Department of Nutritional Sciences, University of
Wisconsin-Madison, Madison, Wisconsin 53706
The doubly labeled water method
for measuring total energy expenditure is subject to error from natural
variations in the background 2H and 18O 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
2H and 18O 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
2H vs.
18O were 6 and 7, respectively. Modeling indicated that
2H and 18O doses yielding a 6:1 ratio of final
enrichments should minimize this error introduced to the doubly labeled
water method.
 |
INTRODUCTION |
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 18O
in body water was in isotopic equilibrium with the oxygen in respiratory CO2 (3, 12). Thus, after a loading
dose of 2H218O, the elimination of
2H from the body is a measure of water flux, whereas the
elimination of 18O is a measure of both water and
CO2 flux. The difference between these two elimination
rates allows for measurement of CO2 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 2H218O 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 CO2, 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
CO2 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 2H and
18O 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
2H and 18O 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 2H and
18O to clearly determine it. Specifically, we believe that
the relationship between 2H and 18O 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 2H218O 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 2H (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 18O-to-16O 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
CO2 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 CO2 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 (
)
enrichment relative to SMOW.
Data analysis.
Sampling for protocol 1 of this study included four separate
mass spectrometric analyses for each of the 2H and
18O samples. Analysis for the second part of this study
followed our typical protocol of two separate mass spectrometric
analyses for 18O and one for 2H. 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 18O
and 0.57
for 2H. Outliers were eliminated on the basis
of replicates displaying SD >0.35
for 18O and >1.16
for deuterium (P < 0.01 vs. average SD,
F-test). There were 2 outliers for 18O out of
192 specimens and 5 out of 192 for 2H. Additional analyses
were performed to replace the outliers.
A correlation analysis between 2H and 18O was
then conducted by linear regression, utilizing the average
18O and 2H 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
A is the analytical error,
P
Cov is the variance of the water source and natural abundance
variation, and
P other is all other physiological error
terms combined. Total error (
T) was calculated as the
average of the within-subject variance.
A was calculated
as above and adjusted for the number of analyses for that subject.
P Cov was calculated as r2
×
T for each subject, and
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 2H
abundance was
41.9 ± 4.5
vs. Vienna SMOW
(vSMOW), and the average 18O abundance
was
5.2 ± 0.7
vs. vSMOW. The median correlation coefficient
between 2H and 18O 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).

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Fig. 1.
Deuterium and 18O abundances for the
nontravelers plotted with the meteoric water line (MTW; see Ref.
1). Abundances are expressed vs. standard mean ocean
water.
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Data for the subjects in protocol 2 of this study, who
traveled away from the Madison area, are displayed in Table
2. 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 2H
abundance was
41.2 ± 6.7
, and the average 18O
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).

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Fig. 2.
Deuterium and 18O abundances for the
travelers plotted with the MLW (1). Abundances are
expressed vs. standard mean ocean water.
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|
Individual values for each error component for the nontravelers of
protocol 1 are displayed in Table
3. The average analytical SE was 0.1
for 18O and 0.3
for 2H. The average total SD
was 0.23
for 18O and 1.7
for 2H. The
average physiological covariant SD was 0.17
for 18O and
1.1
for 2H. And the average noncovariant physiological
SD was 0.23
for 18O and 1.2
for 2H.
Individual values for each component of error for protocol
2, the travelers, were calculated and are displayed in Table
4. The average analytical SE was 0.14
for 18O and 0.6
for 2H. The average total SD
was 0.36
for 18O and 3.4
for 2H. The
average physiological covariant SD was 0.35
for 18O and
3.1
for 2H. The average physiological noncovariant SD
was ~0
for 18O and 1.0
for 2H.
 |
DISCUSSION |
Natural abundance.
The average values for the natural abundance of 2H and
18O for the nontravelers and the travelers are
significantly different from those for the abundance of tap water for
Madison (MTW; 2H =
57, 18O =
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
2H and 18O for the nontravelers were not large.
In terms of the absolute change in the heavy isotope concentration,
this corresponds to an SD for 2H of 0.3 ppm and an SD for
18O 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 CO2
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
2H and 18O, 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 CO2
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 (
T) but not uncorrelated physiological variation (
p). This increase in
T between nontravelers and the travelers was completely
explained by an increase in physiological covariant variance for both
2H and 18O.
Covariant relationship.
The results of these experiments support the existence of a covariant
relationship between 2H and 18O 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 2H and
18O, respectively) were significantly different (P
0.05, F-test) compared with 1.6
and 0.03
for
2H and 18O in the four without a significant
relationship. This indicates that, in those subjects who did not
exhibit covariance between 2H and 18O, 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 2H and 18O (P
0.05), with another individual trending toward a significant correlation (0.05
P
0.10). Of the remaining two
subjects,
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
2H to 18O 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 18O and 2H
elimination rates is calculated for TEE and will not contribute to the total error of the method.
Studies analyzing the relationship between 2H and
18O in vivo have found that the expected slope is
influenced by multiple factors (8). Increases in
CO2 production, increases in H2O 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 CO2 production
result in a change in the isotopic abundance, with a slope of 5.4:1 for 2H to 18O. 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
2H-to-18O 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 2H and 18O (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. Figure
3 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.

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Fig. 3.
Subjects traveling to an arid region plotted against the
MWL, Madison tap water, and the local drinking water (1).
Abundances are expressed vs. standard mean ocean water.
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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 18O analyses with three
replicates per analysis, and one 2H 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
A = 0.02
2 (SD = 0.14
) for 18O and 0.39
2 (SD = 0.62
) for 2H. The total variance then becomes
0.062
2 (SD = 0.25
) for 18O and
3.19
2 (SD = 1.8
) for 2H.
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 18O/kg total body water (TBW) and 0.10 g
2H/kg TBW [assuming 100 atom percent enrichment (APE) of
the doses], which results in a postdose per mil enrichment ratio of
8:1 (2H-18O) and an enrichment ratio of 6:1 at
the end of the collection period. The simulated dose was then altered
such that both 2H and 18O 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 2H
to 18O 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
T and
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 2H and
18O, minimizing any "noise" or baseline fluctuations.
However, the issue of cost then arises, as the amount of
18O administered increases in proportion to the increase in
2H 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 2H to 18O (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
P other variance in the deuterium data.
The effect of this error is successively reduced as the deuterium dose
increases.

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Fig. 4.
Effect of tracer doses on the percent error in
calculations of total energy expenditure (TEE). The dose is expressed
as grams of 100 atom percent 18O water per kg total body
water (TBW). The deuterium dose was increased proportionately, keeping
the end enrichment ratio equal to 6:1.
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Fig. 5.
Effect of altering the end enrichment ratio on the
percent error in TEE calculations. To calculate the dose weights,
0.1 g of 100 atom percent 18O or 2H water
in 1 kg of water increases the postdose isotopic abundances relative to
standard mean ocean water by 45 and 578 , respectively.
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When the isotope cost is considered, especially for 18O,
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 2H and 18O 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
CO2 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
18O dose would be costly.

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Fig. 6.
Effect of analytical precision on the relative standard
deviation (SD) in the estimate of TEE by doubly labeled water at end
enrichment ratios of 6:1 and 12:1.
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Covariance controversy.
The relationship between 2H and 18O in vivo has
been controversial. Ritz et al. (5) analyzed the
within-subject and between-subject relationship between 2H
and 18O, 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
2H and 18O. 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 2H and 18O in vivo because
of a larger analytical error. The total variance in their measurements
was 5.4
2 for 2H and 0.13
2 for
18O, which is large compared with the total error in our
experiments of 3.19
2 for 2H and
0.06
2 for 18O. 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
18O 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 2H218O is
administered to give a final enrichment ratio equal to the relationship
of 2H to 18O 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 18O/kg TBW with a
proportional amount of 2H. 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
18O needed in the dose increases by more than twofold (Fig.
4). This increases the cost per subject for 18O. 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
18O and deuterium, or better, then doses of 0.2 and 0.09 g/kg total body water of 100 AP equivalents of 18O and
deuterated water are acceptable dosages for adults in temperate climates.
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.