Methodologic considerations for measuring energy expenditure differences between diets varying in carbohydrate using the doubly labeled water method

ABSTRACT

Background

Low-carbohydrate diets have been reported to significantly increase human energy expenditure when measured using doubly labeled water (DLW) but not by respiratory chambers. Although DLW may reveal true physiological differences undetected by respiratory chambers, an alternative possibility is that the expenditure differences resulted from failure to correctly estimate the respiratory quotient (RQ) used in the DLW calculations.

Objective

To examine energy expenditure differences between isocaloric diets varying widely in carbohydrate and to quantitatively compare DLW data with respiratory chamber and body composition measurements within an energy balance framework.

Design

DLW measurements were obtained during the final 2 wk of month-long baseline (BD; 50% carbohydrate, 35% fat, 15% protein) and isocaloric ketogenic diets (KD; 5% carbohydrate, 80% fat, 15% protein) in 17 men with a BMI of 25–35 kg/m². Subjects resided 2 d/wk in respiratory chambers to measure energy expenditure (EE_chamber). DLW expenditure was calculated using chamber-determined RQ either unadjusted (EE_DLW) or adjusted (EE_DLWΔRQ) for net energy imbalance using diet-specific coefficients. Accelerometers measured physical activity. Body composition changes were measured by dual-energy X-ray absorptiometry (DXA) which were combined with energy intake measurements to calculate energy expenditure by balance (EE_bal).

Results

After transitioning from BD to KD, neither EE_chamber nor EE_bal were significantly changed (∆EE_chamber = 24 ± 30 kcal/d; P = 0.43 and ∆EE_bal = −141 ± 118 kcal/d; P = 0.25). Similarly, physical activity (−5.1 ± 4.8%; P = 0.3) and exercise efficiency (−1.6 ± 2.4%; P = 0.52) were not significantly changed. However, EE_DLW was 209 ± 83 kcal/d higher during the KD (P = 0.023) but was not significantly increased when adjusted for energy balance (EE_DLWΔRQ = 139 ± 89 kcal/d; P = 0.14). After removing 2 outliers whose EE_DLW were incompatible with other data, EE_DLW was marginally increased during the KD by 126 ± 62 kcal/d (P = 0.063) and EE_DLW∆RQ was only 46 ± 65 kcal/d higher (P = 0.49).

Conclusions

DLW calculations failing to account for diet-specific energy imbalance effects on RQ erroneously suggest that low-carbohydrate diets substantially increase energy expenditure. This trial was registered at clinicaltrials.gov as NCT01967563.

Introduction

There is a great deal of interest in whether low-carbohydrate diets offer a ‘metabolic advantage’ by increasing total energy expenditure (1, 2) – a phenomenon predicted by the carbohydrate-insulin model of obesity (3, 4). In support of this concept, a pair of controlled feeding studies reported substantial increases in average daily energy expenditure during low-carbohydrate diets compared with high-carbohydrate diets as measured by the doubly labeled water (DLW) method (5, 6). However, such results appear to be inconsistent with many studies employing respiratory chambers that failed to detect important energy expenditure differences between isocaloric diets with varying ratios of carbohydrate to fat (7–9).

Our recent inpatient controlled feeding study is the only study to date that compared daily energy expenditure between isocaloric diets widely varying in carbohydrate content using both respiratory chambers and DLW (10). Our primary result was a small but statistically significant increase in daily energy expenditure as measured by respiratory chamber (EE_chamber) of 57 ± 13 kcal/d (P = 0.0004) after 17 men (25 < BMI < 35 kg/m²) transitioned from a 1 mo inpatient run-in period consuming a moderate-carbohydrate baseline diet (BD) (50% carbohydrate, 35% fat, 15% protein) to an immediately subsequent month-long inpatient period consuming an isocaloric ketogenic diet (KD) (5% carbohydrate, 80% fat, 15% protein).

An exploratory aim of our study was to measure changes in daily energy expenditure by DLW (EE_DLW) and we reported a more substantial increase of 151 ± 63 kcal/d (P = 0.03 uncorrected for multiple comparisons) following the KD (10) in 16 of the subjects. At the time, we surmised that the confined environment of the respiratory chamber possibly masked an effect of diet or time that was revealed by the DLW method (10). However, there are methodological considerations that could possibly explain why the energy expenditure differences calculated using the DLW method may not reflect true physiological differences.

Specifically, the DLW method requires an estimate of the overall metabolic fuel utilization of the body as quantified by the average daily respiratory quotient (RQ). It is widely known that RQ depends on the composition of the diet, and most investigators presume that the RQ is equal to the food quotient (FQ) given by the estimated ratio of carbon dioxide (CO₂) produced to oxygen (O₂) consumed if the food itself were oxidized. However, RQ is also related to the overall state of energy and macronutrient balance of the body. Furthermore, the adjustment of RQ for the state of energy imbalance also depends on diet composition (11). Such adjustments are rarely employed in DLW calculations, and most investigators do not have access to RQ measurements determined by respiratory chambers.

Here, we reanalyzed our DLW data taking into account the diet-specific energy imbalance adjustments of chamber-measured RQ and we highlight some key challenges to interpreting DLW data when comparing energy expenditure differences between diets varying in carbohydrate.

Methods

Details of the study and its approval by the Institutional Review Boards have been reported previously (10). Briefly, 17 men with a BMI between 25 and 35 provided informed consent and were admitted as inpatients to metabolic wards (Supplemental Figure 1) where they consumed a standard BD composed of 50% energy from carbohydrate, 35% fat, and 15% protein for 4 wk immediately followed by 4 wk of an isocaloric very low-carbohydrate KD composed of 5% carbohydrate, 80% fat, and 15% protein. Body weight and height were measured to the nearest 0.1 kg and 0.1 cm, respectively, with subjects wearing a hospital gown and undergarments and following an overnight fast. Body fat was measured using dual-energy X-ray absorptiometry (DXA) scanners (Lunar iDXA, GE Healthcare).

Subjects spent 2 consecutive days each week residing in respiratory chambers to measure energy expenditure (EE_chamber). As described previously (10), during the BD period, the daily energy expenditure was calculated as follows:

(1)

where VO₂ and VCO₂ were the volumes of O₂ consumed and CO₂ produced, respectively, and N was the 24 h urinary nitrogen excretion measured by chemiluminescence (Antek MultiTek Analyzer, PAC). During the KD period, the equations were adjusted to account for 24 h urinary ketone excretion, K_excr:

(2)

Energy efficiency of physical activity was measured in the respiratory chamber with subjects exercising at a constant, self-selected, level of moderate-intensity cycle ergometry.

Energy expenditure was calculated by energy balance (EE_bal) using the daily metabolizable energy intake (EI) and the measured rates of change of the body energy storage pools determined from measurements of fat mass (FM) and fat-free mass (FFM) by DXA at the beginning and end of each 2 wk BD and KD period coincident with the DLW measurements as follows:

(3)

where ρ_FM = 9,300 kcal/kg is the energy density of body FM, ρ_FFM = 1,100 kcal/kg is the energy density of FFM.

Energy expenditure was measured by DLW during the final 2 wk of the BD and KD periods to allow sufficient time for fluid shifts as subjects adjusted to each diet. Subjects drank from a stock solution of ²H₂O and H₂¹⁸O water in which 1 g of ²H₂O (99.99% enrichment) was mixed with 19 g of H₂¹⁸O (10% enrichment). An aliquot of the stock solution was saved for dilution to be analyzed along with each set of urine samples. The water was weighed to the nearest 0.1 g into the dosing container. The prescribed dose was 1.0 g/kg body weight and the actual doses were entered in each subject's DLW worksheet. The average daily rate of CO₂ production (rCO₂) was corrected for previously administered isotope doses (12) and was estimated from the rate constants describing the exponential disappearances of the labeled ¹⁸O and deuterated water isotopes (k_O and k_D) in daily spot urine samples collected over 14 d. Isotopic enrichments of urine samples were measured by isotope ratio mass spectrometry. We used the parameters of Racette et al. (13) with the weighted dilution space calculation, R_dil, proposed by Speakman (14):

(4)

where r_GF accounts for the fractionation of the isotopes and (N_D/N_O)_ave is the mean of the N_D/N_O values from the n = 17 subjects.

In our previous report (10), we used the measured 24 h RQ to calculate energy expenditure (EE_DLW) during the baseline period as follows:

(5)

During the KD period, EE_DLW was adjusted for the measured daily urinary ketone excretion rate, K_excr, as follows:

(6)

As previously described (10), derivation of the DLW energy expenditure equations above requires an assumption regarding the fraction of total energy expenditure derived from protein oxidation. We assumed that this protein fraction was equal to the diet proportion of metabolizable energy as protein, which was ∼15%.

Because the energy expended outside the chamber was significantly greater than inside the chamber (10), the chamber RQ values did not accurately represent the overall RQ values during the DLW period. In other words, the relative magnitude of energy imbalance during the DLW period was different than the energy imbalance (EI–EE_chamber) measured during the chamber stays. The overall energy imbalance during the DLW period was defined by the rate of change of body energy stores:

(7)

Therefore, we adjusted the chamber RQ measurements by an amount, ∆RQ, as described in the Supplemental Methods:

(8)

where ΔEB is the difference in energy balance between (EI–EE_chamber) when the RQ measurements were obtained and EB_DLW. Importantly, the value of λ is affected by diet composition and, consequently, the energy equivalence of CO₂ produced in the DLW calculations differs between diets varying in carbohydrate for the same degree of energy imbalance. In particular, λ = 5.28 × 10⁻⁵ d/kcal for the BD and λ = 9.17 × 10⁻⁶ d/kcal for the KD (Supplemental Figure 2).

Thus, the ΔRQ adjustment for each individual subject's diet-specific state of energy imbalance results in the following calculation of DLW energy expenditure (EE_DLWΔRQ) during the baseline period:

(9)

During the KD period, EE_DLWΔRQ was calculated as:

(10)

FQ was not used for our DLW calculations, but we estimated FQ as follows:

(11)

where CI, FI, and PI, were the estimated metabolizable energy intake of carbohydrate, fat, and protein, respectively, as determined by chemical analysis of the 7 d menus. Uncertainties in the FQ estimates were calculated using the SDs of CI, FI, and PI measured by chemical analysis. The values of 1.0 and 0.71 were assumed for the RQ values for carbohydrate and fat oxidation, respectively (15). The assumed RQ of protein oxidation was 0.835, but this value has substantial uncertainty because it depends sensitively on the amino acid composition of oxidized protein, as well as the relative proportion of urea, creatinine, and ammonia end-products of protein oxidation (15).

As opposed to our previous study (10) that reported results during the entire 6 wk period when EI was held constant (i.e., the last 2 wk of the BD phase and the entirety of the KD phase), we now report results based upon data obtained only during the 2 wk DLW phases of both BD and KD periods. In addition to allowing direct comparison with the coincident DLW measures, focusing on the last 2 wk of each diet allowed 2 wk to adapt to the BD from the usual diet as well as to the KD from the BD.

Statistical analysis was performed with SAS (version 9.4) using a paired, 2-sided t-test with significance declared at the P < 0.05 threshold. The data are reported as mean ± SE.

Results

The FQ values estimated from the diet composition measurements by chemical analysis are depicted in Figure 1A along with the RQ values measured in the respiratory chamber during the DLW periods. Interestingly, the chamber RQ measurements were somewhat higher than the estimated FQ during the KD. Therefore, using FQ rather than RQ in the DLW calculations would overestimate EE_DLW during the KD. Accounting for the differences in energy balance between chamber days and the overall DLW period resulted in ∆RQ = −0.027 ± 0.005 during the BD and ∆RQ = −0.003 ± 0.0008 during the KD. Thus, using unadjusted RQ values underestimated EE_DLW during the BD to a greater degree than during the KD.

FIGURE 1.

(A) Estimated food quotient (FQ), daily respiratory quotient (RQ) measured in respiratory chambers, and the adjusted daily respiratory quotient (RQ + ∆RQ) after accounting for the energy imbalance differences between the chamber days and the overall doubly labeled water period. (B) Neither energy expenditure by respiratory chamber (EE_chamber), nor energy expenditure by balance (EE_bal) were significantly different during the baseline diet (BD) compared with the ketogenic diet (KD). However, energy expenditure by doubly labeled water (EE_DLW) was significantly greater during the KD, but not after adjustment of the RQ to account for the differential diet effect of energy imbalance (EE_DLWΔRQ) or after removal of two outliers whose DLW data were incommensurate with other measurements (EE_DLWΔRQ – Outliers). (C) Differences in EE_chamber, EE_bal, EE_DLW, EE_DLWΔRQ, and EE_DLWΔRQ – Outliers between KD and BD phases. Error bars are ± SD in panel (A) and ± SE in panels (B) and (C). P values report the results of a 2-sided, paired t-test test between BD and KD.

During the final 2 wk of the BD, EI was 2,738 ± 107 kcal/d which was significantly higher than EE_chamber = 2,626 ± 104 kcal/d (P < 0.0001) (Table 1 and Figure 1B). EE_DLW was 2,964 ± 126 kcal/d and significantly higher than EI (P = 0.011). After adjusting for the energy imbalance, EE_DLW∆RQ = 3,045 ± 135 kcal/d and was significantly greater than EE_DLW (P = 0.0003). Energy expenditure calculated using EI and the changes in body energy stores was EE_bal = 3,136 ± 171 kcal/d and was not significantly different from EE_DLW (P = 0.23) or EE_DLW∆RQ (P = 0.47). Compared with EE_chamber, EE_DLW was 338 ± 77 kcal/d higher (P = 0.0005), EE_DLW∆RQ was 419 ± 76 kcal/d higher (P < 0.0001), and EE_bal was 509 ± 100 kcal/d higher (P < 0.0001) indicating that subjects expended significantly more energy outside the chamber during the BD phase.

TABLE 1.

Energy intake and expenditure measurements¹

	BD mean ± SE	KD mean ± SE	KD–BD mean ± SE	P value
EI (kcal/d)	2,738 ± 107	2,730 ± 110	−8 ± 5	0.16
EEchamber (kcal/d)	2,626 ± 104	2,650 ± 89	24 ± 30	0.43
EEbal (kcal/d)	3,136 ± 171	2,995 ± 160	−141 ± 118	0.25
EEDLW (kcal/d)	2,964 ± 126	3,173 ± 146	209 ± 83	0.023
EEDLWΔRQ (kcal/d)	3,045 ± 135	3,184 ± 147	139 ± 89	0.14
EEDLW (kcal/d) – Outliers	2,933 ± 122	3,059 ± 134	126 ± 62	0.063
EEDLWΔRQ (kcal/d) – Outliers	3,025 ± 136	3,072 ± 136	46 ± 65	0.49

¹Energy intake (EI) and energy expenditure (EE) measured in the respiratory chamber (EE_chamber), by energy balance (EE_bal), by doubly labeled water (DLW) unadjusted for energy imbalance (EE_DLW) and adjusted for energy imbalance (EE_DLWΔRQ) during the final 2 wk of consuming a baseline diet (BD) or an isocaloric ketogenic diet (KD) in 17 men with a BMI of 25–35 kg/m². EE_DLW and EE_DLWΔRQ are also reported after removing 2 subjects who were clear outliers as described in the main text. P values report the results of a 2-sided, paired t-test between BD and KD.

During the final 2 wk of the KD phase, EI was 2,730 ± 110 kcal/d which, by design, was not significantly different from the BD phase (P = 0.16). Whereas we previously reported a transient increase in EE_chamber during the first 2 wk after introducing the KD (10), neither EE_chamber (2,650 ± 89 kcal/d; P = 0.43) nor EE_bal (2,995 ± 160 kcal/d; P = 0.25) were significantly different during the last 2 wk of the KD compared with the last 2 wk of the BD coincident with the DLW measurement periods (Figure 1B). Likewise, physical activity measured using an accelerometer mounted on the hip was not significantly different (KD relative to BD, −5.1% ± 4.8%; P = 0.3); and energy efficiency of physical activity measured in the respiratory chamber with subjects exercising at a constant level of moderate-intensity cycle ergometry was not significantly different (−1.6% ± 2.4%; P = 0.52) between the BD and KD phases.

Despite no significant differences in EI, EE_chamber, EE_bal, physical activity, or exercise efficiency between the KD and BD phases (Figure 1C), EE_DLW was 209 ± 83 kcal/d higher during the KD phase (P = 0.023). After adjusting for the degree of energy imbalance, EE_DLW∆RQ was 3,184 ± 147 kcal/d during the KD and was not significantly different from EE_bal (P = 0.27). Unlike the unadjusted EE_DLW, the difference in EE_DLW∆RQ between KD and BD phases was not statistically significant (139 ± 89 kcal/d; P = 0.14). Compared with the unadjusted EE_DLW, the adjusted EE_DLW∆RQ substantially increased during the BD, whereas EE_DLW∆RQ was relatively unchanged from EE_DLW during the KD.

There were two clear DLW outliers (individual subject data are plotted in Supplemental Figure 3) whose data indicated large amounts of unaccounted energy. The first outlier, ‘Subject A’, had an EE_DLW that was 1,220 kcal/d in excess of EI during the BD, and was 1,751 kcal/d higher than EI during the KD despite slight body weight and FM gains during these periods. In contrast, the EE_chamber measurements for this subject were 173 kcal/d less than EI during the BD, and 65 kcal/d below EI during the KD. The second outlier, ‘Subject B’, had an EE_DLW during the BD that was only 123 kcal/d higher than EE_chamber, but during the KD his EE_DLW increased by 1,136 kcal/d which was ∼3 SDs greater than the mean increase in EE_DLW, suggesting a severe negative energy balance despite the subject gaining weight during this period and EE_chamber increasing by only 72 kcal/d. Supplemental Tables 1–4 provide summary data on the energy expenditure comparisons between BD and KD phases with and without the exclusion of these subjects. After excluding these subjects with excessive unaccounted energy indicated by DLW measurements of expenditure, EE_DLW during the KD was 126 ± 62 kcal/d greater than during the BD (P = 0.063) and EE_DLW∆RQ during the KD was only 46 ± 65 kcal/d greater than during the BD (P = 0.49).

Discussion

Four days of respiratory chamber measurements that were coincident with each 2 wk DLW period did not detect significant changes in energy expenditure between the BD and KD periods. The increase in unadjusted EE_DLW after transitioning to the KD was substantially greater than could be accounted for by changes in body energy stores. After employing diet-specific RQ adjustments in the DLW calculations to account for energy imbalance, we found that the RQ-adjusted difference in DLW energy expenditure between the diets was attenuated and was no longer statistically significant. After excluding two subjects whose DLW data were highly incommensurate with other measurements, the RQ-adjusted difference in DLW energy expenditure was further reduced to a nonsignificant ∼50 kcal/d increase during the KD.

We previously hypothesized that the discrepancy between the respiratory chamber and DLW measurements was due to increased physical activity on nonchamber days during the KD compared with the BD period (10). However, this potential explanation does not agree with the lack of increase in objectively measured physical activity via accelerometry. Also, the energy expended to perform the same low-intensity exercise in the respiratory chamber was not significantly changed by the KD, making it unlikely that the energy efficiency of skeletal muscle contraction had been altered after transitioning to the KD. Finally, the measured body composition changes were incommensurate with a significant increase in expenditure during the KD. Thus, the unadjusted EE_DLW differences were discordant with several independent measures that suggested no significant energy expenditure changes during the KD compared with the BD. The appropriately adjusted RQ values resulted in DLW estimates that were commensurate with the other data, especially after removing the pair of outliers with large amounts of unaccounted energy.

Another methodological concern with the DLW method is the theoretical possibility that CO₂ production rates can be influenced by the fluxes through biosynthetic pathways that likely vary substantially depending on the carbohydrate content of the diet, especially the de novo lipogenesis pathway (16–18). However, the magnitude of this potential bias in humans is thought to be relatively small, amounting to an energy expenditure difference of only ∼30–60 kcal/d (see Online Supporting Materials). Interestingly, this small potential systematic bias was similar in magnitude to the nonsignificant diet difference in EE_DLW∆RQ after removal of the outliers and would have been sufficient to nullify the statistical significance of the observed difference in unadjusted EE_DLW including all subjects.

Some investigators who promote the carbohydrate-insulin model of obesity have discounted our previously published EE_chamber results and have reinterpreted our exploratory EE_DLW data as underestimating the true physiological effect of low-carbohydrate diets (19, 20). In support of this interpretation, Ebbeling et al. (5, 6) reported significant ∼200–300 kcal/d increases in EE_DLW during low-carbohydrate diets compared with high-carbohydrate diets. However, the measured resting energy expenditure differences failed to corroborate the EE_DLW differences and objectively measured physical activity was not different between the diets. Although body weight was claimed to be stable, body composition changes were unreported. Energy intake was several hundred calories below EE_DLW that was estimated using FQ without adjustment for the subjects’ state of energy balance. Therefore, similar to the current study, unaccounted diet-specific effects of energy imbalance may have contributed to the observed diet differences in EE_DLW. Thus, the data of Ebbeling et al. could be interpreted as supporting the possibility that their unadjusted EE_DLW calculations were systematically biased such that the low-carbohydrate diet resulted in an apparent increase in daily energy expenditure.

In contrast, Bandini et al. (21) found in an outpatient study that EE_DLW was lower during the very low-carbohydrate diet (∼7% of energy) compared with a high-carbohydrate diet (∼83% of energy), but this reduction was attributed to decreased physical activity because the subjects reported nausea and lethargy on the low-carbohydrate diet. No significant differences in resting energy expenditure were found. Stubbs et al. (22) found no significant difference between EE_DLW using a narrower range of diets with 29–67% of energy as carbohydrate. However, the diets were fed ad libitum and energy intake on the low-carbohydrate diet was greater than the moderate-carbohydrate diet which was greater than the high-carbohydrate diet. Thus, the variation in total carbohydrate content of the test diets was attenuated such that daily carbohydrate intake varied by only ∼22% of the mean energy intake between diets which may not have been a sufficient range to observe a systematic bias of the DLW method. Furthermore, the positive energy balance with the low-carbohydrate diet increased RQ whereas the negative energy balance with the high-carbohydrate diet decreased RQ. Thus, the RQ differences during consumption of these diets were attenuated by the differences in energy balance.

It is important to emphasize that our study was not intended to be a DLW validation study and there were several limitations. The DLW measurements were not prespecified as either primary or secondary endpoints of the study. Whereas respiratory chamber measurements have high precision, with an intrasubject coefficient of variation of EE_chamber ∼2–3% (23), the DLW method is less precise, with an intrasubject coefficient of variation of energy expenditure of ∼ 8–15% (24). Therefore, the relatively large inherent variability of the DLW method may have led to an apparent increase in EE_DLW during the KD simply by chance (type-1 error). However, we cannot definitively exclude the possibility of a real increase in energy expenditure, especially at an effect size of ∼50–140 kcal/d after excluding two likely DLW outliers or using diet-specific adjustments of the DLW calculations to account for the energy imbalance.

The DLW method has been validated during 30% caloric restriction with a 55% carbohydrate diet (25) and agrees with our result that EE_DLW and EE_DLW∆RQ were not significantly different from EE_bal during the BD diet phase. Nevertheless, the calculated EE_bal values are somewhat uncertain because DXA has a limited ability to precisely and accurately detect small changes in body energy stores (26). We cannot rule out the possibility that the KD resulted in increased activity-related energy expenditure that was undetected by accelerometers. Finally, the order of the diets was not randomized, and it is possible that the elevated EE_DLW occurred simply because the KD followed the BD. Indeed, others have reported a greater metabolic rate during a low-carbohydrate diet when it followed a high-carbohydrate diet as compared with the reverse order (27).

In summary, when properly employed the DLW method is a robust and valid method for estimating daily average energy expenditure. Our data illustrate important methodological considerations when using the DLW method to estimate daily energy expenditure differences between diets varying widely in the proportion of carbohydrate. We urge caution when interpreting such DLW data that do not appropriately adjust estimated RQ for energy imbalance or when DLW results are not corroborated by quantitatively commensurate observations of energy intake, body composition, or various components of energy expenditure such as resting energy expenditure or physical activity.

Notes

This study was funded by the Nutrition Sciences Initiative (NuSI). This work was also supported, in part, by the Intramural Research Program of the NIH, National Institute of Diabetes and Digestive and Kidney Diseases (KDH, KYC, MLR), NIH UL1 TR00040 (Columbia Clinical and Translational Science Award, MR, and RL), and Nutrition and Obesity Research Center Grant # P30DK072476 (ER).

Supplemental Figures 1–3, Supplemental Methods, Supplemental Tables 1–4, and Supporting Materials are available from the “Supplementary data” link in the online posting of the article and from the same link in the online table of contents at https://academic.oup.com/ajcn/.

Abbreviations used: BD, baseline diet composed of 50% carbohydrate, 35% fat, and 15% protein; CO₂, carbon dioxide; DLW, doubly labeled water; DXA, dual-energy X-ray absorptiometry; EE_bal, energy expenditure measured by balance using energy intake and the rate of change in body energy stores; EE_chamber, energy expenditure measured by respiratory chamber; EE_DLW, energy expenditure measured by doubly labeled water unadjusted for the state of overall energy imbalance; EE_DLWΔRQ, energy expenditure measured by doubly labeled water adjusted for the state of overall energy imbalance; EI, metabolizable energy intake; FFM, fat-free mass of the body; FM, fat mass of the body; FQ, food quotient; KD, ketogenic diet composed of 5% carbohydrate, 80% fat, and 15% protein; RQ, daily respiratory quotient.