Vol. 282, Issue 1, H110-H121, January 2002
Effects of CPAP therapy on cardiovascular
variability in obstructive sleep apnea: a closed-loop
analysis
Vasily
Belozeroff,
Richard B.
Berry,
Catherine S. H.
Sassoon, and
Michael C. K.
Khoo
Biomedical Engineering Department, University of Southern
California, Los Angeles, California 90089; Department of Medicine,
University of Florida, Gainesville, Florida 32610; and Department
Of Medicine, University of California-Irvine/Veterans Affairs
Medical Center, Long Beach, California 90822
 |
ABSTRACT |
To determine the long-term effects
of continuous positive airway pressure (CPAP) therapy on cardiovascular
variability, we measured R-R interval (RR), systolic blood pressure
(SBP) and respiration (
V) in 13 awake, supine patients
with moderate-to-severe obstructive sleep apnea (OSA), before and after
~6 mo of treatment. Using these data, we estimated the
dynamics of the following components of a closed-loop circulatory
control model: 1) the baroreflex component, 2)
the neural coupling of V to RR or respiratory sinus arrhythmia (RSA), 3) the mechanical effects of respiration
(MER) on SBP, and 4) the circulatory dynamics (CID)
component, which is responsible for the feedforward effect of RR
fluctuations on SBP. Baroreflex and RSA gains increased whereas MER and
CID gains decreased in compliant subjects whose average CPAP use was
>3 h/night. In contrast, baroreflex, RSA, and MER gains remained unchanged and CID gain increased in noncompliant subjects. Other summary measures were unchanged in both groups, except for mean RR,
which increased in compliant patients. Closed-loop analysis provides a
simple but sensitive means for quantitatively assessing cardiovascular
control in OSA by using data collected from a single, nonintrusive test procedure.
heart rate variability; blood pressure regulation; sleep-disordered
breathing; baroreflex sensitivity; respiratory sinus arrhythmia; mathematical model; autonomic function
| |
INTRODUCTION |
THERE IS A GROWING
BODY of evidence (35, 44) that suggests a causal
link between obstructive sleep apnea (OSA) and cardiovascular disease.
Although the exact mechanisms that underlie this relationship remain
unresolved, the acute cardiovascular effects of repetitive upper airway
obstruction in sleep are well established. The alternating cycles of
OSA and subsequent arousals with accompanying hyperpnea produce large
fluctuations in intrathoracic pressure and recurring episodes of
hypoxia and hypercapnia. These periodic events lead to dramatic
alterations in hemodynamics and elevations in catecholamine level and
sympathetic neural activity (43, 44). The neural and
humoral consequences of nocturnal apnea carry over into wakefulness in
the daytime (7, 12). Increased sympathetic drive is
believed to be responsible for the elevated heart rate, decreased heart rate variability (HRV) and increased blood pressure variability observed in alert patients with moderate-to-severe OSA (26, 36). The nocturnal application of continuous positive airway pressure (CPAP) over several months has been found to reduce muscle sympathetic nerve activity and plasma catecholamine levels (14, 27, 42) and to increase heart rate variability
(34). Consistent with these changes, autonomic stress
tests also demonstrate improvements in cardiovascular function
(41). Furthermore, daytime blood pressure is lowered
significantly in hypertensive OSA patients after long-term CPAP therapy
(22).
Although the monitoring of autonomic function provides an objective and
noninvasive means of quantifying the effectiveness of long-term CPAP
therapy in patients with OSA, there are practical disadvantages
associated with existing measures. For instance, measurements of muscle
sympathetic nerve activity require considerable technical expertise and
are highly susceptible to artifactual noise introduced by limb
movement. Moreover, microneurography gives only a regionally confined
assessment of sympathetic tone, which can be quantitatively different
in the heart and various parts of the vasculature (20).
The mean ± SD values of heart rate and blood pressure are summary
statistical measures, conveying information that reflects only the net
effect of all the factors that contribute to cardiovascular control,
thus providing little insight into the underlying physiological
mechanisms. Power spectral analysis of HRV and blood pressure
variability offers a promising avenue for investigating the dynamics of
cardiovascular autonomic function (19). However, this type
of analysis is carried out in the frequency domain and provides little
information about the temporal relationships that link dynamic changes
in blood pressure to changes in heart rate. Also, they do not directly take into account the powerful influence of changes in respiration.
In this study, we propose an alternative method for quantifying the
effects of long-term CPAP therapy on cardiovascular variability in OSA.
Our approach takes the form of a closed-loop model of cardiovascular
control, with respiration as an external input. Such a model enables
the characterization of the dynamic interrelationships between various
pairings of the three measured variables: respiration, heart rate, and
arterial blood pressure. Furthermore, the causal structure of the model
allows us to computationally "open the loop" of the closed-loop
system, thereby separating the feedforward from the feedback
components. Spectral analysis does not permit this kind of temporal
delineation. Finally, closed-loop analysis provides a means for
obtaining a comprehensive assessment of the functional mechanisms that
contribute toward HRV and blood pressure variability, using data
measured from a single test procedure.
| |
METHODS |
Subjects.
Thirteen male patients with moderate-to-severe OSA were studied before
(preCPAP) and after (postCPAP) CPAP therapy. The overall duration of
CPAP therapy was 184 ± 15 (SE) days. In each subject, diagnosis
of OSA was confirmed in a prior sleep study (9) using standard polysomnographic instrumentation. Criteria for admission to
the study included an apnea-hypopnea index (AHI) >20/h and the
selection of CPAP as the prescribed therapy. Exclusion criteria included diabetes, significant cardiac arrhythmia, congestive heart
failure, and lung disease. The apnea-hypopnea index during CPAP
application was found to be 3.5 ± 0.8/h in this group of patients. Five subjects were hypertensive. For safety, these subjects continued antihypertensive medication between initial and followup studies. Three patients were on felodopine whereas the other two used
diltiazem. Informed consent was obtained from all subjects. The study
was approved by the Long Beach Veterans Affairs Medical Center Research Committee.
In each of the subjects, the CPAP device (model Aria LX; Respironics;
Pittsburgh, PA) employed contained a memory chip for storing the
duration and pressure level at which the unit was in use. After the
repeat study, compliance information was obtained by downloading the
time at prescribed pressure from the memory chip with the use of
vendor-supplied software (Encore Data Management; Respironics).
Compliance with the prescribed therapy was assessed by evaluation of
the average nightly CPAP use in each subject. Because compliance varied
widely across individuals, we divided the subjects into two groups: the
six compliant subjects (group C) who used CPAP for an
average of >3 h per night, and the seven noncompliant subjects
(group N), whose average nightly CPAP use was <3 h. A
previous study (13) has shown that use of CPAP therapy for
an average of 3.4 h per night over a duration of 4 wk leads to
improved daytime cognitive performance. Hers et al. (15) found that application of CPAP in the first 4 h of sleep resulted in a significant reduction of the severity of OSA over the remainder of
the night, during which treatment was not applied. A recent study
(23) of CPAP compliance in 1,155 OSA patients reported that subjects who used CPAP <2 h per night in the first 3 mo were unlikely to continue with treatment for >1 year. For these reasons, we
felt that the cutoff value of 3 h per night constituted a
reasonable dividing line between the compliant and noncompliant groups.
Table 1 shows the characteristics of
these two groups of subjects. The differences in age, body mass index,
AHI, and prescribed CPAP levels between the two groups were not
statistically significant. Furthermore, there were no
significant changes in body mass index before and after CPAP therapy in
both groups. Application of Fisher's exact test showed that the ratio
of subjects in each group who were hypertensive was not different
between groups. However, although group N used CPAP less,
the total duration of CPAP therapy in these subjects was significantly
longer (P < 0.05). The variability in times between
studies was due primarily to patient accessibility: for example,
subject C5 had to be restudied after only 3 mo due to
impending relocation to another city, whereas subject N4 was studied after ~9 mo because he was temporarily lost to followup.
Experimental procedures and data preprocessing.
Breathing was monitored using calibrated respiratory inductive
plethysmography (Respitrace, Ambulatory Monitoring; Ardsley, NY).
Calibration of the respiratory inductive plethysmograph was performed
against a spirometer with the subject breathing spontaneously in the
supine position. Arterial blood pressure was monitored continuously
using finger arterial plethysmography (Finapres model 2350, Ohmeda;
Boulder, CO). The electrocardiogram (ECG) was measured using a single
bipolar lead and amplified using a bioamplifier (model BMA-831, CWE;
Ardmore, PA).
At the start of each study, the subject lay supine while his ECG, blood
pressure, and spontaneous respiration were monitored for ~5 min. He
was then asked to control his breathing pattern so that it tracked the
respiratory waveform measured in the previous 5 min. Both target and
tracking waveforms were displayed on a computer monitor. This procedure
allowed the subject to become familiarized with the task of tracking
the displayed breathing pattern. Finally, the subject was asked to
control his breathing pattern so that it tracked a waveform with
respiratory durations that varied randomly from breath to breath. The
sequence of randomized breath durations employed in our protocol was
generated from an algorithm that assumed a stationary Poisson noise
process. However, the tidal volumes of the target breath pattern were
selected so that the average minute ventilation could be maintained at
an approximately constant level equal to that deduced from the
subject's previously monitored spontaneous breathing pattern. This
ensured that chemical drive would remain relatively unchanged over the course of the procedure. The purpose of employing a randomized breathing pattern was to improve the accuracy with which the model parameters could be estimated, because such a pattern effectively broadens the bandwidth of the "input" (i.e., respiration)
(17). The entire randomized breathing protocol was
designed to last 5 min. Selection of the 5-min test duration was based
partly on preliminary experiments, which showed that tracking
performance generally deteriorated when longer random breath sequences
were employed. Furthermore, it was important for subsequent analysis to
ensure that stationarity in the heart rate and blood pressure measurements were preserved (39). During each procedure,
the respiratory signal was digitized at 10 Hz while ECG and blood pressure were sampled at 200 Hz; all signals were recorded and stored
in an IBM-compatible computer using custom-designed software based on
the Matlab programming environment (Mathworks; Natick, MA).
To extract an R-R interval (RR) time series from each dataset, the time
locations of the QRS complexes in the ECG tracing were first detected
using a computer algorithm. The results of this procedure were then
reviewed manually and edited when necessary to ensure that no detection
errors were made. Subsequently, the intervals between successive QRS
complexes were computed. Because these spikes occur at irregular
intervals, each sequence of RR was converted into an equivalent
uniformly spaced time-series (sampling rate: 2 Hz) using a resampling
algorithm closely similar to that of Berger et al. (5).
Systolic (SBP) and diastolic (DBP) values were also extracted on a
beat-by-beat basis via computer algorithm from the continuous blood
pressure waveform. The breathing waveform was resampled at 2 Hz so that
each respiratory value would be synchronized with the corresponding
resampled RR, SBP, and DBP values. Each resampled sequence
contained 600 data points (5 min). Before further analyses were
performed, very-low-frequency trends were removed from each dataset by
fitting and subtracting polynomial functions of up to the fifth order.
Modeling and parameter estimation.
A schematic block diagram of the model employed in our analysis is
displayed in Fig. 1. Fluctuations in RR
[RR(t)] are assumed to be produced by two physiological
mechanisms. The first is the baroreflex through which fluctuations in
SBP [SBP(t)] lead to changes in heart rate. The second
mechanism is the direct coupling between respiration
[V(t)] and RR(t), which
accounts largely for what is generally referred to as respiratory sinus
arrhythmia (RSA). It should be noted that fluctuations in heart rate
that occur around the breathing frequency can also be baroreflex
mediated as a result of respiratory-induced changes in arterial blood
pressure. The preceding assumptions are represented mathematically by
the following equation
|
(1)
|
where Trsa and
Tabr are the latencies associated with the RSA
and arterial baroreflex mechanisms, respectively, and
wRR(t) represents the stochastic
component of RR(t) plus any contributions not accounted
for by these two mechanisms. The model is assumed to be linear, and
thus complete characterizations of RSA and baroreflex dynamics are
given by their respective impulse responses. The baroreflex impulse
response [habr(t)], for instance,
quantifies the time course of the change in RR resulting from an abrupt
increase in SBP of 1 mmHg. The RSA impulse response
[hrsa(t)] may be considered as
reflecting the time course of the fluctuation in RR after a very rapid
inspiration and expiration of 1 liter of air. These impulse responses
are assumed to persist for a maximum duration of M sampling
intervals. On the basis of the lengths of our datasets and preliminary
analyses, we found 90 to be a suitable choice for M.
View larger version (12K):
[in this window]
[in a new window]
|
Fig. 1.
Schematic block diagram of the closed-loop model of circulatory
control. V(t), fluctuation in respiration
coupling; hrsa(t), respiratory sinus
arrhythmia (RSA) impulse response;
wRR(t), stochastic component of R-R
intervals (RR); RR(t), fluctuations in RR;
hcid(t), impulse response in
circulatory dynamics; habr(t),
baroreflex impulse response; SBP(t), fluctuations in
stochastic blood pressure; wSBP(t),
stochastic influences on SBP; and
hmer(t), response of mechanical
effects on respiration.
|
|
A portion of SBP(t) is assumed to be produced by changes
in intrathoracic pressure resulting from respiration; we will refer to
this mechanism as the mechanical effect of respiration (MER). Fluctuations in heart rate may be expected to produce changes in SBP
through variations in cardiac output as a consequence of the
Frank-Starling mechanism and windkessel runoff (2, 11). We
have labeled the totality of these effects circulatory dynamics (CID).
These model assumptions take the following mathematical formulation
|
(2)
|
where Tcid is the latency associated with
CID, and wSBP(t) represents
stochastic and other influences on SBP not explained by the model.
Details of the estimation procedure are given in the
APPENDIX.
Statistical analysis.
To facilitate the statistical comparison of the estimated impulse
responses between and within subjects, we derived scalar descriptors
representing the properties related to gain and time course of each
response. There were several descriptors. First, impulse response
magnitude (IRM) was computed as the difference between the maximum and
minimum values of the estimated impulse response. Second, dynamic gain
(DG) was computed by first taking the fast Fourier transform of the
estimated impulse response to obtain the corresponding transfer
function and calculating the average of the transfer function gains
between 0.04 and 0.45 Hz. This range covers the span of frequencies
pertinent to heart rate and blood pressure variability. Third,
characteristic time (
c) provided a measure of
the latency after which the bulk of the impulse response occurs and was
defined as
|
(3)
|
The summary cardiovascular measures that were extracted from the
data and subjected to statistical analysis were mean RR, RR variability
(i.e., standard deviation of RR about the mean), mean SBP, SBP
variability (i.e., standard deviation of SBP), mean DBP, and DBP
variability (i.e., standard deviation of DBP). In addition, two
measures of baroreflex sensitivity (BRS), based on the spontaneous
variability of SBP and RR, were computed for comparison with the
baroreflex gain estimated from the model. The first,
BRSseq, was assessed using the sequence method. Here, the
ratios between short (3-4 beats) increases/decreases in SBP and
corresponding or subsequent increases/decreases in RR were computed and
averaged (30, 31). The second, BRS
, was computed from the power spectra of SBP and RR in the following manner
(30)
|
(4)
|
where PRR and PSBP
represent the spectral powers of RR and SBP, respectively, in the
low-frequency (0.04-0.15 Hz) and high-frequency (0.15-0.45
Hz) bands.
Before statistical testing, each of the aforementioned descriptors was
tested for normality. If the normality assumption was not satisfied,
log transformation was performed. Statistical analysis consisted of
two-way repeated-measures analysis of variance, with the repeated
factor being treatment condition (preCPAP vs. postCPAP) and the other
factor being subject group (C vs. N). Because the subject groups were small and there was significant variability in CPAP
use across individuals, we also applied correlation analysis to the
pooled data from both groups. Here the Pearson correlation coefficient
(r) between average nightly CPAP use and each model parameter or summary cardiovascular measure was computed. The estimated
parameters for the baroreflex model component were also tested for
correlation with BRSseq and BRS. All
statistical procedures were implemented using SigmaStat for Windows
software (SPSS; Chicago, IL). The level of significance was set at
P = 0.05. Numerical results are expressed as means ± SE, unless otherwise stated.
Goodness-of-fit between the model predictions and measurements was
assessed by computing multiple coherence functions (4) for
RR variability and SBP variability, respectively. A multiple coherence
value of unity at all frequencies indicates perfect replication of the
measured output by the model, whereas a value close to zero would mean
that the model has no predictive value. The multiple coherence function
for RR variability was computed in the following way. After estimation
of hrsa(t) and
habr(t), Eq. 1 was used to
predict RR(t). The power spectrum of predicted RR(t) was subsequently calculated and then divided by the
power spectrum of the measured RR(t) on a
frequency-by-frequency basis. The multiple coherence function for SBP
variability was computed in a similar fashion, except that Eq. 2 was used to predict SBP(t).
| |
RESULTS |
Time series.
A representative set of resampled time series of
V(t), RR(t), and
SBP(t) measured from one of the subjects during the
randomized breathing protocol is shown in Fig.
2. It should be noted from the
V(t) waveform that the larger breaths are
associated with longer breath durations; this design helped in
minimizing the breath-to-breath fluctuations in ventilation, and thus
chemical drive. The immediate effects of respiration on
RR(t) and SBP(t) are quite apparent.
However, the presence of significantly lower frequency fluctuations,
not related to the breathing pattern, is also clearly visible.
View larger version (34K):
[in this window]
[in a new window]
|
Fig. 2.
Representative sample of the resampled signals for respiration
(A), RR (B), and SBP (C) in one
obstructive sleep apnea (OSA) subject during the randomized breathing
protocol.
|
|
Changes in summary cardiovascular descriptors.
The effects of long-term CPAP therapy on mean values of RR, SBP, and
DBP, as well as the corresponding measures of variability, are
summarized in Table 2. Repeated-measures
ANOVA revealed no changes in any of these measures, except for
mean RR, which increased significantly (P < 0.03) in
group C after CPAP therapy. The responses of the individual
subjects are shown in Fig. 3. In
group C, every subject demonstrated an increase in mean RR
(or equivalently, a reduction in heart rate); in contrast, in
group N, three subjects showed increases whereas the other
four displayed a reduction in mean RR. The change in mean RR was
significantly correlated with average nightly CPAP use (Table 2). None
of the other summary cardiovascular measures showed any correlation
with CPAP use.
View larger version (13K):
[in this window]
[in a new window]
|
Fig. 3.
Effect of long-term continuous positive airway pressure
(CPAP) therapy on mean RR in the compliant (group C)
patients and the noncompliant (group N) patients. Solid
circles and error bars represent group means ± SE.
|
|
Group-averaged impulse responses.
The estimated group-averaged impulse responses for model components
(RSA and baroreflex) that mediate RR variability are shown in Fig.
4 (A and C for group
C and B and D for group
N). Comparison of the PreCPAP and PostCPAP responses
shows that long-term CPAP therapy produced dramatic increases
in the magnitudes of the RSA and baroreflex impulse responses in
group C but not in group N. The estimated
group-averaged impulse responses for the model components (MER and CID)
responsible for SBP variability are displayed in Fig.
5. CPAP therapy led to reductions in the
MER and CID impulse responses in group C patients. In
group N, the MER impulse response shows little change,
whereas the CID impulse response displays an increase in magnitude in
the followup study.
View larger version (22K):
[in this window]
[in a new window]
|
Fig. 4.
Group-averaged impulse responses for the RSA and
baroreflex model components in group C patients
(A and C) and group N patients
(B and D). Curves with solid circles represent
impulse responses before CPAP therapy, whereas curves with open circles
represent the corresponding postCPAP responses.
|
|
View larger version (24K):
[in this window]
[in a new window]
|
Fig. 5.
Group-averaged impulse responses for model components
mechanical effects in respiration (MER) and circulatory dynamics (CID)
in group C patients (A and C) and
group N patients (B and D). Curves
with solid circles represent impulse responses before CPAP therapy,
whereas curves with open circles represent the corresponding postCPAP
responses.
|
|
Multiple coherence values for RR variability and SBP variability were
>0.5 between 0.15 and 0.25 Hz, demonstrating that the linear
closed-loop model was able to account for >50% of the variance in the
range of frequencies over which respiratory power was highest. This
range largely coincides with the span of frequencies associated with
the estimated impulse responses.
Changes in impulse response descriptors.
Figure 6 displays the CPAP-induced
changes in the individual and group-averaged values of the IRMs for all
four model components. On average, the RSA and baroreflex IRMs
increased almost threefold and MER IRM decreased by ~50% in
group C, whereas there were no changes in the corresponding
descriptors for group N. The group × treatment
interaction was also significant in CID, but in this case, the
group C subjects showed a decrease in IRM with CPAP whereas
there was a tendency for the IRM to increase in group N. The
group-averaged results for all three descriptors (IRM, DG, and
c) in each of the model components are summarized in Table 3. The results for DG closely
paralleled those for IRM. On the other hand, there were no changes in
c for all four model components. As well, CPAP treatment
did not produce any differences in any of the estimated model component
delays. Tabr was 0.96 ± 0.17 s
PreCPAP versus 0.85 ± 0.21 s postCPAP, whereas
Trsa was 
0.88 ± 0.07 s PreCPAP
versus 0.87 ± 0.06 s postCPAP.
View larger version (19K):
[in this window]
[in a new window]
|
Fig. 6.
Effect of CPAP therapy on impulse response magnitude
(IRM) of the RSA (A), baroreflex (B), MER
(C), and CID (D) model components.
|
|
The results of the correlation analysis generally supported the
conclusions arrived at through analysis of variance. The gain parameters for the RSA, baroreflex, and CID model components were significantly correlated with average nightly CPAP use (Table 3).
However, none of the descriptors of MER dynamics was significantly correlated with CPAP use.
Effects of CPAP on BRS.
Although there was a tendency for BRSseq to increase with
CPAP therapy in group C (6.66 ± 0.32 preCPAP vs.
7.60 ± 0.62 postCPAP), the difference was not significant.
There was clearly no change in BRSseq in group N
(7.11 ± 0.41 preCPAP vs. 7.17 ± 0.74 postCPAP). On
the other hand, the preCPAP to postCPAP changes in
BRSseq in both groups were significantly correlated
(r = 0.68, P = 0.009) with the
corresponding changes in baroreflex IRM.
BRS increased significantly (P = 0.018)
in group C with CPAP therapy (4.05 ± 1.23 preCPAP vs.
11.98 ± 7.05 postCPAP); in contrast, in group N,
BRS was unchanged (6.15 ± 1.32 preCPAP vs.
5.29 ± 1.55 postCPAP). BRS was also significantly
correlated (r = 0.69, P = 0.008) with
baroreflex IRM.
| |
DISCUSSION |
A key feature of the analysis employed in this study is the
imposition of causality on the model structure. This modeling constraint allows the unique estimation of the dynamic characteristics of the feedforward and feedback components that compose the closed-loop system, thus eliminating the need to "open the loop" with the use
of pharmacological, surgical, or other invasive procedures. Similar
approaches, with variations in model structure, have been employed in
earlier studies (1, 2, 24, 25, 28) to investigate the
autonomic control of heart rate and blood pressure. The present study,
however, represents the first application of this model-based approach
to determine the effect of CPAP therapy on circulatory control in
OSA. It is also important to note that a major difference between our
study and previous work lies in the mathematical formulation of the
closed-loop model. In previous studies, a multivariate autoregressive
model structure was assumed; in contrast, the impulse responses of our
model components are constructed using Laguerre basis functions. The
important practical advantage of this computational feature is that it
can produce a substantial reduction in the number of unknown parameters
that need to be estimated, thereby allowing greater statistical
reliability to be achieved in the parameter estimates
(21). Another advantage is that this approach introduces a
certain amount of smoothing in the estimated impulse responses.
However, the use of the Laguerre functions as a "shape factor" can
lead to some bias in the estimates.
Apart from a reduction in mean heart rate, the conventional summary
measures of HRV, mean blood pressure, and blood pressure variability in
patients with OSA did not reveal any chronic effects of CPAP treatment.
On the other hand, our closed-loop analysis showed that adequate
application of long-term CPAP therapy produces substantial alterations
in the major physiological mechanisms that influence HRV and blood
pressure variability. We believe that the greater sensitivity of our
technique is because it quantifies the coupling between any two of the
three measured physiological variables: respiration, heart rate, and
blood pressure. For instance, we found that baroreflex gain increased
roughly threefold in group C subjects after CPAP
therapy; this change acting alone would have led to a substantial
increase in HRV. However, RR variability did not increase significantly
after CPAP (see Table 2). We believe that this is due to the
corresponding decrease in CID gain, which cancelled out much of the
effect of the gain increase around the baroreflex loop. Mukkamala et
al. (24) arrived at a similar conclusion regarding the
enhanced sensitivity of this kind of closed-loop analysis in a
different clinical application. They demonstrated that the differences
in cardiovascular control between control subjects and patients with
diabetic autonomic neuropathy that were undetectable using standard
autonomic tests became identifiable using closed-loop modeling. Mullen
et al. (25) demonstrated the physiological validity of
this closed-loop modeling approach to the extent that was achievable in
normal humans. The authors found here that baroreflex and RSA gains
estimated from their model became essentially zero after combined
parasympathetic and 
-sympathetic pharmacological blockade. O'Leary
et al. (28) have also shown that orthostatic stress
induced by head-up tilt leads to a substantial reduction in baroreflex
gain, as estimated using a similar modeling approach.
Baroreflex gain, as quantified by estimates of IRM and DG for the
baroreflex model component as well as BRSseq and
BRS, was substantially lower PreCPAP in the OSA
patients, compared with the ranges reported for normals in the
literature (30, 32). Our estimates of BRSseq
were similar in range to the values for untreated OSA subjects reported
in previous studies (8, 31). After CPAP therapy,
baroreflex gain increased almost threefold in group C
subjects, although c remained statistically unchanged. In contrast, group N subjects showed little change in
baroreflex gain or time course. The changes in estimated baroreflex IRM
and DG were significantly correlated with the corresponding changes in
baroreflex sensitivity determined independently from the sequence and
power spectral methods. On the other hand, the estimates of BRSseq per se were not statistically different preCPAP
versus postCPAP. A possible explanation for this discrepancy is
that the estimates of BRSseq are more susceptible to error
than IRM or DG of the baroreflex component, because the sequence method does not take into account the confounding influences of respiration on
heart rate and blood pressure. Tkacova et al. (40)
recently reported CPAP-induced increases in BRSseq in eight
OSA patients during sleep; the increase in BRSseq persisted
during the second half of the night even after CPAP was withdrawn.
However, all of the OSA patients studied by Tkacova et al. also had
congestive heart failure, whereas in our study, none of our subjects
had any known cardiovascular disease, except for hypertension in five of the patients. Another important difference is that Tkacova's study
focused on the persisting effects of CPAP during sleep in the few hours
after withdrawal of this therapy; in our study, we studied OSA patients
during wakefulness after several months of nocturnal CPAP treatment.
As mentioned earlier, the RSA model component represents the
autonomically mediated coupling between respiration and heart rate. Our
estimated RSA impulse responses were biphasic in form, showing an
initial decrease in RR (or acceleration of heart rate), followed by a
subsequent RR increase (deceleration of heart rate). This dynamic
behavior is compatible with the corresponding estimates that have been
reported previously (24, 25). A key finding in this study
is that RSA gain in group C subjects increased dramatically after CPAP therapy, whereas the corresponding descriptors were unchanged in group N. Because RSA dynamics are mediated
largely through parasympathetic control, this finding is consistent
with previous reports (17, 34) that acute and chronic
application of CPAP in OSA patients led to increases in parasympathetic
activity. These conclusions are also supported by our finding that mean heart rate was dramatically reduced in the group C subjects
after CPAP therapy but remained unchanged in group N.
The CID model component represents the "feedforward" coupling
(1) between changes in RR and changes in SBP. The dynamic behavior of the estimated CID impulse responses (Fig. 5) may be explained as follows. The immediate effect of an increase in RR is a
decrease in the subsequent DBP; this has been termed the "runoff
effect" (2). On the other hand, because of the increased time for filling, the subsequent stroke volume, and thus pulse pressure
(= SBPDBP), would increase, in accordance with the Frank-Starling law. The net effect could be a decrease or increase in the subsequent SBP, depending on the relative strengths of the runoff and Starling effects. In most of our subjects, the CID impulse response showed a
brief initial (next-beat) increase, indicating the predominance of the
Starling effect in these cases. This was followed subsequently by a
more sustained decrease, reflecting the effect of a reduction in
cardiac output produced by the lowered heart rate. The extent to which
the change in cardiac output translates into a corresponding change in
SBP is determined largely by the peripheral resistance. In group
C subjects, long-term CPAP therapy led to substantial reductions
in CID gain, whereas in group N patients, this parameter tended to increase. Based on our understanding of the mechanisms involved, we believe that these changes in CID dynamics reflect a
decrease in peripheral resistance after CPAP therapy in group C and an increased peripheral resistance in some of the
group N subjects. These conclusions are consistent with
previous work showing that sympathetic activity decreased in OSA
patients only if CPAP therapy was applied for an extended duration and
compliance with treatment was high (23).
The dynamic behavior of the estimated MER model component was also
similar in form to previously reported results (2, 24, 25). Immediately after the start of inspiration, there is an abrupt drop in blood pressure as a consequence of the decreased (i.e.,
more negative) intrathoracic pressure. Subsequently, however, the
decreased intrathoracic pressure during inspiration promotes increased
diastolic filling, which also raises DBP and SBP. During expiration,
intrathoracic pressure becomes less negative, thereby negating the
earlier increase in SBP. The mechanical effect of respiration on SBP
thus depends on the amplitude of the resulting change in amplitude of
intrathoracic pressure. The intrathoracic pressure swing that results
from a given tidal volume, in turn, depends on lung volume and/or lung
compliance. One likely interpretation of our finding of a postCPAP
decrease in MER IRM and DG in group C patients is
that long-term CPAP therapy led to increased resting lung volume and/or
lung compliance, thereby reducing the intrathoracic pressure swing per
unit volume of air inspired. This explanation is not unreasonable
because it has been shown (6) that end-expiratory volume
increases during CPAP and remains elevated after CPAP withdrawal in
patients with congestive heart failure. Another study (39) has shown a reduction in intrathoracic pressure swings during CPAP and
that this reduction persists after CPAP withdrawal, suggesting a
CPAP-induced increase in lung compliance.
One strength of the present study is that compliance with the
prescribed CPAP therapy was measured objectively by means of a built-in
microchip that stored the time at which the CPAP device was used at the
physician-assigned pressure. This contrasts with some previous studies
(27, 34), in which CPAP compliance was either not
disclosed or based on self-reported estimated use. It is well known
that self-reported use of CPAP tends to exceed true use
(18). On the other hand, an important weakness of our study design is the use of the noncompliant patients as the
"control" group, because the subjects who ended up in this group
were not randomly preselected. Clearly, it would have been preferable
from a statistical standpoint to compare the treated patients with a
control group of matched subjects who were not administered any CPAP
therapy over the study duration. On the other hand, there were no
significant differences in age, body mass index, apnea-hypopnea index,
or prescribed CPAP levels between the group C and
group N subjects. Nor were there significant differences
between the subject groups in mean heart rate, mean blood pressures,
HRV, and blood pressure variability or any of the model-based descriptors.
Another limitation of the present study is that the randomized
breathing protocol required subject cooperation and mental concentration. Substantial mental stress has been shown to reduce baroreflex sensitivity (37) and RSA magnitude
(29). On the other hand, Cooke et al. (10)
found no appreciable changes in cardiovascular autonomic function when
their subjects switched from uncontrolled to controlled breathing
protocols. In our study, we attempted to minimize the mental stress
associated with the randomized breathing procedure by allowing the
subjects to perform one or two practice runs before actual data
collection; furthermore, the randomized breathing protocol was limited
to 5 min in duration. If mental effort affected our results, it is
likely that the effect was small or uniformly spread among the subjects
because the differences in estimated model component responses between
groups C and N were clearly substantial. To
explore this issue further, we applied our method of analysis to data
segments recorded before the start of the randomized breathing
protocol, during which the subjects were breathing spontaneously.
Comparison of the estimates of baroreflex and RSA gains computed from
these spontaneous breathing segments to corresponding segments in which
the subjects tracked the randomized pattern showed no significant
differences. For instance, the mean changes in baroreflex IRM from
spontaneous breathing to randomized breathing were indistinguishable
from zero: 0.43 ± 0.36 ms/mmHg (P = 0.26) preCPAP
and 0.26 ± 0.71 ms/mmHg (P = 0.72) postCPAP. The
corresponding mean changes in RSA IRM from spontaneous breathing to
randomized breathing were also not significantly different from zero:
27.2 ± 20.1 ms/l (P = 0.20) preCPAP and
6.6 ± 26.9 ms/l (P = 0.81) postCPAP. However,
in making these comparisons, one should keep in mind that the model
estimates obtained during spontaneous breathing were associated with
larger estimation errors, due to the narrow-band frequency spectrum of
the respiratory input (3).
A further weakness in our study design is that we did not monitor
end-tidal PCO2. It is possible that arterial
blood gases and thus chemoreflex drive may have been altered during the
randomized breathing protocol. However, computation of the average
minute ventilation (during randomized breathing) showed that it
remained unchanged in each subject between the preCPAP and postCPAP
studies. In group C subjects, ventilation was 6.3 ± 0.5 l/min preCPAP versus 7.4 ± 0.7 l/min postCPAP; in group
N, the corresponding values were 7.2 ± 0.9 l/min preCPAP
versus 7.2 ± 0.8 l/min postCPAP. Thus it is highly unlikely that
differences in chemoreflex drive were an important contributor to the
differences in autonomic function detected by our model.
In conclusion, our proposed model-based approach represents a
relatively nonintrusive means of assessing the multiple facets of
autonomic control of heart and blood pressure in OSA patients from a
single test procedure. Our findings indicate that long-term CPAP
therapy can lead to a substantial elevation of baroreflex sensitivity
and RSA gain in OSA patients. In addition to improvements in the
autonomic reflexes, CPAP therapy also appears to alter nonneural
mechanisms such as the mechanical effects of respiration on arterial
blood pressure and the feedforward effect of fluctuations in heart rate
on fluctuations in blood pressure, but the physiological bases of these
effects remain unclear. However, improvements in both the autonomically
mediated and nonneural mechanisms of circulatory control depend
strongly only whether there is adequate compliance with the prescribed treatment.
| |
APPENDIX |
Estimation of model impulse responses.
Each of the unknown impulse responses were expanded as the sum of
several weighted Laguerre basis functions (21). For
instance, in the case of the baroreflex and RSA model components
|
(A1)
|
|
(A2)
|
where the Lj(t) represents the
jth-order discrete-time orthonormal Laguerre function, and
c
and
c
are the corresponding
unknown weights that are assigned to
Lj(t) in the baroreflex and RSA
impulse responses, respectively.
Lj(t) is defined as follows over the
interval 0 
t M1
|
(A3)
|
and
|
(A4)
|
In Eqs. A3 and A4, the parameter 
(0 < < 1) determines the rate of exponential decline of
the Laguerre functions and is selected such that, for given
M, qrsa, and
qabr, the values of the constructed impulse
response become insignificant as t approaches M.
Substituting Eqs. A1 and A2 into Eq. 1, we obtain, after some algebraic manipulation
|
(A5)
|
where uj(t) and
vj(t) are new derived variables,
defined as follows
|
(A6)
|
|
(A7)
|
Equation A5 becomes the new linear relation with
unknown parameters c(0 j qabr) and
c (0 j qrsa) that can be
estimated using least-squares minimization. However, note that
Eq. A5 contains far fewer unknown parameters (qrsa + qabr 
2M) than Eq. 1. A similar approach was applied to
Eq. 2.
The least-squares minimization procedure described above was repeated
for a range of values for the delays (Trsa,
Tabr, and Tcid) and
Laguerre function orders (qabr,
qrsa, qcid, and
qmer). For each combination of delays and
Laguerre function orders, a metric of the quality of fit, known as the
minimum description length (MDL), was computed (33). MDL
was computed as
|
(A8)
|
where JR is the variance of the residual
errors between the measured data and the predicted output. Note that
MDL decreases as JR decreases but increases with
increasing model order. Selection of the "optimal" candidate model
was based on a global search for the minimum MDL; in addition, this
optimal solution had to satisfy the condition that the
cross-correlations between the residual errors and past values of the
two inputs [V(t) and SBP(t) in
the case of Eq. 1, and V(t) and
RR(t) in Eq. 2] had to be not significantly
different from zero. Once the optimal parameter values were determined,
the impulse responses of the four model components were computed by
using Eqs. A1, A2, and the analogous equations
for MER and CID. qabr,
qrsa, qcid, and
qmer each ranged from 6 to 8.
Because a closed-loop structure was inherent in the model, it was
necessary to impose causality constraints in an explicit fashion during
the parameter estimation procedure. In the estimation of baroreflex
dynamics, a minimum value of 0.5 s (i.e., 1 sampling interval) was
assumed for Tabr, reflecting the fact that
latencies are present in the baroreception process. In the case of the
CID component, we assumed Tcid = 1 s
to ensure that a change in the current RR can affect pulse pressure,
and thus SBP, only in the following beat (Starling effect). Previous
reports (24, 25) have demonstrated an apparent noncausal
relationship between V(t) and
RR(t), in which changes in heart rate precede changes in lung volume. A reasonable explanation for this observation is that,
although there is simultaneous neural modulation of heart rate and the
drive to breathe, mechanical inspiration takes effect later. Thus we
allowed Trsa to assume negative values. Finally, for MER dynamics, we allowed for the possibility that the mechanical effect of respiration on blood pressure could be virtually
instantaneous; hence, no delay was assumed in this case.
| |
ACKNOWLEDGEMENTS |
We thank Edwin Valladares for technical assistance.
| |
FOOTNOTES |
This study was supported by National Institutes of Health Grants
HL-58725 and RR-01861.
Address for reprint requests and other correspondence:
M. C. K. Khoo, Biomedical Engineering Dept., Univ. of
Southern California, OHE-500, University Park, CA 90089-1451 (E-mail:
khoo{at}bmsrs.usc.edu).
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 26 April 2001; accepted in final form 11 September 2001.
| |
REFERENCES |
1.
Barbieri, R,
Parati G,
and
Saul JP.
Closed-versus open-loop assessment of heart rate baroreflex.
IEEE Eng Med Biol Mag
20:
33-42,
2001[ISI][Medline].
2.
Baselli, G,
Cerutti S,
Civardi S,
Malliani A,
and
Pagani M.
Cardiovascular variability signals: towards the identification of a closed-loop model of the neural control mechanisms.
IEEE Trans Biomed Eng
35:
1033-1045,
1988[ISI][Medline].
3.
Belozeroff, V.
A Model of Cardiorespiratory Autoregulation in Obstructive Sleep Apnea Syndrome (PhD thesis). Los Angeles, CA: Univ. of Southern California, 2001.
4.
Bendat, JS,
and
Piersol AG.
Engineering Applications of Correlation and Spectral Analysis. New York: Wiley, 1980, p. 195-197.
5.
Berger, RD,
Akselrod S,
Gordon D,
and
Cohen RJ.
An efficient algorithm for spectral analysis of heart rate variability.
IEEE Trans Biomed Eng
33:
900-904,
1986[ISI][Medline].
6.
Butler, GC,
Naughton MT,
Rahman MA,
Bradley TD,
and
Floras JS.
Continuous positive airway pressure increases heart rate variability in congestive heart failure.
J Am Coll Cardiol
25:
672-679,
1995[Abstract].
7.
Carlson, JT,
Hedner J,
Elam M,
Ejnell H,
Sellgren J,
and
Wallin BG.
Augmented resting sympathetic activity in awake patients with obstructive sleep apnea.
Chest
103:
1763-1768,
1993[Abstract/Free Full Text].
8.
Carlson, JT,
Hedner JA,
Sellgren J,
Elam M,
and
Wallin G.
Depressed baroreflex sensitivity in patients with OSA.
Am J Respir Crit Care Med
154:
1490-1496,
1996[Abstract].
9.
Carskadon, MA,
and
Rechtshaffen A.
Montoring and staging human sleep.
In: Principles and Practice of Sleep Medicine, edited by Kryger MH,
Roth T,
and Dement WC.. Philadelphia, PA: Saunders, 1989, p. 665-683.
10.
Cooke, WH,
Cox JF,
Diedrich AM,
Taylor JA,
Beightol LA,
Ames JEIV,
Hoag JB,
Seidel H,
and
Eckberg DL.
Controlled breathing protocols probe human autonomic cardiovascular rhythms.
Am J Physiol Heart Circ Physiol
274:
H709-H718,
1998[Abstract/Free Full Text].
11.
DeBoer, RW,
Karemaker JM,
and
Strackee J.
Hemodynamic fluctuations and baroreflex sensitivity in humans: a beat-to-beat model.
Am J Physiol Heart Circ Physiol
253:
H680-H689,
1987[Abstract/Free Full Text].
12.
Dimsdale, JE,
Coy T,
Ziegler MG,
Ancoli-Israel S,
and
Clausen J.
The effect of sleep apnea on plasma and urinary catecholamines.
Sleep
18:
377-381,
1995[ISI][Medline].
13.
Engleman, HM,
Martin SE,
Deary IJ,
and
Douglas NJ.
Effect of continuous positive airway pressure treatment on daytime function in sleep apnoea/hypopnea syndrome.
Lancet
343:
572-575,
1994[ISI][Medline].
14.
Hedner, J,
Darpo B,
Ejnell H,
Carlson J,
and
Caidahl K.
Reduction in sympathetic activity after long-term CPAP treatment in sleep apnoea: cardiovascular implications.
Eur Respir J
8:
222-229,
1995[Abstract].
15.
Hers, V,
Liistro G,
Dury M,
Collard P,
Aubert G,
and
Rodenstein DO.
Residual effect of CPAP applied for part of the night in patients with obstructive sleep apnea.
Eur Respir J
10:
973-976,
1997[Abstract].
16.
Khoo, MCK,
Kim TS,
and
Berry RB.
Spectral indices of cardiac autonomic function in obstructive sleep apnea.
Sleep
22:
443-451,
1999[ISI][Medline].
17.
Kim, TS,
and
Khoo MCK
Estimation of cardiorespiratory transfer under spontaneous breathing conditions: a theoretical study.
Am J Physiol Heart Circ Physiol
273:
H1012-H1023,
1997[Abstract/Free Full Text].
18.
Kribbs, NB,
Kline LR,
Pack AI,
Smith PL,
Swartz AR,
Schubert NM,
Redline S,
Getsy JE,
Henry JN,
and
Dinges DF.
Objective measurements of nasal CPAP treatment for obstructive sleep apnea: patterns of use and comparison to patient reports.
Am Rev Respir Dis
147:
887-895,
1993[ISI][Medline].
19.
Malliani, A,
Pagani M,
Lombardi F,
and
Cerutti S.
Cardiovascular neural regulation explored in the frequency domain.
Circulation
84:
482-492,
1991[Abstract/Free Full Text].
20.
Mancia, G,
Grassi G,
Daffonchio A,
and
Parati G.
Evaluating sympathetic activity in human hypertension.
J Hypertens
11 Suppl:
S13-S19,
1993[Medline].
21.
Marmarelis, VZ.
Identification of nonlinear biological systems using Laguerre expansion of kernels.
Ann Biomed Eng
21:
573-589,
1993[ISI][Medline].
22.
Mayer, J,
Becher H,
Brandengurg U,
Penzel T,
Peter JH,
and
von Wichert P.
Blood pressure and sleep apnea: results of long-term nasal continuous positive airway pressure therapy.
Cardiology
79:
84-92,
1991[ISI][Medline].
23.
McArdle, N,
Devereux G,
Heidarnejad H,
Engleman HM,
MacKay TW,
and
Douglas NJ.
Long-term use of CPAP therapy for sleep apnea/hypopnea syndrome.
Am J Respir Crit Care Med
159:
1108-1114,
1999[Abstract/Free Full Text].
24.
Mukkamala, R,
Mathias JM,
Mullen TJ,
Cohen RJ,
and
Freeman R.
System identification of closed-loop cardiovascular control mechanisms: diabetic autonomic neuropathy.
Am J Physiol Regulatory Integrative Comp Physiol
276:
R905-R912,
1999[Abstract/Free Full Text].
25.
Mullen, TJ,
Appel ML,
Mukkamala R,
Mathias JM,
and
Cohen RJ.
System identification of closed-loop cardiovascular control: effects of posture and autonomic blockade.
Am J Physiol Heart Circ Physiol
272:
H448-H461,
1997[Abstract/Free Full Text].
26.
Narkiewicz, K,
Montano N,
Cogliati C,
van de Borne PJH,
Dyken ME,
and
Somers VK.
Altered cardiovascular variability in obstructive sleep apnea.
Circulation
98:
1071-1077,
1998[Abstract/Free Full Text].
27.
Narkiewicz, K,
Masahiko K,
Phillips BG,
Pesek CA,
Davison DE,
and
Somers VK.
Nocturnal continuous positive airway pressure decreases daytime sympathetic traffic in obstructive sleep apnea.
Circulation
100:
2332-2335,
1999[Abstract/Free Full Text].
28.
O'Leary, DD,
Lin DC,
and
Hughson RL.
Determination of baroreflex gain using auto-regressive moving-average analysis during spontaneous breathing.
Clin Physiol
5:
369-377,
1999.
29.
Patwardhan, AR,
Vallurupalli S,
Evans JM,
Bruce EN,
and
Knapp CF.
Override of spontaneous respiratory pattern generator reduces cardiovascular parasympathetic influence.
J Appl Physiol
79:
1048-1054,
1995[Abstract/Free Full Text].
30.
Parati, G,
Di Rienzo M,
and
Mancia G.
How to measure baroreflex sensitivity: from the cardiovascular laboratory to daily life.
J Hypertens
18:
7-19,
2000[ISI][Medline].
31.
Parati, G,
Di Rienzo M,
Bonsignore MR,
Insalaco G,
Marrone O,
Castiglioni P,
Bonsignore G,
and
Mancia G.
Autonomic cardiac regulation in obstructive sleep apnea syndrome: evidence from spontaneous baroreflex analysis during sleep.
J Hypertens
15:
1621-1626,
1997[ISI][Medline].
32.
Patton, DJ,
Triedman JK,
Perrott MH,
Vidian AA,
and
Saul JP.
Baroreflex gain: characterization using autoregressive moving average analysis.
Am J Physiol Heart Circ Physiol
270:
H1240-H1249,
1996[Abstract/Free Full Text].
33.
Rissanen, J.
Estimation of structure by minimum description length.
Circ Syst Sig Process
1:
395-406,
1982.
34.
Roche, F,
Court-Fortune I,
Pichot V,
Duverney D,
Costes F,
Emonot A,
Vergnon JM,
Geyssant A,
Lacour JR,
and
Barthelemy JC.
Reduced cardiac sympathetic autonomic tone after long-term nasal continuous positive airway pressure in obstructive sleep apnoea syndrome.
Clin Physiol
19:
127-134,
1999[ISI][Medline].
35.
Roux, F,
D'Amrosio C,
and
Mohsenin V.
Sleep-related breathing disorders and cardiovascular disease.
Am J Med
108:
396-402,
2000[ISI][Medline].
36.
Somers, VK,
Dyken ME,
Clary MP,
and
Abboud FM.
Sympathetic neural mechanisms in obstructive sleep apnea.
J Clin Invest
96:
1897-1904,
1995.
37.
Steptoe, A,
and
Sawada Y.
Assessment of baroreflex function during mental stress and relaxation.
Psychophysiology
26:
140-147,
1989[ISI][Medline].
38.
Task Force of the European Society of Cardiology and the North American Society of Pacing and Electrophysiology.
Heart rate variability: standards of measurement, physiological interpretation and clinical use.
Circulation
93:
1043-1065,
1996[Free Full Text].
39.
Tkacova, R,
Rankin F,
Fitzgerald F,
Floras JS,
and
Bradley TD.
Effects of continuous positive airway pressure on obstructive sleep apnea and left ventricular afterload in patients with heart failure.
Circulation
98:
2269-2275,
1998[Abstract/Free Full Text].
40.
Tkacova, R,
Dajani HR,
Rankin F,
Fitzgerald FS,
Floras JS,
and
Bradley TD.
Continuous positive airway pressure improves nocturnal baroreflex sensitivity of patients with heart failure and obstructive sleep apnea.
J Hypertens
18:
1257-1262,
2000[ISI][Medline].
41.
Veale, D,
Pepin JL,
Wuyam B,
and
Levy PA.
Abnormal autonomic stress responses in obstructive sleep apnoea are reversed by nasal continuous positive airway pressure.
Eur Respir J
9:
2122-2126,
1996
TOP
ABSTRACT
INTRODUCTION
