Vol. 89, Issue 6, 2147-2157, December 2000
Periodic breathing in heart failure patients: testing the
hypothesis of instability of the chemoreflex loop
G. D.
Pinna1,
R.
Maestri1,
A.
Mortara2,
M. T. La
Rovere2,
F.
Fanfulla3, and
P.
Sleight4
Departments of 1 Biomedical Engineering,
2 Cardiology, and 3 Pneumology, Fondazione S. Maugeri,
Clinica del Lavoro e della Riabilitazione, IRCCS, Istituto Scientifico
di Montescano, 27040 Montescano (PV), Italy; and
4 Cardiovascular Medicine, John Radcliffe Hospital, Oxford
OX39DU, United Kingdom
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ABSTRACT |
In this study, we applied
time- and frequency-domain signal processing techniques to the analysis
of respiratory and arterial O2 saturation
(SaO2) oscillations during nonapneic periodic
breathing (PB) in 37 supine awake chronic heart failure patients.
O2 was administered to eight of them at 3 l/min.
Instantaneous tidal volume and instantaneous minute ventilation (IMV)
signals were obtained from the lung volume signal. The main objectives
were to verify 1) whether the timing relationship between
IMV and SaO2 was consistent with modeling predictions
derived from the instability hypothesis of PB and 2) whether
O2 administration, by decreasing loop gain and increasing
O2 stores, would have increased system stability reducing
or abolishing the ventilatory oscillation. PB was centered around 0.021 Hz, whereas respiratory rate was centered around 0.33 Hz and was almost
stable between hyperventilation and hypopnea. The average phase shift
between IMV and SaO2 at the PB frequency was 205°
(95% confidence interval 198-212°). In 12 of 37 patients in
whom we measured the pure circulatory delay, the predicted lung-to-ear
delay was 28.8 ± 5.2 s and the corresponding observed delay
was 30.9 ± 8.8 s (P = 0.13). In seven of
eight patients, O2 administration abolished PB (in the
eighth patient, SaO2
did not increase). These results show a remarkable consistency between
theoretical expectations derived from the instability hypothesis and
experimental observations and clearly indicate that a condition of loss
of stability in the chemical feedback control of ventilation might play
a determinant role in the genesis of PB in awake chronic heart failure patients.
respiratory control; spectral analysis; ventilatory oscillations; O2 administration; chemoreceptors
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INTRODUCTION |
A CYCLIC BREATHING
PATTERN characterized by a smooth rise and fall in ventilation
with cycle lengths ranging from ~25 to 100 s (0.01-0.04
Hz) is frequently observed in chronic heart failure (CHF)
patients and is commonly referred to as periodic breathing (PB)
(15, 19, 29, 30, 33) or, usually when separated by apnea,
Cheyne-Stokes respiration (6, 12). Often, the same patient
may exhibit a continuum of different patterns of breathing, ranging
from normal breathing (i.e., without cyclic modulation of ventilation)
to mild PB up to cyclic periods of apnea. These patterns are also
influenced by wakefulness or sleep, posture, and physical and mental activity.
Most studies on the phenomenon of PB in CHF patients have been
performed during sleep (34). The prevalence of PB in awake CHF patients is, however, greater than usually believed. Awake recordings in controlled laboratory conditions showed a sustained PB
pattern in 25-66% of patients with mild to moderate CHF (New York
Heart Association class I to class III) (15, 29, 33).
The physiological mechanisms responsible for PB in CHF patients are
still a matter of debate. Two major hypotheses, however, have received
most attention in the last two decades. The "central" hypothesis
explains PB as the manifestation of a central vasomotor rhythm that
modulates ventilation either indirectly through modulation of blood
flow or directly through central irradiation to respiratory centers
(3, 17, 35). The "instability" hypothesis, on the contrary, explains PB as a self-sustaining oscillation due to the loss
of stability in the closed-loop chemical control of ventilation (5, 6). This loss of stability is thought to be caused by the concurrent presence of slow circulation time between lungs and
chemoreceptors, enhanced loop gain, and underdumping of CO2 and O2 body stores (34).
The instability hypothesis has gained wider acceptance than the central
hypothesis mainly because of its sound theoretical basis, using
mathematical models of the respiratory control system (4, 24,
26). These studies have shown that increased circulatory delay
and loop gain brought about by the decreased cardiac output of CHF
patients may lead to instability in their feedback control of
ventilation. This implies that in some CHF patients there is a critical
frequency (i.e., the PB frequency) at which a perturbation traveling
around the loop is subjected to an overall gain 
1 and to a phase
shift of 180° (4, 24). These are the two well-known necessary and sufficient conditions for an oscillatory behavior in a
closed-loop negative feedback system to be self-sustaining. Definitive
experimental proofs of these modeling predictions in CHF patients,
however, have not been provided. One possible reason is the difficulty
of reliable phase measurements with conventional methods; the other,
even greater, difficulty is the impossibility of open-loop gain
measurement, because it requires opening the ventilatory control loop
at some point. To circumvent these difficulties in this study, we
applied novel signal-processing techniques to estimate the phase shift
of the ventilatory control loop and verified whether theoretical
expectations derived from the instability hypothesis were consistent
with experimental observations. Moreover, we searched for indirect
evidence of a critical role of the loop gain in the development of PB
by acute administration of O2. The rationale was that this
intervention should decrease loop gain and increase O2
stores, leading to increased stability with reduction or abolition of
the ventilatory oscillation.
Because one of the still-unsettled aspects of PB is whether the cyclic
increase of the ventilatory drive acts mainly on tidal volumes,
respiratory frequency, or both, an ancillary aim of the study was to
assess the relationship between changes in tidal volume and
simultaneous changes in minute ventilation.
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METHODS |
Subjects.
We studied 134 subjects with dilated cardiomyopathy and moderate to
severe heart failure consecutively admitted to the Heart Failure Unit
of the Montescano Medical Center for evaluation and therapy of heart
failure, usually in conjunction with evaluation for heart
transplantation. Inclusion criteria were stable clinical condition (no
changes in signs, symptoms, or therapy in the 2 wk preceding the
study), sinus rhythm in the electrocardiogram, and no previous history
of pulmonary or neurological disease or of myocardial infarction or
cardiac surgery within the previous 6 mo. Patients were given
individualized therapy, which included angiotensin I-converting enzyme
inhibitors (87%), nitrates (52%), digoxin (82%), diuretic
drugs (92%), amiodarone (25%), and, in the absence of
contraindications, anticoagulants or antiplatelets agents
(99%). The patients underwent our usual routine assessment of
autonomic function, which included monitoring of resting respiratory and cardiovascular parameters. During this evaluation, 71 (53%) of the
patients demonstrated a sustained PB pattern. We excluded 28 patients
who showed definite apnea between the hyperventilation phases
(Cheyne-Stokes respiration), because these apneas are most likely
triggered by reductions of arterial partial pressure of CO2
(PaCO2) below the apneic threshold (27),
thus involving marked nonlinear relationships between ventilatory
signals that cannot be properly analyzed by the linear techniques used
in this study. We also excluded six patients with poor signal quality in at least one of the ventilatory signals (see below). This selection led to a final sample of 37 patients, who were ~28% of those
admitted to the study.
All subjects gave their informed consent to the study, which was
approved by the local Ethics Committee.
Protocol and signal acquisition.
After instrumentation and a 15-min period for signal stabilization, we
made an 8-min supine resting recording of instantaneous lung volume
(ILV) by inductive plethysmography (Respitrace Plus, Non-Invasive
Monitoring Systems, Miami Beach, FL) and arterial O2
saturation (SaO2) by a fast-response (processing delay
1.5 s) pulse oximeter with an ear probe (Biox 3740, Ohmeda,
Louisville, CO). Calibration of lung volume measurements was carried
out by taking a simultaneous 30-s recording of the respiratory flow at the beginning of each experimental session via a Fleisch
pneumotachograph (model 47304A, Hewlett Packard, Waltham, MA). Flow was
digitally integrated and regressed on the Respitrace signal to obtain
the calibration factor. At the end of the resting recording, 12 of the
37 patients underwent an apnea trial (see the description below), and
nasal O2 was administered to 8 patients at a rate of 3 l/min.
Signal analysis.
An instantaneous tidal volume (ITV) signal was derived from ILV by a
cubic spline interpolation of the end-expiratory and of the
end-inspiratory points and then computing the difference (Fig.
1). A cubic spline was also used to
interpolate the time series of breath duration, giving an instantaneous
breath-duration signal. Dividing the ITV by instantaneous breath
duration gave an instantaneous minute ventilation (IMV) signal (Fig.
1). To validate our method, we produced known minute ventilation
signals by inflating and deflating a standard 1-liter syringe through a
pneumotachograph, following a metronome set at 12 and 15 breaths/min. Flow was digitally integrated to obtain ILV, and the latter was then
processed by our software to obtain IMV, giving, respectively, 12.02 and 15.03 l/min.
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Fig. 1.
Derivation of the instantaneous tidal volume (ITV) and
instantaneous minute ventilation (IMV) signals from the instantaneous
lung volume signal (ILV). Top: end-inspiratory
( ) and end-expiratory ( ) points of the
ILV signal. The two cubic splines fitting these points (upper and lower
envelopes) are also plotted. Their difference is the ITV signal
(bottom). Middle: a cubic spline was also used to
interpolate the time series of breath duration, giving an instantaneous
breath duration signal, plotted by a dashed line. Dividing the ITV
signal by this curve, the IMV signal is obtained, as shown by a solid
line.
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All signals were resampled at 2 Hz and plotted on a personal computer
screen. A portion free from large transients or artifacts with a
duration ranging from 180 to 300 s was interactively selected.
Peaks and troughs (max, min) of the ITV and
SaO2 signals were
derived by special software. Mean breath duration in an 8-s interval
centered in the two phases of each PB cycle (hyperpnea, hypopnea) was
computed and averaged over all cycles.
Univariate spectral analysis was performed by using the autoregressive
method (31), and the central frequency of main oscillatory components was automatically identified and estimated by a spectral decomposition algorithm (22).
Autoregressive bivariate spectral analysis was performed to assess the
relationships between signals, and the coherence and transfer functions
were estimated (28). Phase spectra were plotted using the
conventional "wrapped" format (i.e., representing phase shifts
between 
180° and 180°), but for computations the "unwrapped" format was used. By convention, the phase shift between two signals S1
and S2 was negative if S1 led S2.
Definitions.
The following definitions were used throughout the study. PB was
defined as a sustained oscillation of ventilation characterized by
smooth regularly recurring cycles of hyperventilation and hypopnea or apnea.
The PB frequency (fPB) was defined as the central frequency
of the spectral component of the IMV signal in the band 0.01-0.04 Hz. The lung volume modulation index (LVMI) was defined as the average
depth of modulation of breath amplitude, that is
|
(1)
|
where i = 1, 2 ... L are the PB cycles
within the record analyzed. Hence, the LVMI ranges from 0% (constant
breath amplitude) to 100% (PB with apnea). The peak-to-nadir
O2 saturation was defined as the average peak-to-nadir
change of SaO2 over the observed PB cycles, that is
|
(2)
|
The respiratory frequency was defined as the frequency of the
phasic activity of the ILV signal derived from spectral decomposition.
Modeling assumptions.
A simplified model of the respiratory control system (Fig.
2), which emphasizes the critical delay
elements of the loop, was used throughout the study as a reference for
the analysis and interpretation of observed data. The main elements of
the respiratory control loop are the respiratory network in the central
nervous system (the controller), respiratory muscles (the effectors), the lungs (the plant), arterial blood gas tensions (the controlled variables), the delays between the lungs and carotid bodies and between
the lungs and brain tissue (including the lag from the gas exchange
process in the lungs, the pure time delay due to the convective
transport process, mixing effects in the heart and arterial
vasculature, and the time necessary for the entering blood to impose
its CO2-H+ status on the brain tissue), the
delay between stimulation of carotid chemoreceptors and the reflex
ventilation (peripheral chemoreflex delay), and the carotid and central
chemoreceptors (the feedback sensors). Aortic chemoreceptors have not
been depicted because their contribution to the overall ventilatory
response is much weaker than that of the other chemoreceptors
(16). The model shows the two signals of the loop that
were actually measured in this study, namely IMV and
SaO2, the latter being recorded after the circulatory
delay between carotid bodies and the ear. Major assumptions
relative to this model were that 1) the dynamics of central
chemoreceptors is much slower than that of carotid chemoreceptors,
causing the ventilatory response at the frequency of PB to be mainly
mediated by carotid chemoreceptors and 2) the oscillation of
SaO2 during PB is
accompanied by a concurrent oscillation of PaCO2 and
the two are out of phase (i.e., 180° phase shift).
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Fig. 2.
Simplified model of the respiratory control systems (see
text for details). Dashed-dotted lines with a circle indicate the
signals that were actually measured in the study.
SaO2, O2 saturation at the ear measured by
pulse oximetry;  A, alveolar ventilation; CNS,
central nervous system.
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Phase and time delay estimation.
The phase shift between two signals at the frequency of PB was obtained
as the value of the phase spectrum at that frequency. The corresponding
time delay was estimated by using the relationship
|
(3)
|
where 
and 
are the phase shift in degrees and radians,
respectively, and fPB and TPB are
the PB frequency (in Hz) and the PB wavelength (in s), respectively.
Testing modeling predictions.
To test whether modeling predictions derived from the instability
hypothesis were consistent with experimental observations, we focused
on the phase shift of the PB oscillation around the peripheral
chemoreflex loop (Fig. 2). If the hypothesis of instability is true,
this shift has to satisfy the equation
|
(4)
|
where LC is the phase shift contribution from the
lungs to the carotid body and PR is the lag contribution
between the blood gas oscillation at the carotid body and the
oscillation in ventilation; that is, the peripheral chemoreflex phase
shift. What we could actually measure in our experimental set up,
however, was the overall phase shift LE from the lungs
to the ear lobe, which can be easily derived from the analysis of the
relationship between the IMV and SaO2 signals (Fig.
2). We can express this phase shift as
|
(5)
|
where CE is the lag introduced by the
carotid-to-ear path. Substituting LC from Eq. 5 into Eq. 4, we obtain
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(6)
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Passing now from phase shifts to corresponding time delays (with
the same meanings to the subscripts) using the relationship in
Eq. 3, Eq. 6 becomes
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(7)
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This equation tells us that, under the hypothesis that the PB
oscillation derives from instability in the chemoreflex loop of
ventilation, the overall delay of this oscillation around the loop
(i.e., TLE TCE + TPR) has to equal half the PB wavelength. An estimate
of TCE can be obtained by reasonably assuming
that the carotid-to-ear delay is mostly due to the pure convective process of the blood (i.e., mixing effects are negligible) and, expressing it as a fraction of the pure delay
TLEp between the lungs and the ear,
this fraction being approximately given by the ratio of carotid-to-ear
distance to the lung-to-ear distance. Taking 6 cm and 40 cm as
representative measurements of these distances (21), we
have
|
(8)
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Hence Eq. 7 becomes
|
(9)
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which allows us to predict TLE
having TPB, TLEp,
and TPR. To this purpose, we estimated
TLEp in a subset of 12 patients by asking them to
hold their breath as long as possible at the end of expiration and then
to inspire abruptly with the highest possible vigor. In this way, we
created a step change in ventilation that was followed by a step
increase of SaO2 at the ear. The distance between the
two steps (Fig. 3), averaged over two
consecutive trials, was taken as the desired estimate. A rough estimate
of TPR was obtained from time constants of the
dynamics of the ventilatory response to hypoxia and of mixing effects
in the heart and arteries measured by previous investigators (10,
25). Although these time constants were derived from healthy
subjects, the estimated TPR should not be different from that of CHF patients (see details of this estimation procedure in the APPENDIX).
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Fig. 3.
Estimation of the pure time delay between the lungs and
the ear. SaO2 was corrected for the intrinsic delay of
the oximeter. The subject was asked to hold respiration as long as
possible in 2 consecutive trials and then to inspire with as much vigor
as possible. The time delay was measured as the distance between
beginning of inspiration and nadir of SaO2. Results
(T1 and T2) were averaged
to obtain the final estimate.
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Statistical analysis.
Data are presented as means ± SD. Pairwise comparisons were
performed by the t-test for dependent samples. The
significance level was set at 0.05.
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RESULTS |
Ventilatory oscillations during PB.
The demographic and clinical characteristics of the subjects of the
study are given in Table 1. In the
O2 subgroup, hemodynamic indexes were well representative
of the overall group [left ventricular ejection fraction = 22 ± 8%, cardiac index = 1.8 ± 0.5 (l · min
1 · m2)]. A
typical recording of ILV, ITV, IMV, and SaO2 signals
during PB is shown in Fig. 4,
left. The ITV signal appears as a smooth quasi-periodic
waveform. Note also that the ILV signal shows an oscillation of the
end-expiratory lung volume synchronous with breath amplitude changes.
The respiratory frequency is fairly stable during the different
phases of PB. As a consequence, the IMV signal is very similar to the
ITV signal. An oscillation at the same frequency of the IMV signal
characterizes the behavior of O2 saturation at the ear. In
Fig. 4, right, the corresponding power spectral density
function of all signals is plotted. The spectrum of the ILV signal is
characterized by two well-defined peaks, one at the frequency of PB and
the other at the frequency of phasic respiratory activity, whereas the
spectrum of the other signals is dominated by a peak around 0.02 Hz.
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Fig. 4.
Left: examples of ILV, ITV, IMV, and
SaO2 from a representative congestive heart failure
patient during an episode of periodic breathing. Right:
corresponding spectral density functions.
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The respiratory frequency was 0.33 ± 0.06 Hz (20 ± 4 breaths per minute). Mean breath duration was 3.1 ± 0.4 s in
the hyperpneic phase and 2.9 ± 0.5 s in the hypopneic phase
(P = 0.001). Although statistically significant, this
change is actually very small (<7%). Major parameters describing
ventilation and SaO2 fluctuations during PB are given
in Table 2. To appreciate the
representativeness of the O2 subgroup relative to the
overall group of the study, data from these patients are reported in
the second row of the same table.
The central frequency of the spectral component associated with PB was
0.021 ± 0.004 Hz for ILV, 0.021 ± 0.005 Hz for ITV, 0.021 ± 0.004 Hz for IMV (PB frequency), and 0.021 ± 0.004 Hz for SaO2. By
computing the reciprocal of the PB frequency, we found that the
corresponding length of the PB cycle was 49.8 ± 8 s.
We observed a rather pronounced oscillation of the end-expiratory lung
volume synchronous with the oscillation of breath amplitude in 89% of
the patients. By simultaneously recording ventilatory activity in a
subsample of subjects by use of the Fleisch pneumotachograph (see
METHODS), we found that this end-expiratory volume
oscillation was independent of the technique used for recording
ventilatory activity.
A coherence approaching unity and a near-zero phase shift at the PB
frequency were found both between ILV and ITV (0.96 ± 0.04, 2 ± 11°, not significant) and between ITV and IMV (0.98 ± 0.02, 1 ± 9°, not significant), thus indicating that
during PB there is a very close linear association and synchronicity between the slow component of lung volume and the corresponding oscillation of tidal volume, and between the oscillation of tidal volume and the corresponding oscillation of minute ventilation.
The coherence between IMV and SaO2 at the PB frequency
was very high (0.95 ± 0.05). The phase shift between the two
signals (which, as explained in METHODS, is an estimate of
the phase shift around the ventilatory control loop plus the
carotid-to-ear lag minus the phase shift due to the peripheral
chemoreflex dynamics) exceeded 180° by 25°, with a 95% confidence
interval comprised between 18° and 32°. The corresponding
lung-to-ear delay was 28.3 ± 5.5 s.
Comparing predicted and observed delays.
In the subgroup of 12 patients who underwent the end-expiratory apnea
trial, the PB wavelength was 56.2 ± 9.5 s, corresponding to
a PB frequency of 0.019 ± 0.003 Hz. The lung-to-ear delay was 30.9 ± 8.8 s, with a pure time delay contribution of
13.9 ± 3.7 s. By Eq. 8, the resulting estimate of
the carotid-to-ear delay was 2.1 ± 0.6 s. The
estimate of the delay TPR between the blood gas
oscillation at the carotid body and the oscillation in ventilation was
1.4 ± 0.1 s. Inserting estimated values into Eq. 9, we obtained a predicted lung-to-ear delay of 28.8 ± 5.2 s (P = 0.13 for the comparison with observed values).
O2 administration.
The effect of O2 administration in the patients of the
O2 subgroup, to reduce or minimize the chemoreceptor drive,
was the abolition of PB in 7 of 8 CHF patients. A representative
example of successful O2 administration is given in Fig.
5. In these subjects, the mean
SaO2 passed from 93.4% (basal
condition) to 95.9% (P < 0.03) during O2
administration. It is noteworthy that the only patient in which PB was
not abolished showed a very small increase in
SaO2 (0.7%),
suggesting that probably he did not breathe O2 properly.
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Fig. 5.
Representative tracings of ILV and SaO2
from one patient of the O2 subgroup before (basal
condition) and during O2 administration. Notice the
complete abolition of periodic breathing and the marked increase of
SaO2 after the therapeutic intervention.
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DISCUSSION |
Simultaneous recordings of ventilatory activity and
SaO2 at the ear during episodes of
nonapneic PB in awake CHF patients have been analyzed in this study
through time- and frequency-domain signal processing techniques, and
the phase shift of the oscillation traveling around the peripheral
chemoreflex loop has been estimated to be compared with the predicted
value derived from the instability hypothesis. Given that one of the
leading factors of instability of a feedback control system is
increased loop gain, O2 was administered to a subset of the
patients to assess whether reducing the gain would have eliminated the
ventilatory oscillation. The results of the study were remarkably
consistent with theoretical expectations formulated on the basis of the
instability hypothesis.
Adequacy of modeling assumptions and measurement techniques.
A large body of experimental data has accumulated to support the notion
that central chemoreceptors are characterized by a much slower dynamics
than peripheral chemoreceptors. Previous studies in humans have shown
that the time constant for the ventilatory response of central
chemoreceptors is around one order of magnitude greater than that of
peripheral chemoreceptors (11, 36). We expect this ratio
to be even greater in CHF patients because of their reduced cerebral
blood flow. Therefore, the response of central chemoreceptors at
frequencies ~0.02 Hz (i.e., the typical PB frequency) will be
markedly attenuated and the phase shift will be well below 180°.
Because the overall response of the ventilatory controller can be
modeled as the vectorial summation of the central and peripheral
contributions (24), a dominant role of carotid body
chemoreceptors in the mediation of PB seems well justified. Indeed, in
a simulated study using a brain tissue washout time constant of 80 s, Khoo and co-workers (24) showed that the central
contribution to the overall loop gain of the respiratory control system
is much smaller than the peripheral contribution. We confirmed these
results in our own simulations. The critical role of peripheral
chemoreceptors in the development of PB in cats has been demonstrated
previously (7).
Although intuitive, experimental evidence that SaO2
and PaCO2 oscillate
out of phase during PB has been provided in previous studies (13,
18).
We derived the peripheral chemoreflex delay from the time constants of
the overall ventilatory response and of mixing effects in the heart and
arteries obtained by other investigators in healthy subjects (10,
25). Although these time constants are expected to be markedly
different in CHF patients because of enlarged left heart volumes,
impaired hemodynamic function, and congested lungs, the lag associated
with the response of peripheral chemoreceptors should not be. However,
it is prudent to recognize that several simplifications were introduced
in the overall computing procedure. Taking into account the difficulty
of executing complex or invasive measurements in such severely diseased
patients, we should regard our measurements as approximate estimates of
the true peripheral chemoreflex delay, albeit the best presently possible.
The measurement of SaO2 through pulse oximetry
deserves some final comments. Although this is a widely accepted
technique (accuracy ranges from 2% to 6% when compared with
intra-arterial determinations; Ref. 9), measurements may
be underestimated in the case of perfusion abnormalities. Franklin and
co-workers (17) compared invasively measured
SaO2 during
Cheyne-Stokes breathing with that obtained by the same pulse oximeter
as the one employed in our study and found that periodic desaturations were less severe when measured by the latter. Hence, we cannot exclude
that the peak-to-nadir changes in O2 saturation measured in
this study were somewhat lower than their actual values in arterial blood.
New descriptors of respiratory oscillations during PB.
Using digital signal processing techniques, we derived from the
original lung volume signal two new signals describing, in a continuous
manner, changes over time of tidal volume and minute ventilation. The major advantage offered by these signals was that they could be resampled at the same frequency as that of the other
respiratory signals, thus allowing the application of bivariate
spectral analysis to obtain measurements of phase shifts from phase
spectra. Using this approach, we found a high coherence between the
low-frequency (0.01-0.04 Hz) component of the lung volume signal
and the oscillation of tidal volume, and between the latter and the
corresponding oscillation of minute ventilation, thus making these
three signals virtually interchangeable in describing the cyclic
oscillation of ventilatory activity during PB. In particular, the very
close linear relationship and synchronicity between ITV and IMV and the
very small (<7%) change in breath duration between the hyperpneic and
hypopneic ventilation phases clearly indicate that the oscillation of
minute ventilation during PB is almost totally due to the variation of
tidal volume, with very little contribution from changes in respiratory
rate. These findings are consistent with results from other
investigators obtained in different experimental conditions (2,
15).
A marked wandering of the ventilatory baseline synchronous with the
oscillation of tidal volume was observed in most subjects of the study.
This oscillation has rarely been observed by other investigators and
probably represents a purely mechanical phenomenon, arising from the
fact that the duration of expiration is insufficient to permit complete
exhalation when tidal volume increases during the hyperpneic phases of
PB (37).
PB and the instability hypothesis.
We found that the phase shift between minute ventilation and ear
O2 saturation at the PB frequency was significantly
>180°, a result consistent with Eq. 6 derived from the
instability hypothesis, provided that the carotid-to-ear lag is greater
than the peripheral chemoreflex lag. Indeed, this is what we found in
the apnea trial group. This finding is likely due to the fact that the
carotid-to-ear delay arises from the slow blood transport process,
which is expected to be further slowed down in CHF patients, whereas
the peripheral chemoreflex delay is mainly due to the neural dynamics
of the chemoreflex. We also found that the predicted measurement of the lung-to-ear delay, as given by Eq. 7, was very close to
observed values, the difference being on average ~7% of the expected
value. Hence, these results indicate a remarkable consistency between theoretical expectations from the instability hypothesis and
experimental observations. An example of how this concept is confirmed
by empirical observations is given in Fig.
6, showing the transition phase between
stable and oscillating ventilatory behavior. It can be noticed that a
transient perturbation characterized by a sudden decrease in
ventilation causes a delayed and pronounced decrease in O2
saturation at the ear. This is almost simultaneous with the increase in
ventilation, suggesting a causal relationship. The increase in
ventilation in turn causes a delayed increase in
SaO2 accompanied by
an opposite change in ventilation, and so on.
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Fig. 6.
Onset of periodic breathing in a chronic heart failure
patient. A transient sudden decrease in ventilation causes a delayed
and pronounced decrease in SaO2. This is almost
simultaneous with the increase in ventilation (ILV), suggesting a
causal relationship. The increase in ventilation, in turn, causes a
delayed increase in SaO2 accompanied by an opposite
change in ventilation, and so on.
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Our results, however, do not exclude the possibility that a central
rhythm may play a role in the genesis of PB. Indeed, it seems realistic
to hypothesize that the closed-loop control of ventilation of CHF
patients can be often in a condition of "relative stability"
(4). This is a state of the system characterized by an
open-loop gain <1 at the critical frequency at which the phase shift
of the loop is 180°. In this condition, the corresponding closed-loop
gain shows a pronounced peak at the so-called resonant frequency. The
closer the open-loop gain is to 1, the stronger the magnification and
the narrower the bandwidth at the resonant frequency. This condition
seems highly likely in CHF patients, because the reduced cardiac output
brings about a concurrent increase of both the gain and the phase shift
of the loop (4, 24). Moreover, hypoxic chemosensitivity is
known to be enhanced in CHF patients, likely as a result of increased
catecholamine levels and/or ischemic hypoxia at peripheral
chemoreceptors (8, 14). Hence, if there is even a feeble
central rhythm in the range 0.01-0.04 Hz and its frequency
coincides with the resonant frequency of the loop, a full-blown
oscillation will occur. If the gain increases further up to or over 1, the system becomes unstable and the oscillation tends to get larger and
larger until the nonlinear characteristics of the loop intervene. Two
major criticisms, however, can be addressed to this hypothesis. First,
the frequency of PB is not the same among different populations of
subjects or different physiological conditions. Healthy subjects
at high altitude, for instance, develop PB at a higher frequency
than CHF patients, which would imply a different central rhythm. This
discrepancy seems rather hard to explain. Second, the sudden appearance
of PB after a transient perturbation, such as in the example of Fig. 6,
is also difficult to understand in terms of an underlying central
rhythm, because it would imply either that this rhythm starts abruptly
or that a sudden change in the control loop parameters (e.g., the gain) takes place.
The estimate of the pure convective transport delay between the lungs
and the ear was ~14 s, a result very close to the average circulatory
delay of 12.4 s measured by Ahmed and co-workers (1) from the hypoxic ventilatory response of CHF patients with nocturnal Cheyne-Stokes breathing. In our subjects, this delay accounted for
about half the overall lung-to-ear delay, indicating that the time
constants related to the gas exchange process in the lungs and to
mixing effects in the heart and vasculature play a critical role in the
setting of the PB phenomenon.
The effect of O2 administration on respiration in CHF
patients with Cheyne-Stokes respiration has been previously studied mainly during sleep (20, 34). Results from these
investigations clearly show that supplemental O2 reduces
Cheyne-Stokes respiration, reduces the number of apneas, consolidates
sleep, and reduces cyclic O2 desaturations and the
associated sleep hypoxemia. Differently, in our study, O2
was administered to awake patients with nonapneic PB. In this
condition, changes in central ventilatory drive induced by sleep-waking
transitions (17, 23) are avoided, as are marked system
nonlinearities associated with periodic reductions of
PaCO2 below the apneic threshold (27).
Our experimental setting for O2 administration should
therefore be appropriate to test the instability hypothesis according
to the proposed model. Our experiments do show that elevating the mean
level of O2 saturation in the blood and hence reducing loop
gain and increasing O2 stores abolishes PB in almost all
patients. This finding, again, is consistent with the instability
hypothesis. Similar results have been recently reported by Ponikowski
and co-workers (33) in a group of awake CHF patients with
a mixed composition of apneic and nonapneic PB.
In conclusion, PB is a complex phenomenon that appears in different
pathological conditions as well as in healthy subjects under
different physiological states. It is thus conceivable that several,
perhaps concurrent, mechanisms might contribute to its development. One
of the most frequently claimed mechanisms is instability in the
chemical feedback control of ventilation. We tested this hypothesis in
the specific context of awake CHF patients with nonapneic PB. This
allowed a more precise identification of the underlying
pathophysiological mechanisms, because they are not confounded by large
system nonlinearities in ventilatory regulation and sleep-induced
physiological changes. Two major aspects were specifically considered:
the magnitude of the phase shift and related time delay between minute
ventilation and O2 saturation at the ear and the changes
induced in the breathing pattern by O2 administration.
Experimental observations were consistent with stated expectations.
Although these findings do not represent a conclusive proof in favor of
the instability hypothesis, they clearly indicate that a condition of
loss of stability in the chemical feedback control of ventilation, due
to increased circulatory delay and loop gain, might play a determinant
role in the genesis of PB in awake CHF patients. The analysis of
cardiovascular oscillations during PB further supports this concept
(32).
Our data highlight the critical role played by both the gas exchange
process in the lungs and mixing effects in the heart and arterial
vessels in the development of a long lung-to-carotid delay and,
possibly, enhanced loop gain in CHF patients.
| |
APPENDIX |
To estimate TPR, it is convenient to
express it as (see Eq. 3)
|
(A1)
|
where VR is the phase shift of the PB oscillation
around the ventilatory loop due to the cascade effects of mixing
effects in the heart (H) and arteries (V)
and of the peripheral chemoreflex response (PR). We
attributed 4.9 s to 
VR, which is the median time
constant for the dynamics of the ventilatory response to hypoxia found
by Clement et al. in humans by combining data from different shapes of
the hypoxic input (10). The median was preferred to the
mean value due to the marked skewness of results. Conversely, we
attributed 1 s and 2 s to the time constants for the heart (H) and arteries (V), respectively, as
found by Lange et al. (25) using a dye-dilution technique
in catheterized humans.
| |
ACKNOWLEDGEMENTS |
We gratefully thank Dr. A. Prpa for valuable technical assistance.
| |
FOOTNOTES |
Address for reprint requests and other correspondence: G. D. Pinna, Servizio di Bioingegneria, Centro Medico di Montescano, 27040 Montescano (PV), Italy (E-mail:
bioing.montescano{at}fsm.it).
The costs of publication of this
article were defrayed in part by the
payment of page charges. The article
must therefore be hereby marked
"advertisement"
in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
Received 28 March 2000; accepted in final form 20 July 2000.
| |
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ABSTRACT
INTRODUCTION
