Dilution space ratio of ²H and ¹⁸O of doubly labeled water method in humans

The doubly labeled water method is a precise method for measuring energy expenditure in free-living individuals. Its accuracy, however, is dependent on the ratio the relative dilution spaces of the two tracers. Herein we demonstrate that this ratio is not influenced by most subject characteristics and that a single constant can be used in most studies.

Abstract

Variation of the dilution space ratio (N_d/N_o) between deuterium (²H) and oxygen-18 (¹⁸O) impacts the calculation of total energy expenditure (TEE) by doubly labeled water (DLW). Our aim was to examine the physiological and methodological sources of variation of N_d/N_o in humans. We analyzed data from 2,297 humans (0.25-89 yr old). This included the variables N_d/N_o, total body water, TEE, body mass index (BMI), and percent body fat (%fat). To differentiate between physiologic and methodologic sources of variation, the urine samples from 54 subjects were divided and blinded and analyzed separately, and repeated DLW dosing was performed in an additional 55 participants after 6 mo. Sex, BMI, and %fat did not significantly affect N_d/N_o, for which the interindividual SD was 0.017. The measurement error from the duplicate urine sample sets was 0.010, and intraindividual SD of N_d/N_o in repeats experiments was 0.013. An additional SD of 0.008 was contributed by calibration of the DLW dose water. The variation of measured N_d/N_o in humans was distributed within a small range and measurement error accounted for 68% of this variation. There was no evidence that N_d/N_o differed with respect to sex, BMI, and age between 1 and 80 yr, and thus use of a constant value is suggested to minimize the effect of stable isotope analysis error on calculation of TEE in the DLW studies in humans. Based on a review of 103 publications, the average dilution space ratio is 1.036 for individuals between 1 and 80 yr of age.

NEW & NOTEWORTHY

The doubly labeled water method is a precise method for measuring energy expenditure in free-living individuals. Its accuracy, however, is dependent on the ratio the relative dilution spaces of the two tracers. Herein we demonstrate that this ratio is not influenced by most subject characteristics and that a single constant can be used in most studies.

the doubly labeled water (DLW) method is a unique tool for estimating total energy expenditure (TEE) in free-living condition with minimum constraints. The method was developed and validated by Lifson et al. in animals in 1955 (16). It was not until 27 yr later that Schoeller and van Santen applied first this method in humans (25). The DLW method has been validated against human calorimeter and/or food intake measurements in multiple experiments that targeted lean to obese subjects, infants to adults, and sedentary to exercise conditions (14a, 20, 22, 28, 30). The method has also been applied easily in hundreds of human studies because it provides a measure of TEE during habitual living conditions while imposing only a small subject burden only requiring that the subjects provide a modest number of specimens (any of urine, saliva, or plasma) before and after administration of DLW (usually by mouth) (14a, 28).

The DLW method makes use of the observation that the deuterium (²H) and oxygen-18 (¹⁸O) kinetics differ because ²H is eliminated from the body as water, while ¹⁸O is eliminated as water and carbon dioxide (16). Specifically, the rate of carbon dioxide production (rCO₂) is calculated from the difference of the products of isotope elimination rate and isotope dilution space of the two stable isotopes (7, 8, 17). These isotope dilution spaces are close to that of total body water (TBW), but both ²H and ¹⁸O also exchange with nonaqueous body components and thus are slightly larger than TBW. The extent of the nonaqueous exchange is estimated to be approximately 4∼5 and 1% for ²H and ¹⁸O, respectively, in humans (13, 19). Although the variation around these estimates is small, any variation would propagate through the calculations and have a measureable effect on the calculated of rCO₂, and hence TEE. For example, in the average adult human, if the actual dilution space ratio (N_d/N_o) was 0.01 lower than the N_d/N_o used in the calculation (1.027 vs 1.037), TEE is underestimated by 4–5%, which is not negligible for many applications of the method (18).

Currently, the most widely used equation for human subjects assumes N_d/N_o is a constant of 1.034 and not different between individuals (19); however, the individual values reported for this ratio have been reported to vary and there is concern that the variation might depend on physical or diet characteristics of the subjects or animals (10, 11). For example, female subjects have higher fat and slightly lower protein masses per unit of TBW, which may affect the fractional isotopic exchange into nonaqueous, organic compounds, and thus N_d/N_o. Indeed, Goran et al. (10) reported significantly higher N_d/N_o in males than in females (1.052 and 1.044, respectively). In contrast, Racette et al. (19) reported that females tended to have a higher N_d/N_o than males although neither difference was significant (P = 0.07). These studies, however, were based on a small sample size and might be biased by sampling or measurement technique (6).

The aim of this study was to examine the physiological and methodological effects on variation of N_d/N_o in human DLW studies and determine the N_d/N_o value and range using a large sample. In the past 30 yr, we have conducted quite a large number of the DLW studies providing a database large enough to detect smaller differences than in previous studies.

MATERIALS AND METHODS

Subjects.

We analyzed the N_d/N_o data from 2,297 human subjects. Subjects included males and females with ages between 0.25 and 89 yr. All of the subjects lived in United States at the time of measurement. The subjects had been recruited to various research studies and the physical characteristics are summarized in Table 1. Each of the studies that contributed to the database as well as the creation of the deidentified database were approved by the IRBs of the institutions with which DAS was affiliated at the time of study (University of Wisconsin-Madison or the University of Chicago). Additional IRB approvals were obtained from the various institutions comprising the clinical sites at which the subjects were enrolled in the study.

Table 1.

Physical characteristics and body composition for human subjects

Age, yr	Height, cm	BW, kg	BMI, kg/m2	Body fat, %	FM, kg	FFM, kg	(n)
Male
<1 yr	62.1 ± 2.3	6.2 ± 0.8	17.7 ± 11.1	16.1 ± 1.3	1.1 ± 0.7	5.1 ± 0.7	(20)
2–5 yr	94.4 ± 8.7	14.7 ± 3.1	24.1 ± 6.0	16.4 ± 1.2	3.7 ± 1.6	11.0 ± 1.8	(44)
6–11 yr	130.5 ± 16.6	35.0 ± 17.9	27.3 ± 10.7	19.2 ± 5.2	11.1 ± 9.5	23.9 ± 9.1	(44)
12–19 yr	174.0 ± 9.4	65.6 ± 10.4	22.5 ± 8.0	21.7 ± 3.4	15.1 ± 7.4	50.4 ± 7.6	(81)
20–29 yr	179.1 ± 5.7	80.5 ± 16.8	21.6 ± 7.5	25.1 ± 5.0	18.1 ± 10.5	62.4 ± 9.2	(36)
30–39 yr	181.4 ± 7.3	88.5 ± 17.9	24.7 ± 9.5	27.0 ± 5.8	23.0 ± 13.3	65.5 ± 7.9	(21)
40–49 yr	177.9 ± 8.0	85.5 ± 15.1	29.8 ± 5.5	26.9 ± 4.0	25.9 ± 8.1	59.6 ± 9.2	(111)
50–59 yr	176.4 ± 6.6	89.6 ± 15.7	32.7 ± 5.7	28.7 ± 4.6	29.8 ± 9.4	59.8 ± 8.5	(102)
60–69 yr	175.8 ± 6.9	88.9 ± 15.7	34.6 ± 5.4	28.7 ± 4.2	31.3 ± 9.5	57.6 ± 7.8	(81)
70–79 yr	173.4 ± 7.5	82.5 ± 13.2	33.4 ± 6.2	27.5 ± 4.2	28.0 ± 8.4	54.5 ± 7.0	(148)
80–89 yr	172.0 ± 6.2	79.0 ± 13.4	34.0 ± 6.2	26.8 ± 4.5	27.4 ± 8.3	51.6 ± 6.9	(54)
Total	165.0 ± 28.6	73.7 ± 27.0	29.6 ± 8.3	25.4 ± 5.7	23.1 ± 12.0	50.6 ± 17.2	(742)
Female
<1 yr	60.9 ± 1.5	5.8 ± 0.5	23.2 ± 6.8	15.5 ± 1.1	1.3 ± 0.4	4.4 ± 0.5	(25)
2–5 yr	93.3 ± 8.7	14.3 ± 3.1	25.7 ± 6.2	16.2 ± 1.4	3.8 ± 1.6	10.5 ± 1.8	(46)
6–11 yr	129.4 ± 16.9	35.1 ± 19.1	32.8 ± 10.7	19.6 ± 6.4	13.1 ± 11.4	22.0 ± 8.6	(39)
12–19 yr	164.7 ± 6.7	60.6 ± 10.4	33.4 ± 5.5	22.3 ± 3.3	20.5 ± 6.6	40.0 ± 5.4	(151)
20–29 yr	164.7 ± 5.5	64.4 ± 13.5	33.2 ± 7.4	23.8 ± 5.2	22.0 ± 9.8	42.4 ± 6.1	(87)
30–39 yr	166.3 ± 6.0	75.2 ± 19.1	36.6 ± 7.9	27.1 ± 6.4	28.5 ± 13.2	46.6 ± 7.8	(42)
40–49 yr	164.3 ± 7.0	74.8 ± 20.4	38.7 ± 7.9	27.6 ± 7.0	30.2 ± 13.9	44.6 ± 7.8	(115)
50–59 yr	163.3 ± 6.4	76.9 ± 18.2	42.7 ± 6.7	28.8 ± 6.3	33.8 ± 12.6	43.1 ± 6.8	(121)
60–69 yr	161.9 ± 6.6	75.4 ± 15.3	42.8 ± 6.1	28.8 ± 5.7	33.0 ± 10.8	42.4 ± 5.7	(359)
70–79 yr	160.4 ± 6.0	71.9 ± 14.7	42.3 ± 6.2	27.9 ± 5.5	31.0 ± 10.2	40.9 ± 5.8	(461)
80–89 yr	158.5 ± 6.3	66.9 ± 11.4	40.2 ± 6.4	26.7 ± 4.7	27.4 ± 8.0	39.5 ± 5.1	(109)
Total	157.6 ± 19.0	67.8 ± 20.8	39.5 ± 8.1	26.5 ± 6.3	28.0 ± 12.6	39.8 ± 9.8	(1,555)

Values are the mean ± SD; n = number of subjects.

BW, body weight; BMI, body mass index; FM, fat mass; FFM, fat-free mass.

DLW administration and sample collection.

Subjects provided a baseline urine sample and were given an oral dose containing ¹⁸O- and ²H-labeled water. The dose was typically between 1.9 and 2.5 g/kg estimated TBW (10 atom% H₂¹⁸O) and between 0.01 and 0.016 g/kg estimated TBW (99.9 atom% ²H₂O). Urine samples were collected at approximately 2, 3, and 4 h after dosing. Subjects were allowed a maximum of 250 ml of liquid after the 1-h postdose time point and up to 500 ml total water consumption through the 4-h time point but were usually less than 250 ml. These volumes were subtracted from the TBW values but not the dilution space. Urine samples were stored at −20°C until the stable isotope abundances of the physiologic samples were measured by isotope ratio mass spectrometry (IRMS). For geriatric populations, plasma or saliva samples were obtained and used for those who had evidence of delayed isotopic equilibration into urine likely caused by urine postvoid retention in the bladder (3). If no saliva was available, subjects for whom the dilution spaces at 3 and 4 h after the dose differed by more than 5% were dropped from the data set. Isotope dilution spaces were calculated by the plateau method according to Cole and Coward (5) using gravimetric dilutions of the dose water. These dilutions were performed in triplicate once for each batch of DLW dose water and those values used in the dilution space calculations for each individual whose dose water came from the batch. Two laboratory standards, one natural abundance and enriched to mimic postdose enrichments, were run daily to correct for day-to-day variations in the IRMS systems. Carbon dioxide production was calculated over ca. 7 or 14 days using the two-point DLW method with Eq. A6 of Schoeller et al. (23), as modified by Racette et al. (19), and energy expenditure using the modified Weir equation (29).

Stable isotope analysis.

Urine (<5 ml) was mixed with <200 mg carbon black to remove impurities and filtered through a 0.45-μm filter. Saliva was centrifuged (4°C, 1 h, relative centrifugal force: 12,000 g) to remove dense proteins. One milliliter of urine or saliva was placed into an autosampler vial and deuterium was measured by IRMS after reduction over chromium (Delta Plus mass spectrometer; Finnigan MAT, Bremen, Germany). From each 1 ml of sample, 1 μl was injected into a quartz tube packed with chromium powder held at 850°C to reduce the water to hydrogen gas. Each run included three injections of the sample with independent analysis. Data were corrected for both H³⁺ and memory. Results were corrected to the standard mean ocean water (SMOW) scale using laboratory-working standards. A second 1 ml of saliva or carbon black-cleaned urine was allowed to equilibrate with CO₂ at 25°C for 48 h. The ¹⁸O concentration was measured by continuous flow IRMS (Delta V; Thermo Scientific, Bremen, Germany). Isotopic abundances were expressed on SMOW scale using calibrated laboratory standards.

Blind analysis for test-retest precision.

Urine samples from 54 subjects were blinded and analyzed twice. The samples were prepared by investigators outside of our institute. The samples were aliquoted into different tubes and labeled with a different ID. After all analyses had been finished, matching by IDs was done by an investigator who did not conduct any of the isotope analyses.

Redosing after 6 mo for intraindividual variability.

A total of 55 subjects received the second DLW experiment after 6 mo. The DLW administration and sample collection protocols were identical to those of the first study. The samples were analyzed after being labeled by an investigator outside our institute to blind the analysis and an investigator who did not perform any of the analyses matched the data after all analyses had been completed.

Statistical analysis.

The subjects were categorized by body mass index (BMI) into underweight (<18.5 kg/m²), normal healthy weight (18.5–24.99 kg/m²), overweight (25–29.99 kg/m²), class I obese (30–34.99 kg/m²), class II obese (35–39.99 kg/m²), and class III obese (>40 kg/m²). The subjects were also categorized by age group based on date of birth.

Results were presented as mean ± SD. Two-way ANOVA was conducted for N_d/N_o with BMI category and sex as between-subject factor. Regression analysis was conducted for N_d/N_o with age, sex, BMI, and body fat (%fat) as independent variables. All analyses were performed using IBM SPSS 23.0 for Mac (IBM, New York, NY). For all of the analyses, an α of 0.05 was used to denote statistical significance.

RESULTS

Physiological effects.

Figure 1 displays the frequency distribution N_d/N_o of all subjects, which was normally distributed. The mean N_d/N_o for all human subjects (n = 2,297) is 1.0374 ± 0.0167 and 95% confidence interval (CI) for the mean was 1.0367–1.0381 (Table 2). The mean N_d/N_o and 95% CI are shown for each of the 11 age groups and sex in Table 2.

Fig. 1.

Dilution space ratio (N_d/N_o) histogram for all human subjects. CI, confidence interval.

Table 2.

N_d/N_o ratio for human subjects

Age	Male (n)	Female (n)	All (n)	95% CI
<1 yr	1.0363 ± 0.0230 (20)	1.0342 ± 0.0164 (25)	1.0351 ± 0.0194 (45)	1.0295–1.0408
2–5 yr	1.0505 ± 0.0149 (44)	1.0419 ± 0.0223 (46)	1.0461 ± 0.0194 (90)	1.0421–1.0501
6–11 yr	1.0382 ± 0.0138 (44)	1.0412 ± 0.0237 (39)	1.0396 ± 0.0190 (83)	1.0355–1.0437
12–19 yr	1.0364 ± 0.0130 (81)	1.0324 ± 0.0121 (151)	1.0338 ± 0.0126 (232)	1.0322–1.0354
20–29 yr	1.0385 ± 0.0145 (36)	1.0375 ± 0.0156 (87)	1.0378 ± 0.0152 (123)	1.0351–1.0405
30–39 yr	1.0377 ± 0.0158 (21)	1.0437 ± 0.0153 (42)	1.0417 ± 0.0156 (63)	1.0378–1.0456
40–49 yr	1.0385 ± 0.0178 (111)	1.0364 ± 0.0168 (115)	1.0374 ± 0.0173 (226)	1.0352–1.0397
50–59 yr	1.0350 ± 0.0182 (102)	1.0375 ± 0.0200 (121)	1.0363 ± 0.0192 (223)	1.0338–1.0388
60–69 yr	1.0433 ± 0.0147 (81)	1.0420 ± 0.0127 (359)	1.0422 ± 0.0131 (440)	1.0410–1.0434
70–79 yr	1.0325 ± 0.0185 (148)	1.0366 ± 0.0162 (461)	1.0356 ± 0.0168 (609)	1.0342–1.0369
80–89 yr	1.0282 ± 0.0169 (54)	1.0320 ± 0.0180 (109)	1.0308 ± 0.0177 (163)	1.0281–1.0335
Total	1.0370 ± 0.0174 (742)	1.0376 ± 0.0163 (1,555)	1.0374 ± 0.0167 (2,297)	1.0367–1.0381

Values are the mean ± SD; n = number of subjects.

CI, confidence interval.

As shown in Table 3, there were no significant age groups-by-sex interactions for BMI classification N_d/N_o (adults: 20–89 yr, P = 0.386). There were no significant BMI group main effects (P = 0.576) or sex main effect (P = 0.080).

Table 3.

N_d/N_o ratio for human adult subjects in categorized BMI

BMI Classification	Male (n)	Female (n)	All (n)	95% CI
Underweight	1.0306 ± 0.0295 (5)	1.0344 ± 0.0098 (19)	1.0336 ± 0.0151 (24)	1.0275–1.0396
Normal	1.0376 ± 0.0168 (164)	1.0376 ± 0.0168 (451)	1.0376 ± 0.0168 (615)	1.0363–1.0390
Overweight	1.0345 ± 0.0181 (244)	1.0384 ± 0.0166 (435)	1.0370 ± 0.0173 (679)	1.0357–1.0383
Class I obese	1.0374 ± 0.0184 (105)	1.0384 ± 0.0152 (234)	1.0381 ± 0.0162 (339)	1.0363–1.0398
Class II obese	1.0353 ± 0.0152 (25)	1.0378 ± 0.0132 (96)	1.0373 ± 0.0136 (121)	1.0349–1.0397
Class III obese	1.0309 ± 0.0148 (10)	1.0392 ± 0.0167 (57)	1.0380 ± 0.0166 (67)	1.0340–1.0420
Total	1.0359 ± 0.0177 (553)	1.0381 ± 0.0161 (1,292)	1.0374 ± 0.0166 (1,845)	1.0367–1.0382

Values are the mean ± SD; n = number of subjects.

N_d/N_o, dilution space ratio. The subjects were categorized by BMI into underweight (<18.5 kg/m²), normal weight (18.5–24.99 kg/m²), overweight (25–29.99 kg/m²), class I obese (30–34.99 kg/m²), class II obese (35–39.99 kg/m²), and class III obese (>40 kg/m²). Values were calculated by two-way ANOVA. There were no significant BMI groups-by-sex interactions for (P = 0.386), main effect of BMI (P = 0.576), and main effect of sex (P = 0.080).

The potential factors (sex, age, BMI, and %fat) that might influence the N_d/N_o were investigated by linear regression analysis for all subjects. None of these correlations with sex, BMI, and %fat were statistically significant. There was poor negative correlation for age (r = −0.050, P = 0.017, slope = −0.00003, and intercept = 1.0391; Table 4). The effect was most apparent at the extreme ends of the age spectrum (Table. 2).

Table 4.

Correlation coefficients between dilution space ratio and selected physiological parameter

		r	P
Sex (male: 742; female: 1,555)		0.019	0.375
Age, yr	52.3 ± 25.4	−0.050	0.017
BMI, kg/m2	26.2 ± 6.1	−0.010	0.619
Body fat, %	36.3 ± 9.4	−0.020	0.335

Values are the mean ± SD; n = 2,297.

P, significance level; r, correlation coefficient.

Methodological effects.

The intraindividual and measurement variability (n = 54, BMI = 26.7 ± 5.4, and %fat = 38.4 ± 8.8) were determined by two repeated methods analyses (blind analysis for test-retest precision and redosing after 6 mo). Blind analysis test-retest precision shows that inter- and intraindividual SD (0.013 and 0.010, respectively). In addition, redosing after 6 mo for intraindividual variability (n = 55, BMI = 26.7 ± 5.9, and %fat = 32.7 ± 10.1) shows that intraindividual SD over time and measurement SD were 0.015 and 0.013, respectively. Because both of these studies were analyzed as using the same determination of the gravimetric DLW dose dilutions, they underestimate the analytical variation compared with that cross-sectional data analyses, which involved ∼50 DLW dose batches. The SD for the gravimetric dilutions expressed, as a SD of N_d/N_o, was 0.008. Thus the intraindividual SD and analytical SD including adjustment for the gravimetric dilutions were 0.017 and 0.015, respectively (Table 5).

Table 5.

Sources of variation in N_d/N_o dilution space ratio in blind repeat test for same samples and repeat experiment after 6 mo

Source	SD
Interindividual (total)	0.0167
Measurement error	0.010
Duplicate samples	0.008
Intraindividual (6 mo)	0.013
Intraindividual physiologic	0.002
Interindividual physiologic	0.011

For same samples, n = 54; for repeat experiment after 6 mo, n = 55 by ANOVA.

Literature review.

To avoid any bias from the average dilution space ratio in our single laboratory, we reviewed reported dilution space ratios from 103 published articles (see Supplemental Material; Supplemental Material for this article is available online at the Journal website). For individuals between 1 and 80 yr, the average dilution space ratio was 1.036. For newborns and infants <1 yr of age, the average was 1.028, and for individuals over 80 yr was 1.024.

DISCUSSION

We found the mean N_d/N_o and variance of all subject groups categorized by age, BMI status, or sex were tightly clustered and that none of these variables displayed a significant correlation with N_d/N_o. The group mean N_d/N_o for 2,297 human subjects was 1.037, which was quite similar to the value of 1.034 that Racette et al. reported previously (19), although there was a significant difference between two. The difference between these two estimates translates to a 1.5% difference in rCO₂ and TEE for studies in which the deuterium elimination rate 25% larger than oxygen-18 elimination rate.

By deduction, our findings that common physiologic variables do not explain the cross-sectional variability in interindividual N_d/N_o suggest that the variation is mainly due to analytical error. Far more direct evidence, however, is that our adjusted SD for N_d/N_o of 0.015 is only slightly smaller than the interindividual SD of 0.0167 from the cross-sectional analysis. The difference corresponds to the fact that the physiologic variability in N_d/N_o under the above conditions would propagate to a SD of 3% in rCO₂ and TEE.

Other investigations regarding the variation of N_d/N_o have given divergent results. Król and Speakman (15) conducted a careful study in which they examined the variation in N_d/N_o using ²H, tritium (³H) and ¹⁸O in mice. They hypothesized that if the variation of N_d/N_o is dependent on physiological factors rather than analytical error, the dilution space ratio of ²H and ¹⁸O would be highly correlated with the dilution space ratio of ³H and ¹⁸O. They observed the significant correlation between these two-dilution space ratios and concluded the variation of the observed N_d/N_o was mostly physiological rather than analytical. In contrast, Reilly and Fedak (21) and Arnould et al. (1) examined the dilution space difference between ²H and ³H using desiccation method to measure actual TBW in seals (Halichoerus grypus and Arctocephalus gazella, respectively). The dilution spaces of ²H and ³H, relative to TBW, were not correlated, which, if one assumes that most physiological variation in N_d/N_o is derived from N_d, suggests that the variability of the dilution space ratio is mostly analytical. Our study is consistent with the latter. We can suggest two possible explanations for this disagreement. It may be that larger animals have slower weight-normalized metabolic flux rates and thus lesser influences of any metabolic reactions that result in exchange or incorporation of the isotopes into nonaqueous pools, thereby a more constant dilution space ratio. The other possibility is there may have been a type II error in one or both of these prior studies because the sample size in both these studies was small (Halichoerus grypus: 4; Arctocephaus gazelle: 5; and mice: 26, respectively). In the present study, we conducted careful experiments that could examine whether the variability of N_d/N_o is dependent on physiological or analytical factors in humans, using blinded test-retest analysis and reexperimentation of DLW dosing after 6 mo and a propagation of error analysis to differentiate between analytical and physiological variation.

As summarized by Racette et al. from our laboratory (19), the variability of N_d/N_o in humans from the majority of DLW studies reported by others was small. Thus we would conclude the variability of N_d/N_o in larger animals such as human is mostly the result of random analytical error. It is possible, however, that for small animals such as mice (<40 g) there might be physiological variation, just as there is a difference in the best fit equation for calculating rCO₂ in small animals that results from a difference in the nonaqueous routes of loss for the stable isotope tracers (27).

Most other reports did not test for differences as a function of age, BMI, or sex. There was a trend, however, with adults male and females having average N_d/N_o values that were only 0.2% different, which was not statistically significant (1.0359 and 1.0381, respectively, P = 0.080). Thus there is a trend for sex effect, but it is not statically significant despite the large sample size and we therefore do not support use of different values for males and females. More importantly, the difference between 1.0359 and 1.0381 would only induce a difference of approximately 0.7% in TEE, which is negligible for most DLW applications.

The mechanism that results in the isotope dilution spaces being larger than the TBW is due isotope exchange and/or incorporation of tracer into nonaqueous pools (24). In the case of N_d, it is known that the hydrogen in water exchanges with the labile protons in protein and estimates of the number of labile protons suggest that the N_d space would be ∼5% larger than TBW (9). In the case of oxygen, the primary route of exchange into inorganic pools is during the formation of ester bonds, with the most rapid being movement into phosphate groups during oxidative phosphorylation (12). We have estimated that these routes would expand the ¹⁸O space relative to TBW by 0.7 to 1% (24).

Validation studies of the DLW method discuss whether to use the measured (normalized observed value) or constant (fixed value) for N_d/N_o. Previous research has shown that using the individual ratios does not enhance the fit of individual data to the reference methods (2, 4, 19, 23, 26). Moreover, the DLW validation studies of Coward and Prentice (7), Wong et al. (31), and Bevan et al. (2) suggested there was an improved fit of DLW data to the reference method when individual ratios were used. Herein, the notion that the variation is physiological is supported by propagating error from the mass spectrometric determinations of hydrogen and oxygen enrichment. Such error propagation calculations indicate that most of the observed variation is analytical, and thus we predict that using individual data will actually increase the variability in TEE and recommend again against it to minimize error in TEE (18). Thus the use of the constant value of N_d/N_o (1.036) for each subject is suggested to minimize the effect of stable isotope analysis error on calculation of TEE in the DLW studies in humans. We reviewed the literature and found measured N_d/N_o ratio in 103 references (Supplemental Table S1). The values was 1.036 in 158 groups of subjects, which excluded <1 and >80 age groups. This constant is not very different from the previous observation of 1.034 by Racette et al. (19) from our laboratory but is preferable to that of Racette because it is based on a much larger sample and is probably not biased by specific analytical methods used in a single laboratory. We recommend the 1.036 as revised constant value of N_d/N_o for individuals between 1 and 80 yr of age, 1.029 for those <1 yr of age, and 1.025 for those >80 yr of age. The effect of using 1.036 in place of 1.034 on TEE is ∼1% for most conditions. If a laboratory is finding its average dilution space ratios does not agree with what is reported here or our variance is out of range reported here, we recommend it reevaluates its analytical methodologies. We suggest that the differences for by age results from systematic change in the water to protein ratio as both groups have slightly higher hydration of their fat-free mass (14).

Using data from our single laboratory and thus minimizing systematic error due to differences in laboratory methods, we found no differences in the N_d/N_o ratio due to sex, gender, or BMI status and only a small difference due to age between 0.25 and 89 yr. Thus we recommend the use of a single value 1.036 for the N_d/N_o ratio in calculating rCO₂ and TEE from DLW with the exception of infants and advanced elderly, since this value was based on measures of N_d/N_o from our large subjects and multiple laboratories literature.

GRANTS

These investigators were supported by multiple National Institutes of Health Grants. The data analysis was supported by a Research Fellowships of the Japan Society for the Promotion of Science for Young Scientists Research Grant (14J11761; to H. Sagayama).

DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the author(s).

AUTHOR CONTRIBUTIONS

H.S., Y.Y., N.M.R., T.C.S., and D.A.S. analyzed data; H.S., Y.Y., and D.A.S. interpreted results of experiments; H.S., Y.Y., and D.A.S. prepared figures; H.S., Y.Y., and D.A.S. drafted manuscript; H.S., Y.Y., N.M.R., and D.A.S. edited and revised manuscript; H.S., Y.Y., N.M.R., T.C.S., and D.A.S. approved final version of manuscript; Y.Y. and D.A.S. conception and design of research; N.M.R., T.C.S., and D.A.S. performed experiments.