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VO_{2} and VCO_{2} variabilities through indirect calorimetry instrumentation
SpringerPlus volume 2, Article number: 688 (2013)
Abstract
The aim of this paper is to understand how to measure the VO_{2} and VCO_{2} variabilities in indirect calorimetry (IC) since we believe they can explain the high variation in the resting energy expenditure (REE) estimation. We propose that variabilities should be separately measured from the VO_{2} and VCO_{2} averages to understand technological differences among metabolic monitors when they estimate the REE. To prove this hypothesis the mixing chamber (MC) and the breathbybreath (BbB) techniques measured the VO_{2} and VCO_{2} averages and their variabilities. Variances and power spectrum energies in the 0–0.5 Hertz band were measured to establish technique differences in steady and nonsteady state. A hybrid calorimeter with both IC techniques studied a population of 15 volunteers that underwent the clinoorthostatic maneuver in order to produce the two physiological stages. The results showed that interindividual VO_{2} and VCO_{2} variabilities measured as variances were negligible using the MC while variabilities measured as spectral energies using the BbB underwent 71 and 56% (p < 0.05), increase respectively. Additionally, the energy analysis showed an unexpected cyclic rhythm at 0.025 Hertz only during the orthostatic stage, which is new physiological information, not reported previusly. The VO_{2} and VCO_{2} interindividual averages increased to 63 and 39% by the MC (p < 0.05) and 32 and 40% using the BbB (p < 0.1), respectively, without noticeable statistical differences among techniques. The conclusions are: (a) metabolic monitors should simultaneously include the MC and the BbB techniques to correctly interpret the steady or nonsteady state variabilities effect in the REE estimation, (b) the MC is the appropriate technique to compute averages since it behaves as a lowpass filter that minimizes variances, (c) the BbB is the ideal technique to measure the variabilities since it can work as a highpass filter to generate discrete time series able to accomplish spectral analysis, and (d) the new physiological information in the VO_{2} and VCO_{2} variabilities can help to understand why metabolic monitors with dissimilar IC techniques give different results in the REE estimation.
Background
Indirect calorimetry (IC) has been considered by physicians, clinical nutritionists, and researchers as the gold standard to estimate the resting energy expenditure (REE) and the metabolic substrate utilization in humans (Ferrannini 1988; Branson and Joahanningam 2004). The IC technique has been implemented through the respiratory gas exchange measurement in order to calculate mainly the averages of the oxygen consumption (VO_{2}) and carbon dioxide production (VCO_{2}) using different kinds of metabolic monitors with dissimilar instrumental techniques that can possibly produce different results in the estimation of the REE (McClave and Snider 1992).
The general clinical view assumes that the REE estimation inconsistency is the result of uncertainties in the instruments at the time they compute de VO_{2} and VCO_{2} averages in ambulatory or critical care patients (Matarese 1997). However, this high REE variation is not only consequence of instrumental precision problem since it has different causes other than sensors and electronics noise.
We believe that the variation in the REE estimation mainly depends on how the VO_{2} and VCO_{2} variabilities are detected and measured during the standard VO_{2} and VCO_{2} average estimations. The variabilities basically depend on the patients’ physiological state, since each one responds differently, during the IC studies, to the stimuli produced by their diseases, environmental stress conditions (temperature, noise, humidity, etc.) and to the metabolic monitoring connector devices such as face masks, canopies and mouth connectors (Garby and Lammert 1994).
The problem is that the commercial metabolic monitors do not separate and measure the VO_{2} and VCO_{2} variabilities from their average computation in order to correctly interpret whether these variabilities are noise, artifacts, or if they can contain physiological information that may help to understand the variation in the REE estimation (Karsegard et al. 2010; Sundstrom et al. 2013). How to measure the VO_{2} and VCO_{2} variabilities in steady or nonsteady state is an open question since metabolic monitors have been designed only to compute the VO_{2} and VCO_{2} averages in IC clinical studies which respond to a different type of patient needs such as the pediatric, ambulatory, intensive care or those subjects in free movement conditions (Simonson and DeFronzo 1990).
The premise is that the metabolic monitors use different instrumental IC techniques which can filter or enhance the VO_{2} and VCO_{2} variabilities depending on the design of the pneumatic hardware. For instance, in calorimeters with mass exchange, which can be considered as an opendesign pneumatic system, the VO_{2} and VCO_{2} measurements of averages are carried out faster even in a portable manner but with more sensitivity to detect the embedded variabilities (Brown et al. 1984; Myers et al. 1990). On the other hand, in metabolic monitors with closeddesign pneumatic circuit the VO_{2} and VCO_{2} variabilities are filtered because their frequency bandwidth response is probably limited by the great size of their instrumental setups (Holdy 2004). In both cases, no study exists that would suggest which type of pneumatic hardware would be more suitable to measure the variabilities separately. Thus, metabolic monitor manufacturers are free to promote their own hardware designs, which have the sole purpose to obtain the best estimation of the VO_{2} and VCO_{2} averages.
Currently most of the commercial metabolic monitors in use are open circuit systems with the capability to perform IC studies in the range of 15–20 minutes. The bench performance in their accuracy has been evaluated in the range of 2 to 3%, which does not explain the high variation in the REE estimation, in critical care and ambulatory patients (Reeves et al. 2004 and Cooper et al. 2009). The REE variation has been reported as intersubject or intrasubject variability despite following the clinical guide for standardizing IC studies. Therefore, we assume this guide is only focused on controlling the patient’s steady state in order to facilitate the prediction of the REE in 24 hours without taking into account unsteady patients (AARC Clinical Practice Guideline 2004). The second assumption is that the IC studies in nonsteady state, as part of the clinical routine, are accountable for the high variability in the REE estimation (Wessel et al. 1979). Then, current guidance has a limited scope since it only describes measurement conditions when patients are in steady state such that their physiological reaction to thermal and noise environment is monitored and controlled only through the measurement of the variation coefficient (VC) that should be maintained by no more than ± 5% in any single 5 minute measurement interval (McClave et al. 2003).
Consequently, any proposal for a new IC clinical guide with the capability to define studies in steady and nonsteady state should consider the following facts: (a) only 54% of ambulatory patients who are submitted to REE estimation comply with the current VC defined threshold (McClave and Snider 1992; Damask et al. 1983). (b) Different IC studies in ambulatory subjects have reported intraindividual REE variability of 12.5% and 23% during two consecutive days and over a period of 2 years, respectively (Mindy et al. 1986). (c) Studies in critically ill patients have reported interindividual REE variability up to 64% with different metabolic monitors (Schadewaldt et al. 2013). (d) Investigations have shown increments beyond 15% in the VC due to what is called physiological reactivity which is associated to the effect of the connecting devices such as face masks, mouth connectors and canopies (McAnena et al. 1986; Segal 1987; Isbell et al. 1991; Forse 1993). (e) Metabolic monitors for patients in a hospital or the ambulatory environment having different pneumatic techniques and algorithms have not been evaluated to perform IC studies in steady and nonsteady state conditions, and (f) the most frequently used open circuit calorimeters have two different design concepts known as the breath by breath (BbB), and the mixing chamber (MC) techniques that may produce different REE estimation results (Faver et al. 1998; Arch et al. 2006).
Observations, such as those previously mentioned, have triggered our main assumption that the VO_{2} and VCO_{2} variability analysis can help to understand the variation in the REE estimation. Therefore, we propose that variabilities should be separately measured from their VO_{2} and VCO_{2} averages with the purpose to identify the monitors’ technological differences in the measurement of the variabilities and to search for possible physiological information in them during steady and nonsteady IC studies. To prove this hypothesis, the VO_{2} and VCO_{2} averages and their variabilities were simultaneously measured by using the MC and the BbB techniques. Specifically, variances were used with the MC technique and power spectrum functions in the 0–0.5 Hertz band were constructed and measured in the BbB method. The gas exchange in the first method was sampled every 20 seconds while the gas exchange in the second technique was sampled breath by breath in order to generate a stochastic process measurement as a manner of a discrete time series. Both gas exchanges were measured in two consecutive 15 minute windows in order to obtain enough data to measure trends and to have high frequency resolution when exploring cyclical rhythms.
The objective of this work was to develop a pilot study where young healthy volunteer population was submitted to the physiological clinoorthostatic maneuver (COM) with the idea to generate steady/clinostatic and nonsteady/orthostatic stages as a manner of an instrumental bench test (Gonzalez et al. 2013; Cadena et al. 2010). A hybrid calorimeter with the MC and the BbB techniques was applied to compare interindividual variability changes during the COM stages. The interindividual variabilities’ energy measurement was considered as appropriate since it can reflect physiological phenomena. Then, variance averages (SD _{ VO 2} ^{2}, SD _{ VCO 2} ^{2}) were used as time energy measurement in the MC technique and power spectrum functions (vVO2(f), vVCO2(f)) were used as frequency energy measurement in the BbB method. Finally, the interindividual VO_{2} and VCO_{2} averages were computed with the purpose to compare the techniques’ performance in the REE estimation.
Results and discussion
Variabilities’ energy by power spectrum functions
The Figure 1 shows the BbB intersubjects VO_{2} and VCO_{2} variabilities in terms of their averaged power spectrum functions vVO2(f) and vVCO2(f) with units in (ml/bth)^{2}/Hz in the frequency range of 0–0.5 Hertz. Thus, individual spectrum functions were generated when each subject (N = 15) was submitted to the steady/clinostatic and then to the nonsteady/orthostatic stages of the COM.
The averaged functions vVO2(f) and vVCO2(f) showed that their main energy was concentrated in the low frequency (LF) and medium frequency (MF) bands, where the analysis bands were defined as LF = 0–0.04, MF = 0.04–0.15 and HF = 0.15–0.50 Hertz. Here, it is noteworthy that the band definition for the variabilities was analogous to how the heart rate variability is analysed with the purpose to facilitate their physiological interpretation (Task Force of the European Society of Cardiology 1996). The Figure 1 clearly shows that the vVO2(f) and vVCO2(f) have an unexpected cyclic rhythm energy with central frequency at 0.025 Hz that is generated only during the nonsteady/orthostatic stage of the COM with an energy increment of 71% and 56%, respectively, when this is compared with the steady state energy.
The Figure 2 shows the variabilities’ total energy (ml/bth)^{2} increments by frequency bands. For instance, the total energy of vVO2(f) was computed as the integral below the function so that in orthostatic stage is approximately 50% higher in magnitude than the total energy of the vVCO2(f) for the same stage. A comparative analysis for the variability energies as a consequence of the COM application is shown in the Table 1.
Comparative analysis of the variabilities’ energy
The Table 1 shows the comparative analysis of the variabilities’ energy obtained by the MC and the BbB techniques application. The variances averages (SD _{ VO 2})^{2} and (SD _{ VCO 2})^{2} are compared against the total variabilities’ averaged energy obtained from the vVO2(f) and vVCO2(f) functions.
The variance averages increment due to the COM were not statistically significant (p > 0.1), while the spectral total energy increment were 71% for vVO2(f) and 56% for the vVCO2(f) (p < 0.05) as it is also seen in Figure 2.
Comparative analysis of averages
The Table 2 shows the VO_{2} and VCO_{2} average comparison according to the model of the Figure 3. A discrete gas exchange (VO2[n] and VCO2[n]) model was considered in order to compute separately the averages for the MC and BbB techniques. Then, the averages for the MC technique (V\dot{O}2{\left[n\right]}_{\mathit{MC}} and VĊO 2[n]_{ MC }) were incremented 63% and 39% (p < 0.05), while the averages for the BbB technique (V\dot{O}2\left[n\right] and VĊO 2[n]) were only increased 32% and 40% (p < 0.1), when the COM was applied. The statistical differences analysis was based on the Welch ttest for unequal variances.
Although all computed averages in Table 2 show independent significant statistical differences due to the COM, the Figure 4 shows no differences between the IC techniques. The posthoc statistical analysis corroborates none differences (p > 0.1) using a Welch ttest for the interindividual VO_{2} and VCO_{2} averages, after applying an ANOVA onefactor test for multiple measurements. However, it is worth to observe that the difference between the V\dot{O}2{\left[n\right]}_{\mathit{MC}} and the V\dot{O}2\left[n\right] averages shows a slight tendency (p = 0.39) to reject the null hypothesis only during the orthostatic stage.
Discussion
In view of the results, the hypothesis is proved in the sense that it is necessary to analyze the VO_{2} and VCO_{2} variabilities in order to understand the causes of variations in the REE estimation. The Table 1 shows the interindividual variabilities’ energies computed as variances which did not show statistical differences during the COM test. These unchanged variances lead to the interpretation that the MC technique is a better method to perform IC studies with patients in steady and nonsteady state since the REE is much less affected by the VO_{2} and VCO_{2} variabilities. The MC technique works as a low pass filter such that it suppresses the high frequencies of the variabilities generating more adequacies to measure the averages of the VO_{2} and VCO_{2}. Thus, the analysis of averages in Table 2 is consequent with the MC technique performance when an increment of 63% for the V\dot{O}2{\left[n\right]}_{\mathit{MC}} is observed while the V\dot{O}2\left[n\right] only shows an increment of 32%. Additionally, this result can be interpreted as the MC technique having the right sensitivity to faithfully follow any physiological low frequency change that affects the VO_{2} and VCO_{2} averages (Bruce 1996).
These outcomes lead us to understand why the old instrument Delta Track II (Datex Finland) has been accepted as the reference instrument when new metabolic monitors are compared against its performance, mainly during IC studies in critical care patients. It is clear that the canopy in the Delta Track II performs as an open circuit MC technique with the capability to reject high frequency variabilities. Deltra Track’s hardware can be modelled as a time average filter so that the VO_{2} and VCO_{2} variabilities from unstable patients produce minimum interindividual variations in the REE estimation (Severine et al. 2013; Miodownik et al. 2000).
On the other hand, the power spectrum functions in Figure 1 show how IC studies in steady or nonsteady state can be separated using their energy computation. The interindividual variabilities’ energies in Table 2 show increments of 71% for the vVO2(f) and 53% for the vVCO2(f) when subjects are submitted to the orthostatic stage. These results suggest, the BbB technique is more suitable for monitoring and controlling the subjects’ physiological condition. This is an improvement over only using the traditional concept of CV. In addition, the cyclical rhythms found at 0.025 Hz in Figure 1 can be used as a new figure of merit to describe how stable or unstable the patient is during an IC study. Although this finding can be used as new physiological control information, the interpretation of its origins needs more research work. One first approach was carried out by dividing the energy of the vVO2(f) and vVCO2(f) in frequency bands similarly to the way that heart rate variability (HRV) is processed; after which, one second step would be to correlate the energy found in LF and MF with the LF energy of the HRV in order to discard whether or not the rhythmicity is due to sympathetic neural control or not (Taylor et al. 2001; Satue and Méndez 2012).
Conclusions
New and advanced IC metabolic monitors designs should consider the following issues: (a) the VO_{2} and VCO_{2} variabilities should be separately measured using the MC and BbB techniques simultaneously in order to carry on IC studies in steady or nonsteady state and to distinguish the origin of the variation of the REE estimation. (b) The MC technique is the appropriate method to estimate the VO_{2} and VCO_{2} averages, whereas the BbB technique is the most suitable procedure to provide physiological information to determine how stable or unstable an IC study is. (c) The cyclical rhythm in the BbB technique cannot be interpreted as instrumental noise since the O_{2} and CO_{2} transducers are performing independent measurements in open circuit calorimeters that allow to compute the vVO2(f) and vVCO2(f) separately. (d) The discrete gas exchange modeling of the Figure 3 contributes to understand why the MC technique is a lowpass filter or a moving average measurement system while the BbB technique is a highpass filter able to generate a random process measurement system. Therefore, both techniques have different effects in the REE estimation. (e) Finally, it is important to notice that the COM physiological test combined with the VO_{2} and VCO_{2} variability measurements can be considered as an input–output paradigm assessment in order to search for the metabolic monitors’ performance.
Methodology
Model for the MC and BbB variabilities and averages definition
The Figure 3 shows a hybrid calorimeter model with the MC and the BbB techniques where the VO_{2} and VCO_{2} variabilities are defined at the output as SD _{ VO2 } and SD _{ VCO2 } and vVO2[n] and vVCO2[n], respectively. Likewise, the averages are defined as V\dot{O}2{\left[n\right]}_{\mathit{MC}} and VĊO 2[n]_{ MC } for the MC technique and V\dot{O}2\left[n\right] and VĊO 2[n] for the BbB method.
This model for the MC and BbB techniques considers a discrete gas exchange at the input of the mouth (VO2[n] and VCO2[n]) in which the variabilities are implicitly included before they are separately measured. The argument n = 1,2,3… stands for a discrete time series that represents the breath by breath gas exchange during an IC study. The model in Figure 5 explains how the discrete gas exchange is formed at the alveolar level.
Model for the alveolar discrete gas exchange
The alveolar discrete gas exchange is modelled in Figure 5. The assumption is that the continuous gas exchange at the alveoli (VO2(t) and VCO2(t)) is sampled by the lung’s mechanical ventilation. Then a discrete gas exchange VO2[n] and VCO2[n] is generated when the breath by breath instant flow f(t) works as a sampling function as in Equations (1) and (2).
Where: f (t) is the instant expired flow (L/sec). V _{ T } is the tidal volume (ml) without BTPS (body, temperature, pressure, saturated) to STPD (standard, temperature, pressure, dry) volumetric corrections in order to preserve the simplicity of the model, FIO _{2}(t) – FEO _{2}(t) is the inspiredexpired oxygen fraction difference and the FECO _{2}(t) is the expired CO_{2} gas fraction. All gas fractions are in atmospheric percentages (%).
The products f(t) × VO2(t) and f(t) × VCO2(t) generate the continuous sampling for the O_{2} and CO_{2} uptake during each expired breath with time duration D _{ 1 }, D _{ 2 }, …D _{ n }. Hence, individual and different breathbybreath sample volumes are produced as VO2[Dn] and VCO2[Dn]. These volumes are computed as in Equations (3) and (4). The instantaneous products are done between signals analog to digital converter (A/D) at the rate of 10 milliseconds per sample in order to avoid numerical integration errors and to be according with the sampling Nyquist theorem when it is assumed signals with bandwidths below 100 Hz (Proakis and Manolakis 1998).
The g (t – D _{ n }) are continuous gate functions with the same time duration D_{1}, D_{2},..D_{n} that allow synchronization to integrate the products between the instant flow and the instant gas fractions as it is seen in Figures 6 and 7. Normalized products f(t) × VO2(t) and f(t) × VCO2(t) are needed in order to match with the f(t) peak amplitude the VO2(t) and VCO2(t) values so that Equations (3) and (4) should be divided by 1/V _{ T }. Figure 6 shows a real example how gas fractions signals and the expired instant flow signal are synchronized to compute each VO2[Dn] and VCO2[Dn].
BbB discrete time series analysis
The VO2[n] and VCO2[n] discrete time series in Figure 7 are generated when the computations of each VO2[Dn] and VCO2[Dn] are carried out over the continuous signal outputs corresponding to the flow, O_{2} and CO_{2} sensors. The constant time delay of 800 msec in Figure 6 is for the synchronization between the instantaneous flow f(t) and the time gas fraction signals (FEO2(t) and FECO2(t)). This time lag depends on the sensors’ time response and the delay produced by the tubing length which utilizes a flow of 150 ml/min to sample the sensors. The hybrid calorimeter with the open pneumatic circuit is sketched in Figure 9. Each VO2[Dn] and VCO2[Dn] value is placed in a time series using the sequence δ[n] with mathematical proprieties that allow the generation of the BbB discrete time series according to Equations (5) and (6).
Then, the sequence δ [n – D _{ n }] is used to geometrically place each value of VO2[Dn] and VCO2[Dn] as a series of coefficients at the end of each f(t) as it is seen in Figure 7. Here, the meaning of Dn is extended as a dumb variable (Dn = 1,2,..n) just to be interpreted as an index to generate the BbB discrete time series VO2[n] and VCO2[n]. The Figure 7 shows an example of a discrete time series from which the νVO2[n] and νVCO2[n] variabilities are computed. The average values (V\dot{O}2\left[n\right] and VĊO 2[n]) are calculated from the discrete gas exchange as in Equations (7) and (8).
Where:
The above averages are computed with approximately N = 225 breaths, which are equivalent to a data acquisition window of 15 minutes.
An example of the power spectrum analysis of the νVO2[n] and νVCO2[n] is shown in the Figure 8. A linear data interpolation function was used to reformat the discrete time series VO2[n] and VCO2[n]. Then, one sample per second was used to resample the reformatted discrete time series in order to obtain a frequency domain analysis in the range of 0.0 to 0.5 Hz. The processing window was selected to capture at least 15 minutes of data so that a Welch power spectrum estimator allowed a maximum resolution of 0.005 Hertz using 50% of data overlapping. The frequency band analysis was defined in three main regions: low frequencies (LF = 0–0.04 Hz), medium frequencies (MF = 0.05–0.15 Hz) and high frequencies (HF = 0.16–0.5 Hz). These band divisions are similar to the heart rate variability analysis with special emphasis in the LF and MF bands since the HF band is assumed to be related with instant flow’s frequency (respiratory frequency) activity as it is seen in the example of the Figure 8.
Averages and variabilities in the MC technique
The measurement of the averages and variabilities using the MC technique requires modeling the effect of the mixing chamber upon the discrete gas exchange VO2[n] and VCO2[n], having the model in Figure 3 in mind. The MC averages should be computed as in Equations (11) and (12) using a digital moving average which depends on the chamber volume and the number of breaths that the chamber storages as a manner of pipeline, prior to obtaining one sample average every 20 seconds. In our case, the hybrid calorimeter has a chamber with a volume of 1.8 Liters so that the number of breaths storage in the MC, when the patient’s respiratory frequency is approximately 15 breaths/min, is approximately M = 4 in Equations (11) and (12). And the V\dot{O}2{\left[n\right]}_{\mathit{MC}} and VĊO 2[n]_{ MC } are computed using the criteria of 30 averages to smooth enough the gas exchange. Thus, each one of the 30 averages is formed with M breaths to obtain one average sample during a total of 15 minutes per each IC study.
The measurement of the variabilities in the MC technique was computed as in Equations (13) and (14). Even, these equations allow the calculation of the VCs according to the clinical practice guidelines as it is shown in (15).
Hybrid indirect calorimeter hardware
A specific opencircuit hybrid indirect calorimeter (MGM3) was designed and manufactured for the purpose of this work which was based in the design of Westenskow et al. (1984). The MC and the BbB techniques were fused in the MGM3 as it can be seen in Figure 9. The patient’s half mask works either by passing the expired gas through the 1.8 L mixing chamber to implement the MC technique or by directly connecting the expired gas to a hotwire flowmeter (TSI Inc, USA) to implement the BbB technique.
The MGM3 calibration and quality control unit was a microprocessor based design and was calibrated every 5 minutes using a reference gas cylinder with a certified mixture of 21% O_{2}, 10% CO_{2}, complemented with N_{2}. Additionally, two more gas certified mixture cylinders (15% O_{2}, 4% CO_{2} and 18% O_{2}, 3% CO_{2}, Praxair) were used to adjust the transducer offsets and gains for the case of doing IC studies in ambulatory patients. The MC technique was implemented by displaying values of V_{E} (expired volume minute in L · min^{1}), RF (respiratory frequency in breaths · min^{1}), VO_{2} (ml · min^{1}), VCO_{2} (ml · min^{1})_{,} V_{T} (tidal volume in ml · breath^{1}) and RQ (respiratory quotient VO_{2}/VCO_{2}) every 20 seconds. These readings were automatically corrected and displayed at STPD conditions after measuring volumes and fractions at BTPS conditions (2400 meters above the sea level at Mexico City, 590 ± 3 mmHg, and expired gases’ temperature). The VO_{2} was computed using the Haldane correction.
Experimental design and data processing
A population of 15 young normal volunteer subjects without a history of any chronic disease was studied. The ages ranged from 18 to 30 years with a body mass index (BMI) average of 24.2 ± 3.8 Kg · m^{2}. All subjects gave signed informed consent to be studied in the morning after 8 hours of fasting. Subjects were asked to perform the active clinoorthostatic maneuver (COM). First, a 5 minute period of relaxing was used before he/she lied down on a couch and was then submitted to the COM while connected to the MGM3 calorimeter. Two 30 minutes periods were used to implement the measurement protocol: 15 minutes for the MC technique and 15 min for the BbB technique in each COM position. All of the measurements were made in the same room maintaining constant temperature and data collection by the same expert team in all cases.
Comparative statistical paired data analysis was applied intragroups. The MC averages V\dot{O}2{\left[n\right]}_{\mathit{MC}} and VĊO 2[n]_{ MC } were compared against the BbB averages V\dot{O}2\left[n\right] and \dot{V}\mathit{CO}2\left[n\right]. Similarly, variances averages (SD _{ VO 2})^{2} and (SD _{ VCO 2})^{2} were compared against total spectral energy averages. The statistics analysis was parametric since the variables were considered to be Gaussians, once they were tested by the Kolmogorov–Smirnov test. Then, twotailed paired ttests (Welch version) were used as appropriate for unequal variances. In all cases, the null hypothesis was rejected when p ≤ 0.1 since this experiment was considered to be a pilot study.
Abbreviations
 IC:

Indirect calorimetry
 COM:

Clinoorthostic maneuver
 REE:

Resting energy expenditure (Kcal/day)
 VO_{2} :

Oxygen consumption (ml/min)
 VCO_{2} :

Dioxide production (ml/min)
 MC:

Mixing chamber technique
 BbB:

Breathbybreath technique
 VC:

Variation coefficient (SD/average)
 SD:

Standard deviation
 SD^{2}VO2:

VO_{2} variance (energy) (ml/breath)^{2}
 SD^{2}VCO2:

VCO_{2} variance (energy) (ml/breath)^{2}
 vVO2(f):

VO_{2} variability average power spectrum function (ml/breath)^{2}/Hz
 vVCO2(f):

VCO_{2} variability average power spectrum function (ml/breath)^{2}/Hz
 Total energy:

=\frac{1}{2}{\displaystyle {\int}_{\infty}^{\infty}\mathit{vVO}2\left(f\right)\mathit{df}} (ml/breath)^{2}
 V\dot{O}2{\left[n\right]}_{\mathit{MC}} :

VO_{2} average by the MC technique (ml/min)
 VĊO2[n]MC:

VCO_{2} average by the MC technique (ml/min)
 V\dot{O}2\left[n\right] :

VO_{2} average by the BbB technique (ml/min)
 VĊO2[n]:

VCO_{2} average by the BbB technique (ml/min)
 VO2[n] and VCO2[n]:

Discrete gas exchange at the mouth
 VO2(t) and VCO2(t):

Continuous gas exchange at the alveoli
 vVO2[n]:

VO_{2} time discrete series variability (ml/min)
 vVCO2[n]:

VCO_{2} time discrete series variability (ml/min).
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Acknowledgments
This work was supported by grants from the Universidad Autónoma MetropolitanaIztapalapa, the Institute of Science and Technology from the DF in México City (project number PICSA1175), and from the Universidad Nacional Autónoma de México (project PAP IIT IN11361) during the period from 2008 to 2012.
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The four authors declare that they have no competing interests since they are working for public institutions supported by the Mexican government.
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MCM, OIV, and JAL participated in the conception and design of the pilot study as well as the data collection, analysis and interpretation. BER participated in the supervision of the experimental design as well as the digital signal processing of the signals. MCM was the primary author of the manuscript. All authors read, revised and approved the final manuscript.
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CadenaMéndez, M., EscalanteRamírez, B., AzpirozLeehan, J. et al. VO_{2} and VCO_{2} variabilities through indirect calorimetry instrumentation. SpringerPlus 2, 688 (2013). https://doi.org/10.1186/219318012688
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DOI: https://doi.org/10.1186/219318012688
Keywords
 VO2 and VCO2 variabilities
 Gas exchange variability
 Variability
 Open circuit hybrid calorimeter
 VO2 and VCO2 power spectrum