EE: Application of RQ (2005)


Elia M, Livesey G. Energy expenditure and fuel selection in biological systems: The theory and practice of calculations based on indirect calorimetry and tracer methods. In Simopoulos AP (ed): Metabolic control of eating, energy expenditure and the bioenergetics of obesity. World Rev Nutr Diet. Basel, Karger, 1992, vol 70, pp. 68-131.

Study Design:
Meta-analysis or Systematic Review
M - Click here for explanation of classification scheme.
Quality Rating:
Neutral NEUTRAL: See Quality Criteria Checklist below.
Research Purpose:
Consider the stoichiometries of fuel oxidation that allowed the development of classical indirect methods of calorimetry. These methods depend on the estimation of heat production from measurements of oxygen consumption, carbon dioxide production, and the excretion of other substances, such as urinary nitrogen, methane and hydrogen. Precise interpretation requires detailed understanding of the assumptions and optimal use of calculation procedures.
Inclusion Criteria:
Not specified.
Exclusion Criteria:
Not specified.
Description of Study Protocol:
  • There were no search procedures specified nor was study quality assessed.
  • Types of outcomes investigated include errors associated with the use of CO2 production alone, use of O2 consumption alone, and Use of O2 consumption pluse CO2 production when calculating energy expenditure.
  • Populations included: Mostly stoichimetry so no individuals targeted for research. Indirectly, however, assumptions are based on healthy populations.
  • Of note, studies where individual data is reported is from early 1900’s.
Data Collection Summary:

Outcome(s) and other measures

Information abstracted:

  1. Calimetric Coefficients for fat, CHO and protein using O2 consumption & CO2 production
  2. RQ of substrates oxidation
  3. Estimation of proportion of energy derived from the oxidation of different fuels
  4. Assessment of the errors
Description of Actual Data Sample:
  • # 55 articles included
  • No of articles identified not given

Of the 55 articles, 7 met sorting criteria and were reviewed for sample size of studies, and characteristics of the study participants. Within this 7, 2 were rejected as they were written by primary author of article at earlier dates; 1 was a dietary intake survey; and 1 was related to doubly-labelled water studies. The remaining 3 articles:

Ben-Porat M et al. Energy metabolism rate equatin for fasting and post-absorptive subjects, 1983 (stoichemetry hypothesis testing); Frayn K. Calculation of substrate oxidation rates in vivo from gaseous exchange, 1983(stoichemetry hypothesis testing); and Bursztein S et al. Utilization of protein, carbohydrate and fat in fasting and post-absorptive subjects, 1980. The latter included 10 healthy subjects.

20 reference book citations were used; 2 Consensus Statements, 3 animal studies, and 18 primary scientific research (stoichemistry or within individuals) were used. Of the latter, the earliest publication date was 1897 (a foreign language publication in German) and up to a book published in 1991.

Summary of Results:

Authors have adopted different coefficients (RQ and Energy equivalent O2) for the same fuels of fat-carbohydrate and protein oxidation mixtures. Therefore, different equations for calculating energy expenditure have emerged. (Tables 19 & 20 lists 10 formulations)


Types of studies that use only CO2 production include tracers, such as doubly-labelled water or the labeled bicarbonate method. Direct measurement of CO2 (unlabelled) has been used to estimate energy expenditure in some ventilated patients, where the administration of high concentrations of O2 may make it difficult to obtain accurate measurements of oxygen consumption using the following equation:

EE(kJ)=CO2 production (l) times Energy equivalent of one liter of CO2 (kJ/l) varies considerably more than one liter of energy equivalent of O2. Thus, considering the food eaten and change in body composition is important. (Source Fig. 9)


(Mixed diet reflects almost 100% CHO intake; i.e., close to RQ=1.00)

Negative energy balance   RQ
25% EE 0.78 25.2
50% EE


75% EE


100% (When the mixed diet RQ is 0.95 and meets needs)  
100% 0.95 21.9 (5 kcal/L)

Positive energy balance RQ

125% EE 

1.0       21.0

150% EE 

1.05      20.0

175% EE 

1.14      19.0

200% EE 

1.25      18.5

When RQ of a dietary intake =0.95 meets 100% energy expenditure, the energy equivalent CO2 of the diet =21.87 kJ/l (or approximately 5 kcals/L).

SCENARIO 2 (Diet closely reflects 100% high fat intake; i.e., RQ=0.70): MIXED DIET RQ=0.80 

Negative energy balance RQ
25% EE 0.74 26.5
50% EE


75% EE


100% (When the mixed diet RQ is 0.80 and meets needs)
100% 0.80 25.0 (6 kcal/l)

Positive energy balance RQ EeqCO2body

125% EE

0.81 26.5

150% EE

0.82 25.8

175% EE

0.84 25.0

200% EE

0.85 23.5

Overall, over- or underfeeding to the extent of 50% energy expenditure will alter the energy equivalent CO2 body and RQbody by only 4-11% depending on the composition of the diet. Such degrees of energy imbalance over 2 weeks (the length of doubly labeled water study in adults) should be detectable by weighing the subject and used to make appropriate corrections.


O2 is a better predictor of energy expenditure than CO2 production. If a constant value of Energy equivalent O2 mix of 20.22 kJ/l (4.8 kcal/L) is used to calculate energy expenditure in situations where the RQ is between 1 and 0.71, the maximum error is <4%. Since the energy equivalent O2 for different fuels is much less variable than the Energy equivalent of CO2, when different proportions of fuels are oxidized (e.g., fat-carbohydrate-protein-alcohol mixture), the variation in Energy equivalent O2mix is 3- to 4-fold less than that for Energy equivalent of CO2 mix.

[Abstractors note: if the Scenarios above were constructed to reflect variation in Energy equivalent of O2, they are 3-4 fold less as per authors calculations].

The percent variation in the Energy equivalent O2 between the highest and lowest value is 2.5%, while the variation in Energy equivalent CO2diet and are 8.8%. These errors are relatively small, even in the presence of nutrient imbalance, some workers simply report O2 consumption as an index of energy expenditure.


The errors associated with the use of O2 consumption plus CO2 production for predicting energy expenditure (with or without estimates of protein oxidation) are less than those associated with either O2 consumption alone or CO2 production alone. The absolute errors are small even when alcohol or atypical fuels are included in the oxidation mixture.

When a combination of O2 consumption or CO2 production is used to estimate energy expenditure, the effect of an error in the measurement of one gas may be “buffered” or even counteracted by an error in the measurement of the other gas. O2 consumption has a 3-fold greater impact than CO2 production on the estimated energy expenditure as deduced by consideration of the constants associated with O2 consumption and CO2 productions in the energy equation:

  • EE (kJ)=15.818 O2+5.176 CO2


When the amount of CO2 produced by a biological system is either > or < than the amount of O2 consumed, the volume of dry air entering the system will differ from the volume leaving the system.

When RQ is <1.0, less CO2 is produced than O2 consumed; therefore, the volume of outgoing air < volume of ingoing air. This implies concentrations of gases in the outgoing air are higher than those which would exist if there was no volume change. The reverse happens when the RQ is >1.0.

When there is such a volume inequality, there is scope for error in the calculations of gaseous exchange, particularly when measurements are made of only O2 or only CO2. When measurements are made of both O2 and CO2 concentrations, the problem of volume inequality can be taken into account by relating the measurements to the predicted concentration of N2 (100-%CO2-%O2), which I assumed to be neither consumed nor produced by the biological system.


For RQs ranging between 0.718 and 1.3, the % errors in oxygen consumption vary from -6.1 to +6.3% when the O2 concentration in dry air is 21%.

For RQs ranging between 0.718 and 1.3, the % errors in oxygen consumption vary from -29% to +30% when the ingoing O2 concentration is 100%.

Overall, the % error in O2 consumption < than when estimates are made on the volume of outgoing air, but the errors are now influenced by the rate of gaseous exchange.

Author Conclusion:

As stated by the author in body of report:

Accurate determination of energy expenditure and fuel selection based on measurements of O2 consumption and CO2 production is dependent on the correct choice of calorimetric coefficients and equations. A rigorous examination of the principles used to derive the coefficients for fats, carbohydrates, proteins, individual amino acids and other fuels shows that a number of anomalies and errors exist in the derivation of some existing coefficients.

The general calorimetric equations may provide acceptable estimates for energy expenditure, with errors up to about ±0-5%, even when unusual fuels are predominantly being oxidized, the errors in fuel selection can be magnified severallfold. With a typical fat-carbohydrate oxidation mixture, errors in the estimation of either CO2 production or O2 consumption leads to errors in the estimation of fat or carbohydrate utilization (as a proportion of energy expenditure) that are 3-12 times greater than the erros in energy expenditure.

The paper concludes that it is possible to use indirect calorimetry to assess energy expenditure and fuel selection and deposition when there is no lipid synthesis from carbohydrate. It is possible to modify the general equations for use in situations where there are multiple or unusual fules utilized.

With the correct measurements and “correct” general coefficients and calculation procedures, it is estimated that the errors in energy expenditure are usually within ±1.5% when both Ox consumption and CO2 production are measured; ±2-3% when oxygen consumption alone is measured; and <5 to >10% when CO2 production alone is measured, depending on the period of measurement, and on whether or not appropriate “checks” are used.

The theoretical framework is recommended for optimal interpretation of measurements obtained by indirect calorimetry and tracer methods, such as the doubly-labeled water and labeled bicarbonate, that primarily measure CO2 production.”
Funding Source:
Reviewer Comments:

Elia and Livesey have comprehensively discussed the calorimetry known from foods and applied to individual metabolism. Their writings reflect brilliance in mathematics and the minute details of heat combustion and exchange.

The publication year range is immense and thus limits biases. The truths reported hold up today.
Quality Criteria Checklist: Primary Research
Relevance Questions
  1. Would implementing the studied intervention or procedure (if found successful) result in improved outcomes for the patients/clients/population group? (Not Applicable for some epidemiological studies) Yes
  2. Did the authors study an outcome (dependent variable) or topic that the patients/clients/population group would care about? Yes
  3. Is the focus of the intervention or procedure (independent variable) or topic of study a common issue of concern to dieteticspractice? Yes
  4. Is the intervention or procedure feasible? (NA for some epidemiological studies) Yes
Validity Questions
1. Was the research question clearly stated? Yes
  1.1. Was (were) the specific intervention(s) or procedure(s) [independent variable(s)] identified? N/A
  1.2. Was (were) the outcome(s) [dependent variable(s)] clearly indicated? N/A
  1.3. Were the target population and setting specified? N/A
2. Was the selection of study subjects/patients free from bias? No
  2.1. Were inclusion/exclusion criteria specified (e.g., risk, point in disease progression, diagnostic or prognosis criteria), and with sufficient detail and without omitting criteria critical to the study? N/A
  2.2. Were criteria applied equally to all study groups? N/A
  2.3. Were health, demographics, and other characteristics of subjects described? N/A
  2.4. Were the subjects/patients a representative sample of the relevant population? N/A
3. Were study groups comparable? No
  3.1. Was the method of assigning subjects/patients to groups described and unbiased? (Method of randomization identified if RCT) N/A
  3.2. Were distribution of disease status, prognostic factors, and other factors (e.g., demographics) similar across study groups at baseline? N/A
  3.3. Were concurrent controls or comparisons used? (Concurrent preferred over historical control or comparison groups.) N/A
  3.4. If cohort study or cross-sectional study, were groups comparable on important confounding factors and/or were preexisting differences accounted for by using appropriate adjustments in statistical analysis? N/A
  3.5. If case control study, were potential confounding factors comparable for cases and controls? (If case series or trial with subjects serving as own control, this criterion is not applicable.) N/A
  3.6. If diagnostic test, was there an independent blind comparison with an appropriate reference standard (e.g., "gold standard")? N/A
4. Was method of handling withdrawals described? Yes
  4.1. Were follow-up methods described and the same for all groups? N/A
  4.2. Was the number, characteristics of withdrawals (i.e., dropouts, lost to follow up, attrition rate) and/or response rate (cross-sectional studies) described for each group? (Follow up goal for a strong study is 80%.) N/A
  4.3. Were all enrolled subjects/patients (in the original sample) accounted for? N/A
  4.4. Were reasons for withdrawals similar across groups? N/A
  4.5. If diagnostic test, was decision to perform reference test not dependent on results of test under study? N/A
5. Was blinding used to prevent introduction of bias? Yes
  5.1. In intervention study, were subjects, clinicians/practitioners, and investigators blinded to treatment group, as appropriate? N/A
  5.2. Were data collectors blinded for outcomes assessment? (If outcome is measured using an objective test, such as a lab value, this criterion is assumed to be met.) N/A
  5.3. In cohort study or cross-sectional study, were measurements of outcomes and risk factors blinded? N/A
  5.4. In case control study, was case definition explicit and case ascertainment not influenced by exposure status? N/A
  5.5. In diagnostic study, were test results blinded to patient history and other test results? N/A
6. Were intervention/therapeutic regimens/exposure factor or procedure and any comparison(s) described in detail? Were interveningfactors described? Yes
  6.1. In RCT or other intervention trial, were protocols described for all regimens studied? N/A
  6.2. In observational study, were interventions, study settings, and clinicians/provider described? N/A
  6.3. Was the intensity and duration of the intervention or exposure factor sufficient to produce a meaningful effect? N/A
  6.4. Was the amount of exposure and, if relevant, subject/patient compliance measured? N/A
  6.5. Were co-interventions (e.g., ancillary treatments, other therapies) described? N/A
  6.6. Were extra or unplanned treatments described? N/A
  6.7. Was the information for 6.4, 6.5, and 6.6 assessed the same way for all groups? N/A
  6.8. In diagnostic study, were details of test administration and replication sufficient? N/A
7. Were outcomes clearly defined and the measurements valid and reliable? Yes
  7.1. Were primary and secondary endpoints described and relevant to the question? N/A
  7.2. Were nutrition measures appropriate to question and outcomes of concern? N/A
  7.3. Was the period of follow-up long enough for important outcome(s) to occur? N/A
  7.4. Were the observations and measurements based on standard, valid, and reliable data collection instruments/tests/procedures? N/A
  7.5. Was the measurement of effect at an appropriate level of precision? N/A
  7.6. Were other factors accounted for (measured) that could affect outcomes? N/A
  7.7. Were the measurements conducted consistently across groups? N/A
8. Was the statistical analysis appropriate for the study design and type of outcome indicators? Yes
  8.1. Were statistical analyses adequately described and the results reported appropriately? N/A
  8.2. Were correct statistical tests used and assumptions of test not violated? N/A
  8.3. Were statistics reported with levels of significance and/or confidence intervals? N/A
  8.4. Was "intent to treat" analysis of outcomes done (and as appropriate, was there an analysis of outcomes for those maximally exposed or a dose-response analysis)? N/A
  8.5. Were adequate adjustments made for effects of confounding factors that might have affected the outcomes (e.g., multivariate analyses)? N/A
  8.6. Was clinical significance as well as statistical significance reported? N/A
  8.7. If negative findings, was a power calculation reported to address type 2 error? N/A
9. Are conclusions supported by results with biases and limitations taken into consideration? Yes
  9.1. Is there a discussion of findings? N/A
  9.2. Are biases and study limitations identified and discussed? N/A
10. Is bias due to study's funding or sponsorship unlikely? Yes
  10.1. Were sources of funding and investigators' affiliations described? N/A
  10.2. Was the study free from apparent conflict of interest? N/A