Sleep, 15(6):556-561
© 1992 American Sleep Disorders Association and Sleep Research Society
Distribution of Period,·Analyzed Delta Activity
During Sleep
Roseanne Armitage and Howard P. Roffwarg
University of Texas Southwestern Medical Center at Dallas,
Dallas, Texas, US.A,
Summary: The distribution of delta EEG activity was evaluated during sleep in eight healthy adults. Digital period
analysis, including an amplitude measurement, was used to quantify delta activity. The average percentages of delta
half- and full-wave zero-crosses, mean delta power, and mean total power were computed for each nonrapid eye
movement (NREM) period. The distribution of these de:lta measures was examined across NREM periods (NREMPs).
No significant linear trends were evident in the zero-cross or power measures. Four subjects showed the highest
delta power and greatest incidence of delta in the second rather than first NREMP. Regression analyses of individual
delta incidence data revealed that only 62.5% of recording nights could be described with an exponential equation.
Exponential regressions described 81 % of delta amplitude cases. Further, delta activity in some subjects could be
described by either linear or exponential regression. The findings suggest that the temporal changes of delta activity
may not be entirely systematic across NREMPs and are variable across subjects. Key Words: Computer-analyzed
EEG-Period analysis-REM-NREM sleep cycle-Slow wave sleep.
It is widely held that delta activity, assessed eitht~r
by visual scoring or by a variety of computer quantification techniques, decreases from the first to last nOflrapid eye movement period (NREMP) of sleep (14,13). It is debatable, however, whether the suggested
distribution of delta shows an exponential decay, linear
decline, or bimodal change throughout the night (4)..
U sing power density estimates from spectral or fast
Fourier analyses (FFTs), Dijk et al. (3) have described
delta changes in both slow-wave sleep and recovery
from extended sleep with an exponential function.
However, Feinberg (4), using period-amplitude analysis, claims that an exponential decay in delta is only
evident in peak-amplitude delta activity, corresponding to visually scored stage 4 sleep. Kupfer et al. (11)
have also reported that normals consistently show
counts of7 5-fJ, V delta to be greater in the first NREMP,
and secondly, that more delta in the second NREMP
may be associated with psychopathology. Howeve:r,
Feinberg (5) has also reported anecdotally that normal
young adults often show more delta activity in the
second NREMP than in the first. He suggests a more
apt description of delta change may be a decrease from
the first half to the second half of the night.
Accepted for publication July 1992.
Address correspondence and reprint requests to Roseanne Armitage, Ph.D., University of Texas Southwestern Medical Center,
Dallas Department of Psychiatry, 5323 Harry Hines Blvd., Dallas,
Texas 75235-9070, U.S.A.
Spectral analysis, yielding power density measures,
cannot distinguish low-amplitude, high-incidence electroencephalographic (EEG) from high-amplitude, lowincidence activity (6). Accordingly, it is not possible
to determine whether it is the amplitude and/or the
incidence of delta activity that show a linear change
across the night.
This report presents the distribution of period-analyzed delta amplitude and incidence during nocturnal
sleep in healthy adults.
METHODS
Subjects
Six females and two males with an average age of
32.0 ± 7.1 years spent two consecutive nights in the
Sleep Study Unit at UT Southwestern. All subjects
were medically fit and had no personal or family history of drug or alcohol abuse, depression, or other
major psychopathology. Subjects maintained a 5-day
sleep diary prior to participating in the study to ensure
regularity of sleep habits.
Procedure
EEG, electrooculogram (EOG), annd electromyogram (EMG) data were recorded simultaneously on
FM tape and polygraphic paper (GRASS Model 78
556
557
PERIOD-ANALYZED DELTA
polygraph) on each subject during two consecutive
nights in the laboratory. The FM tapes were digitized
and analyzed off-line at a sampling rate of 256 Hz. The
EEG was recorded from the left central (C3) site, which
was referenced to right mastoid on GRASS P511 AC
amplifiers at a sensitivity of 5. The half-amp low- and
high-bandpass filters were set at 0.3 and 30 Hz (24 dB/
octave). A 60-Hz notch filter attenuated electrical noise.
The digital period analysis (DPA) algorithm and procedures used here have been described in detail previously (7-9). The algorithm evaluates the length of
time between successive zero-cross and first-derivative
EEG events in five conventional frequency categories:
delta (0.5 to <4 Hz); theta (4 to <8 Hz); alpha (8 to
< 12 Hz); sigma (12 to < 16 Hz); and beta (16-32 Hz).
After analog-to-digital (AID) conversion, four different
analyses are performed on the EEG data: full-wave
zero-cross, half-wave zero-cross, first-derivative, and
power. First-derivative analyses are not included here
as they preferentially quantify fast-frequency EEG.
A zero-cross event is a polarity shift in the signal
voltage. Half-wave zero-crosses evaluate both negative-to-positive and positive-to-negative signal changes,
whereas full-wave zero-crosses evaluate only negative
inflections. The algorithm for both the half-wave and
full-wave zero-cross analyses computes the time interval between successive zero-voltage crossings,
thereby determining the frequency of each wave. A
time-in-frequency category accumulator is incremented and, at the end of each 30-second epoch, the percentage of total zero-cross time in each frequency is
computed. A power measure is also derived for each
frequency category based on the sum of the squared
amplitude of the corresponding half-waves. This analysis produces power estimates that are roughly equivalent to FFT power in slower frequencies (4,10) and
perhaps in some faster frequencies as well (10). A total
power value for all frequencies is also calculated.
Polygraph paper speed may drift more than 5 minutes per night, prohibiting the use of stage scores from
paper records to identify epochs ofDPA data for analysis by NREMP unless a synchronizing event marker
is available. Because the data were quantified from FM
tape without such an event marker, definitions of
NREM periods were based on visual scoring of computerized, "paperless" polygraph displays of EEG in
30-second epochs.
We have previously questioned the propriety of ineluding stage 1 and low-amplitude stage 2 sleep in
NREM averages intended for contrast with REM sleep
(8). In keeping with this viewpoint, stage 1 sleep was
excluded from our analysis. Epochs of movement or
wakefulness were also excluded. No minimum REM
period (REMP) duration criterion was used for the first
or later REMPs. A REMP was considered ended at the
last REM epoch of the period if no additional REM
epochs supervened within a half hour. The first NREMP
was defined as the interval between stage 2 onset and
the first REM epoch. Subsequent NREMPs were defined as the time interval between REMPs, minus stage
1, movement time, and wakefulness. All NREMPs were
terminated by REM, except for the last NREMP, which
was directly succeeded by REM sleep or a morning
awakening.
The means and standard deviations were computed
by NREMP for delta half-wave zero-cross (DHZ), delta
full-wave zero-cross (DFZ), delta power (DP), and total
power (TOTP). Following computation, separate repeated-measures ANOVAs were conducted on each
DPA measure (NREMP as a four-level, within-subject
factor), using BMDP-4V statistical routines. Night-instudy was treated as a two-level, between-subject variable. ANOV As were used to determine linear changes
in de1ta activity (16).
Exponential regression analyses, using SAS NUN
procedures, were also conducted on the delta percentages and power values for each individual subject, with
time of night as the predictor variable. These analyses
evaluated nonlinear changes in the distribution of delta. Individual, rather than group, regressions were chosen because a substantial number of sleep measures,
such as total sleep time and the number and length of
NREMPs, varied among subjects.
RESULTS
Seven of the eight subjects had four NREMPs on
both nights. The remaining subject had three distinct
NREMPs. The average NREMP length, excluding stage
1 sleep and wakefulness (53.6 ± 18.2 minutes), did
not change significantly during the night (F = 1.20, df
= 3,21, p = 0.31), although a very small linear decrease
in period length was evident. The average interval between NREMPs was 56.5 ± 28.3 minutes. The average
total sleep time was 418 ± 32.4 minutes.
Only one subject demonstrated a visually discernable linear decrease in the DPA data that was evident
in both DHZ and DP from the first to the fourth
NREMP, and only on the first night of study. The
largest DP and also the highest incidence of delta were
found in the second NREMP on both nights in four
subjects. One subject had the largest amount of delta
in the third NREMP. The remaining two subjects
showed no difference between NREMP 1 and 2.
Repeated-measures ANOVA indicated that none of
the delta percentages or power measures revealed either a significant main effect for NREMP or night-instudy or significant interactions. The largest F ratio
was obtained for DHZ by NREMP (F = 1.89; df =
3,21; p = 0.28). The means and standard deviations
Sleep. Vol. 15. No.6. 1992
558
R. ARMITAGE AND H. P. ROFFWARG
DELTA CHANGES BY NREM PERIODS
DELTA CHANGES BY NREM PERIODS
DELTA MEASURE
DELTA MEASURE
_
DELTA HALF-ZERO
D
_
DELTA FULL-ZERO
DELTA POWER
D
TOTAL POWER
500
%
400
P
D
E
L
T
A
60
0
300
40
W
E
R
200
20
100
o
FIG. 1. Average percentages of delta half-wave zero-cross (DELTA
HALF-ZERO) and delta full-wave zero-cross (DELTA FULL-WAVE)
by NREM period, averaged across nights. Error bars denote standard
deviations.
for each NREMP are illustrated in Figs. 1 and 2. Neither DHZ nor DFZ showed evidence oflinear changes
across NREMPs. The means for total power and delta
power did show very slight evidence of a decline during
the night, although no significant effects were obtained.
Comparing the absolute amounts of delta power
among subjects is somewhat problematic insofar as the
variability of this measure is usually quite large. To
explore whether intersubject variability obscured potential trends, we created a relative index of delta power by computing the ratio of delta power to total power
for each NREM epoch. The average ratios and standard deviations were then compared across NREMPs.
Analyses were also conducted on the standard deviations in delta ratios to determine shifts in the distribution of delta variances. A repeated-measures ANOVA was conducted on this variable, yielding results
that did not achieve statistical significance (F = 1.07,
df= 3,21, p = 0.38). The means were very similar for
all NREMPs (0.60, 0.57, 0.56, and 0.60; standard deviations were on the order of 0.08 for each NREMP).
A ratio was also derived within DP alone: from DP
in the first NREMP relative to DP in all other NREMPs.
This ratio was computed on the chance that changes
in total power might obscure trends in DP across
NREMPs. A repeated-measures ANOVA was also
computed on this ratio, producing a nonsignificant effect (F = 1.69, df = 3,21, p = 0.20).
Nonlinear, exponential regression analyses were also
computed on delta measures, using epoch (i.e. continuous time) as the predictor variable, based on the equation y = b*exp(c*time), where parameter b is the estimated delta value at time 0 and parameter c is the
exponent rate of decay multiplied by time. All reported
Sleep, Vol. 15, No.6, 1992
FIG. 2. Average delta power and total power values by NREM
period, averaged across nights. Error bars denote standard deviations.
r2 values are based on the asymptotic correlation coefficients determined by the nonlinear regressions. Note
that r 2 statistics obtained from linear regression cannot
be interpreted as the proportion of variance attributable to the effect (20). It is the statistic that is used to
determine the significance of exponential fits beyond
chance probabilities.
None of the DFZ regression analyses was significant,
indicating no exponential decline in this delta measure
(average r2 = 0.08 ± 0.23).
For DHZ, 10 of the 16 exponential regression equations were significant (average r2 = 0.71 ± 0.05). Two
of the regression equations were significant in the opposite direction, indicating an increase in DHZ across
NREMPs (r2 = 0.77 ± 0.15). Four of the exponential
regressions did not reach significance (r2 = 0.19 ±
0.13). It should be noted that the data from four subjects who demonstrated significant exponential regressions could also be described by a linear equation (r 2
= 0.81 ± 0.16).
The parameters from the regression analyses of DP
data are presented in Table 1. Exponential regression
equations were significant (r2 = 0.64 ± 0.05) in 13 of
16 cases, although the rate of decay was considerably
faster than showed by the DHZ regressions. Thus,
maximal exponential change in DP may occur after
the second NREMP. Two of the subjects-one on both
nights-showed no exponential decline in delta power.
The exponential rate of decay can be solved from the
formula above, with a rate of 0.1 % per minute, approximately 50 minutes. The time at which delta activity is '12 the initial value is approximately 350 minutes into the night.
Previous comparisons of the distribution of delta
have been conducted without regard to amplitude,
PERIOD-ANALYZED DELTA
TABLE 1. Average parameters from significant exponential
regression analyses of delta power. Seven subjects exhibited
13 nights with significant trends, based on the model (delta
power = b·exp(c·time of night)], where b is the expected delta
power value at time = 0, and c is exponential change. A
negative value of c represents an exponential decay, whereas
a positive value ref/ects exponential growth
PARAMETERS FROM EXPONENTIAL
REGRESSIONS OF DELTA POWER
PARAMETER
ESTIMATE
ST!;1 ERROR
B
113.6
99.7
C
-0.001
0.0004
ASYMPTQTIQ 25 %
QQNFIDENQE INTEBVAL
upper
lower
156.5
64.5
-0.002
-0.001
ASYMPTOTIC CORRELATION
-0.80 +/- 0.22
n-13 nights. 7 S8 with significant regressions
whereas other analyses have evaluated temporal
changes only in delta waves >75 /lV. Although we did
not use a minimum-voltage excursion for delta waves,
an approximation of high-amplitude delta was obtained by restricting the analysis to epochs in which
40% or more delta half-wave zero-crosses occurred (2).
Repeated-measures ANOV As were also computed on
these delta measures, resulting in nonsignificant differences. The biggest trend was a main effect for night
on the DHZ measure (F = 2.45; df = 1,7, p = 0.16),
but not for NREMP.
The final analysis of the delta data compared changes
from the first to second half of the night. Three independent repeated-measures ANOV As were performed
on the average DHZ, DFZ and DP, and TOTP values
across halves of the night. A marginally significant effect was obtained for DHZ (F = 5.77; df = 1,6; p =
0.06), indicating a lower percentage of DHZ in the
second half of the night. None of the remaining measures showed any indication of a significant trend in
delta across the night.
DISCUSSION
Neither the incidence nor the amplitude of delta
activity across NREMPs showed strong group evidence ofa linear decline. Delta amplitude showed only
a trivial tendency to decrease in the second half of the
night compared to the first half. Delta incidence, as
measured by the DHZ variable, did show a trend toward less delta in the second half of the night that
approached significance. In contrast to the findings of
Borbely et al. (2) and Dijk et al. (3), we found no
559
evidence of a systematic decline in delta across
NREMPs. However, in the exponential regression
analyses of individual subject data, 62.5% of DHZ
regressions showed a decline across NREMPs. Although these findings provide some support for Dijk
and Boberly's data, we question the robustness of the
exponential trends in delta. Changes in delta activity
appear to be considerably more variable and less replicable than earlier data suggest. Further, four subjects'
data could be described with either a linear or an exponential equation. Dijk et al. (3) have acknowledged
that exponential changes may not be evident in all
subjects.
The delta power measures, reflecting amplitude, did
show an overall exponential decay in 81 % of cases, but
with a rate of about 50 minutes. Further, the time at
which delta was 1/2 the initial amplitude was nearly 350
minutes into the night. The data from Borbely's group
suggest a decay rate more on the order of 100 minutes.
It is somewhat difficult to reconcile the disparate findings from ANOVA, nonlinear regressions and time
series analysis. One possibility is that trends in delta
change from the first to second half of the night. Perhaps the change in delta in the first half of the night is
a sharper exponential decline than in NREMPs in the
second half of the night, whereas changes in delta in
the latter half of the night may be more linear. Such
an effect could result in a marginally significant timeof-night effect as well as significant linear and exponential regressions. The observation that all subjects
showed rhythmic, sinusoidal variation in delta through
the use of time series analysis (18) does not, however,
argue in favor of a shift in the distribution of delta
from the first to the second half of the night. This
possibility can't be excluded, however, especially in
light of the weak time-of-night effect. These issues are
discussed in more detail below.
Nevertheless, it continues to be critical to distinguish
between delta amplitude and delta incidence, as the
nonlinear changes in delta appear to be more consistent
for power measures than for delta zero-cross analyses.
None of the full-wave delta regressions were significant,
suggesting that temporal changes in delta incidence
may be more prevalent at the faster end of the delta
band (2-4 Hz).
It is known that the distribution of delta activity
may be modified by sleep deprivation or fragmentary
sleep, and recovery from slow-wave deprivation may
produce a more stable exponential change in delta activity due to slow-wave rebound in recovery sleep. It
is also possible that some subjects who do not demonstrate strong temporal variation in delta have more
sleep disruption or perhaps less slow wave sleep in
general, though no support for this speculation is evident in our data. Differences in subjects' sleep quality
Sleep. Vol. 15. No.6. 1992
560
R. ARMITAGE AND H. P. ROFFWARG
just prior to the study can also contribute to tempoml
variability in delta. For example, studies showing
stronger exponential changes in delta may have used
subjects who had irregular sleep/wake habits or were
mildly sleep deprived. In a recent follow-up study,
exponential trends in delta were stronger and had a
slower rate of decay in university students, who did
not maintain as rigid a sleep schedule as the eight subjects reported here (19).
It should be noted, however, that our findings are
based on an amplitude-independent algorithm that
quantifies all delta waves, not just those in excess of
75 J.N. Peak-amplitude delta, corresponding to stage
4 sleep, may, in fact, decrease systematically ov~:r
NREM periods (1). Inasmuch as we did not utilize a
specific amplitude criterion for the period analysis, we
cannot evaluate this suggestion. In a previous study,
however, the number of delta waves (>75 p,V) per
minute did not show a significant decrease from the
first to the second NREMP (15). Further, restricting
analysis to those epochs with greater than 40% delta
activity did not enhance the linear trend.
The exponential regression results imply a relatively
sharp plateau in delta amplitude without recovery,
whereas rhythmic data from time series analysis suggest that both delta amplitude and incidence recur ev~ry 100 minutes, although the rhythm is stronger in
DHZ. There are few data to suggest divergent distributions of delta amplitude and incidence across the
night, although few studies separate these two delta
events. Our data support divergent trends. That is,
delta amplitude appears to be better described as an
exponential change, whereas the percentage of delta is
better characterized by ultradian trends.
Alternatively, one or the other statistical technique
has produced artifactual trends in delta across the night.
A comparison of actual DPA data to the two statistical
treatments may address these issues. In several previouspublications, we have shown that delta incidence
shows a recurrent increase about every 80-120 minutes, in agreement with the spectral analysis. The recurrence of delta, especially later in the night, does not
support a linear or exponential decline in either amplitude or incidence.
It is possible, although unlikely, that methodological
differences in EEG quantification contributed to the
discrepant findings of this study and the work of other
groups. Several laboratories have noted that the delta
zero-cross power measure, derived from period analysis, is virtually identical to delta power from FFTs
(4,5,7,9,10). The two quantification techniques show
their maximal overlap in the slow frequencies. It seems
unlikely that the distribution of delta activity across
the night would differ depending on whether FFTs lOr
period analysis were used. Further, Dijk et al. (3) have
Sleep, Vol. 15, No.6, 1992
plotted the time course of delta power in two subjects
at baseline. Only one showed reduced power across
successive NREMPs. In the second subject, there was
virtually no difference between the first two NREMPs
and considerably less delta in the second half of the
night, as in our results. These findings suggest considerable individual differences in the distribution of delta
activity across NREMPs. The Dijk et al. study, however, included only young male subjects.
Because age and gender have been suggested to moderate both the periodicity and phase of ultradian
rhythms (14), the amount of delta activity (4,13), and
other sleep macroarchitectural characteristics (l, 13),
these factors have to be taken into account with respect
to the divergent results in several studies of slow-wave
sleep. Too few subjects were included in this study to
evaluate age and gender effects. A follow-up study is
currently underway.
Factors that are likely to produce discrepancies
among studies include definitions of REM and
NREMPs, inclusion or exclusion of stage 1 sleep in
NREM averages, and the demographic characteristics
of samples. Kupfer's group routinely uses a 3-minute
minimum first REMP criterion (11). Borbely et al. and
Dijk et al. use a minimum 5-minute REM duration,
but only for middle REMPs and not for the first and
last cycles (2,3). Our laboratory does not use any minimum REM criterion, which conforms with the standard scoring criteria of Rechtschaffen and Kales (17).
If, for example, a REMP was 1 minute in length, we
would delineate two NREMPs about it, whereas Kupfer would consider it a single NREMP and Borbely's
group would identify two NREMPs only if it occurred
in the first or last cycle. These differences result in an
altered delta distribution based on period definition.
Whether stage 1 sleep is included or excluded affects
delta distributions in a similar manner.
In terms of demographic characteristics of sample
populations, family or personal history of alcohol or
drug abuse and psychiatric illness, for example, if not
used specifically as exclusion criteria, may contribute
to the differences among studies. Depression is usually
associated with a decrease in delta activity, among
other sleep abnormalities, and perhaps an alteration
in the distribution of delta across NREMPs (11). Inasmuch as sleep abnormalities have been uncovered
in first-degree relatives of depressed patients (12), if
such subjects are not excluded from study on the basis
of family history, they may bias the sleep EEG data in
a way that is not characteristic of normal controls.
Beyond the considerations already mentioned, sleep
hygiene, i.e. the regularity of sleep habits prior to laboratory evaluation, may also influenc~ the outcome of
research. The subjects in our study maintained regular
sleep habits for 1 week before sleeping in the labora-
PERIOD-ANALYZED DELTA
tory, and few awakenings occurred during the recording night.
We strongly recommend that normal control subjects be chosen with explicit and detailed exclusion
criteria and normalized sleep so as to minimize uncontrolled influences on sleep EEG. We look to future
research with appropriate controls to help identify the
individual differences that contribute to variability in
the distribution of EEG frequencies during sleep.
7.
8.
9.
10.
Acknowledgements: We thank Kenneth Z. Altshuler,
chairman of the Department of Psychiatry, for administrative support; Paula Pechacek for assistance in the preparation
of data and this manuscript; and the Mental Health Clinical
Research Center, directed by Dr. A. John Rush, for conducting clinical evaluations on all normal controls. We also
thank the technicians of the Sleep Study Unit, under the
supervision of Darwynn Cole, for data collection. This research was supported by NIMH-MH4115 (R.A.), Biological
Humanics Foundations (R.A. and H.P.R.), and from departmental research funds (R.A.).
12.
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