Vol. 283, Issue 1, H434-H439, July 2002
Evidence for fractal correlation properties in variations of
peripheral arterial tone during REM sleep
I.
Dvir1,
Y.
Adler2,
D.
Freimark2, and
P.
Lavie3
1 Itamar Medical Limited, Caesarea 38900;
2 Cardiac Institute, Heart Failure Clinic, and
Cardiac Rehabilitation Institute, Sheba Medical Center,
Tel-Hashomer, Tel Aviv University, Tel Aviv 52620; and
3 Sleep Laboratory, Faculty of Medicine,
Technion-Israel Institute of Technology, Haifa 32000, Israel
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ABSTRACT |
Previous studies utilizing detrended
fluctuation analysis (DFA) of heart rate variability during sleep
revealed a higher fractal exponent during rapid eye movement (REM)
sleep than non-REM sleep. The aim of this study was to determine
whether the same difference exists in the variations of peripheral
arterial tone (PAT). Finger pulse wave measured by a novel
plethysmographic technique was monitored during sleep in 12 chronic
heart failure patients, 8 heavy snorers, and 12 healthy volunteers. For
each subject, at least two 15-min time series were constructed from the
interpulse intervals and from pulse wave amplitudes during REM and
non-REM sleep. Fractal scaling exponents of both types of time series were significantly higher for REM than non-REM sleep in all groups. In
each of the groups and in both sleep stages, the fractal scaling exponents based on pulse wave amplitude were significantly higher than
those based on pulse rate variability. A repeat of the analysis for
short-, intermediate-, and long-term intervals revealed that the
fractallike exponents were evident only in the short- and intermediate-term intervals. Because PAT is a surrogate of sympathetic activation, our results indicate that variations in sympathetic activation during REM sleep have a fractallike behavior.
detrended fluctuation analysis; congestive heart failure; heavy
snoring
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INTRODUCTION |
DETRENDED FLUCTUATION
ANALYSIS (DFA) has been used extensively for extracting
hidden information from physiological time series, particularly from
heart rate variability data (5-7). This has been
successfully used in sleep. The fractal exponent of the
electrocardiogram-derived RR interval variability during rapid eye
movement (REM) sleep, or dream sleep, was shown to be very similar to
that during wakefulness, whereas it declined significantly during
non-REM sleep (4, 17). Heart rate variability, however, is
under the simultaneous control of both the sympathetic and
parasympathetic branches of the autonomic nervous system. Therefore, it
is not possible to determine whether the fractal correlation properties
of heart rate variability reflect a unique interaction between the two branches of the autonomic regulating mechanisms or whether fractal correlations characterize the activity of only one of the branches. REM
sleep is associated with augmented sympathetic activation relative to
non-REM sleep, as determined by spectral analysis of heart rate
variability (2, 3, 13) and by muscle sympathetic nerve
recordings (16). Using a newly developed plethysmographic technique to measure peripheral arterial tone (PAT), we demonstrated that the PAT signal can be used as a sensitive surrogate of sympathetic activation during sleep. Transient attenuation of the PAT signal, indicating vasoconstriction, or increased sympathetic activation, accompanied apneas, hypopneas, and periodic leg movements during sleep
(10, 15), and tonic attenuation accompanied REM sleep (9). Furthermore, transient deeper attenuation events
associated with bursts of rapid eye movements, termed phasic REM
events, were superimposed on the tonic PAT attenuation
(11).
In the present study we applied DFA to the PAT signal during REM sleep
and sleep stage 3-4 (non-REM) sleep, and we demonstrate for the
first time fractal correlation properties in PAT during REM sleep. We
also show that the magnitude of the fractal exponent based on the PAT
amplitude was higher than that based on pulse rate variability.
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STUDY DESIGN |
Subjects.
Thirty-two subjects participated in this study (see Table
1 for selected demographic, clinical, and
sleep data). Twelve chronic heart failure patients [CHF group; 9 men,
3 women; age 60.9 ± 11.9 yr, body mass index (BMI) 25.9 ± 4.6 kg/m2, 4 current smokers] with New York Heart
Association score stage 3-4. Their mean ejection fraction was
22.36 ± 4.63%. Five patients had Cheyne-Stokes respiration
during sleep. The mean respiratory disturbance index (RDI, defined as
total number of central apneas plus hypopneas divided by hours of
sleep) was 34.6 ± 21.9. Periodic breathing was associated with
periodic oscillations in arterial oxygen saturation
(SaO2). The mean saturation nadir was 85.5 ± 6.5%. All medications [long-acting nitrates (7),
-blockers (7), angiotensin-converting enzyme inhibitors
(12), benzodiazepines (2)] were continued
during the study, but none of the patients used 
-blocking
medications, which could affect PAT. The second group comprised
eight adults (SN group; 3 men, 5 women; age 48.9 ± 9.9 yr, BMI
27.5 ± 5.3 kg/m2, 3 current smokers) who were
referred to the Technion Sleep Laboratory because of suspected sleep
apnea and were found to have only heavy snoring (mean RDI 4 ± 3.25; none had a meaningful decrease in oxygen saturation). The third
group comprised 12 healthy volunteers without any sleep disorders (Norm
group; 9 men, 3 women; age 25.6 ± 10.9 yr, BMI 21.9 ± 2.7 kg/m2, 1 current smoker, RDI 7.6 ± 5.4; none had any
meaningful decrease in oxygen saturation). All participants were
recorded in the sleep laboratory for either one or two nights. Wherever
two nights were available, data from the second night were analyzed.
All participants gave signed informed consent before being enrolled in
the study, which was approved by the Institutional Human Subjects
Review Committee.
Method.
Polysomnographic recordings included electrooculography,
electrocardiography, submental electromyography, electroencephalography (EEG, C3-A2), respiratory abdominal motion (respiratory
belt), air flow (orobuccal thermistors), SaO2 (finger
oximetry), body movements, and breathing sound intensity. All
were recorded into computer memory after amplification and signal
conditioning via a multichannel polygraph (EEG 4214; Nihon Kohden,
Kogyo, Tokyo, Japan). Studies were performed from about 10-11 PM
to 6 AM the following day. The polysomnographic signals were scored
from the computer screen according to standard practice. The PAT signal was sampled at 128 Hz and digitized with the SITE PAT-200 (Itamar Medical, Cesarea, Israel). The data were automatically analyzed off-line as described below. First, polysomnographic data were conventionally scored for sleep stages (1, 2, 3-4, and REM) based on 30-s epochs. A 15-min sliding window with 1-min increments was then
applied to the data, and the percentage of sleep stages was determined
in each of the 15-min windows. Only windows containing 15 min of either
REM or sleep stage 3-4 were selected for further analysis. In each
window PAT pulses were digitally detected, artifacts and noise sections
were removed (but not premature beats), and time series were
constructed by concatenation of artifact-free PAT pulse sections
1) from the pulse period (difference of 2 locations of
adjacent maxima) and 2) from the upstroke amplitude (the
difference of maximum and its preceding minimum). Each subject could
have multiple windows of either REM or stage 3-4 because of the
1-min increments of the sliding window. Windows containing at least 7.5 min (50%) of valid PAT pulses were included in the analysis. DFA
(14) was performed on each of the time series
(amplitude/pulse period) and averaged across all available REM and
stage 3-4 windows. The average percentage of PAT pulses in each
window that was included in the analysis was 94.9% ± 7.3% (minimum
65%). The total number of windows was 1,375: 557 for REM and 818 for
stage 3-4.
The DFA method is briefly described here. First, the original time
series was integrated, and then detrending was performed locally, that
is, the time series was subdivided into windows of equal length and, in
each window, the local trend was subtracted. Standard deviations of the
integrated and detrended time series were computed for windows of the
same length, and the mean of the standard deviations of all windows of
the same size (n) was computed. The above process was
repeated over an increasing window size. The outcome of the DFA
analysis was the fractal exponent , which represents the slope, on a
log-log scale, of a line fitted to the mean standard deviations vs. the
window sizes across the relevant range of scales (Fig.
1). Because previous results of DFA
applied to interbeat interval sleep data indicated that the fitted DFA
plot was not strictly linear (4) but consisted of at least
two regions with different slopes (crossover phenomenon), we calculated
the scaling exponent for three different regions: a short-term
interval time series over periods of 4-10 pulses (1), an
intermediate-term interval from 10 to 100 pulses (2), and the
long-term interval from 100 to 25% of the total number of PAT pulses
in a window (~250; 3). We also calculated the fractal exponent
based on the entire range of 4-25% of the total number of pulses.
Thus eight fractal exponents were calculated for each 15-min window,
four based on the time series constructed from the pulse rate
variability and four from the pulse amplitude variability. Each of the
exponents was averaged across all available 15-min windows for each
subject, for REM and stage 3-4 separately, to provide the final
individual outcome measures.
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Fig. 1.
Detrended fluctuation analysis (DFA) of pulse amplitude
and pulse period variability of rapid eye movement (REM) and sleep
stage 3-4 (non-REM) time series for a representative normal
volunteer. Left: 900 s of the peripheral arterial tone
(PAT) raw signal during the 2 stages of sleep and the corresponding PAT
amplitudes and interpulse intervals. Right: results of the
fractal scaling analysis for the pulse interval and pulse amplitude
time series. Note that in both cases the scaling exponent was higher in
REM sleep and that the pulse amplitude exponents were higher than the
pulse interval exponents in both sleep stages. PR, pulse
rate.
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Statistical analysis.
Differences between the groups were assessed by analysis of variance
followed by Duncan's multiple-range test for parametric variables and
by Kruskal-Wallace test for nonparametric variables. The fractal
exponents are presented as means ± SD. Because fractal exponents
were normally distributed, analysis of covariance, followed by planned
post hoc comparisons, was used to compare between the fractal exponents
of REM and stage 3-4 and among the three groups. The fractal
exponents based on the pulse amplitude (pulsea) and pulse rate
(pulsev) variability were compared with t-tests. Pearson product-moment correlations were used to determine the relationship between the fractal exponents and age and BMI. Univariate analysis was
followed by multiple stepwise regression analysis to predict (pulsev) and (pulsea) with sleep stage, group, age, gender, BMI,
smoking, rates of hypertension and diabetes, and RDI as predictors. Logistic regression analysis, followed by calculation of the
receiver-operating characteristic (ROC), was used to determine whether
the fractal exponents could differentiate between the REM and stage
3-4 windows across all three groups. This was done separately for
(pulsev) and (pulsea), as well as for both exponents combined.
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RESULTS |
There was no statistically significant difference in gender among
the three groups (
2 = 3.74, P < 0.16). However, there was a statistically significant difference in age
among the three groups, with the CHF group being older than the SN
group, who were older than the Norm group (F = 31.33, P < 0.0001). In addition, there was a statistically
significant difference in BMI (F = 4.89, P < 0.02). Post hoc Duncan's multiple-range test
revealed that the Norm group was statistically significantly less obese
than the other two groups. The CHF group had a higher prevalence of
hypertension (2 = 14.93, P < 0.0006) than the other two groups and a higher prevalence of diabetes
than the Norm group (2 = 9.88, P < 0.002). The three groups differed in the percentage of smokers
(2 = 6.59, P < 0.04) but not in
the number of packs smoked per year. Post hoc testing revealed that the
SN group had a larger percentage of smokers than the Norm group
(2 = 6.71, P < 0.02). There was a
borderline statistically significant difference in minimum oxygen
saturation among the three groups (Kruskal-Wallace test
2 = 5.34, P < 0.07).
Figure 1 depicts a representative example of the REM and stage 3-4
time series constructed from the interpulse intervals and PAT signal
amplitudes and the outcome of DFA for a normal volunteer. Both
(pulsev) and (pulsea), which were based on the entire range, significantly increased in REM relative to stage 3-4 sleep (Table 2). It is also evident from Fig. 1 that
there was a crossover point in the DFA plots at ~100 pulses, for both
sleep stages, particularly in those based on pulse amplitudes, at which
the fractal exponents became smaller. Table
3 presents the REM and stage 3-4
fractal exponents for the three groups determined separately for the
short-, intermediate- and long-term intervals. In almost all of
the cases, both (pulsea) and (pulsev) were significantly higher
in REM than in stage 3-4 sleep. In only a few cases were t-test results insignificant or bordering on statistical
significance. Of note, both in REM and stage 3-4 sleep,
1(pulsea) was either slightly greater than 1.0 or very close to 1.0, indicating the existence of self-similar fluctuations over this range
of time scales in PAT amplitude variability in both stages of sleep.
The fractal exponents for the intermediate-term interval were close to
1.0 only during REM sleep, whereas for the long-term interval time
series fractal exponents were much smaller than 1.0 in both sleep
stages, which indicates the loss of fractallike behavior in intervals
longer than 100 pulses.
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Table 3.
Mean (pulsea) and (pulsev) time series for REM and sleep stage
3-4 for short, intermediate, and long-term time series
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In view of the consistency of the differences between REM and stage
3-4 sleep across the three regions, we used the -exponent based
on the entire region to compare the three groups as well as the two
methods of calculating the exponents, i.e., interpulse variability vs.
interamplitude variability. Because the groups significantly differed
from each other with respect to age, BMI, smoking, and the rates of
hypertension and diabetes, these variables were used as covariates.
Analysis of covariance revealed significant differences between REM and
stage 3-4 sleep for both (pulsev) (F = 39.45;
P < 0.0001) and (pulsea) (F = 93.0;
P < 0.0001) but no significant difference between the
groups for either variable or any interaction between group and sleep
stage. Across all groups there was a significant correlation between
(pulsea) and age in both REM sleep (0.52; P < 0.002) and stage 3-4 sleep (0.49; P < 0.004). Age
was unrelated to (pulsev), and there was no significant relationship
between gender, BMI, smoking, hypertension, and diabetes and fractal
exponents. The two fractal exponents were only marginally correlated
with each other during stage 3-4 sleep (0.38, P < 0.028) and were unrelated during REM sleep (
0.03, not significant).
Multiple stepwise regression analysis confirmed the univariate
analysis. The fractal exponent based on pulse amplitude variability could be predicted by sleep stage, which accounted for 54.7%
(P < 0.0001) of the total variability, and age, which
accounted for 11.8% (P < 0.0001) of the total
variability; (pulsev) was predicted only by sleep stage, accounting
for 39.4% of the variability.
Comparison of the magnitude of the two fractal exponents revealed that
(pulsea) was significantly higher than (pulsev) in all three
groups and in both sleep stages (each comparison was significant
at at least P < 0.0008). Likewise, using the two
fractal exponents in a logistic regression analysis to differentiate
REM from sleep stage 3-4 time series, we found a better
discrimination when using (pulsea) than (pulsev), as indicated by
a larger area under the ROC curve [95.2% (P = 0.001)
vs. 87.6% (P = 0.005)]. The use of both fractal
exponents in the regression analysis only slightly improved on these
results (96%, P = 0.001).
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DISCUSSION |
Our present results demonstrate that PAT, as measured by the pulse
wave amplitude, shows fractal correlation properties similar to those
reported previously in RR interval variability and, as found in the
present study, also in pulse rate variability. The DFA technique
quantifies the presence or absence of long-term correlations in a time
series. A fractallike signal results in an -value of ~1.
Deviations from a value of 1.0 to either greater or smaller values
indicate the breakdown of the long-term correlations in the data
(14). The finding that the short-term fractal exponents extracted from the variability in the PAT signal amplitude during REM
sleep and stage 3-4 were closer to 1.0 may reflect the powerful modulation of cardiac activity by respiration in both sleep stages. This was evident in all three of the groups, healthy controls, heavy
snorers, and CHF patients. In contrast, in the intermediate-term time
series, fractallike exponents were found only in REM sleep. These
findings confirm and extend the results of Bunde et al. (4) and Togo and Yamamoto (17), who reported
on similar findings for DFA of heart rate variability data. No attempt,
however, was made in those studies to differentiate between the
contribution of short- and long-term regions to the fractal exponents.
Furthermore, in agreement with the results of Bunde et al.
(4), who showed that apneic events during sleep did not
influence the outcome of the DFA, episodes of Cheyne-Stokes breathing
in CHF patients also did not influence our results. Regardless of the
occurrence of disordered breathing during sleep, the magnitude of
fractal exponent was higher by 17.7-29.1% during REM than
during sleep stage 3-4.
A comparison of the fractal exponents among the three groups after
adjustment for confounding variables revealed no significant differences in either fractal exponent. Previously, CHF patients were shown to have deviations from the normal value of ~1.0 in the
fractal exponent of heart rate variability (1). Although CHF patients in our study also showed the highest fractal exponent during REM sleep (1.11 vs. 1.06 and 1.02), this could be accounted for solely by the age difference between the groups. Age was
significantly correlated with the fractal exponent based on pulse wave
amplitude variability and was also found to be a significant predictor
of this fractal exponent by stepwise multiple logistic regression. Previously, short-term fractal exponent of heart rate variability during wakefulness was shown to increase in aged individuals
(18). Of note, during sleep only the exponent based on
pulse amplitude variability was related to age.
In each of the groups and in both sleep stages, the magnitude of the
fractal exponent based on the pulse wave amplitude variability was
significantly higher than the exponent based on the pulse rate
variability. Overall, it was higher by 40% and 32.5% during sleep
stage 3-4 and REM, respectively. The results of the logistic regression analysis also indicated that the fractal exponent based on
the pulse wave amplitude provided a better discrimination than the
exponent based on pulse variability between REM and sleep stage
3-4 time series.
This suggests that the variations in pulse amplitudes behave more as a
fractallike signal than the variations in pulse rate. Unlike heart rate
variability, or its pulse wave surrogate, which reflects the interplay
between sympathetic and vagal influences on the heart, the finger pulse
wave amplitude measured with the PAT device is a sensitive surrogate of
purely sympathetic activation. The peripheral vascular beds located at
the distal parts of the limbs are major sites of sympathetic
vasoconstrictor activity. This is particularly true of the soles of the
feet, the plantar surfaces of the toes, and the palmar surfaces of the
hands and fingers, where there is a high density of arteriovenous
anastomoses and a correspondingly high density of -adrenergic
sympathetic innervation (12). During wakefulness as well,
increased sympathetic activation was shown to be associated with
increasing magnitude of the fractal exponent of heart rate variability
(18, 19). Thus the pattern of sympathetic activation that
modulates the peripheral tone during REM sleep is characterized by
fractal correlation properties for intervals up to 100 pulses. The
finding that the pulse rate variability and amplitude variability
fractal exponents were uncorrelated during REM sleep and were only
marginally correlated during sleep stage 3-4 may indicate that
they reflect at least partially independent processes. On the basis of
previous and present findings, it can be concluded that the fractal
correlation properties of heart rate variability during REM sleep are
primarily the result of the intense sympathetic activation during this
sleep stage.
In conclusion, our present findings demonstrate that the regulation of
PAT during REM sleep, which is a surrogate of sympathetic activation,
behaves as a fractal signal. This behavior is similar to that of the
heart rate variability and was found in healthy controls, in heavy
snorers, and in CHF patients.
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ACKNOWLEDGEMENTS |
The editorial help of G. Nathanzon and A. Jaffe-Katz is greatly appreciated.
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FOOTNOTES |
This study was supported by a grant from Itamar Medical.
Address for reprint requests and other correspondence: P. Lavie, Sleep Laboratory, Gutwirth Bldg, Technion City, Haifa 32000, Israel (E-mail:
plavie{at}tx.technion.ac.il).
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.
First published March 7, 2002;10.1152/ajpheart.00336.2001
Received 25 April 2001; accepted in final form 27 February 2002.
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Am J Physiol Heart Circ Physiol 283(1):H434-H439
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ABSTRACT
INTRODUCTION
