Abstract
Busso, Thierry, PeiJi Liang, and Peter A. Robbins.Breathtobreath relationships between respiratory cycle variables in humans at fixed endtidal Pco _{2} and Po _{2}. J. Appl. Physiol. 81(5): 2287–2296, 1996.—This study examined the statistical properties of breathtobreath variations in the inspiratory and expiratory volumes and times during rest and light exercise. Sixty data sets were analyzed. Initial data and residuals after fitting timeseries models were examined for 1) sustained periodicities with use of spectral analysis, 2) temporal changes in signal power with use of evolutionary spectral analysis, and 3) auto and cross correlations with use of a portmanteau test. The major findings were as follows: 1) no sustained periodic components were detected;2) temporal changes in signal power were normally present, but these did not affect significantly the results from timeseries modeling; 3) for all variables, a simple autoregressive moving average (ARMA) AR_{1}MA_{1} model generally described the autocorrelation; 4) considerable cross correlation remained between residuals from the AR_{1}MA_{1} model; 5) relationships between variables could be described by using a multivariate timeseries model; 6) residual fluctuations in endtidal Pco _{2} had little influence; and 7) responses were broadly similar between rest and exercise, although some quantitative differences were found. The multivariate model provides a description of the structure of the interrelationships between cycle variables in a quantitative and a qualitative form.
 control of breathing
 chemoreflex feedback loop
 correlated variability
 timeseries models
 constant power spectrum
as demonstrated by Priban (26), the breathbybreath fluctuations in respiratory cycle variables are not purely random. Correlations between successive breaths were observed for tidal volume (Vt) and cycle duration (Tt). This result was extended by Bolton and Marsh (5) to include inspiratory and expiratory volumes (Vt _{I} and Vt _{E}) and times (Ti and Te).
Timeseries models, or autoregressive moving average (ARMA), models have been used to analyze the autoregressive structure of these data sequences. The application of a firstorder model to steadystate breathing in humans showed that the values for Vt and Tt in a given breath were dependent on the values from the preceding breath (3, 4). The interpretation of these results, however, has been complicated by the influence of the feedback loops involving blood gas tensions. Periodic oscillations arising from chemical feedback have been observed for Vt and Tt(7, 18, 21). It thus becomes unclear whether the autocorrelation is due to these feedback loops or to other intrinsic factors.
To try to resolve this issue, animal preparations have been employed in which the respiratory controller has been isolated from the effects of chemical feedback and where the properties of the respiratory controller can be studied independently of any instability induced by chemical feedback. The results from such experiments on the respiratory controller in an openloop state have not been clearcut. On the one hand, breathtobreath correlations in Ti, Te, and phrenic activity have been observed in an “isolated respiratory centre” preparation by Benchetrit and Bertrand (2) in the anesthetized cat. On the other hand, Khatib et al. (20) did not observe such correlation in phrenic activity in anesthetized, vagotomized, and artificially ventilated rats. These authors suggested that the discrepancy between their findings and those of Benchetrit and Bertrand could be due to failure of Benchetrit and Bertrand to check their data sequences for nonstationarity, which could have corrupted the analysis of the breathtobreath correlation.
In humans, the respiratory controller can be investigated in a quasiopenloop state by use of the technique of dynamic endtidal forcing, where a computercontrolled gasmixing system is used to adjust the inspiratory gas composition on a breathbybreath basis to maintain the subject’s endtidal O_{2} and CO_{2}pressures (Pet _{O2} and Pet _{CO2}, respectively) close to target values, despite variations in ventilation. In essence, this system attempts to break the physiological feedback loop at the point where ventilation influences Pet _{CO2} and Pet _{O2}. Liang et al. (22) demonstrated the presence of breathbybreath correlation of minute ventilation (V˙e) in data that had been obtained using this technique. In most cases, there was also a slow change over time in the variance of the data that was detected by using evolutionary spectral analysis (28). However, these slow variations over time in variance did not affect the observed breathtobreath correlations for ventilation.
The purpose of the present study was to extend the work of Liang et al. (22) to the respiratory cycle variables, Vt _{I}, Vt _{E}, Ti, and Te. The first aim was to determine whether these respiratory variables have statistical properties similar to or different from breathbybreath ventilation and whether their statistical properties fit with the findings of Benchetrit and Bertrand (2) or Kathib et al. (20) for the isolated respiratory center preparation. The second aim was to study the cross correlations between these variables within and between breaths. As with the study by Liang et al. (22), all data analyzed had been gathered by using the endtidal forcing technique to keep the chemical stimulation at as constant a level as possible.
METHODS
The experimental data were taken from a study described in a previous report (25). Most of the statistical methods employed in this study have been fully described and discussed by Liang et al. (22) in relation to ventilation.
Recording and treatment of the data.
Ventilatory data were available from five subjects over periods of 43 min, with the subject seated at rest or performing exercise at 70 W on a cycle ergometer. Each protocol was repeated six times by each subject. During each experiment, Pet _{O2} was held constant at 100 Torr and Pet _{CO2} at 2–3 Torr (4–5 Torr in subject 807) above the subject’s natural value during rest or exercise. Breathbybreath Vt _{I}, Vt _{E}, Ti, and Te were recorded continuously during each 43min experiment. Details of the experimental methods have been described elsewhere (25).
The first 50 breaths in the rest experiments and the first 300 breaths in the exercise experiments were discarded to remove any initial transient responses. The mean values and the coefficients of variation of each variable for the remainder of the data sequences are listed for each subject in Table 1.
Before any further analysis, the mean value, together with any linear trend, was removed from each respiratory cycle variable for each data sequence. The resulting deviations were analyzed before and after the application of the demodulation process proposed by Liang et al. (22), which aims to remove any slow variations in variance of the respiratory variables. Demodulation of the original sequence consisted of dividing the ith observation of each respiratory cycle variable,x
_{i}, by the corresponding value of the modulating function (an autoregressive estimate of the variance),c
_{i}, computed as follows
Specific periodicities.
The data were examined for the presence of any specific periodicity by use of spectral analysis. A smoothed periodogram was calculated for each data set with use of a combination of three Daniell windows with lengths of 3, 5, and 7. Then the six individual spectra calculated for each subject and protocol were averaged. The 95% confidence interval for the mean spectral density was calculated on the basis that the estimates of spectral density follow a χ^{2} distribution (27). The procedure is described in more detail by Liang et al. (22).
Evolutionary spectral analysis.
The data sequences were examined for the presence of variations in power over time by use of evolutionary spectral analysis (28). The principle of this technique is to apply a double window in time and frequency domains. The width of the window used in the time domain was 100 breaths, and the bandwidth used in the frequency domain was 3/40. Values for evolutionary spectral density were then calculated for the corresponding times and frequencies. A twoway analysis of the variance was applied on the logarithmic values of spectral density with use of factors of time and frequency to test for differences in spectral density with time. The χ^{2} tests were used to examine the significance of the factors of “time” and “interaction + residual error.” When the interaction and the time terms were not significant, it was concluded that the power of the data sequence was constant. When the time term but not the interaction term was significant, the data sequence was considered to be uniformly modulated. A significant interaction term led to the conclusion that the data sequence was not uniformly modulated. On a similar set of simulated respiratory data, evolutionary spectral analysis was found to yield a test statistic that was somewhat oversensitive, and for this reason a level of significance of P < 0.0025 was employed for the χ^{2} test (22).
Simple ARMA model fitting.
The data were fitted with ARMA models, which may be written in the form
Multivariate ARMA model fitting.
The data were fitted with multivariate models of the form
The parameters of the different multivariate models were estimated by maximum likelihood.
Portmanteau test.
A modified portmanteau test (6) was used to examine the whiteness of each variable and the independence of any pair of variables within each data set. The test is based on the statistic Q, defined as follows
Comparison of the model coefficients among protocols, models, or data treatments was undertaken using analysis of variance. All the statistical calculations were done using Splus statistical software (Statistical Sciences, Oxford, UK).
RESULTS
Specific periodicities.
Smoothed periodograms were estimated for each data set for Vt _{I}, Vt _{E}, Ti, and Te. No obvious peaks in the power spectrum were apparent. Examples of smoothed periodograms for Vt _{I}, Vt _{E}, Ti, and Te averaged for the six data sets forsubject 797 at rest are shown in Fig.1. The power is concentrated in the lower frequencies, and a smooth decline in the power can be traced within the 95% confidence intervals, with no peaks occurring at any particular frequency. These results generally indicate that there were no marked specific periodic components within the data for any of the respiratory variables examined.
Variations in power spectrum over time.
Variability over time of the power spectrum was tested for each respiratory variable by evolutionary spectral analysis. The number of data sets for which the null hypothesis of having a constant power spectrum over time could be accepted, according to the respiratory variable, was 2–6 of 30 data sets for rest and 4–9 of 30 data sets for exercise (Table 2). The number of uniformly modulated data sets, where the overall shape of the power spectrum can be accepted as constant but where the total power may vary, was 17–28 for rest and 24–27 for exercise. “Demodulation” of the data sets by use of the autoregressive estimate of the variance altered these results considerably. After demodulation, 16–28 data sets for rest and 22–27 for exercise could be accepted as having a constant power spectrum. The number of uniformly modulated data sets rose to 24–29 for rest and 28–29 for exercise. These results generally indicate that, for each variable tested, the absolute variance associated with the variable changes over time but that the relative distribution of power within the power spectrum remains constant over time.
Correlations within data before modeling.
Table 3 illustrates the degree of auto and cross correlation for the individual respiratory cycle variables in the original data before and after demodulation. The results generally indicate that 1) few sequences could be accepted as white and/or independent of the other sequences, 2) the results were similar for the data sequences before and after demodulation, and 3) in approximately onehalf of the data sequences, no dependence on Pet _{CO2} was detected.
Simple ARMA models.
For each data set, Vt _{I}, Vt _{E}, Ti, and Te were fitted with AR_{1}, AR_{2}, and AR_{1}MA_{1} models. The whiteness of the corresponding residuals was used to assess the goodness of fit. The number of data sets accepted as having white residuals is given for each variable and protocol in Table 4. The results clearly indicate that the AR_{1}MA_{1} model accounted best for the autocorrelation in the data sets before and after the demodulation process.
The model parameter estimates averaged for each protocol are given in Table 5. The major findings were that1) the coefficients for Vt _{E} and Vt _{I} were significantly greater (P < 0.01) for the exercise data than for the data obtained at rest and 2) no statistical difference was observed between the parameters estimated from the original data and the demodulated data.
Having modeled the autocorrelative structure of each respiratory variable, the next step is to determine whether this also accounts adequately for the cross correlation observed between respiratory variables. This has been done by examining the degree of cross correlation in the residuals after fitting of the AR_{1}MA_{1} model. The results are shown in Table6. The conclusions that can be drawn are as follows: 1) the results are similar for rest and exercise protocols, 2) the residuals for Vt _{E}and Te generally could not be accepted as independent of the residuals for Vt _{I} and Ti in most of the data sets, and 3) Vt _{I} and Ti were commonly dependent on Vt _{E}and Te, respectively. Thus the cross correlations observed between respiratory variables cannot be due entirely to the autocorrelation within respiratory variables.
Multivariate ARMA models.
To model the cross correlation between variables, a multivariate ARMA model structure was employed. The design of the model, in terms of which coefficients should be nonzero, was based on the following:1) the AR_{1}MA_{1} model could be taken as a good model of the autoregressive structure, and 2) the coefficients for cross correlation should be based on the marked dependencies that remained between the residuals after the fit of the AR_{1}MA_{1} model. The particular model employed was as follows
The estimates for the coefficients for the above model are given in Table 7. The coefficient of Vt _{E(n − 1)} in fitting Vt _{E(n)} was not statistically different from zero for the rest and exercise protocols. The coefficient of the moving average term in fitting Vt _{E(n)}and Te _{n} was not statistically different from zero for the exercise protocol. The coefficient of Vt _{I(n)} in fitting Vt _{E(n)} those of Vt _{I(n − 1)} in fitting Vt _{E(n)} and those of Te _{n − 1} in fitting Ti _{n} were statistically greater for the exercise data than for the data obtained at rest. Conversely, the coefficient of Ti _{n − 1} in fitting Ti _{n} and those of Te _{n − 1} in fitting Te _{n} were statistically lower for the exercise data.
To determine the degree of success or otherwise of the multivariate model in describing the correlations between the respiratory variables, the independence of the residuals after fitting of the multivariate model was again examined using the portmanteau test. The results are shown in Table 8. Only the residuals for Te during exercise failed to be independent of the other variables in a reasonable number of cases.
Influence of Pet_{CO2} on model coefficients.
The influence of residual fluctuations of Pet _{CO2} not controlled by the endtidal forcing system on the above results was examined by fitting the data sets with a multivariate model that matched the one above, but where Pet _{CO2} andV˙e had been included as additional variates. For each respiratory cycle variable (apart from Pet _{CO2}), a further coefficient for Pet _{CO2} at breathn − 2 was added to the model. The lag of n − 2 was used to allow for the pure delay associated with the transport delay of the respiratory gases from the lung to the chemoreceptors (9). The structure for modeling Pet _{CO2} was as described by Liang et al. (22). The overall model structure was as
follows
The coefficients of the multivariate model including Pet _{CO2} were then compared with those from the model excluding Pet _{CO2}. Only the coefficient of Vt _{En − 1} in the fitting of Vt _{In} was significantly reduced by the inclusion of Pet _{CO2} (0.381 vs. 0.374,P < 0.05). The independence or otherwise of the residuals for Vt _{I}, Vt _{E}, Ti, and Teon the residuals for Pet _{CO2} was tested by the portmanteau test. The residuals for Vt _{I}, Vt _{E}, Ti, and Te could be accepted as independent of the residuals for Pet _{CO2} in 42–47 of 60 data sets for each variable for rest and exercise protocols. Thus it appears that residual fluctuations in Pet _{CO2} not controlled by the endtidal forcing system had little influence on the results obtained.
DISCUSSION
The findings of this study concern the statistical properties of the breathing pattern associated with the human respiratory controller when dynamic endtidal forcing has been used in an attempt to open the feedback loop between ventilation and blood gas tensions. Vt _{I}, Vt _{E}, Ti, and Te were shown to have properties similar to the composite variable of ventilation, as previously described for the same data set by Liang et al. (22). The breathtobreath fluctuations of each respiratory variable could be fitted with a simple AR_{1}MA_{1} model, the coefficients of which were not affected by the slow variations in variance over time that were observed in the majority of data sets. However, there remained considerable cross correlations between different variables for the residuals after fitting of the AR_{1}MA_{1} model. The use of a multivariate statistical analysis enabled these correlations between the respiratory variables within and between breaths to be modeled in many of the data sequences. The significant correlations, as determined by the multivariate approach, are summarized in Fig.2. Before the physiological implications of these outcomes are discussed, possible confounding factors need to be considered. These factors include 1) the influence of any instability in chemical stimulation arising through imperfections in the technique of endtidal forcing and 2) the nonstationarity and/or nonlinearity of many of the data sequences examined.
Instability arising from chemical feedback.
Systems with intact feedback loops commonly display specific periodicities. However, no such sustained specific periodicities were detected within our data with use of spectral analysis. This result is in keeping with the result for ventilation for the same data (22) and is similar to that from one other study of respiratory cycle variables in conscious humans where no endtidal forcing had been employed (19). However, in other studies of the human respiratory system with intact chemical feedback loops, periodic components of respiratory variability have often been observed (18, 21, 23). The fairly tight control exercised on the endtidal gases by the endtidal forcing technique in our study would be expected to reduce instability arising from chemical feedback. However, spectral analysis cannot totally exclude brief periods of periodicity or instability arising through small fluctuations in alveolar gas tensions. Variations in Pet _{O2} and Pet _{CO2} can potentially influence breathing pattern. For the data of the current study, Pet _{O2} was maintained at ∼100 Torr. This mean value is associated with a very low level of sensitivity of the respiratory controller to small changes in Po _{2} (11). Thus it is most unlikely that any fluctuations in Pet _{O2} affect the correlational structure of the breathing pattern. For CO_{2}, this is not the case, and for about onehalf of the original data sequences some dependence of the respiratory variables on Pet _{CO2} was detected. Consequently, the influence of fluctuations in Pet _{CO2} on the observed correlations between respiratory cycle variables has to be examined, despite the fact that the endtidal forcing system was employed to minimize these. For this purpose, the influence of Pet _{CO2} was examined within the multivariate ARMA model. Only one coefficient (relating Vt _{I} to the preceding Vt _{E}) was significantly depressed by the inclusion of Pet _{CO2} in the model, and this effect was small (2% change). Moreover, the residuals for the respiratory cycle parameters from the multivariate model were in most cases independent of the residuals for Pet _{CO2}. Therefore, although the endtidal forcing technique did not eliminate all the fluctuations in the chemical stimuli, the residual fluctuations do not seem to affect the correlational structure of the breathing pattern to any very great extent.
Slowly changing variance.
Evolutionary spectral analysis was used to assess whether the power spectrum of the data sequences was constant over time. For most of the sequences of respiratory variables, the associated power spectrum was not constant, although it was often uniformly modulated, as observed for ventilation (22). Using a likelihood ratio test, Ackerson et al. (1) suggested that respiratory data sequences were often nonstationary. Unfortunately, they did not give any results that could be compared with ours.
In keeping with previous results for ventilation (22), a modulating function built from an autoregressive estimate of the variance could often be used to reduce the original data to sequences that could be accepted as having a constant power spectrum. Thus the observed variations in power spectrum can be treated as arising from slow variations in variance over time of the respiratory sequences.
The application of ARMA models requires the data sequence to be stationary, and therefore the application of ARMA models to our data is potentially inappropriate. However, because our data sequences could often be reduced to those that could be accepted as stationary by demodulation, the AR_{1}MA_{1} model could be applied to original and demodulated data to test the influence of the observed slowly changing variance of the data on the estimates of the model coefficients. No statistical difference was observed between the results from the two sets of data. Thus we conclude that the variance of the data changes too slowly to affect the shortterm breathtobreath correlations in our time series.
Correlations between successive breaths.
Autocorrelative structure within variables of the respiratory cycle has been observed previously in humans with intact chemical feedback loops and described using AR_{1} and AR_{2} models (3, 4, 19, 23). During sleep, a firstorder autoregressive structure has been observed for Vt and Ti, although variability in Te appeared mostly to be due to periodic oscillations without underlying autoregressive structure (23). In the current study where dynamic endtidal forcing has been used to open the chemical feedback loops, an AR_{1}MA_{1} model described the fluctuations of all the respiratory cycle variables more satisfactorily than AR_{1} and AR_{2} models. However, inasmuch as we are not aware of any other study of an AR_{1}MA_{1} model in humans with intact chemical feedback loops, it is not possible to conclude that there are any differences in autoregressive structure between the different states.
In animal studies of the respiratory controller where the chemical feedback loops have been opened, the observations have been somewhat contradictory. The anesthetized cat showed breathtobreath correlations for Ti and Te and phrenic activity in an isolated respiratory center preparation (2). On the other hand, although they observed correlations between successive breaths for Vt in spontaneously breathing bivagotomized rats, Khatib et al. (20) failed to find such correlations for phrenic activity in paralyzed and artificially ventilated bivagotomized rats. These authors suggested that the autoregressive structure of Vt resulted from the presence of chemical feedback. Khatib et al. suggested that the discrepancy between their results and those of Benchetrit and Bertrand (2) might be due to differences between the species studied or to nonstationarity within the data of Benchetrit and Bertrand.
Our results in conscious humans, where we have used dynamic endtidal forcing to open the chemical feedback loops in a functional sense, are in much closer agreement with the findings of Benchetrit and Bertrand (2) than with Khatib et al. (20). Although the original data sequences could not be accepted as stationary in almost all cases, they could be transformed into sequences that could be accepted as stationary by demodulation, and this process did not modify significantly the coefficients of the ARMA models fitted to the data. Thus we can be reasonably confident that the difference between our result and that of Khatib et al. is not due to nonstationarity within our data sets.
Interrelationships between respiratory variables.
In the original data sets, almost every pair of variables describing the respiratory cycle was correlated. To make progress, the autocorrelation within the data was first modeled using the AR_{1}MA_{1} model. Once this autocorrelative structure had been removed by eliminating those pairs of variables for which cross correlation may have been induced by intrinsic autocorrelation, the residuals from the model could then be examined for any remaining cross correlation. This reduced the pairs of variables for which cross correlation was detected. After this procedure, however, there remained a considerable dependence of Vt _{E} and Te on preceding Vt _{I} and Ti and a considerable dependence of Vt _{I} on preceding Vt _{E} and Ti on preceding Te. These results led us to fit a multivariate ARMA model that included the above dependencies together with the AR_{1}MA_{1} structure for the autocorrelative components.
Model coefficients corresponding to the cross correlations were statistically different from zero, but the autocorrelation of Vt _{E} became nonsignificant in rest and exercise protocols with the inclusion of Vt _{I} in the multivariate model. Thus the autoregressive structure for Vt _{E} in the simple ARMA model would appear to arise because of its dependence on the preceding Vt _{I}, rather than through a true breathtobreath dependence independent of Vt _{I}. This may be explained by the relatively passive nature of expiration (14) and its mechanical dependence on the volume of the previous inspiration. It appeared with the exercise data that the cross correlation between Vt _{E} and the previous Vt _{I} was increased and that the moving average term for Vt _{E} was not statistically different from zero. It is possible that a greater Vt would induce a greater mechanical dependence between Vt _{E} and the previous Vt _{I} for the exercise protocol than for the rest protocol.
The cross correlations between Vt _{I} and Vt _{E} will be affected in rest and exercise protocols by the fact that over time the total volume inspired will be approximately equal to the total volume expired. The fact that the dependence of Vt _{E} on the previous Vt _{I} is much greater than the dependence of Vt _{I} on Vt _{E} reflects the greater variability of endinspiratory volumes than endexpiratory volumes, as can be observed on a standard spirometer record.
The significance of the weak, but statistically significant, negative relationship between Vt _{E} and preceding Ti is not clear. We are not aware of any results comparable to ours concerning this negative cross correlation.
The link between, on the one hand, Te and, on the other hand, preceding Ti and Vt _{I} has been previously documented in conscious humans. Correlations between Te and preceding Ti were shown during steady breathing at a constant inspiratory gas composition in resting humans (10, 24). Te has also been shown to be dependent on preceding Ti in some subjects with use of a multivariate timeseries model (19). However, the true dependence of Teon Vt _{I} is not supported by all observations. Rafferty et al. (29) investigated the separate effects on Te of changes in Ti and Vt _{I} by using auditory feedback to enable the subjects to fix some of the variables of the breathing pattern. This study showed that Te changed in parallel with Ti when Vt _{I} was maintained constant but that Te did not change with Vt _{I}when Ti was maintained constant. In addition, the study by Benchetrit and Bertrand (2) of the anesthetized cat with open chemical feedback loops has shown in most cases a dependence of Teon preceding Ti but no dependence on the value of integrated phrenic activity (2).
The link that we observed between Ti and preceding Te in our study is less well established. Such a link has been observed in some subjects in a previous study using a multivariate timeseries model in conscious humans (19). However, in this study, the stationarity of the data was not tested, and the influence of the chemical feedback loops on the respiratory instability was not clearly identified. Although not demonstrated in the majority of studies, Ti has been shown to vary with changes in Temediated by electrical activation of vagal afferents and mechanical activation of the receptors in animals (12, 15, 30). Using a multivariate ARMA model, Benchetrit and Bertrand (2) observed in the isolated respiratory center preparation a correlation between Ti and preceding Te. As in our study, the link between Te and subsequent Ti was generally weaker in these studies than the converse relationship between Ti and subsequent Te.
The multivariate ARMA model yielded broadly similar results between the rest and exercise protocols. Nevertheless, some quantitative differences were found. These included a decrease in the autocorrelation for Ti and for Te and an increase in the cross correlation between Ti and preceding Te for exercise compared with rest. Additionally, the movingaverage term for Te was not statistically different from zero for the exercise protocol. These findings may suggest that the nextneighboring events have a greater importance for the timing variables during exercise than during rest.
From the results above, it appears that the breathtobreath relationships between the respiratory cycle variables observed in this study in conscious humans are generally in good agreement with the results of Benchetrit and Bertrand (2) in an isolated respiratory center preparation in the anesthetized cat. These authors concluded that the dependence of a given breath on preceding breaths in the absence of chemical and vagal feedback loops was the result of a central mechanism acting as a shortterm memory. Since then, memorylike mechanisms in the brain stem contributing to the smoothing of the respiratory output have received additional support (13).
In the current study, the chemical respiratory drive was maintained as constant as possible to study the respiratory controller isolated from the effects of the chemoreflex feedback loop. Furthermore, there is also evidence that the vagal feedback mediated by the pulmonary stretch receptors does not affect breathing pattern in humans, provided that the overall level of ventilation is not too high (16, 17). It is thus likely that the relationships between respiratory cycle variables observed for the data in resting subjects arise essentially from central mechanisms within the respiratory controller. During exercise, the increase in ventilation, and thus in Vt, may well enhance the role of the mechanical feedback loop in determining breathing pattern (8, 14). Despite this possibility, only the magnitudes of some auto and cross correlations fitted using the multivariate model were modified during exercise compared with rest.
Acknowledgments
We thank Dr. J. J. Pandit for the material that made this study possible. T. Busso is grateful to the Laboratoire de Physiologie and the Groupement d’Intérêt Public Exercise, SaintEtienne (France) for financial support.
Footnotes

Address for reprint requests: P. A. Robbins, University Laboratory of Physiology, Parks Rd., Oxford OX1 3PT, UK.

Present address of T. Busso: Laboratoire de Physiologie, CHU de SaintEtienne, Hôpital de SaintJeanBonnefonds, Pavillon 12, 42055 SaintEtienne Cedex 2, France.
 Copyright © 1996 the American Physiological Society