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Dysrhythmias of breathing occur in several clinical disorders, but their mechanistic basis is obscure.
To understand their pathophysiology, factors responsible for the variability of breathing need to be
defined. We studied the effect of hyperoxic hypercapnia (CO2) on the variational activity of breathing in 14 volunteers before and after delivering CO2 nonobstrusively via a plastic hood. Compared
with air, CO2 increased the gross variability of minute ventilation (
I) and tidal volume (VT), and decreased that of inspiratory time (TI) and expiratory time (TE) (all p < 0.03). CO2 increased the autocorrelation coefficient at a lag of one breath for I (p < 0.05), the number of consecutive breath lags
having significant autocorrelation coefficients for I and VT (both p < 0.01), and the cycle time of oscillations in I (p = 0.03) and VT (p = 0.04). Uncorrelated random behavior constituted 
80% of the
variance of each breath component, correlated behavior represented 9 to 20%, and oscillatory behavior represented < 1% during both air and CO2. CO2 increased the correlated behavior of volume
components, which was accompanied by development of low-frequency oscillations with a cycle time
consistent with central chemoreceptor activation.
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We and others have shown that breath components display considerable breath-to-breath variability in healthy human subjects (1). This variability in breathing can be considered to be composed of a fixed part, namely, the mean of the entire breath series, and a variable part, which is the deviation of the magnitude of each breath from the mean. This variable deviation from the mean, in turn, can be considered to have a non-random (correlated) fraction and an uncorrelated random fraction. In a study of steady-state ventilation of eucapnic healthy subjects, we (8) performed autocorrelation analysis to determine the fraction of variational activity that was correlated on a breath-to-breath basis. The group mean autocorrelation coefficient at a lag of one breath for each of the primary breath components, tidal volume (VT), inspiratory time (TI), and expiratory time (TE), were significantly different from zero, indicating that the magnitude of each component in a given breath was positively correlated with the magnitude of the same component in the immediately preceding breath. The autocorrelation coefficients for each component remained significant for approximately three consecutive breaths, suggesting the presence of short-term memory (9).
The factors that determine the variational activity in breathing are largely unknown. Breathing is controlled by multiple feedback loops, and factors such as central neural networks and chemical stimulation are likely to be important in determining the extent of breath-to-breath variability of breathing, which may be important in the development of dyspnea (10). Although an enormous literature pertains to the influence of hypercapnia on mean changes in respiratory motor output, research on the effect of carbon dioxide (CO2) on the variability of breathing in humans is scant to non-existent. On the basis of studies in vagotomized animals, it has been suggested that hyperoxic hypercapnia may strengthen the interrelationship between breath components in neighboring breaths because of the dominant activation of the central chemoreceptors under these conditions (11). The central chemoreceptors have a prolonged time constant, and, thus, induced deviations from the mean level of ventilation should return more slowly to the mean level, leading to an increase in correlated behavior. Several investigators (2, 12) have postulated that CO2 stabilizes the respiratory controller and decreases the occurrence of ventilatory oscillations. This reasoning is partly based on the linear ventilatory response to an increase in CO2, indicating that the gain of the chemoreceptors is constant, and, therefore, a more stable breathing pattern is expected during hypercapnia (2). Indeed, irregularities of breathing have been reported to disappear with CO2 inhalation (2). In addition, CO2 may act as a stabilizing influence by raising the apneic threshold (13).
Ventilatory oscillations are thought to be mediated largely by the peripheral chemoreceptors (12). However, Waggener and colleagues (14) observed ventilatory oscillations in premature infants that had a cycle time considerably longer than that expected for oscillations originating in the peripheral chemoreceptors. They attributed these low-frequency ventilatory oscillations to central chemoreceptor activity, although the role of the latter was not systematically investigated. Ventilatory oscillations are particularly common in the setting of combined hypoxia and sleep (13). In a study of sleeping subjects exposed to hypoxia, Chapman and colleagues (15) found that CO2 gain, quantitated as the ventilatory response to hypercapnia (16), was higher in subjects who developed ventilatory oscillations than in those who remained free of oscillations. The role of CO2 gain as a determinant of this and other fractions of variational activity in breathing has not been systematically examined in awake subjects.
To investigate the role of central chemoreceptor stimulation on variational activity of breathing, we recorded ventilation in healthy volunteers before and after the induction of a steady-state increase in end-tidal CO2 tension (PETCO2). The study was conducted in the presence of hyperoxia since the latter diminishes peripheral chemoreceptor activity in humans, and, in this setting, step changes in PETCO2 are considered to represent a relatively pure central chemoreceptor stimulus (17). The subjects inhaled CO2 through an open-ended plastic hood, and ventilation was measured nonobtrusively with an inductive plethysmograph to avoid the confounding effects resulting from instrumentation attached to the face (18). We tested the following hypotheses: (1) hyperoxic hypercapnia increases the nonrandom fraction of variational activity in breathing; (2) the change in the nonrandom fraction with hyperoxic hypercapnia is a function of CO2 gain.
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Subjects
Fourteen nonsmoking volunteers (12 men and two women) with a mean age of 35 yr (range, 26 to 44 yr) participated in this study. All had normal pulmonary function. Informed consent was obtained from all subjects, and the study was approved by the Human Studies Subcommittee of Edward Hines Jr. Veterans Administration Hospital.
Respiratory Inductive Plethysmograph
Ventilation was measured nonobtrusively with a respiratory inductive
plethysmograph (Non-Invasive Monitoring Systems, Miami Beach,
FL). The inductive plethysmograph was calibrated against spirometry
by the least squares method (7, 18). Validation was checked during
tidal breathing in the horizontal and semirecumbent positions. Inductive plethysmographic data were considered acceptable if they displayed a 
10% difference from spirometry at both the beginning and
the end of the study. Validation of the inductive plethysmograph
against spirometry in the horizontal and semirecumbent positions revealed mean ± SD arithmetic differences of 3.5 ± 2.8% and 4.9 ± 3.1%, respectively, before the experiments and 4.2 ± 3.3 and 5.0 ± 3.9%, respectively, after the experiments. The signals from the inductive plethysmograph were recorded on a microprocessor system (Non-Invasive Monitoring Systems, Miami Beach, FL), which sampled the
data at 20 Hz. On a breath-by-breath basis, the microprocessor continuously calculated the values of minute ventilation (I), VT, TI, and TE.
The data were processed by taking the duration of the respiratory cycle (Ttot) as the unit of time.
End-tidal CO2
PETCO2 was recorded from nasal prongs using an infrared CO2 analyzer (No. 4700; Ohmeda, Louisville, CO). The infrared analyzer was calibrated before each study. Continuous breath-by-breath recordings of PETCO2 were obtained and stored on a computer disk.
Inspired Gas Administration
To avoid the significant changes in breathing pattern induced by instrumentation attached to the face (19), an open-ended hood was employed for the delivery of CO2. The hood consisted of transparent material that was not in direct contact with the subject's head and did not produce uncomfortable feelings such as claustrophobia. The hood was loosely positioned over the subject's head and it was ventilated with the desired gas composition. Compressed gas cylinders of pure oxygen (O2) and pure CO2 were connected to a flowmeter (Fischer and Porter Co., Warminister, PA), and the outlet of the latter was connected to the hood.
Protocol
The study was conducted while the subject lay semirecumbent on a bed in a quiet room. After successful validation of the inductive plethysmograph, the plastic hood was positioned over the subject's head while he or she rested quietly for 15 min before the initiation of data recording. Subjects were instructed to remain motionless, keeping arms by the side, and to remain awake for the duration of the study; electroencephalography was not monitored. The subjects watched a single recording of a video tape player. Subjects first breathed room air through the hood for 60 min. Then, the mixture of O2 and CO2 flowing into the hood was adjusted to achieve an increase in PETCO2 of ~ 10 mm Hg from baseline; in reality, PETCO2 increased from 33.7 ± 3.4 to 46.6 ± 4.0 mm Hg. This level of PETCO2 was maintained for at least 60 min. Breathing pattern and PETCO2 were continuously recorded on a computer and stored on disk for later analysis (Figure 1).
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Ventilatory Response Progressive Hypercapnia
On a separate day, the CO2 gain was assessed by measuring the ventilatory response to hypercapnia using a modification of the Read rebreathing technique (16). The subjects rebreathed a 7% CO2-93% O2 mixture from a 6-L anesthesia bag, and ventilation was measured by a pneumotachograph (Hans Rudolf; Kansas City, MO) attached to the inspiratory side of a mouthpiece. Expired gas was continuously sampled by an infrared CO2 analyzer (Datex, Helsinki, Finland). Signals from the recording amplifiers were digitized continuously at 50 Hz using a 16-bit analog-to-digital converter (DATAQ Instruments, Inc., Akron, OH) connected to a computer and stored on disk. To reduce random variability, three CO2 response curves (separated by a 15-min rest period) were obtained and averaged. In each subject, the ventilatory response to CO2 was linear with a high correlation coefficient (mean, 0.97 ± 0.01).
Data Analysis
Breath components in a breath series display breath-to-breath variability, which may consist of correlated, oscillatory, and random components. Autocorrelation and spectral analysis enable the determination of the relative magnitudes of these components.
Gross variability. The standard deviation, viz., the square root of the variance, for each breath component was calculated in each subject during air and hyperoxic hypercapnia. To ensure that the standard deviations approximated a Gaussian distribution, they were logarithmically transformed. Then, the log-transformed data for each breath component during air were compared with those during hyperoxic hypercapnia using paired t tests.
Autocorrelation analysis. Autocorrelation analysis was employed to determine what fraction of variational activity is correlated on a breath-to-breath basis (see APPENDIX). By its ability to extract correlated activity from data obscured by random noise, autocorrelation analysis can determine if there is a strong relationship between one breath and another at some interval (or lag) away. It also determines the relative strength of "short-term memory" for each breath component, i.e., a given breath is followed by several breaths that persist in similar magnitude, as if by "memory" (19). Although memory is the term used to describe this statistical relationship, it does not necessarily signify that the consecutive serial autocorrelation coefficients have a neural origin (8, 9).
Spectral analysis. Power spectral analysis can also be used to quantitate breath-to-breath variability in a breath component (20). The power spectrum expresses the variance of a signal as a function of frequency. The presence of a significant peak (see APPENDIX) in the spectrum indicates that some of the variance in the data is due to a periodic oscillation with a period equal to the inverse of the frequency of the peak. The area inscribed by the peak (amount of power) reflects the degree of variability in the signal resulting from fluctuations at that frequency (19).
Although spectral analysis and autocorrelation analysis are mathematically related, periodic oscillations as detected by spectral analysis can represent physiologic mechanisms other than autoregressive behavior (4); in particular, spectral analysis can reveal low-frequency (slow) oscillations of breath components that might be missed by autocorrelation analysis; it has also been shown (4) that both types of analysis should be done in order to correctly partition the total variability of breathing without corrupting the autocorrelation coefficients.
Fractionation of variational activity. The variational activity of breathing was partitioned into autoregressive, periodic, and white noise fractions employing the approach described and validated by Modarreszadeh and colleagues (4) (see APPENDIX). This model enables the quantification of each fraction and its contribution to the entire variational activity of breathing. Fractionation of variational activity allows the influence of hyperoxic hypercapnia on the composition of the total variational activity to be investigated.
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Mean Change in Breathing Component
Mean values of the breath components in each subject during
air and hyperoxic hypercapnia are shown in Figure 2. I increased from 6.47 ± 1.20 (SD) L/min during air breathing to
20.66 ± 6.33 L/min during hyperoxic hypercapnia (p < 0.001);
the respective values for VT were 0.47 ± 0.13 and 1.14 ± 0.27 L (p < 0.001); the respective values for TI were 1.7 ± 0.4 and 1.5 ± 0.3 s (p = 0.14); the respective values for TE were
2.6 ± 0.5 and 1.9 ± 0.4 (p < 0.001).
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Gross Variability of Breath Components
Frequency histograms of I, VT, TI, and TE during air and hyperoxic hypercapnia in a representative subject are shown in Figure 3. Standard deviations of the breath components in
each subject during air and hyperoxic hypercapnia are shown
in Figure 4. The standard deviation of I for the group increased from 1.45 ± 0.83 L/min during air breathing to 3.07 ± 1.19 L/min during hyperoxic hypercapnia (p < 0.001); the
respective values for VT were 0.143 ± 0.118 and 0.241 ± 0.146 L (p < 0.005); the respective values for TI were 0.46 ± 0.53 and 0.26 ± 0.14 (p < 0.025); the respective values for TE
were 0.66 ± 0.38 and 0.35 ± 0.14 (p < 0.001).
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Nonrandom Variability Analysis
Autocorrelograms of I during air and hyperoxic hypercapnia
in our representative subject are shown in Figure 5. Hyperoxic hypercapnia increased the autocorrelation coefficient at a lag of one breath and the number of breath lags with significant
(p < 0.01) serial correlations. Power spectra of I during air
and hyperoxic hypercapnia in our representative subject are
shown in Figure 6. Although no oscillations were observed
during air breathing, a low frequency oscillation was detected
during hyperoxic hypercapnia.
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Autocorrelation analysis. The autocorrelation coefficients
at a lag of one breath for each breath component during air
and hyperoxic hypercapnia in the 14 subjects are shown in Figure 7. The autocorrelation coefficient for I increased from
0.194 ± 0.163 during air breathing to 0.329 ± 0.212 during hyperoxic hypercapnia (p < 0.05); the respective values for VT
were 0.302 ± 0.171 and 0.342 ± 0.157 (p = 0.41); the respective values for TI were 0.232 ± 0.167 and 0.278 ± 0.135 (p = 0.29); the respective values for TE were 0.286 ± 0.137 and
0.286 ± 0.144 (p = 0.99).
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The number of consecutive breath lags having significant
(non-zero, p < 0.01) autocorrelation coefficients for I increased from 2.7 ± 4.8 during air breathing to 22.5 ± 25.1 during hyperoxic hypercapnia (p < 0.01); the respective values for
VT were 3.2 ± 4.2 and 15.1 ± 16.3 lags (p < 0.01); the respective values for TI were 3.7 ± 4.6 and 6.3 ± 6.3 lags (p = 0.17);
the respective values for TE were 4.1 ± 4.9 and 4.4 ± 2.7 lags
(p = 0.82).
Spectral analysis. The centroid frequency, i.e., the mathematically weighted median frequency of the entire spectrum
(0.0 to 0.5 cycle/breath), decreased from 0.16 ± 0.09 cycle/
breath for I during air breathing to 0.11 ± 0.08 cycle/breath
during hyperoxic hypercapnia (p < 0.05); the respective values for VT were 0.14 ± 0.06 and 0.09 ± 0.07 cycle/breath (p < 0.05); the respective values for TI were 0.17 ± 0.07 and 0.13 ± 0.05 cycle/breath (p = 0.11); the respective values for TE were
0.14 ± 0.06 and 0.12 ± 0.05 cycle/breath (p = 0.17).
The number of subjects who displayed a significant peak,
and the corresponding frequency and power of the significant
oscillations for each breath component in the combined low-
and high-frequency bands, are listed in Table 1. An increase in
the number of subjects with significant peaks during hyperoxic hypercapnia was observed for VT only. Hyperoxic hypercapnia caused a significant shift in the oscillations for I (p = 0.03) and VT (p = 0.04) to lower frequencies, whereas it had
no effect on those of TI and TE. Hyperoxic hypercapnia
tended to decrease the power of the oscillations for TI (p = 0.11) and TE (p = 0.09), whereas it had no effect on the power
of the oscillations for I and VT.
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Fractionation of variational activity of breathing. The fractions of variational activity of breathing secondary to oscillatory behavior, correlated behavior, and uncorrelated random [w(n)] behavior for each breath component during air and hyperoxic hypercapnia are listed in Table 2. During both air and hyperoxic hypercapnia, uncorrelated random [w(n)] behavior constituted > 80% of the variance of each breath component, correlated behavior represented 9 to 20%, and oscillatory behavior represented < 1%.
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The effect of hyperoxic hypercapnia resulted in an increase
in the total variational activity in I (p < 0.01) and a decrease in the total variational activity in TE (p < 0.04). Hyperoxic hypercapnia decreased the uncorrelated random [w(n)] fraction of I (p = 0.05), and it tended to increase the correlated fraction of I (p = 0.06) (Table 2 and Figure 8). Hyperoxic hypercapnia produced a very small, although statistically significant,
increase in the oscillatory fraction for VT (p = 0.03).
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Ventilatory Response to Progressive Hypercapnia
CO2 gain, quantitated as the slope of the ventilatory response
to CO2 rebreathing, was 4.29 ± 2.09 (range, 1.29 to 8.00) L/ min/mm Hg in the 14 subjects. The autocorrelation coefficient at a lag of one breath for any breath component during air
breathing or hyperoxic hypercapnia was not related to CO2
gain (Table 3). The number of consecutive breath lags having
significant (non-zero) autocorrelation coefficients for the breath
components was not related to CO2 gain, with the exception of
a negative correlation with TI (r = 
0.52, p = 0.05) during hyperoxic hypercapnia
that is, the number of significant lags
were increased in subjects with a low CO2 gain. Likewise, the
fractions of variational activity in each breath component during air and hyperoxic hypercapnia were not related to CO2 gain
(Table 4).
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We were surprised by the lack of a relationship between
measurements of the variational activity in breathing and CO2
gain. We wondered if this occurrence might be due to the fact
that the variational activity of breathing was assessed under
steady-state conditions, whereas CO2 rebreathing was not.
Also, the CO2 rebreathing maneuver and the steady-state
measurements were not performed on the same day. Accordingly, we derived a quasi-steady-state measurement of CO2
gain in each individual subject by taking the difference in
mean I between air and hyperoxic hypercapnia and dividing
it by the mean change in PETCO2 between air and hyperoxic hypercapnia. This quasi-steady-state measurement of CO2 gain
was negatively correlated with the autocorrelation coefficient
at a lag of one breath for I during hyperoxic hypercapnia
(r = 0.52, p = 0.05). None of the other measurements of variational activity of any breath component was related to this
measurement of CO2 gain.
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Hyperoxic hypercapnia increased the gross variability of I
and VT, and decreased that of TI and TE. It increased the autocorrelation coefficient at a lag of one breath for I and the
number of consecutive breath lags having sufficient autocorrelation coefficients for I and VT. Hyperoxic hypercapnia increased the number of subjects displaying oscillations in VT
and it produced about a three-fold increase in the cycle time
of oscillations in I and VT. Fractionation revealed that at
least 80% of the total variance of each breath component was
due to uncorrelated random [w(n)] behavior, correlated behavior represented 9 to 20%, and oscillatory behavior constituted substantially less than 1% during both air and hyperoxic
hypercapnia. Hyperoxic hypercapnia decreased the fraction of
variational activity in I because of noise, largely by increasing its fraction of correlated behavior.
Significance of CO2 Stimulus
In human studies, investigators have concluded that hypercapnic stimulation in the presence of hyperoxia causes central chemoreceptor stimulation with little or no contribution of the peripheral chemoreceptors (17, 21, 22); indeed, hyperoxic hypercapnia has been regarded as "an almost pure intracranial chemoreceptor stimulus" (17). Ledlie and colleagues (23) examined the effects of hyperoxic hypercapnia in an "open loop" system in dogs, in which respiratory motor output was prevented by paralysis from affecting ventilation and, thus, influencing the input chemical signals. They found that phrenic nerve activity and TE responses to hypercapnia were the same whether or not the carotid sinus nerves were severed. This further supports the notion that the response to hyperoxic hypercapnia stimulation is mediated by the central chemoreceptors.
Effect of Hypercapnia on Mean Change and Gross Variability of Breathing
CO2 produced increases in I and VT, a decrease in TE, and
no change in TI. Other investigators (24) have reported findings qualitatively similar to ours, although they used instrumentation requiring the use of a mouthpiece and noseclips
factors that produce marked alterations in the pattern of
breathing (18).
In a study that focused primarily on the interrelationships
between VT, TI, and TE during air breathing, Newsom-Davis
and Stagg (5) studied six healthy subjects who inhaled mixtures of 1.5 and 3% CO2 in air. Unfortunately, these investigators provided few details on this aspect of their investigation,
except to state that the coefficients of variation of VT, TI, and
TE tended to decrease in one subject, although numerical values were not given (see Figure 5 of their report). However, coefficients of variation are influenced by a change in the mean
value (as occurs with CO2) and thus imperfectly reflect the
true variability of breath components. We quantitated gross
variability in terms of standard deviations, which increased for
the volume components and decreased for the time components during hyperoxic hypercapnia (Figure 4). The increase in gross variability of I with hyperoxic hypercapnia was also supported by inspection of the frequency histogram plots,
which exhibited a broader dispersion of values with hyperoxic
hypercapnia in 13 of the 14 study subjects. Moreover, the absolute variance of I because of correlated behavior increased
from 0.20 L/min during air breathing to 1.57 L/min during hyperoxic hypercapnia (p < 0.03), and the absolute variance of
I because of random behavior increased from 2.52 L/min
during air breathing to 7.92 L/min during hyperoxic hypercapnia (p < 0.009). We are not aware of other systematic studies
of gross variability of breath components in awake human
subjects during steady-state hypercapnic stimulation with which
to compare our results.
Interrelationships between Breath Components
The nonrandom fraction of breathing variability was first examined by Priban (6). Using the analysis of "run lengths" as a
measure of randomness of data, Priban found that the average run length was 1.79 breaths compared with a value of 1.50 breaths per run that is expected for a random series. In four
rebreathing experiments, he reported that CO2-induced hyperpnea (level of PCO2 or I not stated) did not alter the number of breaths per run. A similar experimental approach was
employed by Bolton and Marsh (25) in three healthy men.
They also reported that hyperoxic hypercapnia (magnitude
not stated) did not alter the run length. These results suggest
that hypercapnia does not influence the overall variability of
breathing; however, the investigators did not attempt to determine if correlated or oscillatory behavior was altered by CO2.
Khatib and colleagues (11) fitted a first-order autoregressive model to consecutive values of VT in anesthetized, vagotomized spontaneously breathing rats. While breathing air,
five of seven rats had negative autoregressive coefficients, signifying that when VT of a given breath had a value above the
mean, the value of the next breath was likely to be below the
mean. In contrast, none of our subjectsnor in our previous
study of 33 subjects (8)had negative autocorrelation coefficients for VT while breathing air. When the rats breathed 4%
CO2 in O2, however, three of three had positive autoregressive
coefficients with an estimated average of ~ 0.29 (extrapolated
from Figure 3) (11). We also found a positive autocorrelation
coefficient at a lag of one breath for VT in all subjects during
hyperoxic hypercapnia with an average autocorrelation coefficient of 0.34comparable to that of Khatib and colleagues
(11).
Hyperoxic hypercapnia increased the strength of the relationship of I in immediately adjoining breaths, and it also
increased the number of breath lags having significant autocorrelation coefficients for I and VT. Of interest, this conditioning influence was confined to the volume components,
which is consistent with the predominant effect of hypercapnia on the mean values (Figure 2). The mechanism underlying
the dependence of breath components on the characteristics of the preceding respiratory cycle is not known. We (8) and others (26) have speculated that it might be related to after-discharge (facilitatory memory), that is, the augmentation of
ventilatory output that persists after cessation of a primary
stimulus (9). Indirect evidence suggests that the level of preceding hyperpnea contributes to the manifestation and magnitude of ventilatory afterdischarge (1, 27). Thus, the considerable hyperpnea in our subjectsa greater than threefold
increase in Imight have enhanced afterdischarge and so
contributed to the increase in correlated variational activity.
Afterdischarge is extremely sensitive to the prevailing level of
PCO2, and even a slight decrease in PCO2, accompanying the increase in I, greatly attenuates the magnitude and duration of
afterdischarge (28). Conversely, Engwall and colleagues (29)
showed in awake goats that quite mild hypercapnia (~ 2 mm
Hg increase in arterial PCO2) substantially enhanced the magnitude of afterdischarge and prolonged its duration 2.4-fold.
The investigators attributed the enhancement of afterdischarge to central CO2 chemical drive rather than to the level
of ventilation.
Another contributor to the stronger relationship between volume components of neighboring breaths during hyperoxic hypercapnia may be the blunting of the peripheral chemoreceptors (17). The fast response time of the peripheral chemoreceptors makes them especially important in achieving rapid adjustments around the mean level of ventilation from one breath to the next. Blunting their activity with hyperoxia could have reduced this fine-adjustment mechanism, causing deviations to return more slowly to the mean level, with consequent increase in correlated behavior.
Employing the same mathematical techniques, we recently examined the effect of increasing inspiratory elastic loads on variational activity of breathing in healthy subjects (30). Loading decreased the total variational activity of VT and TE without altering the correlated behavior. The differing responses suggest that the alteration in variational activity of breathing is specific to the nature of the stimulus, probably reflecting behavioral (cortical) influences on the respiratory controller during elastic loading, and automatic (subcortical) influences during hypercapnia.
Oscillatory Behavior
Hyperoxic hypercapnia increased the number of subjects displaying significant ventilatory oscillations and altered their cycle time (Table 1). The development of ventilatory oscillations is thought to result from unstable dynamics in chemical feedback of the respiratory control system (2). In a mathematical model, Khoo and colleagues (12) demonstrated that an increase in loop gain of the respiratory control system resulted in oscillatory behavior. Hypercapnia is considered to decrease loop gain and it eliminates the periodic breathing induced by hypoxia (12, 13). However, the action of CO2 as a stabilizing influence has generally been demonstrated in a system rendered unstable through use of hypoxia, whereas we compared hyperoxic hypercapnia with a stable state, viz., normal resting breathing. Another factor that can lead to ventilatory oscillations is increased circulation time; however, this is an unlikely source of the oscillations with hypercapnia since the latter increases cardiac output (12). Decreased dampening of the respiratory system secondary to a decrease in lung volume can also cause oscillations (9), but this is a less likely mechanism since hypercapnia does not consistently decrease functional residual capacity.
The most striking action of hyperoxic hypercapnia on the
oscillatory behavior of breathing was the threefold reduction
in the frequency of significant oscillations in I and VT. For
I, the frequency of oscillations decreased from 0.12 cycle/
breath during air breathing to 0.04 cycle/breath during hyperoxic hypercapnia; this signifies an increase in the number of
breaths per cycle from eight during air breathing to 25 during
hyperoxic hypercapniaalternatively, this can be considered
in terms of an increase in cycle time from ~ 28 to 88 s (assuming an average breath duration of 3.5 s) (7). This prolongation
of cycle time during hyperoxic hypercapnia is compatible with
the slower response of the central chemoreceptors compared
with the peripheral chemoreceptors (14). Swanson and Bellville (31) quantitated the response time to step changes in
PETCO2 while keeping end-tidal O2 concentration constant. The average time constant of the slow component, considered to
reflect central chemoreceptor activity, was 75 s. This response
time is compatible with the cycle length of the low-frequency
oscillations during hyperoxic hypercapnia in our subjects, suggesting that activation of the central chemoreceptors plays an
important role in their development. Employing a system to
buffer breath-to-breath variations in PETCO2, Modarreszadeh
and Bruce (32) achieved a marked reduction in spontaneous
variability in I in healthy subjects. Although the experimental conditions in their study were necessarily constrained compared with the free breathing permitted in our subjects, the
results of the two studies complement each other. Modarreszadeh and Bruce (32) found that a decrease in spontaneous
fluctuations of PCO2 had its greatest effect on the low-frequency band of the power spectrum for I, and we found that
an increase in mean PCO2 also had its predominant influence on the low-frequency band of the spectra for I and VT (Figures 6 and 8 and Table 1).
Activation of the peripheral chemoreceptors are considered to play an important role in the development of ventilatory oscillations (2, 12, 13). In awake ponies, however, Brown
and colleagues (33) observed ventilatory oscillations when the
carotid bodies were denervated, indicating that the peripheral
chemoreceptors are not essential for the development of oscillatory behavior. In elderly subjects displaying ventilatory oscillations during sleep, Pack and colleagues (34) observed virtual synchrony of electroencephalographic and I time series
on cross-correlation analysis. This result led them to conclude
that the ventilatory oscillations were due to changes occurring
in the state-dependent input to the respiratory control system
at sleep onset, rather than resulting from instability in the peripheral chemoreceptors. In addition to chemical feedback
loops, nonchemical factors almost certainly contribute to the
variational activity in breathing (32). Multiple central pattern
generators are believed to exist in the neuronal networks of
the brainstem (35), which generate a coordinated output to
different groups of respiratory motor neurons resulting in
multiple breathing patterns (33). It is conceivable that hyperoxic hypercapnia may have a direct effect, or an indirect effect
via release of neurotransmitters, on the central pattern generators resulting in altered oscillatory behavior of the type observed in our subjects.
Ventilatory Response to Hypercapnia (CO2 Gain)
Virtually none of the fractions of the variational activity in
breathing was related to CO2 gain (Tables 3 and 4). This may
be partly due to limitations of the technique for measuring CO2 gain since the ventilatory response to CO2 has limited reproducibility. We sought to minimize this factor by selecting
responses that showed a high correlation between I and
PCO2, and taking the average of three measurements. Another
reason for the lack of a relationship between the fractions of
variational activity and CO2 gain might be the relatively small
range of measured CO2 gains; however, the observed four-fold increase in CO2 gain makes this a less likely possibility. In
addition to this technical consideration, the lack of a significant relationship between the variability fractions and CO2
gain suggest that primary neuronal processes rather than direct chemoreceptor activity might be responsible for the observed changes in variational activity of breathing.
The lack of a significant relationship between variational
activity in breathing and CO2 gain might also be related to the fact that the measurements were obtained on separate days.
To overcome this problem, we examined the relationship between the various components of variational activity and a
measure of quasi-steady-state CO2 gain, based on the ratio of
change in I between breathing air and hyperoxic hypercapnia to the change in PETCO2 between air and hyperoxic hypercapnia. A negative correlation was observed between the autocorrelation coefficient at a lag of one breath for I during
hyperoxic hypercapnia and this measurement of CO2 gain (r = 0.52, p = 0.05). That is, subjects with a high CO2 gain exhibited a weak correlation between values of I in immediately adjoining breaths during hyperoxic hypercapnia. This negative correlation suggests that the higher the CO2 gain, the more
random or "noisy" the breath-to-breath variability in I during hyperoxic hypercapnia.
In summary, hyperoxic hypercapnia produced an increase
in the gross variational activity of I and VT and a reduction
in that of TI and TE. Greater than 80% of the variational activity for each breath component consisted of uncorrelated random fluctuations (white noise), correlated behavior represented 9 to 20%, and oscillatory behavior represented much
less than 1% of the variational activity during both air and hyperoxic hypercapnia. Hyperoxic hypercapnia increased the relationship of I in immediately adjoining breaths, and it increased the number of consecutive significant autocorrelation coefficients (i.e., short-term memory) of I and VT. Hyperoxic hypercapnia induced low-frequency oscillations in I and VT. Virtually none of the fractions of variational activity in breathing correlated with CO2 gain, although the autocorrelation
coefficient at a lag of one breath for I during hyperoxic hypercapnia was negatively correlated with a quasi-steady-state
measure of CO2 gain. In conclusion, although the increase in
variability of volume components with hyperoxic hypercapnia
was predominantly due to uncorrelated random fluctuations, a
significant portion resulted from increased correlated behavior accompanied by the development of low-frequency oscillations with a cycle time consistent with central chemoreceptor
activation.
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Footnotes |
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Correspondence and requests for reprints should be addressed to Amal Jubran, M.D., division of Pulmonary and Critical Care Medicine, Edward Hines Jr. Veterans Administration Hospital, Route 111N, Hines, IL 60141.
(Received in original form January 24, 1997 and in revised form June 4, 1997).
Acknowledgments: The writers gratefully thank Rebecca Young, Malinda Mazur, Christine Mullner, and Wilbert Armstrong for their technical assistance, and Eugene N. Bruce, Ph.D., for repeated advice regarding data analysis.
Supported by a Merit Review grant from the Veterans Administration Research Service.
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References |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
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APPENDIX |
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Mathematical Methods
Stationary. Time-series analysis such as autocorrelation requires stationary data, i.e., the statistical properties of the breath series should be time-invariant. To ensure data stationarity, 700 consecutive breaths during air and hyperoxic hypercapnia in which the values of I, VT, TI, and TE did not display large deviations from the mean on visual inspection were
chosen for data analysis. Because a small number of outliers
can substantially affect a correlogram (19), we employed the
clamping technique described by Pack and colleagues (20).
Data points that were more than 2 SD above or below the
mean value were identified and replaced by values that were
equal to the mean plus 2 SD or the mean minus 2 SD, respectively. Next, polynomial equations of increasing order were
employed to detrend the chosen data strings. The polynomial equation, with the breath number as the independent variable
and the corresponding breath component as dependent variable, that best fitted the clamped data was found by multiple
regression (8, 19). This entails calculation of the residual sum
of squares as each successive term was added, then calculating
the F-value as follows:
![F=[(RSS<SUB>n</SUB>−RSS<SUB>n+1</SUB>)/(P<SUB>n+1</SUB>−P<SUB>n</SUB>)]/[RSS<SUB>n+1</SUB>/(N−P<SUB>n+1</SUB>)]](/content/vol156/issue4/fulltext/1129/img001.gif)
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where RSS is the residual sum of squares, subscript n refers to the lower order polynomial, subscript n + 1 is the next higher order polynomial, P is the number of adjustable parameters (order of polynomial plus 1 for intercept), and N is the number of points in the data string. The F-value was calculated for successive orders of polynomials, and the highest order with a significant F-value signified the polynomial that yielded the best fit to the data string. The order of the polynomials were similar for air and hyperoxic hypercapnia for all breath components. The data were detrended by subtracting the polynomial fit from the breath series on a breath-by-breath basis. Autocorrelation analysis was then performed on the detrended data.
Autocorrelation analysis. Autocorrelation analysis was performed to calculate the fraction of variational activity that is correlated among serial breaths, as opposed to random, uncorrelated fluctuations (white noise) in breathing (8, 19). Autocorrelation coefficients at a lag of one breath for I, VT,
TI, and TE were calculated for each data string. The relative
strength of short-term memory of each breath component was
computed as the number of consecutive lags, starting at a lag
of one breath, that displayed autocorrelation coefficients that
were statistically different from zero at p < 0.01. Thus, memory extended to the point at which the autocorrelation coefficient first lost statistical significance at the p < 0.01 level.
We rigorously investigated the adequacy of this detrending
procedure in achieving stationarity. The data strings of 640 breaths during air and hyperoxic hypercapnia were each divided into two segments: an "early" segment consisting of
breaths 0 to 320, and a "late" segment consisting of breaths
321 to 640. Then, polynomial equations of increasing order
were fitted to each segment of the clamped data. The data
were detrended by subtracting the polynomial fit from the
breath series on a breath-by-breath basis. Next, the autocorrelation coefficients and the number of lags with significant serial correlations during air breathing for each breath component were calculated for the early and late segments; a similar
analysis was performed on the data obtained during hyperoxic
hypercapnia. the autocorrelation coefficients at a lag of one
breath for I, VT, TI, and TE were equivalent in the early and
late segments during both air breathing (p > 0.49 in all instances) and hyperoxic hypercapnia (p > 0.22 in all instances).
Likewise, the number of breath lags displaying significant correlations for I, VT, TI, and TE were not different between the
early and late segments during either air breathing (p > 0.21 in all instances) or hyperoxic hypercapnia (p > 0.20 in all instances).
The distribution of sample values of a correlation coefficient (r) is restricted to r values between 1.0 and +1.0, and is, in general, asymmetrical (i.e., not Gaussian); thus, a Fisher's z
transformation was performed on each r value. After each r
value was transformed to a function z, standard parametric
statistics were performed. Specifically, the autocorrelation coefficients and number of lags with significant serial correlations for breath components during air breathing were compared with those during hyperoxic hypercapnia using Fisher's
z transformation with paired t tests.
Spectral analysis. Power spectra of the data strings during air and hyperoxic hypercapnia were obtained using a fast Fourier transform (FFT) algorithm to detect significant oscillations and to quantify their magnitude. After removing any linear trend, the data were multiplied by a cosine-tapered rectangular (Hanning) window, and a FFT was applied to obtain the power spectrum. Spectral analysis was performed on 640 consecutive breaths, subdivided into 10 segments of 64 breaths each; final spectral estimates were calculated by averaging the spectra of the 10 subsegments (4). Each power spectrum was first characterized by calculation of the centroid frequency, which is the mathematically weighted median frequency of the spectrum. To allow for the possibility of nonuniform baseline power, we divided the spectrum into a low-frequency (0.0 to 0.2 cycle/breath) and high-frequency band (0.2 to 0.5 cycle/ breath); otherwise, the number of significant oscillations in the low-frequency band are likely to be overestimated, whereas the number of significant oscillations in the high-frequency band are likely to be underestimated (4). Significant peaks were detected in each of the frequency bands by comparing the power at each frequency with the mean power in that band. Peaks were considered significant when at least two consecutive data points lay above the 95% confidence interval of each spectral estimate (15). The presence of a significant peak in the power spectrum indicates that part of the variance in the data is due to an oscillation with a period equal to the inverse of the frequency of the peak. The area inscribed by the peak (amount of power) reflects the degree of variability in the signal resulting from oscillations at that frequency. Differences in centroid frequencies, number of significant peaks, frequencies of significant peaks, and the power of significant peaks were compared during air and hyperoxic hypercapnia by paired t tests.
Fractionation of variational activity. The total variational activity of the data was modeled as a mixture of autoregressive variations using a first-order autoregressive model (AR1), oscilatory variations, and uncorrelated white noise [w(n)] using the technique described by Modarreszadeh and colleagues (4):
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![<LIM><OP>∑</OP><LL>j=1</LL><UL>ρ</UL></LIM>[b<SUB>j1</SUB>sin (2πf<SUB>j</SUB>n)+b<SUB>j2</SUB>cos (2πf<SUB>j</SUB>n)]+w(n)](/content/vol156/issue4/fulltext/1129/img003.gif)
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where x = ventilatory variable, n = breath number, a1 = autoregressive coefficient, 
= the maximal number of significant peaks, fj = frequency of significant peaks, and bj1 and bj2 = amplitudes of the sinusoids. The expression within the brackets is the contribution of each discrete oscillation, having a frequency of fj, to the variance of the data. The coefficients a1,
bj1, and bj2 were calculated by the least-squares method. The
variance secondary to autoregressive components and w(n),
i.e., 
2AR, was calculated using the standard error of the estimate (SEE): (SEE)2/1 a12; the variance caused by w(n) was
calculated as (SEE)2, whereas the variance caused by the autoregressive fraction was calculated as 2AR (SEE)2. If the
a1 coefficient of the data string for a breath component in a
subject was statistically different from zero, a second-order autoregressive model (AR2) was then fitted to the data and
the entire fractionating process was repeated (19). For the
AR2 model, the variance secondary to the autoregressive fraction and w(n), i.e., 2AR2, was calculated as: