Beta (20-28 Hz) and Delta (0.3-3 Hz) EEGs Oscillate Reciprocally Across l~rem and REM Sleep

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1 Sleep, 15(4): 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 < ) 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-Beta Delta-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 Address correspondence and reprint requests to Sunao Uchida, MED: Psychiatry TB 148, University of California, Davis, CA , U.S.A. 352 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 (Ss) SUBJECTS AND METHODS 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

2 RECIPROCAL OSCILLATION OF BETA AND DELTA points 25.6 sec 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 (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 20- second 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, , ,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, and Hz. These frequency bands were designed to examine the delta and beta band EEG in detail. A 3.5-Hz, 200- J,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 = ). 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 Hz for delta and 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 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 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 Hz. Sleep, Vol. 15, No.4, 1992

3 354 S. UCHIDA ET AL. A :- I '.. OJ 0 () Cf) "0 C1l "0 C C1l Cf) B " ~~~~~~~?-~.... I 4500 i DeltaPower Density (J.1V 2 ) -2~~~~ ~_~_~_~~~~_~ o Minutes from lights-out o NREM o REM -- Delta... Beta FIG. 2. (A) Standard scores of the FFf power density of delta (0.3-3 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 %. 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 ep- 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,

4 RECIPROCAL OSCILLATION OF BETA AND DELTA 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 to -0.76, mean = (p < 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 < (two-tailed t test) and at p < 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 < (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 % 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 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); %, 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 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 (16-32 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

5 356 S. UCHIDA ET AL. a previous analysis for six of these subjects. The beta frequency bands available to us included Hz and Hz; the delta band available was 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 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 (range to -0.69). For the same six Ss, mean r for the log of the FFT measures was (range 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 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 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 Hz band led to confusing results because the EEG between 15 and 20 Hz sometimes behaved like sigma and sometimes like 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,

6 RECIPROCAL OSCILLATION OF BETA AND DELTA 357 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. 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