Sleep, 15(4):352-358
© 1992 American Sleep Disorders Association and Sleep Research Society
Beta (20-28 Hz) and Delta (0.3-3 Hz) EEGs Oscillate
Reciprocally Across l~REM and REM Sleep
Sunao Uchida, Tom Maloney and Irwin Feinberg
Department of Psychiatry, University of California, Davis, VA Medical Center, Martinez
Summary: Across-night oscillations of beta (20-28 Hz) and delta (0.3-3 Hz) electroencephalograms (EEGs) were
examined with spectral analysis in 10 normal young adult subjects (Ss). In each S, power densities of beta were
found to oscillate reciprocally with delta power density across both nonrapid eye movement (NREM) and rapid
eye movement (REM) sleep. Linear correlation coefficients between log power density of delta vs. beta were significant
(p < 0.0001) for each S. An incidental observation was that beta power within REM was reliably lower in epochs
with more eye movement activity. The reciprocal relationship between beta and delta holds implications for sleep
physiology and supplements our earlier finding that sigma (12-15 Hz) oscillates reciprocally with delta within
NREM sleep. These descriptions of the continuously varying EEG across sleep provide information not available
when EEG measures are tabulated by discrete NREM periods and REM periods. Key Words: Sleep-EEG-BetaDelta-Rapid eye movements-Fast Fourier transform-Period amplitude-Computer analysis.
Early applications of automated analysis reveal~:d
that a continuous graph of electroencephalographic
(EEG) amplitude across sleep clearly exhibits the cyclic
fluctuations that underlie visually scored sleep stages
(1,2). Lubin et al. (3), using fast Fourier transform
(FFT), and Sinha et al. (4), using an analog tracing with
a compressed time scale, interpreted these oscillations
as a "damped sinusoid".
These early descriptions of continuous EEG measurements were followed by a different approach: computer measurement ofEEG but with tabulation by visually defined nonrapid eye movement (NREM) periods
and rapid eye movement (REM) periods (5,6). This
more discrete analysis provides useful information but
tends to obscure the continuously fluctuating patterns
of EEG activity across sleep.
There has been renewed interest in examining oscillatory patterns as primary sleep data (7,8). This interest has been mainly directed to the delta frequencies.
This focus on delta is due to several features: delta
frequencies contain the preponderant energy of the sleep
EEG, these frequencies show the most marked changes
across the night and with age, and they appear to be
Accepted for publication March 1992.
Address correspondence and reprint requests to Sunao Uchida,
MED: Psychiatry TB 148, University of California, Davis, CA 956168657, U.S.A.
correlated with a homeostatic process that reverses
waking effects on the brain (9,10).
Higher EEG frequencies have received less attention. However, they also show systematic oscillations
across sleep. Thus, we recently reported that the power
density of sigma (12-15 Hz) shows clear-cut oscillations across sleep that are out of phase with delta during
NREM sleep and in phase (at low levels) in REM sleep
(11). Here, we report a similar analysis of beta-delta
dynamics. This analysis reveals that power densities
of beta and delta oscillate inversely across both NREM
and REM sleep. We also show that this reciprocal oscillation can be observed with period amplitude (PA)
analysis.
SUBJECTS AND METHODS
Subjects (Ss)
Ss were 10 normal young adult college students (4
male,6 female) who ranged in age from 18.6 to 25.4
years (mean = 21.8; SD = 2.14 years). Six of the 10
Ss were included in the previous report of sigma-delta
dynamics (11). All Ss were in good health and had no
sleep disturbance. The Ss for this report were randomly
selected from a larger group (n = 16) who participated
in a study of waking duration-sleep EEG relations.
InitiallY the data of 13 Ss were examined but it was
necessary to eliminate 3 Ss, 2 because of artifact and
352
RECIPROCAL OSCILLATION OF BETA AND DELTA
2048 points
25.6 sec.
1600 points
20.0 sec.
>.
FIG. I. Treatment ofFFT analysis epochs. Both edges of224 points
were cosine tapered and 448 points were overlapped. Thus the waveform in the 20-second epoch was not modified by the window operation, nor was there a strong convolution effect.
1 because of recording problems. The data below are
for one baseline night that immediately followed one
adaptation night for each S.
Recordings
Baseline sleep EEG (C3-A2, C4-Al) and electrooculogram (EO G) (each outer canthus to forehead) were
recorded in standard fashion on a Grass model 78
polygraph with the low frequency, half-amp (high pass)
filter set at 0.3 Hz (time constant of 250 milliseconds)
and with the low pass filter set at 100 Hz. The 60-Hz
filter was not used. Data were recorded on a Honeywell
101 instrumentation tape recorder. A time code was
written every 10 seconds on both paper tracing and
tape.
EEG analysis
Visual sleep stage scoring was carried out for each
20-second time-code-delimited epoch according to
modified (9) Rechtschaffen and Kales criteria (12). Visually scored epochs corresponded exactly to the computer-analyzed epochs. For the analysis of beta-delta
dynamics, we used epochs scored as stage 2, 3, 4 and
REM; epochs of wake and stage 1 were deleted. Epochs
containing electromyographic (EMG) or other artifacts
in the EEG lead were also eliminated.
The tape-recorded C3-A2 lead was played at four
times recorded speed into a 12-bit ND converter
[Contec ADI2-16(98)], through a 40-Hz anti-aliasing
analog high-cut filter (by Kohden Medical Co.) and
sampled at 80 Hz, in real time. An FFT analysis was
carried out by an NEC9801 computer on each 2,048
points (25.6 seconds), during which the longest analyzed wave (0.3 Hz) could continue more than seven
times. Both edges (224 points; 2.8 seconds) of each
analysis epoch were cosine tapered, such that 448 points
353
(5.6 seconds) in each epoch overlapped with preceding
and succeeding epochs (Fig. 1). (These methods were
originally developed by Drs. Y. Atsumi and S. Uchida
for a period amplitude system using an FFT-IFFT
filter (13).) With this operation, waveforms in the 20second epoch were not modified by the taper window;
nor were there strong convolution effects. The real and
imaginary terms for each frequency in the FFT were
squared and summed to obtain a power spectrum of
1,024 bins. This power spectrum was compressed into
19 frequency bands of 0-0.3, 0.3-0.75, 0.75-1,1-1.5,
1.5-2,2-2.5,2.5-3, 3-8, 8-12, 12-14, 14-16, 16-18,
18-20, 20-22, 22-24, 24-26, 26-28, 28-30 and 30-32
Hz. These frequency bands were designed to examine
the delta and beta band EEG in detail. A 3.5-Hz, 200J,L V (peak-trough) sine curve calibration signal was also
analyzed, and the average value in the 3-8 Hz band
from seven epochs of different phases of the signal was
taken to represent 10,000 J,LV2. The values from the
seven epochs analyzed were highly consistent (SDI
mean = 0.000459). The absolute power in each frequency band was scaled to the power of this calibration
signal. The data presented here are simple sums of
power in the bins of each frequency band, rather than
averaged values.
The frequency bands used for the dynamic analysis
were 0.3-3 Hz for delta and 20-28 Hz for beta. Although the upper limit of delta is not standardized, a
point between 2 and 4 Hz is usually employed. In our
laboratory, we have used 3 Hz since 1978 (5), although
all frequency bands are analyzed.
Our definition of the lower limit of beta was the
result of preliminary exploration of the behavior of
frequencies above the usual upper limit (15-16 Hz) of
sigma. We initially sought patterns in frequencies between 15 and 23 Hz (beta-l band). We found that 1523-Hz activity did not exhibit a clear cyclic pattern.
Power in these frequencies varied inversely with delta
power during NREM but showed inconsistent patterns
in REM, sometimes being in phase and at other times
being out of phase. We therefore raised the lower limit
of beta until clear patterns emerged. We found that the
20-28 Hz band displayed clear cyclic oscillations systematically related to those of delta in both NREM
and REM.
The 28-Hz upper limit of beta used here was determined by our sampling rate (80 Hz). Although theoretically we could have examined frequencies to 40 Hz
(the Nyquist frequency), we were concerned that such
data might not be reliable, as only two points would
be sampled in one complete sinusoidal wave. We therefore set the upper limit at 28 Hz. We think that higher
EEG frequencies (to the extent that they are biologically meaningful) would also show the patterns observed for 20-28 Hz.
Sleep, Vol. 15, No.4, 1992
354
S. UCHIDA ET AL.
9
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FIG. 2. (A) Standard scores of the FFf power density of delta (0.33 Hz) and beta (20-28 Hz) EEGs across sleep for a representative
subject. Each point is a 3-minute average. Epochs of wake and artifact
have been removed. NREM and REM are distinguished by shading.
Both beta and delta showed a cyclic pattern across sleep. Beta oscillated reciprocally with delta across both NREM and REM sleep.
(B) Standard scores of delta (0.3-3 Hz) zero-cross integrated amplitude and beta (23-30 Hz) zero first derivative curve length by period
amplitude analysis from the same subject as A. Beta~elta dynamics
are highly similar to the FFf findings.
EOG analysis
EOGs were visually scored to evaluate eye movement (EM) density during REM sleep. Each 20-second
REM epoch was divided into five 4-second sections
that were scored for the presence of eye movement.
Thus a 20-second epoch could have 0-100% (by 20%
increments) eye-movement-positive 4-second epochs.
Each 20-second REM epoch was then classified into
one of three categories on the basis of these values:
epochs scored 0%, epochs scored 20-60%, and epochs
scored 80-100%.
RESULTS
The across-night dynamics of beta and delta power
densities are shown in Fig. 2A for a representative S.
Visually scored NREM and REM are distinguished by
shading. Time-coded epochs visually scored as wake
or with body movement or other artifact were excluded, and values were averaged for 3 minutes (nine epSleep. Vol. 15. No.4. 1992
FIG. 3. Scattergram of beta vs. delta power density ofa1l20-second
epochs of NREM and REM sleep from the same subject as Fig. 2.
Delta and beta show a consistent curvilinear relationship in both
NREM and REM sleep.
ochs}. When epochs were eliminated, averaging was
performed using adjacent epochs so that no time deletions occurred. Thus, each data point in Fig. 2 represents 3 minutes although for a relatively small number of points, fewer than nine 20-second epochs
contributed to the average value.
The beta and delta measures were then converted to
standard (Z) scores. This conversion was necessary because delta power is so much greater than that of beta
that absolute values could not be graphically depicted
on the same scale. Conversion from raw to standard
scores had no effect on the temporal fluctuations of the
data.
Figure 2A shows that beta power exhibited cyclic
variations across sleep that were as clear as those of
delta, and that these cycles were systematically related:
delta and beta power oscillated reciprocally across both
NREM and REM sleep.
Figure 2B shows that PA analysis (5) reveals the
same inverse relation found with FFT although the
curves differ in detail. Where these differences occur,
we offer no opinion as to whether FFT or PAis valid.
Each method has limitations, and these issues will be
discussed in a future systematic comparison of FFT
and PA analysis of an extensive data set. The PA analysis is presented here because of a discrepancy between
our FFT findings and those of a recent PA analysis by
Armitage et al. (14) (see Discussion).
Figure 3 is a scattergram of beta and delta power
density of all 20-second epochs scored as stages 2, 3,
i.
RECIPROCAL OSCILLATION OF BETA AND DELTA
1
I.
~.
4 and REM from the subject whose across-night curves
are shown in Fig. 2. A curvilinear relation is clearly
apparent. In contrast to the sigma-<ielta relation, which
showed this pattern only during NREM sleep (11), the
curvilinear relationship for beta-<ielta held across both
NREM and REM sleep.
To evaluate the reliability of the inverse relation of
beta and delta, we carried out log transformations of
both data sets; this procedure tended to normalize both
distributions (see Fig. 3) and enabled us to compute
linear correlation coefficients. Pearson r values were
significant for each S; r ranged from -0.34 to -0.76,
mean = -0.57 (p < 0.0001 for all).
We also examined beta activity by visually scored
sleep stage, combining stages 3 and 4 as slow-wave
sleep (SWS). As expected, beta power increased progressively from SWS to stage 2 to REM. The mean
values (SD) were 2.39 (0.66), 3.21 (0.70) and 4.19 (0.68)
(J,L V2), respectively. The beta power in each of these
sleep stages differed from the other two at p < 0.0002
(two-tailed t test) and at p < 0.005 for the Wilcoxon
signed-rank test.
Figure 2 shows that the beta curve was relatively
smooth during NREM but appeared jagged during
REM. This difference was observed in all subjects. To
evaluate this phenomenon statistically, we examined
the residual values from the smoothed beta curve (vertical distance of each point from the smoothed curve)
across the night. The smoothed curves were produced
by nonlinear techniques used in the SMOOTH program of Delta software. The rationale of nonlinear
smoothing is given by Velleman and Hoaglin (15), and
previous applications of these methods to sleep EEG
have been reported (8,16).
We examined the residual values by visually scored
sleep stages. They increased progressively from SWS
to stage 2 to REM: the mean values (SD) were 0.23
(0.11),0.35 (0.14) and 0.51 (0.16) (J,LV2), respectively.
The residuals in each visually scored sleep stage differed from the other two at p < 0.006 (two-tailed t
test) and at p < 0.02 with the Wilcoxon signed-rank
test.
To investigate the origin of the sharp fluctuations of
beta power within REM (Fig. 1), one of us (S.U.) reexamined the ink-written records. This review suggested that epochs with EM bursts contained fewer
organized, sinusoidal bursts of beta than epochs without EMs. We therefore carried out an analysis to determine whether beta power is lower in REM epochs
that have more EM. (EM scoring was entirely independent of the computer analysis.)
Mean beta power density in 20-second REM epochs
that contained 80-100% EM-positive 4-second epochs
was lower than in epochs with 0% or 20-60% EM in
all 10 subjects. Conversely, beta power was highest in
355
epochs with 0% EM in 8 of the 10 subjects. Mean beta
power density (SD) for each of the EM categories was:
0%,4.4 (0.74); 20-60%, 4.2 (0.70); 80-100%, 3.9 (0.66)
(J,L V2). The difference between any two of these values
was significant at p < 0.03 (Wilcoxon signed-rank test).
DISCUSSION
These findings show that beta EEG in the 20-28-Hz
frequency band oscillates inversely with delta throughout both NREM and REM sleep. Thus, these beta
frequencies behave similarly to sigma (12-15 Hz) during NREM sleep but differ during REM, where sigma
and delta are at their lowest levels (11). Although beta
and sigma frequencies are usually considered to reflect
different neurophysiological mechanisms, it is worth
emphasizing that their behavior is similar throughout
the 75% of sleep made up ofNREM. In addition, sigma
and beta frequencies respond similarly to benzodiazepine administration: these drugs stimulate beta and
sigma and suppress delta (17-19). The similarity in
drug response, taken in association with the similar
oscillatory behavior within NREM sleep, raises the
possibility that beta and sigma EEG share a common
mechanism.
Previous computer analyses of beta by sleep stage
gave results consistent with an inverse relation between
beta and delta. Thus, a number of investigators found
that beta power (or its equivalent) is highest in wake
(stage 1) or REM and lowest in stage 4 (20-26). Moreover, Fig. 1 of Dumermuth et al. (23, p. 328) clearly
shows an inverse relation between delta and beta, although these authors did not emphasize this finding.
The failure of previous investigators to describe explicitly these beta dynamics may have been due to the
focus on developing computer methods that could
mimic visual sleep stage scoring. These rhythms could
also have been missed because the very low power of
beta can be obscured by the high power in other frequency bands.
Although our FFT results are consistent with the
findings of most previous investigators, they are diametrically opposite those of a recent report by Armitage et al. (14), which appeared after this article was
initially submitted for publication. Using PA analysis,
Armitage and co-workers found that delta (0.5-4 Hz)
(half-wave) zero-cross time-in-frequency and beta (1632 Hz) (full-wave) first-derivative time-in-frequency
oscillate in phase across sleep in normal subjects; however, these investigators also observed 90-minute beta
rhythms.
In an attempt to trace the source ofthis discrepancy
we first investigated the possibility that it was due to
a basic difference between FFT and period amplitude
methods. We randomly selected PA data available from
Sleep. Vol. 15. No.4. 1992
356
S. UCHIDA ET AL.
a previous analysis for six of these subjects. The beta
frequency bands available to us included 15-23 Hz
and 23-30 Hz; the delta band available was 0.3-3 Hz.
The PA analysis of this laboratory has used (half-wave)
zero-cross integrated amplitude to measure delta and
peak-trough amplitude measured by (half-wave) zero
first derivative points to measure beta [for algorithms,
see (5)].
We first examined the beta-delta relations of these
PA measures for the 23-30 Hz beta band. Figure 2B
(see Results) shows that beta-delta dynamics measured
in this way were highly similar to the FFT findings in
the same S. We next computed Pearson correlation
coefficients for log beta vs. log delta for each S. Mean
r for the six Ss was -0.55 (range -0.43 to -0.69). For
the same six Ss, mean r for the log of the FFT measures
was -0.52 (range -0.34 to -0.76). Thus, the discrepancy between our findings and those of Armitage
et al. is not due to a fundamental difference between
FFT and PA methods.
We next tested the possibility that the discrepancy
resulted from the fact that the above PA analysis does
not include the lower end of the beta band. We repeated
the analysis using PA measures for 15-30 Hz. This
analysis confirmed the FFT results described above:
there was a strong inverse beta delta relation in NREM
and a more variable pattern in REM.
Thus, we are unable to account for the discrepancy
between our results and those of Armitage et al. (14).
We have confidence in our findings because they were
obtained with two entirely independent methods of
analysis. Moreover, our results are consistent with the
wide range of studies cited above [including one by
Hoffmann et al. (25), whose method appears to have
been employed by the Armitage group] that show that
beta activity is lowest in stage 4 and highest in REM
or wake.
What is the functional significance of the reciprocal
beta-delta rhythm? In general, greater EEG synchrony
(lower frequencies, higher amplitudes) is associated with
lower levels of arousal. It is, therefore, tempting to
speculate that the beta-delta oscillations are correlated
with, or directly represent, fluctuations in central
arousal level during sleep. One might object that arousal thresholds during REM are about the same as those
in NREM stage 2. However, behavioral arousal thresholds during phasic REM activity are higher than those
during tonic REM which, in fact, are significantly lower
than those in NREM stage 2 [see the study and extensive review by Price and Kremen (27)]. The fact that
phasic REM is associated with relatively high thresholds may be due to sensory occlusion. The intense
endogenous activity in sensory pathways during REM
may intermittently block cortical transmission of an
incoming exogenous stimulus, raising the apparent
Sleep. Vol. 15. No.4. 1992
sensory threshold. This occlusion effect could produce
variable arousal thresholds during stage REM even
though central arousal levels are consistently elevated.
Central arousal level may also be implicated in our
finding, which was unexpected, that beta power varies
inversely with EM activity during stage REM. Elsewhere, Feinberg et al. (28,29) proposed that EM activity during REM is proportional to central arousal level.
This interpretation accounts for most of the known
experimental variation of EM activity, including its
increase across successive rapid eye movement periods
(REMPs) within the normal sleep period, its spectacular increase in late REMPs when sleep is extended,
and its reduction by sleep deprivation and sedativehypnotic agents (which depress arousal level). Thus,
one would wonder why, if higher beta power signifies
increased arousal, EM activity within stage REM should
vary inversely with beta power.
This apparent paradox may be explained by the fact
that intermittent bursts of sinusoidal (organized) beta
have much higher power than the sporadic waves in
this frequency band. When organized waking alpha is
de synchronized by arousing stimuli the power of8-12
Hz is reduced. An analogous phenomenon may occur
with beta. Thus, organized or more synchronized sinusoidal beta bursts may represent lower arousal levels
within the beta spectrum. This hypothesis can be subjected to experimental test.
There are three methodological points that bear brief
discussion. First, those who may be interested in replicating our results should pay careful attention to recording technique, as EMG can easily obscure these
low amplitude patterns. In addition, for any method
of computer EEG analysis, issues of calibration and
filtering assume greater significance than in visual scoring [see discussion in (30)].
A second point concerns the definition of frequency
bands applied to sleep EEG analysis. Sleep investigators have usually adopted the conventions used for
waking EEG. These conventions may require modification for sleep research. Thus, as mentioned above,
our first attempt to investigate the 15-23-Hz band led
to confusing results because the EEG between 15 and
20 Hz sometimes behaved like sigma and sometimes
like 20-28 Hz frequencies. The appropriate frequency
bands for sleep studies should be evaluated empirically
on the basis of their lawful behaviors. It is also possible
that the frequency ranges to be studied may differ for
different experimental problems or populations.
The third point is more fundamental. It concerns
analysis of sleep EEG as a continuous biological signal
rather than a succession of discrete neurophysiologic
events. Haustein et al. (7) have noted that continuous
analysis can overcome some of the limitations of visual
sleep stage scoring. We strongly agree with this view,
RECIPROCAL OSCILLATION OF BETA AND DELTA
..
and we have proposed methods suitable for quantifying the temporal dynamics of the sleep EEG. These
methods involve nonlinear smoothing and automatic
computation of peaks, troughs and areas under the
curve. They have already shed light on the "skipped"
first REMP. This phenomenon, an apparent absence
of REM at the expected time, had been reported anecdotally in children and in young adults after total sleep
deprivation. Using objective curve-smoothing measures, we showed that the first trough is not delayed
but occurs at the usual time in children and also after
sleep deprivation (8,16). Obviously, both phenomena
are of interest: that the first delta trough is not delayed,
and that eye movement is usually absent in this trough
in children and after sleep deprivation. The absence
of eye movement in these conditions is consistent with
our hypothesis that eye movement activity during sleep
varies inversely with central arousal levels. These levels must be quite low early in the sleep of children and
in young adults after total sleep deprivation.
The idea that continuous measures of sleep EEG
contain information lost by discrete categorization is
not new. Thus, John R. Knott and colleagues (31),
introducing one of the earliest applications of Fourier
analysis to the sleep EEG, wrote "Categorical descriptions of any phenomena mask the dimensionality of
the data to which they are applied and may thus be
somewhat incomplete, if not misleading. In the case
of the EEG, categorizing masks the fact that the record
is composed of a continuous series of frequencies and
amplitudes" (31, p. 465). We believe that, so far as
sleep dynamics are concerned, categorization has produced incomplete information.
Obviously, there should be considerable overlap in
the information provided by sleep stage scoring (including tabulation by NREMs and REMs) and dynamic, automated analyses of the continuously varying sleep
EEG. Whether the latter approach proves scientifically
advantageous will depend upon its ability to discover
new or more reliable relations between sleep EEG and
such variables as behavior and physiology.
Acknowledgements: This study is supported by research
funds from the Department of Veterans Affairs (I.F.), from
NIA 5 ROI AG02274 (I.F.), from Japan Research Foundation for Clinical Pharmacology (S.U.) and from Tokyo
Ikashika Daigaku Seishinkai no Kai (S.U.). The authors thank
Jonathan D. March of Delta Software, San Francisco, for his
computer support, Dr. Rahman Azari for statistical advice
and Edward Wakabayashi for his assistance in various stages
of this study.
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