chromosorb-Q, and introduced into the source for continuous flow isotopic analysis (9). During each mass spectrometric analysis, two separate injections and isotope analyses were performed. Results were expressed in per mil (δ‰) enrichment relative to SMOW.

#### Data analysis.

Sampling for *protocol 1* of this study included four separate mass spectrometric analyses for each of the ^{2}H and^{18}O samples. Analysis for the second part of this study followed our typical protocol of two separate mass spectrometric analyses for ^{18}O and one for ^{2}H. The standard deviation (SD) for the replicate analyses for each sample was calculated. The median value for the SD of the eight subjects in*protocol 1* was determined to be 0.17‰ for ^{18}O and 0.57‰ for ^{2}H. Outliers were eliminated on the basis of replicates displaying SD >0.35‰ for ^{18}O and >1.16‰ for deuterium (*P* < 0.01 vs. average SD,*F*-test). There were 2 outliers for ^{18}O out of 192 specimens and 5 out of 192 for ^{2}H. Additional analyses were performed to replace the outliers.

A correlation analysis between ^{2}H and ^{18}O was then conducted by linear regression, utilizing the average^{18}O and ^{2}H value for each sample. For the nontravelers, for whom six specimens per subject were used, a Pearson correlation coefficient (*r*) ≥ 0.754 was considered significant (*P *< 0.05). Because of the varying number of samples per subject in the second part of this study, the significant*r *value varied. Because the slope and correlation coefficients were not normally distributed, both the median and mean values were calculated.

Finally, analysis of total variance from each study was calculated, and the contribution from analytical error and source water to the total variance was determined. Total error possible in this method can be expressed by the equation
where ε_{A} is the analytical error, ε_{P Cov} is the variance of the water source and natural abundance variation, and ε_{P other} is all other physiological error terms combined. Total error (ε_{T}) was calculated as the average of the within-subject variance. ε_{A} was calculated as above and adjusted for the number of analyses for that subject. ε_{P Cov} was calculated as *r*
^{2}×ε_{T} for each subject, and ε_{P other} was calculated by the difference.

## RESULTS

The data for the nontravelers in *protocol 1* are presented in Table 1. The week-to-week shifts in the isotope abundances did not trend with time but fluctuated above and below their average values. As such, the variations were unlikely to be seasonal trends. The average ^{2}H abundance was −41.9 ± 4.5‰ vs. Vienna SMOW (vSMOW), and the average ^{18}O abundance was −5.2 ± 0.7‰ vs. vSMOW. The median correlation coefficient between ^{2}H and ^{18}O abundance was 0.78, and the median slope was 6.1 ± 2.5 for subjects exhibiting a significant relationship. This covariant relationship between isotopes was significant for four of the eight subjects (*P *≤ 0.05) and trended toward significance for two more subjects (0.05 ≤ *P*≤ 0.10; Fig. 1).

Data for the subjects in *protocol 2* of this study, who traveled away from the Madison area, are displayed in Table2. Isotopic changes were detected in all travelers, and the change tended to be systematic with time. Changes were unidirectional during the period of travel, with a return toward baseline upon return to Madison, WI. The average ^{2}H abundance was −41.2 ± 6.7‰, and the average ^{18}O abundance was −4.2 ± 1.0‰. The median correlation coefficient was 0.93, and the median slope was 7.2 ± 6.5 for those subjects exhibiting a significant correlation (average *r *= 0.88, average slope = 7.3). A significant relationship between the two isotopes was found for 11 of the 14 subjects (*P *≤ 0.05), with a trend for one more subject (0.05 ≤ *P *≤ 0.10; Fig. 2).

Individual values for each error component for the nontravelers of*protocol 1* are displayed in Table3. The average analytical SE was 0.1‰ for ^{18}O and 0.3‰ for ^{2}H. The average total SD was 0.23‰ for ^{18}O and 1.7‰ for ^{2}H. The average physiological covariant SD was 0.17‰ for ^{18}O and 1.1‰ for ^{2}H. And the average noncovariant physiological SD was 0.23‰ for ^{18}O and 1.2‰ for ^{2}H.

Individual values for each component of error for *protocol 2*, the travelers, were calculated and are displayed in Table4. The average analytical SE was 0.14‰ for ^{18}O and 0.6‰ for ^{2}H. The average total SD was 0.36‰ for ^{18}O and 3.4‰ for ^{2}H. The average physiological covariant SD was 0.35‰ for ^{18}O and 3.1‰ for ^{2}H. The average physiological noncovariant SD was ∼0‰ for ^{18}O and 1.0‰ for ^{2}H.

## DISCUSSION

#### Natural abundance.

The average values for the natural abundance of ^{2}H and^{18}O for the nontravelers and the travelers are significantly different from those for the abundance of tap water for Madison (MTW; ^{2}H = −57, ^{18}O = −8.7‰), which is located on the meteoric water line (MWL). This isotopic displacement is similar to previous reports (4, 6,8) and can be explained by the effects of fractionation during evaporative water loss, because light isotopes will be eliminated from the body water pool faster, leaving behind heavy or enriched body water (8).

The standard deviations surrounding the average isotopic abundances of^{2}H and ^{18}O for the nontravelers were not large. In terms of the absolute change in the heavy isotope concentration, this corresponds to an SD for ^{2}H of 0.3 ppm and an SD for^{18}O of 0.5 ppm, but these changes are not unimportant. If the baseline changes had occurred during an actual DLW experiment, and if we assume that no covariant relationship exists and no other errors occur, the resulting error in calculations of CO_{2}production would have been 7%. These variations probably result from daily modifications in the water and food consumed throughout the course of the experimental period. For example, consumption of bottled water and canned goods, as well as fruits grown in different parts of the world, contributes to changes in the natural abundance of^{2}H and ^{18}O, as food and bottled beverages will have an isotopic abundance that reflects the enrichment of the water in the location where they are grown or bottled. In addition, changes in water turnover, fractional evaporative water loss, and CO_{2}production can result in small isotopic changes (8).

The results from travelers better illustrate the effect of water source on the background isotopic abundances. By changing geographical locations, subjects were changing their water source, which resulted in an increase in total variance (ε_{T}) but not uncorrelated physiological variation (ε_{p}). This increase in ε_{T} between nontravelers and the travelers was completely explained by an increase in physiological covariant variance for both^{2}H and ^{18}O.

#### Covariant relationship.

The results of these experiments support the existence of a covariant relationship between ^{2}H and ^{18}O in vivo. Among nontravelers, six of eight subjects demonstrated a significant correlation or strong trend between the two isotopes. The failure of all eight to demonstrate a covariant relationship is due to the small total variance in several subjects. The geometric averages in the four with significant covariance (4.1‰ and 0.08‰ for ^{2}H and^{18}O, respectively) were significantly different (*P*≤ 0.05, *F*-test) compared with 1.6‰ and 0.03‰ for^{2}H and ^{18}O in the four without a significant relationship. This indicates that, in those subjects who did not exhibit covariance between ^{2}H and ^{18}O, the variations in natural abundance were just too small to be detected above analytical error. Because the total variance is low in these individuals, the effect on the accuracy of DLW is small (Table 3), and there is no need to adjust the ratio of tracer doses beyond the need for the dose to minimize the effects of analytical error (10).

Among the travelers, 11 of 14 subjects exhibited a covariant relationship between ^{2}H and ^{18}O (*P*≤ 0.05), with another individual trending toward a significant correlation (0.05 ≤ *P *≤ 0.10). Of the remaining two subjects, ε_{T} values were also small, and thus covariance was harder to detect above the analytical error (Table 4).

In a typical DLW experiment, subjects are informed that traveling during the study is not appropriate, and it is more typical for subjects to remain in the location where they began the study than to travel. Therefore, we felt that the linear regression results for the nontravelers were more representative of a typical experiment than results from the travelers, because the nontravelers did not travel or introduce new water sources. For the nontravelers, there does appear to be a significant covariance, with a median correlation coefficient of 0.79. This value is similar to the cross-sectional value previously found by Schoeller et al. (6), a correlation of 0.83. Not all subjects for DLW studies, however, refrain from travel during the study, and in some studies travel occurs by study design, and thus the results from the travelers are also important.

#### Slope.

When the relationship between deuterium and 18-oxygen is covariant, the slope of the linear regression line determines the ratio of^{2}H to ^{18}O in the dose that should be given to minimize error in the DLW method. If the two isotopes are covariant, then when subjects are dosed in a ratio equal to the slope of their covariance, error introduced by the variation of these isotopes will be canceled when the difference between ^{18}O and ^{2}H elimination rates is calculated for TEE and will not contribute to the total error of the method.

Studies analyzing the relationship between ^{2}H and^{18}O in vivo have found that the expected slope is influenced by multiple factors (8). Increases in CO_{2} production, increases in H_{2}O turnover, fractionated gas loss, and changes in the water source all affect the slope of the relationship between the two isotopes. One previous model (8) predicted that increases in CO_{2} production result in a change in the isotopic abundance, with a slope of 5.4:1 for^{2}H to ^{18}O. Effects of altering the rate of water turnover resulted in a slope of 3:1. Increases in fractionated gas loss resulted in a slope of 7:1, and the effect of changing water sources to a new source on the MWL resulted in a shift in the^{2}H-to-^{18}O ratio to 10:1.

Individuals' slopes from the experiments described here did vary; however, most were within the expected range. The slope values found for these experiments were 6.1 ± 1.7 for the nontravelers and 7.2 ± 6.5 for the travelers. Although most individuals exhibited a relationship within the expected range of slopes, there were several individuals with slopes outside the predicted range (*subjects 7*′, *8*′, *10*, and*12*). These subjects also exhibited significant correlations between ^{2}H and ^{18}O (*P *≤ 0.05). In two of these subjects, we were able to determine the reasons for these results. *Subjects 7*′ and *8*′ traveled together to Arizona in the southwest United States. We obtained a sample of the local water of Arizona (AZ tap water) and determined that the water source from Arizona was not on the MWL, although its abundance is typical of water from an “arid” region. Figure3 shows that the subjects' enrichments changed in the direction proportional to the change from MTW to AZ tap water. Thus the unusual slope for the relative changes in the isotope abundances of urinary water in these two subjects resulted from the failure of the AZ tap water to fall on the MWL.

#### Error analysis.

The influence of these variances and their covariance in the precision of the DLW technique were determined by use of a propagation of error analysis. The average error components for the nontravelers were determined from repeated analysis of individual samples. In our hands, a typical DLW analysis includes two ^{18}O analyses with three replicates per analysis, and one ^{2}H analysis, with two replicates per analysis. When adjusted for the difference between our typical DLW analysis and our multiple analyses for the nontravelers, the predicted ε_{A} = 0.02‰^{2} (SD = 0.14‰) for ^{18}O and 0.39‰^{2} (SD = 0.62‰) for ^{2}H. The total variance then becomes 0.062‰^{2} (SD = 0.25‰) for ^{18}O and 3.19‰^{2} (SD = 1.8‰) for ^{2}H.

To determine the effect the covariant relationship has on the amount of dose administered, these errors were propagated through the calculation of TEE in a representative 70-kg male subject with a TEE of 2,800 kcal/day. Initially, we modeled the propagation of error for a dose of 0.24 g ^{18}O/kg total body water (TBW) and 0.10 g^{2}H/kg TBW [assuming 100 atom percent enrichment (APE) of the doses], which results in a postdose per mil enrichment ratio of 8:1 (^{2}H-^{18}O) and an enrichment ratio of 6:1 at the end of the collection period. The simulated dose was then altered such that both ^{2}H and ^{18}O doses were decreased to 25 or 50% of the original dose, or increased 125, 150, or 200% while the 6:1 dose ratio in delta per mil enrichment of ^{2}H to ^{18}O was maintained. The effect of error on TEE was then calculated with and without inclusions of the covariant relationship. To do this, we modeled analytical error on baseline and *day 1* and total error on *day 14*. Thus the within-day variations in background were assumed to be zero over the first part of the dose day. For the noncovariant model, we performed the propagation of error analysis separately for both isotopes and then summed the variances. For the covariant analysis, the ε_{T} and ε_{P cov} terms were applied simultaneously for both isotopes, which allowed the errors to cancel.

The results of this model are displayed in Fig.4 as the percent error in calculations of TEE. When error is added assuming noncovariance, the percent error in TEE calculations is increased relative to the covariant case. As the dose amount is increased, the error occurring with or without covariance is reduced. This is due to the effect of “flooding” the body with a high enrichment of ^{2}H and^{18}O, minimizing any “noise” or baseline fluctuations. However, the issue of cost then arises, as the amount of^{18}O administered increases in proportion to the increase in^{2}H dose given, and thus the method becomes more costly. A second model analysis was performed to simulate the effect of altering the enrichment ratio of ^{2}H to ^{18}O (Fig.5). With the same theoretical male as used in the previous model, we simulated the effect of error at different final enrichment ratios on the percent error in calculations of TEE with and without a covariant relationship. At the standard end-period enrichment ratio of 6:1, error occurring from assumed noncovariance increased the percent error in calculations of TEE to 6.7%. When the error was treated as covariant, the percent error in TEE calculations was decreased to 3.0%, bringing the measured TEE closer to the true expenditure of 2,802 kcal. When the enrichment ratio began to deviate from the 6:1 ratio, the effects of introductions of error were magnified. This effect was largest for the final enrichment ratio of <4:1, resulting in an error of 8% when noncovariance was assumed and 4% when covariance was assumed. As the enrichment ratio increased, the effect of an increase in total error without modeling the covariant relationship did begin to decrease because of the effect of the large dose. When covariance was modeled, the error increased with increasing deuterium dose, but the increase was quite modest even up to an enrichment ratio of 12:1. The error does not increase as rapidly with increasing enrichment ratios as with decreasing ratios because of the ε_{P other} variance in the deuterium data. The effect of this error is successively reduced as the deuterium dose increases.

When the isotope cost is considered, especially for ^{18}O, there is great interest in decreasing the dose. This model indicates that the dose can be decreased ∼20–25% from our previously recommended dose of 0.24 g/kg body water, with only a modest decrease in DLW precision. Further reduction, however, sufficiently increases the relative error. The use of these lower doses does require^{2}H and ^{18}O precisions of 0.62‰ and 0.14‰, respectively. Not all labs attain this precision, and in this case the larger doses are needed (10). The effect of poorer analytical precision on the precision of TEE is modeled in Fig.6. The rapid increase in the modeled error in TEE illustrates the need to assess and improve analytical error in individual analytical centers (10). At these lower doses, it is also important to limit the metabolic period to <2.5 tracer half-lives to control the error in the rate of CO_{2} production (6). Proportionally larger doses and careful attention to the length of the metabolic period are still recommended for young children (6). The major exception to this would be someone undergoing an unusual isotopic shift. The two individuals who traveled to Arizona might appear to be such a case. The relative errors in TEE modeled for these subjects were 7 and 9% at a 6:1 enrichment ratio (Table 4). Unfortunately, the background effect cannot be compensated for by adjusting the enrichment ratio, because the isotopic backgrounds of the two tracers are changing in opposite directions. Errors can only be reduced by using larger doses, moderate periods of sample collection, or the use of unlabeled subjects to determine correction factors. Had the city of origin had an isotopically heavier water source, then the slope might have been positive but small. For slopes of <5:1, matching the enrichment ratio to the slope is generally not recommended, because reducing the deuterium dose to reach this ratio would increase the effect of the analytical error on the relative error in TEE, whereas increasing the^{18}O dose would be costly.

#### Covariance controversy.

The relationship between ^{2}H and ^{18}O in vivo has been controversial. Ritz et al. (5) analyzed the within-subject and between-subject relationship between ^{2}H and ^{18}O, and they found a significant between-subject relationship but not a significant within-subject relationship between the two isotopes.

Our studies reinvestigated the within-subject relationship between^{2}H and ^{18}O. Results indicated that there was a significant relationship between the two isotopes in vivo (median *r *= 0.78). Although the individual slopes determined here exhibited a range of values, the confidence intervals are such that there is no reason to discard the null hypothesis for constancy of the slopes among the nontravelers. Surprisingly, the slopes exhibited in the study by Ritz et al. demonstrated a much tighter range than did those of our subjects, although the differences were not significant. The range of the slopes displayed by the subjects in the Ritz experiments was 4.1 ±1.4 to 5.4 ±1.2, not dramatically different from the range seen by subjects in our studies here, indicating that although slopes varied, they were within expected limits (8).

It is possible that Ritz et al. (5) did not find a correlation between ^{2}H and ^{18}O in vivo because of a larger analytical error. The total variance in their measurements was 5.4‰^{2} for ^{2}H and 0.13‰^{2} for^{18}O, which is large compared with the total error in our experiments of 3.19‰^{2} for ^{2}H and 0.06‰^{2} for ^{18}O. This could result from a larger physiological variation or a larger analytical variation. Unfortunately, they did not directly measure the analytical variation but calculated the analytical noise with previous mass spectrometric precision values (5) and a mathematical model (4). Their findings recommended a 12:1 enrichment ratio. The advantage of the 6:1 enrichment ratio decreases with increasing analytical variance, and thus 12:1 may be the preferred ratio under their circumstances (Fig. 6).

One last possible reason could be that the abundances of^{18}O and deuterium in food, food moisture, and beverages in the United States exhibit a different relationship from those in the United Kingdom (as in Ref. 5), whether due to packaging and preparation of food or the water source. It is possible that if some of the food in the UK displayed a different relationship from that of the MWL, the circumstance might introduce noncovariant error and thus mask a covariant relationship.

#### Cost analysis.

If the dose of ^{2}H_{2}
^{18}O is administered to give a final enrichment ratio equal to the relationship of ^{2}H to ^{18}O in the body, then error will be minimized such that less total isotope will be needed, and the total cost of the method will be decreased. If a 6:1 final enrichment ratio is used and covariant changes occur, then to decrease the total error occurring in calculations of TEE to 3%, the amount of dose administered must be 0.2 g ^{18}O/kg TBW with a proportional amount of ^{2}H. However, if a noncovariant error occurs, as would be the case if tritium were used instead of deuterium, to decrease the error in the method to <3%, the amount of^{18}O needed in the dose increases by more than twofold (Fig.4). This increases the cost per subject for ^{18}O. This cost analysis illustrates the importance of understanding the error structure of this expensive stable isotope tracer as it applies to the DLW method. This should be done in each individual laboratory, particularly with respect to analytical error, to determine appropriate tracer doses to obtain a given level of precision in TEE. When analytical precision is 0.14 and 0.6 per mil for^{18}O and deuterium, or better, then doses of 0.2 and 0.09 g/kg total body water of 100 AP equivalents of ^{18}O and deuterated water are acceptable dosages for adults in temperate climates.

## Footnotes

Address for reprint requests and other correspondence: D. Schoeller, Univ. of Wisconsin-Madison, 1415 Linden Drive, Madison, WI 53706 (E-mail: dschoell{at}nutrisci.wisc.edu).

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked “

*advertisement*” in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

- Copyright © 2001 the American Physiological Society