Eur J Appl Physiol DOI 10.1007/s00421-015-3169-x
ORIGINAL ARTICLE
Assessment of breath‑by‑breath alveolar gas exchange: an alternative view of the respiratory cycle V. Cettolo1 · Maria Pia Francescato1
Received: 10 November 2014 / Accepted: 3 April 2015 © Springer-Verlag Berlin Heidelberg 2015
Abstract Purpose Breath-by-breath (BbB) determination of the O2 flux at alveolar level implies the identification of the start and end points of each respiratory cycle; Grønlund defined them as the times in two successive breaths showing equal expiratory gas fractions. Alternatively, the start and end points of each breath might be linked to the ratio between the exchangeable and non-exchangeable gases. The alternative algorithm is described and evaluated with respect to the algorithm proposed by Grønlund. Methods Oxygen and carbon dioxide fractions, and ventilatory flow at the mouth were continuatively recorded in 20 subjects over 6 min at rest and during a cycloergometer exercise including 4 increasing intensities lasting 6 min each. Alveolar BbB oxygen uptake was calculated from the gas and flow traces by means of the two methods at stake. Results Total number of analysed breaths was 14,257. The data obtained with the two methods were close to the identity line (average slope 0.998 ± 0.004; R > 0.994; n > 334 in all subjects). Average difference between the O2 uptake data obtained by the two methods amounted to −0.27 ± 1.29 mL/ min, whilst the standard deviation of the differences was 11.5 ± 4.6 mL/min. The relative percentage difference was independent from the O2 uptake and showed an average bias amongst subjects close to zero (−0.06 ± 0.15 %). Communicated by Susan Hopkins. Electronic supplementary material The online version of this article (doi:10.1007/s00421-015-3169-x) contains supplementary material, which is available to authorized users. * Maria Pia Francescato [email protected] 1
Department of Medical and Biological Sciences, University of Udine, P.le Kolbe 4, 33100 Udine, Italy
Conclusions The alternative timing of the respiratory cycle provided congruent O2 uptake data and made the identification of the start and end points of each breath more robust without introducing systematic errors. Keywords Breath-by-breath oxygen uptake · Alveolar gas exchange · Gas lung stores · Gas fractions Abbreviations BbB Breath-by-breath FO2 Oxygen fraction at the mouth FOA 2 Oxygen fraction at alveolar level FN2 Nitrogen fraction at the mouth FNA 2 Nitrogen fraction at alveolar level vA Variation of the alveolar gas volume vOS2i Variation of pulmonary oxygen stores OG Original Grønlund’s algorithm SG Simplified Grønlund’s algorithm STPD Standard temperature pressure dry t1 Starting time of the ith breath t2 Final time of the ith breath defined on the FO2 trace or on the FO2/FN2 trace t3 Final time of the ith breath defined on the FN2 trace A Alveolar volume at the beginning of the ith breath vi−1 vNA 2 Volume of nitrogen exchanged at alveolar level vOA 2 Volume of oxygen taken up at alveolar level vOM 2 Volume of oxygen exchanged at the mouth ˙ V COA 2 Alveolar carbon dioxide release Alveolar oxygen uptake V˙ OA 2
Introduction The study of O2 uptake, and/or of CO2 release, under various conditions still attracts the interest of several
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researchers involved in different fields of investigation. Non-invasive measurements are usually made at the mouth, from which researchers try to get information about the gas transfer occurring at alveolar level. Nevertheless, changes of the volume of gas contained in the lungs (the “pulmonary stores”) from one breath to the following unbind the values measured at the mouth from the gas transfer at the alveoli in terms of signal intensity and time. Several computational algorithms have been proposed to determine the alveolar gas transfer on a breath-by-breath (BbB) basis (Wessel et al. 1979; Beaver et al. 1981; Swanson and Sherrill 1983; Busso and Robbins 1997). All of them are based on the Auchincloss et al. approach (1966), but each of them takes into account the alveolar volume at the beginning of the breath A ) in a different way. di Prampero and Lafortuna (1989), (vi−1 A result however, showed that different values assigned to vi−1 in a different BbB gas exchange variability. It then appears that “true” alveolar gas exchange could be correctly determined only A could be assessed on a BbB basis. if the actual vi−1 An alternative algorithm was proposed by Grønlund A by con(1984), who got rid of the need of estimating vi−1 sidering the respiratory cycle as the period of time elapsing between equal expiratory gas fractions in two successive breaths. This algorithm was resumed and extensively tested by Capelli et al. (2001). The algorithm proposed by Grønlund (1984) and its implementation might seem quite complex and the difficulties of developing appropriate software might have hindered its diffusion. We propose an alternative view of the respiratory cycle, which results in the removal of unnecessary mathematics as compared to that of Grønlund (1984). The simplified algorithm was then evaluated by comparing breath-by-breath alveolar gas transfer values with the corresponding values obtained by means of the original algorithm.
Theory During the ith breath, the volume of oxygen taken up at the alveoli, vOA 2i, can be determined from the volume of oxygen exchanged at the mouth, vOM 2i , minus the volume change of pulmonary oxygen stores vOS2i: M S vOA 2i = vO2i − vO2i
(1)
According to Auchincloss et al. (1966), the change of volume of pulmonary O2 stores can be divided into two
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terms: the first dependent on the variation of the fraction of alveolar oxygen, FOA 2 , from the i−1 breath to the ith breath, the second due to the variation of the volume of alveolar gas, vA, between the two subsequent breaths: A vOS2i = vi−1 · FOA2i − FOA2i−1 + FOA2i · vA (2) i where vA i−1 is the end-expiratory alveolar volume at the beginning of the current breath i. To determine viA, we can suppose that the assumptions made above are valid also for the nitrogen (Auchincloss et al. 1966), and that the N2 volume exchange at the alveolar level, vNA 2 , during any time interval was null:
A A M A A A =0 + FN · v vNA = vN − v · FN − FN 2i i 2i 2i i−1 2i 2i−1
whereby:
viA =
1 M A A A vN − v · FN − FN 2i i−1 2i 2i−1 FNA 2i
(3)
By substituting Eq. (3) into Eq. (2) and then in Eq. (1), the following equation is obtained:
FOA A A 2i vi−1 × FOA 2i − FO2i−1 + FNA 2i A A A × vNM 2i − vi−1 × FN2i − FN2i−1
M vOA 2i = vO2i −
FOA A A A 2i × vNM 2i - vi−1 × FO2i − FO2i−1 A FN2i A FO2i A A A − A vi−1 × FN2i − FN2i−1 FN2i
= vOM 2i −
(4)
In this equation, the only quantity not directly measurable A (di Prampero and on a breath-by-breath basis is the term vi−1 Lafortuna 1989). To circumvent this problem, according to the assumptions of Grønlund (1984), the integration interval can be identified on both the O2 (or CO2) trace and N2 trace as the time period elapsed between a common starting time (t1) and two final times, one specific for the O2 (or CO2) trace (t2) and the other for the N2 trace (t3); whenever t2 and t3 do not overlap, a correction factor has to be introduced (Fig. 1). Capelli et al. (2001) developed a software that applies the definition of the respiratory cycle according to Grønlund (1984). The alternative view of the integration interval results from the reasoning outlined below. Indeed, Eq. (4) can be simplified by factorising the term A as follows: vi−1
Eur J Appl Physiol
Subsequently, bringing the two terms in curly braces to the same denominator (FNA 2i), Eq. (5) is obtained: M vOA 2i = vO2i −
×
FOA A 2i × vNM 2i +vi−1 FNA 2i
A A A FOA 2i−1 × FN2i − FO2i × FN2i−1
FNA 2i
(5)
Two times t1 and t2 can be appropriately chosen on two consecutive breaths so that the numerator within the curly braces becomes zero, i.e.: A A A FOA 2i−1 (t1 ) · FN2i (t2 ) = FO2i (t2 ) · FN2i−1 (t1 ).
(6)
Under these conditions, the third part of Eq. (5) disapA unnecessary. pears, making the knowledge of vi−1 The condition described in Eq. (6) can be rewritten as:
FOA 2i−1 (t1 ) FNA 2i−1 (t1 )
=
FOA 2i (t2 ) A FN2i (t2 )
This equation shows that the start and end points of each respiratory cycle can be defined in a new way, i.e. as the times in successive breaths where identical FO2/FN2 ratios are observed. Hence, the calculation of vOA 2i over the interval from t1 to t2 is limited to the first two parts of Eq. (5): M vOA 2i = vO2i −
=
t2
t1
FOA 2i × vNM 2i FNA 2i
FOA 2i V˙ M · FOM 2 dt − FNA 2i
t2
V˙ M · FNM 2 dt
t1
where V˙ M is the respiratory flow, whose sign depends on the phase considered (inspiration or expiration), FOM 2 and M FN2 are the O2 and N2 fraction, respectively, as measured at the mouth. A The ratio FOA 2i FN2i is unknown, but if t1 and t2 are selected towards the end of the expiration of two consecutive breaths, the fractions of oxygen and nitrogen at the mouth approximate those in the alveoli (Grønlund 1984):
FOA FOM 2i 2 (t1 ) ≈ A FNM FN2i 2 (t1 ) The alveolar volume of oxygen taken up in a breath can thus be determined by variables all measurable at the mouth:
vOA 2i
=
t2
t1
FOM 2i (t1 ) V˙ M · FOM · 2 dt − FNM 2i (t1 )
t2
V˙ M · FNM 2 dt
t1
The oxygen uptake, at alveolar level and during the temporal interval between t1 and t2, is given by the quotient of vOA 2i divided by (t2−t1). With appropriate modifications (i.e. substituting FO2 with FCO2), alveolar CO2 transfer can also be obtained with the same approach.
Fig. 1 Traces of O2 and N2 fractions and of the calculated ratio FO2/ FN2 at rest for a typical subject, as seen at the mouth. “Exp” and “Insp” are the inspiration and expiration phases. Time t1 is chosen according to specific criteria (see text). Times t2 and t3 on the FO2 and FN2 traces are chosen to yield O2 and N2 fractions, respectively, which are identical to that at t1. Time t2 on the FO2/FN2 trace is chosen to yield a ratio identical to that at t1. Note that, the FN2 scale was expanded twice as compared to the other vertical scales
Methods Subjects Twenty healthy adults (11 males and 9 females of mean (±SD) age 33.3 ± 12.2 years), after having been thoroughly informed of the nature, purpose, and possible risks,
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gave their voluntary written consent to participate in the study. Average (±SD) stature and body mass of the subjects were 1.74 ± 0.10 m and 67.5 ± 12.6 kg, respectively. All subjects were healthy and moderately active; none was smoker. The study was approved by the local Ethics Committee and was conducted according to the Declaration of Helsinki. Experimental protocol The subjects were equipped with the face mask and then sat quietly on the bicycle ergometer (Ergomed 839E; Monark, Vansbro, Sweden) for about 8 min. Afterwards, the subject started pedalling keeping throughout the exercise period the pedalling frequency as close as possible to 60 rpm with the aid of the inbuilt led bar. Four exercise steps of increasing intensity (corresponding to 0.6, 0.9, 1.2, and 1.5 W/kg body mass and 0.5, 0.8, 1.0, and 1.3 W/kg body mass in men and women, respectively) were performed, lasting 6 min each. In addition, to evaluate if the newly proposed algorithm was still able to cope with changes in lung volume, 8 out of the 20 recruited volunteers were asked to return to the lab in a following day. In this occasion, a short (about 1 min) data collection period was performed at rest during which the volunteers were asked to voluntarily change the endexpiratory and the inspiratory volumes. Measurements Oxygen and carbon dioxide fractions, and ventilatory flow at the mouth were continuatively recorded throughout the tests (6 min at rest + 4 × 6 min during exercise) by means of a metabolic cart (Quark B2, Cosmed, Italy). Subjects breathed through a facemask mounted on a turbine flowmeter. Gases were sampled continuously through a 2-m-long capillary line inserted in the outer frame of the flowmeter and analysed by fast-response O2 (chemical; t90 ~ 170 ms) and CO2 (infra-red; t90 ~ 190 ms) sensors embedded in the equipment. The software operating it allowed us to record gas and flow signals with a sampling frequency of 25 Hz and to save them as text files. Before each test, following the procedures indicated by the manufacturer, the analysers were calibrated with a gas mixture of known composition (FO2 = 0.16; FCO2 = 0.04; N2 as balance) and ambient air; the flowmeter was calibrated by means of a 3-L syringe (Hans Rudolph Inc., USA). Data treatment Alveolar breath-by-breath oxygen uptake (V˙ OA 2 ) and carbon dioxide production (V˙ COA ) were calculated from the 2 original gas and flow traces, by means of the two methods to be compared. Computerised procedures were specifically
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developed in C language under the Unix-like Cygwin environment (Red Hat Cygwin, version 1.7.30). In the present investigation, the final equation used to calculate the alveolar O2 uptake during one breath by means of the original algorithm proposed by Grønlund (1984) (OG), described also by Capelli et al. (2001), was the following:
V˙ OA 2i =
t2
V˙ M · FOM 2 dt −
t1
FOM 2 (t1 ) FNM 2 (t1 )
·
t3
M V˙ M · FNM 2 dt + FO2i (t1 ) ·
t3
V˙ M dt
t2
t1
t2 − t 1
In comparison, the final equation used to implement the simplified algorithm (SG), as proposed in the present paper, was the following:
V˙ OA 2i =
t2
t1
V˙ M · FOM 2 dt −
FOM 2i (t1 ) FNM 2i (t1 )
t2 − t 1
·
t2
V˙ M · FNM 2 dt
t1
It should be remembered here that the t1 and t2 time points, although having the same conceptual meaning, are defined in a different manner for the two equations (see Theory). Analogous equations were used to compute the carbon dioxide production by means of the two methods. Finally, for both methods: 1. One minus the sum of measured O2 and CO2 fractions was assumed to be represented only by N2, as also assumed by others (Cautero et al. 2005). 2. After correction for the water-vapour partial pressure, inspired and expired gases have been converted to STPD conditions. The temperature in the alveoli was assumed to be 37 °C; the expiratory gas temperature at the flowmeter, the ambient temperature, the barometric pressure and the relative humidity were assumed to be equal to those measured by the metabolic cart. 3. To avoid incoherent data likely arising from coughs, sighs or swallows, the breaths were considered valid only if the inspiratory and/or the expiratory volumes were greater than 150 mL; in the other cases, the invalid breath was incorporated with the following one. 4. The same reference value for the FO2 (for OG) or for the FO2/FN2 ratio (for SG) was used to identify the t1 times of all the breaths. The reference value (fraction or ratio) was determined by preliminarily identifying the minimum of the fractions (or of the ratios) for all the expirations. Subsequently, the histogram of the obtained values was generated and the reference value was set to the 97.5th highest percentile. For both methods, the t1 times were identified in all the expirations as the time points where the FO2 (or the FO2/FN2 ratio) corresponded to the reference value. Subsequently, the t2 times were the
Eur J Appl Physiol
t1 times of the following breaths; when the t1 value could not be identified in that breath, data pertaining to this breath were merged with the preceding one. 5. A similar procedure as the previous one was applied to determine the t1 times used to compute the carbon dioxide production, with the difference that maximum FCO2 factions (or FCO2/FN2 ratios) were analysed. 6. The t3 times, required for the OG method, were determined as the time points that satisfied contemporarily two conditions: closest in time to the corresponding t2 and showing the closest N2 fraction to that found at the corresponding t1. In addition, for about 1 min data collections (during which the volunteers changed the end-expiratory and the inspiratory volumes), the “gross” oxygen uptake at the mouth was calculated by simply integrating the product of flow and exhaled concentration, after conversion to STPD conditions. Data analysis and statistics All the results are reported as mean ± SD. Oxygen uptake data (and CO2 production) were compared by linear regression and Bland–Altman’s analysis. Bland and Altman’s limits-of-agreement plot (Bland and Altman 1986) allowed assessing the agreement between the two investigated methods (OG and SG, respectively). According to this analysis, the differences between the corresponding values obtained applying the two methods were plotted against the averages of the two figures. The average of the differences represents the bias between the two methods.
Bland–Altman analysis of a typical subject is illustrated in Fig. 2. Average difference (i.e. the bias) amongst subjects amounted to −0.27 ± 1.29 mL/min, whilst the standard deviation of the differences amounted on average to 11.5 ± 4.6 mL/min. Figure 2 clearly shows that, with increasing the average V˙ OA 2 , the differences between the values yielded by the two methods become more widespread. Nevertheless, the relative percentage difference (i.e. the difference normalised according to the correspondent average value and expressed as percentage) was independent from the average values (Fig. 3), showing an average bias amongst subjects close to zero (−0.06 ± 0.15 %) and an average standard deviation of 1.47 ± 0.68 %. Similar results as those described for V˙ OA 2 were obtained also for V˙ COA 2 (data not shown). Supplemental materials summarise the parameters obtained for V˙ OA 2 on the individual subjects. Figure 4 illustrates the data obtained on a typical subject who voluntarily changed the end-expiratory and the inspiratory volumes during a short data collection period at rest. The figure shows that, by simply integrating the product of flow and exhaled concentration (“gross” O2 uptake, i.e. neglecting the changes of the pulmonary gas stores), very high values were obtained when inspiration exceeded expiration (breath n. 6); in contrast, negative values were obtained when expiration exceeded inspiration (breath n. 13). Similar results were obtained for all the other subjects. Indeed, the Bland–Altmann analysis performed on these data showed an average bias of 1.5 mL/min and a standard deviation of 8.1 mL/min. Despite the resting condition, where there is a worse signal-to-noise ratio, these values are not far from the corresponding figures reported for the exercise trials.
Results Overall, considering the whole data recording periods (lasting about 30 min for each subject), the total number of analysed breaths was 14,257 (range from 334 to 1007 for an individual subject), which corresponded to an average breath frequency of 21.6 ± 5.3 breaths per min amongst subjects (range from 11.1 to 31.5 breaths per min). The two methods have identified the breaths at different times in about 0.1 % of cases (18 and 14 cases out of 14,257 for OG and SG methods, respectively). Regressions lines between the corresponding V˙ OA 2 data determined using the two methods were close to the identity line in all subjects, showing an intercept of 2.8 ± 4.8 mL/min and a slope amounting to 0.998 ± 0.004 (R > 0.994; n > 334 in all cases).
Fig. 2 Differences (OG-SG) versus the averages of the values yielded by the two methods at stake to calculate V˙ OA 2 (OG and SG)
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Fig. 3 Percentage relative differences (2 × (OG−SG)/ (OG + SG) × 100 %) versus the averages of the values yielded by the two methods at stake to calculate V˙ OA 2 (OG and SG)
Fig. 4 Upper panel Oxygen uptake data obtained by simple integration (“gross” VO2; full diamonds), by the SG algorithm (open dots) and the OG algorithm (asterisks) are illustrated as a function of time. Lower panel The respiratory flow at the mouth is shown (negative values are inspiration). The times of the O2 uptake data obtained by means of the three methods do not coincide since they correspond to the midpoint between start of inspiration and end-expiration for the simple integration method, whereas they are the midpoint between two subsequent t1 times identified during the expirations for OG and SG
Discussion The present investigation shows that the alternative identification of the start and end points of each respiratory cycle,
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based on the ratio between the gas exchanged at alveolar level (e.g. O2) and the non-exchangeable gas fraction (essentially N2) yields reliable breath-by-breath O2 uptake (or CO2 release) data. Indeed, the simplified method to calculate the BbB gas exchange yielded overlapping V˙ OA 2 (or A ˙ V CO2 ) data as compared to those provided by the original method of Grønlund (1984). The computation of the O2 uptake on a BbB basis necessarily requires the knowledge of breath duration, i.e. the identification of the start and end points of the respiratory cycles. Traditionally, the respiratory cycle was defined on the basis of the time points where the measured flow change orientation, i.e. a breath starts at the onset of inspiration and ends when expiratory flow had entirely or largely ceased (Auchincloss et al. 1966). Although researchers are aware that the computation of the O2 uptake at alveolar level has to take into account the pulmonary O2 stores, the traditional definition of the respiratory cycle was used for a long time, assuming arbitrary amounts A ). for the alveolar volume at the beginning of the breath (vi−1 More recently, however, Grønlund (1984) proposed a new timing of the respiratory cycle, where the start and end points have equal alveolar oxygen (or carbon dioxide) tensions. By A selecting this integration interval, the measurement of vi−1 is circumvented. A drawback of Grønlund’s algorithm is the necessity of defining also a time point on the FN2 trace (i.e. time point t3) having equal alveolar N2 tension as compared to the start of the breath. Under these assumptions, the same breath could be associated with four different durations (i.e. for the O2 fraction, the N2 fraction referred to the O2 uptake calculation, the CO2 fraction, and the N2 fraction referred to the CO2 release calculation), and the integral of flow between t2 and t3 is warranted when the breath duration associated with the N2 fraction does not coincide with that of the gas under investigation. The timing of the respiratory cycle of the present work, based on the fractions between alveolar exchangeable gas (O2 and/or CO2) and non-exchangeable gas (N2), reduces each breath cycle to two durations (i.e. one for the O2/N2 ratio referred to the O2 uptake calculation and the other for the CO2/ N2 ratio referred to the CO2 release calculation). In addition, the ratio FO2/FN2 (or FCO2/FN2) amplifies the signal changes as compared to the simple gas fractions, making the identification of the start and end times of the breaths (i.e. of the t1 and t2 time points) more robust on the digitalized data. An advantageous method to estimate the gas transfer occurring at alveolar level from measurements made at the mouth should be able to cope with possible changes of the lung gas stores, which are due essentially to imbalances between inspired and expired volumes. This condition can be stressed by changing voluntarily the end-expiratory and inspiratory volumes; after such manoeuvres, Wüst et al. (2008) showed a reduction of about 84 % in the variability of the O2 uptake when they took into account the changes in gas lung stores. Even the original Grønlund’s
Eur J Appl Physiol
algorithm, extensively investigated by Capelli et al. (2001), was designed to correct the gas transfer at alveolar level for the lung gas stores. The simplified algorithm illustrated in the present work essentially maintains the Grønlund’s approach. As a matter of fact, the simplified algorithm provided overlapping values as compared to those obtained with the original Grønlund’s algorithm; the agreement between the two algorithms was maintained also when deliberate lung volume changes were induced (see Fig. 4). Data were acquired continuously for about 30 min, including a period of rest and four different exercise intensities, resulting in at least 334 consecutive breaths (range from 334 to 1007) for each volunteer. The relative percentage difference between the V˙ OA 2 calculated by means of the two methods at stake was small (i.e. −0.06 % ± 1.47 %) and remained constant with increasing the V˙ OA 2 (Fig. 3), independent of the steady state or transient phases. These results support the view that the alternative timing of the respiratory cycle did not introduce systematic errors as compared to the original algorithm of Grønlund. Strengths and limitations of the study In the present investigation, a comparison with the values obtainable by means of a golden standard method (e.g. the classical open circuit method with a Douglas bags gas collection) was not carried out. Nevertheless, the original Grønlund’s algorithm was already extensively validated both at rest and in steady state conditions (Grønlund 1984; Capelli et al. 2001) and it was also applied during the transients (Aliverti et al. 2009; Cautero et al. 2002). In all these studies, the volunteers performed low-intensity exercises (up to a maximum of 120 W) to allow an easier detection of the limitations of the algorithm. Similarly, in the present investigation, the data acquisition was limited to the low exercise intensity domain. Undoubtedly, a validation at higher workloads, and/or under pathological conditions (e.g. lung disease where ventilation and/or blood flow heterogeneity may occur), is warranted. A further limitation of Grønlund’s algorithm is that the instantaneous end-expiratory fraction reflects the “average” alveolar fraction for each gas species. The lung, however, is not homogeneous, thus it might not be adequate to assume that breath-by-breath differences in the end-tidal measurements are a reliable measurement of the BbB differences in alveolar composition (Busso and Robbins 1997). A peculiarity of the present work is that the two methods (OG and SG) were compared using exactly the same O2, CO2 and flow digital traces, using the same C calculation routines, applied on the appropriate data, and adding a specific routine only to determine the t3 times on the N2 trace, required for the OG method. Consequently, whatever systematic error derived from the acquisition of the original
data has affected in the same way the results obtained with the two methods. A drawback of the two algorithms is that gas exchange values can be calculated only during off-line analysis of the gas fractions and respiratory flow signals, i.e. after the end of the data collection (Capelli et al. 2011). Despite this drawback, it is mathematically attractive to eliminate alveA from the equations, making the two BbB olar volume vi−1 algorithms appealing. Technical and methodological implications The calculation of BbB gas exchange data at alveolar level requires an appropriate algorithm and reliable information acquired at the mouth by means of proper and well-known hardware. In the present investigation, gas and flow signals at the mouth were recorded using the sensors embedded in a commercial metabolic cart, which included a 2-m-long gas sampling capillary and a bidirectional turbine as flowmeter. The acquired O2 and CO2 signals showed delay times, lasting about 720 ms, compared to the flow signal, as reported also by other authors (Aliverti et al. 2004); these delay times were provided by the calibration procedure and were automatically corrected by the software operating the metabolic cart before yielding the digital data in the text file. Should this correction be neglected, it would heavily affect the BbB values, up to an underestimation of about 30 % compared to the true values (Capelli et al. 2011). Of note, the delay times might also change with respect to changes in the breathing pattern (Roecker et al. 2005), thus the software ideally should include variable correction factors for each breath. The manufacturer of the metabolic cart certified, for the flowmeter, a volume resolution of 12 mL with the lowest detectable flow of 30 mL s−1. This last figure provides an estimate of the inertia of the turbine, which could affect the recorded dynamics of the actual flow. Despite this drawback, the turbine has the advantage that it is not sensitive to variations in viscosity between inspiration and expiration. The analogue-to-digital converters (ADCs) allowed us to record the signals every 40 ms (i.e. 25 Hz), where the responding time of the O2 and CO2 sensors (t90) lasted about 180 ms. Ideally, faster responding gas analysers should be used (Capelli et al. 2011) to avoid the distortion in the temporal pattern of the measured variables. Oxygen uptake (or carbon dioxide production) values are usually expressed in STPD conditions, which implies the thermodynamic conversion of the inspiratory and expiratory flows starting from the appropriate temperature, pressure and humidity values. The correctness of the thermodynamic transformations can be verified by analysing the multibreath N2 balance, whose drift theoretically
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should remain zero. In the present investigation, the values of temperature, pressure and relative humidity provided by the metabolic cart were used and the same thermodynamic transformations of flows were performed for the OG and SG algorithms. Under these conditions, the possible drift in the N2 balance of a specific subject would affect in the same way the data to be compared, i.e. the V˙ OA 2 data calculated with the two algorithms.
Conclusions Results support the view that the alternative timing of the respiratory cycle, linked to the ratio between the exchangeable gas fraction and the non-exchangeable gas fraction at alveolar level, results in a simplification of the computational algorithm. The proposed algorithm yielded congruent O2 uptake data, without introducing systematic errors. Acknowledgments This work was supported by the Department of Medical and Biological Sciences funding of the University of Udine to M. Pia Francescato. Conflict of interest None of the authors has conflicts of interest to declare.
References Aliverti A, Kayser B, Macklem PT (2004) Breath-by-breath assessment of alveolar gas stores and exchange. J Appl Physiol 96:1464–1469. doi:10.1152/japplphysiol.01198.2003 Aliverti A, Kayser B, Cautero M, Dellacà RL, di Prampero PE, Capelli C (2009) Pulmonary kinetics at the onset of exercise is faster when actual changes in alveolar O2 stores are considered. Resp Physiol Neurobiol 169:78–82. doi:10.1016/j. resp.2009.08.012 Auchincloss JH Jr, Gilbert R, Baule GH (1966) Effect of ventilation on oxygen transfer during early exercise. J Appl Physiol 21:810–818
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Eur J Appl Physiol Beaver WL, Lamarra N, Wasserman K (1981) Breath-by-breath measurement of true alveolar gas exchange. J Appl Physiol 51:1662–1675 Bland JM, Altman DG (1986) Statistical methods for assessing agreement between two methods of clinical measurement. Lancet 1:307–310 Busso T, Robbins PA (1997) Evaluation of estimates of alveolar gas exchange by using a tidally ventilated nonhomogenous lung model. J Appl Physiol 82:1963–1971 Capelli C, Cautero M, di Prampero PE (2001) New perspectives in breath-by-breath determination of alveolar gas exchange in humans. Pflugers Arch 441:566–577. doi:10.1007/ s004240000429 Capelli C, Cautero M, Pogliaghi S (2011) Algorithms, modelling and VO2 kinetics. Eur J Appl Physiol 111:331–342. doi:10.1007/ s00421-010-1396-8 Cautero M, Beltrami AP, di Prampero PE, Capelli C (2002) Breathby-breath alveolar oxygen transfer at the onset of step exercise in humans: methodological implications. Eur J Appl Physiol 88:203–213. doi:10.1007/s00421-002-0671-8 Cautero M, di Prampero PE, Tam E, Capelli C (2005) Alveolar oxygen uptake kinetics with step, impulse and ramp exercise in humans. Eur J Appl Physiol 95:474–485. doi:10.1007/s00421-005-0038-z di Prampero PE, Lafortuna CL (1989) Breath-by-breath estimate of alveolar gas transfer variability in man at rest and during exercise. J Physiol 415:459–475 Grønlund J (1984) A new method for breath-to-breath determination of oxygen flux across the alveolar membrane. Eur J Appl Physiol 52:167–172 Roecker K, Prettin S, Sorichter S (2005) Gas exchange measurements with high temporal resolution: the breath-by-breath approach. Int J Sports Med 26:S11–S18. doi:10.1055/s-2004-830506 Swanson G, Sherrill D (1983) A model evaluation of estimates of breath-to-breath alveolar gas exchange. J Appl Physiol Respir Environ Exerc Physiol 55:1936–1941 Wessel H, Stout R, Bastanier C, Paul M (1979) Breath-by-breath variation of FRC: effect on VO2 and VCO2 measured at the mouth. J Appl Physiol Respir Environ Exerc Physiol 46:1122–1126 Wüst RCI, Aliverti A, Capelli C, Kayser B (2008) Breath-by-breath changes of lung oxygen stores at rest and during exercise in humans. Resp Phys Neurobiol 164:291–299. doi:10.1016/j. resp.2008.06.002
ORIGINAL ARTICLE
Assessment of breath‑by‑breath alveolar gas exchange: an alternative view of the respiratory cycle V. Cettolo1 · Maria Pia Francescato1
Received: 10 November 2014 / Accepted: 3 April 2015 © Springer-Verlag Berlin Heidelberg 2015
Abstract Purpose Breath-by-breath (BbB) determination of the O2 flux at alveolar level implies the identification of the start and end points of each respiratory cycle; Grønlund defined them as the times in two successive breaths showing equal expiratory gas fractions. Alternatively, the start and end points of each breath might be linked to the ratio between the exchangeable and non-exchangeable gases. The alternative algorithm is described and evaluated with respect to the algorithm proposed by Grønlund. Methods Oxygen and carbon dioxide fractions, and ventilatory flow at the mouth were continuatively recorded in 20 subjects over 6 min at rest and during a cycloergometer exercise including 4 increasing intensities lasting 6 min each. Alveolar BbB oxygen uptake was calculated from the gas and flow traces by means of the two methods at stake. Results Total number of analysed breaths was 14,257. The data obtained with the two methods were close to the identity line (average slope 0.998 ± 0.004; R > 0.994; n > 334 in all subjects). Average difference between the O2 uptake data obtained by the two methods amounted to −0.27 ± 1.29 mL/ min, whilst the standard deviation of the differences was 11.5 ± 4.6 mL/min. The relative percentage difference was independent from the O2 uptake and showed an average bias amongst subjects close to zero (−0.06 ± 0.15 %). Communicated by Susan Hopkins. Electronic supplementary material The online version of this article (doi:10.1007/s00421-015-3169-x) contains supplementary material, which is available to authorized users. * Maria Pia Francescato [email protected] 1
Department of Medical and Biological Sciences, University of Udine, P.le Kolbe 4, 33100 Udine, Italy
Conclusions The alternative timing of the respiratory cycle provided congruent O2 uptake data and made the identification of the start and end points of each breath more robust without introducing systematic errors. Keywords Breath-by-breath oxygen uptake · Alveolar gas exchange · Gas lung stores · Gas fractions Abbreviations BbB Breath-by-breath FO2 Oxygen fraction at the mouth FOA 2 Oxygen fraction at alveolar level FN2 Nitrogen fraction at the mouth FNA 2 Nitrogen fraction at alveolar level vA Variation of the alveolar gas volume vOS2i Variation of pulmonary oxygen stores OG Original Grønlund’s algorithm SG Simplified Grønlund’s algorithm STPD Standard temperature pressure dry t1 Starting time of the ith breath t2 Final time of the ith breath defined on the FO2 trace or on the FO2/FN2 trace t3 Final time of the ith breath defined on the FN2 trace A Alveolar volume at the beginning of the ith breath vi−1 vNA 2 Volume of nitrogen exchanged at alveolar level vOA 2 Volume of oxygen taken up at alveolar level vOM 2 Volume of oxygen exchanged at the mouth ˙ V COA 2 Alveolar carbon dioxide release Alveolar oxygen uptake V˙ OA 2
Introduction The study of O2 uptake, and/or of CO2 release, under various conditions still attracts the interest of several
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researchers involved in different fields of investigation. Non-invasive measurements are usually made at the mouth, from which researchers try to get information about the gas transfer occurring at alveolar level. Nevertheless, changes of the volume of gas contained in the lungs (the “pulmonary stores”) from one breath to the following unbind the values measured at the mouth from the gas transfer at the alveoli in terms of signal intensity and time. Several computational algorithms have been proposed to determine the alveolar gas transfer on a breath-by-breath (BbB) basis (Wessel et al. 1979; Beaver et al. 1981; Swanson and Sherrill 1983; Busso and Robbins 1997). All of them are based on the Auchincloss et al. approach (1966), but each of them takes into account the alveolar volume at the beginning of the breath A ) in a different way. di Prampero and Lafortuna (1989), (vi−1 A result however, showed that different values assigned to vi−1 in a different BbB gas exchange variability. It then appears that “true” alveolar gas exchange could be correctly determined only A could be assessed on a BbB basis. if the actual vi−1 An alternative algorithm was proposed by Grønlund A by con(1984), who got rid of the need of estimating vi−1 sidering the respiratory cycle as the period of time elapsing between equal expiratory gas fractions in two successive breaths. This algorithm was resumed and extensively tested by Capelli et al. (2001). The algorithm proposed by Grønlund (1984) and its implementation might seem quite complex and the difficulties of developing appropriate software might have hindered its diffusion. We propose an alternative view of the respiratory cycle, which results in the removal of unnecessary mathematics as compared to that of Grønlund (1984). The simplified algorithm was then evaluated by comparing breath-by-breath alveolar gas transfer values with the corresponding values obtained by means of the original algorithm.
Theory During the ith breath, the volume of oxygen taken up at the alveoli, vOA 2i, can be determined from the volume of oxygen exchanged at the mouth, vOM 2i , minus the volume change of pulmonary oxygen stores vOS2i: M S vOA 2i = vO2i − vO2i
(1)
According to Auchincloss et al. (1966), the change of volume of pulmonary O2 stores can be divided into two
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terms: the first dependent on the variation of the fraction of alveolar oxygen, FOA 2 , from the i−1 breath to the ith breath, the second due to the variation of the volume of alveolar gas, vA, between the two subsequent breaths: A vOS2i = vi−1 · FOA2i − FOA2i−1 + FOA2i · vA (2) i where vA i−1 is the end-expiratory alveolar volume at the beginning of the current breath i. To determine viA, we can suppose that the assumptions made above are valid also for the nitrogen (Auchincloss et al. 1966), and that the N2 volume exchange at the alveolar level, vNA 2 , during any time interval was null:
A A M A A A =0 + FN · v vNA = vN − v · FN − FN 2i i 2i 2i i−1 2i 2i−1
whereby:
viA =
1 M A A A vN − v · FN − FN 2i i−1 2i 2i−1 FNA 2i
(3)
By substituting Eq. (3) into Eq. (2) and then in Eq. (1), the following equation is obtained:
FOA A A 2i vi−1 × FOA 2i − FO2i−1 + FNA 2i A A A × vNM 2i − vi−1 × FN2i − FN2i−1
M vOA 2i = vO2i −
FOA A A A 2i × vNM 2i - vi−1 × FO2i − FO2i−1 A FN2i A FO2i A A A − A vi−1 × FN2i − FN2i−1 FN2i
= vOM 2i −
(4)
In this equation, the only quantity not directly measurable A (di Prampero and on a breath-by-breath basis is the term vi−1 Lafortuna 1989). To circumvent this problem, according to the assumptions of Grønlund (1984), the integration interval can be identified on both the O2 (or CO2) trace and N2 trace as the time period elapsed between a common starting time (t1) and two final times, one specific for the O2 (or CO2) trace (t2) and the other for the N2 trace (t3); whenever t2 and t3 do not overlap, a correction factor has to be introduced (Fig. 1). Capelli et al. (2001) developed a software that applies the definition of the respiratory cycle according to Grønlund (1984). The alternative view of the integration interval results from the reasoning outlined below. Indeed, Eq. (4) can be simplified by factorising the term A as follows: vi−1
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Subsequently, bringing the two terms in curly braces to the same denominator (FNA 2i), Eq. (5) is obtained: M vOA 2i = vO2i −
×
FOA A 2i × vNM 2i +vi−1 FNA 2i
A A A FOA 2i−1 × FN2i − FO2i × FN2i−1
FNA 2i
(5)
Two times t1 and t2 can be appropriately chosen on two consecutive breaths so that the numerator within the curly braces becomes zero, i.e.: A A A FOA 2i−1 (t1 ) · FN2i (t2 ) = FO2i (t2 ) · FN2i−1 (t1 ).
(6)
Under these conditions, the third part of Eq. (5) disapA unnecessary. pears, making the knowledge of vi−1 The condition described in Eq. (6) can be rewritten as:
FOA 2i−1 (t1 ) FNA 2i−1 (t1 )
=
FOA 2i (t2 ) A FN2i (t2 )
This equation shows that the start and end points of each respiratory cycle can be defined in a new way, i.e. as the times in successive breaths where identical FO2/FN2 ratios are observed. Hence, the calculation of vOA 2i over the interval from t1 to t2 is limited to the first two parts of Eq. (5): M vOA 2i = vO2i −
=
t2
t1
FOA 2i × vNM 2i FNA 2i
FOA 2i V˙ M · FOM 2 dt − FNA 2i
t2
V˙ M · FNM 2 dt
t1
where V˙ M is the respiratory flow, whose sign depends on the phase considered (inspiration or expiration), FOM 2 and M FN2 are the O2 and N2 fraction, respectively, as measured at the mouth. A The ratio FOA 2i FN2i is unknown, but if t1 and t2 are selected towards the end of the expiration of two consecutive breaths, the fractions of oxygen and nitrogen at the mouth approximate those in the alveoli (Grønlund 1984):
FOA FOM 2i 2 (t1 ) ≈ A FNM FN2i 2 (t1 ) The alveolar volume of oxygen taken up in a breath can thus be determined by variables all measurable at the mouth:
vOA 2i
=
t2
t1
FOM 2i (t1 ) V˙ M · FOM · 2 dt − FNM 2i (t1 )
t2
V˙ M · FNM 2 dt
t1
The oxygen uptake, at alveolar level and during the temporal interval between t1 and t2, is given by the quotient of vOA 2i divided by (t2−t1). With appropriate modifications (i.e. substituting FO2 with FCO2), alveolar CO2 transfer can also be obtained with the same approach.
Fig. 1 Traces of O2 and N2 fractions and of the calculated ratio FO2/ FN2 at rest for a typical subject, as seen at the mouth. “Exp” and “Insp” are the inspiration and expiration phases. Time t1 is chosen according to specific criteria (see text). Times t2 and t3 on the FO2 and FN2 traces are chosen to yield O2 and N2 fractions, respectively, which are identical to that at t1. Time t2 on the FO2/FN2 trace is chosen to yield a ratio identical to that at t1. Note that, the FN2 scale was expanded twice as compared to the other vertical scales
Methods Subjects Twenty healthy adults (11 males and 9 females of mean (±SD) age 33.3 ± 12.2 years), after having been thoroughly informed of the nature, purpose, and possible risks,
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gave their voluntary written consent to participate in the study. Average (±SD) stature and body mass of the subjects were 1.74 ± 0.10 m and 67.5 ± 12.6 kg, respectively. All subjects were healthy and moderately active; none was smoker. The study was approved by the local Ethics Committee and was conducted according to the Declaration of Helsinki. Experimental protocol The subjects were equipped with the face mask and then sat quietly on the bicycle ergometer (Ergomed 839E; Monark, Vansbro, Sweden) for about 8 min. Afterwards, the subject started pedalling keeping throughout the exercise period the pedalling frequency as close as possible to 60 rpm with the aid of the inbuilt led bar. Four exercise steps of increasing intensity (corresponding to 0.6, 0.9, 1.2, and 1.5 W/kg body mass and 0.5, 0.8, 1.0, and 1.3 W/kg body mass in men and women, respectively) were performed, lasting 6 min each. In addition, to evaluate if the newly proposed algorithm was still able to cope with changes in lung volume, 8 out of the 20 recruited volunteers were asked to return to the lab in a following day. In this occasion, a short (about 1 min) data collection period was performed at rest during which the volunteers were asked to voluntarily change the endexpiratory and the inspiratory volumes. Measurements Oxygen and carbon dioxide fractions, and ventilatory flow at the mouth were continuatively recorded throughout the tests (6 min at rest + 4 × 6 min during exercise) by means of a metabolic cart (Quark B2, Cosmed, Italy). Subjects breathed through a facemask mounted on a turbine flowmeter. Gases were sampled continuously through a 2-m-long capillary line inserted in the outer frame of the flowmeter and analysed by fast-response O2 (chemical; t90 ~ 170 ms) and CO2 (infra-red; t90 ~ 190 ms) sensors embedded in the equipment. The software operating it allowed us to record gas and flow signals with a sampling frequency of 25 Hz and to save them as text files. Before each test, following the procedures indicated by the manufacturer, the analysers were calibrated with a gas mixture of known composition (FO2 = 0.16; FCO2 = 0.04; N2 as balance) and ambient air; the flowmeter was calibrated by means of a 3-L syringe (Hans Rudolph Inc., USA). Data treatment Alveolar breath-by-breath oxygen uptake (V˙ OA 2 ) and carbon dioxide production (V˙ COA ) were calculated from the 2 original gas and flow traces, by means of the two methods to be compared. Computerised procedures were specifically
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developed in C language under the Unix-like Cygwin environment (Red Hat Cygwin, version 1.7.30). In the present investigation, the final equation used to calculate the alveolar O2 uptake during one breath by means of the original algorithm proposed by Grønlund (1984) (OG), described also by Capelli et al. (2001), was the following:
V˙ OA 2i =
t2
V˙ M · FOM 2 dt −
t1
FOM 2 (t1 ) FNM 2 (t1 )
·
t3
M V˙ M · FNM 2 dt + FO2i (t1 ) ·
t3
V˙ M dt
t2
t1
t2 − t 1
In comparison, the final equation used to implement the simplified algorithm (SG), as proposed in the present paper, was the following:
V˙ OA 2i =
t2
t1
V˙ M · FOM 2 dt −
FOM 2i (t1 ) FNM 2i (t1 )
t2 − t 1
·
t2
V˙ M · FNM 2 dt
t1
It should be remembered here that the t1 and t2 time points, although having the same conceptual meaning, are defined in a different manner for the two equations (see Theory). Analogous equations were used to compute the carbon dioxide production by means of the two methods. Finally, for both methods: 1. One minus the sum of measured O2 and CO2 fractions was assumed to be represented only by N2, as also assumed by others (Cautero et al. 2005). 2. After correction for the water-vapour partial pressure, inspired and expired gases have been converted to STPD conditions. The temperature in the alveoli was assumed to be 37 °C; the expiratory gas temperature at the flowmeter, the ambient temperature, the barometric pressure and the relative humidity were assumed to be equal to those measured by the metabolic cart. 3. To avoid incoherent data likely arising from coughs, sighs or swallows, the breaths were considered valid only if the inspiratory and/or the expiratory volumes were greater than 150 mL; in the other cases, the invalid breath was incorporated with the following one. 4. The same reference value for the FO2 (for OG) or for the FO2/FN2 ratio (for SG) was used to identify the t1 times of all the breaths. The reference value (fraction or ratio) was determined by preliminarily identifying the minimum of the fractions (or of the ratios) for all the expirations. Subsequently, the histogram of the obtained values was generated and the reference value was set to the 97.5th highest percentile. For both methods, the t1 times were identified in all the expirations as the time points where the FO2 (or the FO2/FN2 ratio) corresponded to the reference value. Subsequently, the t2 times were the
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t1 times of the following breaths; when the t1 value could not be identified in that breath, data pertaining to this breath were merged with the preceding one. 5. A similar procedure as the previous one was applied to determine the t1 times used to compute the carbon dioxide production, with the difference that maximum FCO2 factions (or FCO2/FN2 ratios) were analysed. 6. The t3 times, required for the OG method, were determined as the time points that satisfied contemporarily two conditions: closest in time to the corresponding t2 and showing the closest N2 fraction to that found at the corresponding t1. In addition, for about 1 min data collections (during which the volunteers changed the end-expiratory and the inspiratory volumes), the “gross” oxygen uptake at the mouth was calculated by simply integrating the product of flow and exhaled concentration, after conversion to STPD conditions. Data analysis and statistics All the results are reported as mean ± SD. Oxygen uptake data (and CO2 production) were compared by linear regression and Bland–Altman’s analysis. Bland and Altman’s limits-of-agreement plot (Bland and Altman 1986) allowed assessing the agreement between the two investigated methods (OG and SG, respectively). According to this analysis, the differences between the corresponding values obtained applying the two methods were plotted against the averages of the two figures. The average of the differences represents the bias between the two methods.
Bland–Altman analysis of a typical subject is illustrated in Fig. 2. Average difference (i.e. the bias) amongst subjects amounted to −0.27 ± 1.29 mL/min, whilst the standard deviation of the differences amounted on average to 11.5 ± 4.6 mL/min. Figure 2 clearly shows that, with increasing the average V˙ OA 2 , the differences between the values yielded by the two methods become more widespread. Nevertheless, the relative percentage difference (i.e. the difference normalised according to the correspondent average value and expressed as percentage) was independent from the average values (Fig. 3), showing an average bias amongst subjects close to zero (−0.06 ± 0.15 %) and an average standard deviation of 1.47 ± 0.68 %. Similar results as those described for V˙ OA 2 were obtained also for V˙ COA 2 (data not shown). Supplemental materials summarise the parameters obtained for V˙ OA 2 on the individual subjects. Figure 4 illustrates the data obtained on a typical subject who voluntarily changed the end-expiratory and the inspiratory volumes during a short data collection period at rest. The figure shows that, by simply integrating the product of flow and exhaled concentration (“gross” O2 uptake, i.e. neglecting the changes of the pulmonary gas stores), very high values were obtained when inspiration exceeded expiration (breath n. 6); in contrast, negative values were obtained when expiration exceeded inspiration (breath n. 13). Similar results were obtained for all the other subjects. Indeed, the Bland–Altmann analysis performed on these data showed an average bias of 1.5 mL/min and a standard deviation of 8.1 mL/min. Despite the resting condition, where there is a worse signal-to-noise ratio, these values are not far from the corresponding figures reported for the exercise trials.
Results Overall, considering the whole data recording periods (lasting about 30 min for each subject), the total number of analysed breaths was 14,257 (range from 334 to 1007 for an individual subject), which corresponded to an average breath frequency of 21.6 ± 5.3 breaths per min amongst subjects (range from 11.1 to 31.5 breaths per min). The two methods have identified the breaths at different times in about 0.1 % of cases (18 and 14 cases out of 14,257 for OG and SG methods, respectively). Regressions lines between the corresponding V˙ OA 2 data determined using the two methods were close to the identity line in all subjects, showing an intercept of 2.8 ± 4.8 mL/min and a slope amounting to 0.998 ± 0.004 (R > 0.994; n > 334 in all cases).
Fig. 2 Differences (OG-SG) versus the averages of the values yielded by the two methods at stake to calculate V˙ OA 2 (OG and SG)
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Fig. 3 Percentage relative differences (2 × (OG−SG)/ (OG + SG) × 100 %) versus the averages of the values yielded by the two methods at stake to calculate V˙ OA 2 (OG and SG)
Fig. 4 Upper panel Oxygen uptake data obtained by simple integration (“gross” VO2; full diamonds), by the SG algorithm (open dots) and the OG algorithm (asterisks) are illustrated as a function of time. Lower panel The respiratory flow at the mouth is shown (negative values are inspiration). The times of the O2 uptake data obtained by means of the three methods do not coincide since they correspond to the midpoint between start of inspiration and end-expiration for the simple integration method, whereas they are the midpoint between two subsequent t1 times identified during the expirations for OG and SG
Discussion The present investigation shows that the alternative identification of the start and end points of each respiratory cycle,
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based on the ratio between the gas exchanged at alveolar level (e.g. O2) and the non-exchangeable gas fraction (essentially N2) yields reliable breath-by-breath O2 uptake (or CO2 release) data. Indeed, the simplified method to calculate the BbB gas exchange yielded overlapping V˙ OA 2 (or A ˙ V CO2 ) data as compared to those provided by the original method of Grønlund (1984). The computation of the O2 uptake on a BbB basis necessarily requires the knowledge of breath duration, i.e. the identification of the start and end points of the respiratory cycles. Traditionally, the respiratory cycle was defined on the basis of the time points where the measured flow change orientation, i.e. a breath starts at the onset of inspiration and ends when expiratory flow had entirely or largely ceased (Auchincloss et al. 1966). Although researchers are aware that the computation of the O2 uptake at alveolar level has to take into account the pulmonary O2 stores, the traditional definition of the respiratory cycle was used for a long time, assuming arbitrary amounts A ). for the alveolar volume at the beginning of the breath (vi−1 More recently, however, Grønlund (1984) proposed a new timing of the respiratory cycle, where the start and end points have equal alveolar oxygen (or carbon dioxide) tensions. By A selecting this integration interval, the measurement of vi−1 is circumvented. A drawback of Grønlund’s algorithm is the necessity of defining also a time point on the FN2 trace (i.e. time point t3) having equal alveolar N2 tension as compared to the start of the breath. Under these assumptions, the same breath could be associated with four different durations (i.e. for the O2 fraction, the N2 fraction referred to the O2 uptake calculation, the CO2 fraction, and the N2 fraction referred to the CO2 release calculation), and the integral of flow between t2 and t3 is warranted when the breath duration associated with the N2 fraction does not coincide with that of the gas under investigation. The timing of the respiratory cycle of the present work, based on the fractions between alveolar exchangeable gas (O2 and/or CO2) and non-exchangeable gas (N2), reduces each breath cycle to two durations (i.e. one for the O2/N2 ratio referred to the O2 uptake calculation and the other for the CO2/ N2 ratio referred to the CO2 release calculation). In addition, the ratio FO2/FN2 (or FCO2/FN2) amplifies the signal changes as compared to the simple gas fractions, making the identification of the start and end times of the breaths (i.e. of the t1 and t2 time points) more robust on the digitalized data. An advantageous method to estimate the gas transfer occurring at alveolar level from measurements made at the mouth should be able to cope with possible changes of the lung gas stores, which are due essentially to imbalances between inspired and expired volumes. This condition can be stressed by changing voluntarily the end-expiratory and inspiratory volumes; after such manoeuvres, Wüst et al. (2008) showed a reduction of about 84 % in the variability of the O2 uptake when they took into account the changes in gas lung stores. Even the original Grønlund’s
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algorithm, extensively investigated by Capelli et al. (2001), was designed to correct the gas transfer at alveolar level for the lung gas stores. The simplified algorithm illustrated in the present work essentially maintains the Grønlund’s approach. As a matter of fact, the simplified algorithm provided overlapping values as compared to those obtained with the original Grønlund’s algorithm; the agreement between the two algorithms was maintained also when deliberate lung volume changes were induced (see Fig. 4). Data were acquired continuously for about 30 min, including a period of rest and four different exercise intensities, resulting in at least 334 consecutive breaths (range from 334 to 1007) for each volunteer. The relative percentage difference between the V˙ OA 2 calculated by means of the two methods at stake was small (i.e. −0.06 % ± 1.47 %) and remained constant with increasing the V˙ OA 2 (Fig. 3), independent of the steady state or transient phases. These results support the view that the alternative timing of the respiratory cycle did not introduce systematic errors as compared to the original algorithm of Grønlund. Strengths and limitations of the study In the present investigation, a comparison with the values obtainable by means of a golden standard method (e.g. the classical open circuit method with a Douglas bags gas collection) was not carried out. Nevertheless, the original Grønlund’s algorithm was already extensively validated both at rest and in steady state conditions (Grønlund 1984; Capelli et al. 2001) and it was also applied during the transients (Aliverti et al. 2009; Cautero et al. 2002). In all these studies, the volunteers performed low-intensity exercises (up to a maximum of 120 W) to allow an easier detection of the limitations of the algorithm. Similarly, in the present investigation, the data acquisition was limited to the low exercise intensity domain. Undoubtedly, a validation at higher workloads, and/or under pathological conditions (e.g. lung disease where ventilation and/or blood flow heterogeneity may occur), is warranted. A further limitation of Grønlund’s algorithm is that the instantaneous end-expiratory fraction reflects the “average” alveolar fraction for each gas species. The lung, however, is not homogeneous, thus it might not be adequate to assume that breath-by-breath differences in the end-tidal measurements are a reliable measurement of the BbB differences in alveolar composition (Busso and Robbins 1997). A peculiarity of the present work is that the two methods (OG and SG) were compared using exactly the same O2, CO2 and flow digital traces, using the same C calculation routines, applied on the appropriate data, and adding a specific routine only to determine the t3 times on the N2 trace, required for the OG method. Consequently, whatever systematic error derived from the acquisition of the original
data has affected in the same way the results obtained with the two methods. A drawback of the two algorithms is that gas exchange values can be calculated only during off-line analysis of the gas fractions and respiratory flow signals, i.e. after the end of the data collection (Capelli et al. 2011). Despite this drawback, it is mathematically attractive to eliminate alveA from the equations, making the two BbB olar volume vi−1 algorithms appealing. Technical and methodological implications The calculation of BbB gas exchange data at alveolar level requires an appropriate algorithm and reliable information acquired at the mouth by means of proper and well-known hardware. In the present investigation, gas and flow signals at the mouth were recorded using the sensors embedded in a commercial metabolic cart, which included a 2-m-long gas sampling capillary and a bidirectional turbine as flowmeter. The acquired O2 and CO2 signals showed delay times, lasting about 720 ms, compared to the flow signal, as reported also by other authors (Aliverti et al. 2004); these delay times were provided by the calibration procedure and were automatically corrected by the software operating the metabolic cart before yielding the digital data in the text file. Should this correction be neglected, it would heavily affect the BbB values, up to an underestimation of about 30 % compared to the true values (Capelli et al. 2011). Of note, the delay times might also change with respect to changes in the breathing pattern (Roecker et al. 2005), thus the software ideally should include variable correction factors for each breath. The manufacturer of the metabolic cart certified, for the flowmeter, a volume resolution of 12 mL with the lowest detectable flow of 30 mL s−1. This last figure provides an estimate of the inertia of the turbine, which could affect the recorded dynamics of the actual flow. Despite this drawback, the turbine has the advantage that it is not sensitive to variations in viscosity between inspiration and expiration. The analogue-to-digital converters (ADCs) allowed us to record the signals every 40 ms (i.e. 25 Hz), where the responding time of the O2 and CO2 sensors (t90) lasted about 180 ms. Ideally, faster responding gas analysers should be used (Capelli et al. 2011) to avoid the distortion in the temporal pattern of the measured variables. Oxygen uptake (or carbon dioxide production) values are usually expressed in STPD conditions, which implies the thermodynamic conversion of the inspiratory and expiratory flows starting from the appropriate temperature, pressure and humidity values. The correctness of the thermodynamic transformations can be verified by analysing the multibreath N2 balance, whose drift theoretically
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should remain zero. In the present investigation, the values of temperature, pressure and relative humidity provided by the metabolic cart were used and the same thermodynamic transformations of flows were performed for the OG and SG algorithms. Under these conditions, the possible drift in the N2 balance of a specific subject would affect in the same way the data to be compared, i.e. the V˙ OA 2 data calculated with the two algorithms.
Conclusions Results support the view that the alternative timing of the respiratory cycle, linked to the ratio between the exchangeable gas fraction and the non-exchangeable gas fraction at alveolar level, results in a simplification of the computational algorithm. The proposed algorithm yielded congruent O2 uptake data, without introducing systematic errors. Acknowledgments This work was supported by the Department of Medical and Biological Sciences funding of the University of Udine to M. Pia Francescato. Conflict of interest None of the authors has conflicts of interest to declare.
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