Sleep
10(6):523-536, Raven Press, Ltd., New York
© 1987 Association of Professional Sleep Societies
Period-Amplitude Analysis of Rat
Electroencephalogram: Stage and Diurnal
Variations and Effects of Suprachiasmatic
Nuclei Lesions
Bernard M. Bergmann, *Ralph E. Mistlberger, and Allan Rechtschaffen
Sleep Research Laboratory, University of Chicago, Chicago, Illinois; and *Department of
Physiology and Biophysics, Harvard Medical School, Boston, Massachusetts, U.S.A.
Summary: Period-amplitude analysis was used to measure the number of
waves per unit time (wave incidence) and wave amplitude for 19 wavelength
categories in the lateral cortical electroencephalogram (EEG) of five intact and
four suprachiasmatic nuclei-lesioned rats during NREM sleep, waking, and
paradoxical sleep (PS) over a period of 24 h. The analysis confirmed several
parallels between rat electroencephalogram (EEG) and human EEG: The wave
incidence and amplitude at all wavelengths are both practically indistinguishable between wake, PS, and NREM sleep onset. As NREM sleep EEG amplitude increases, slow wave incidence and amplitude increase. The incidence
and amplitude of slow waves are greatest at the start of the diurnal NREM
sleep period and lowest at its end. The pattern of diurnal variation of the
NREM EEG may be modeled using two wave generators (sources of variation), one between 1 and 4 Hz, and the other between 5 and 16 Hz. The diurnal
patterns for wake and PS are less clear, but both appear to require three generators, one below 3 Hz, one between 3.5 and 6 Hz, and one above 9 Hz. The
EEG of suprachiasmatic nuclei-lesioned rats does not show any shift to longer
wavelengths in NREM sleep. Wake, PS, and NREM EEG in these rats have a
lower incidence and amplitude of slow waves than the corresponding stages in
intact rats. One explanation is an inhibition of the slow wave generator as a
result of the lesions. Key Words: Rat electroencephalogram-Period-amplitude analysis-Diurnal rhythms-Sleep-Suprachiasmatic nucleus lesions.
This paper presents data on wave incidence and amplitude of the rat electroencephalogram (EEG) (period-amplitude analysis, or PAA) as a function of wavelength, sleep
state, diurnal time, and suprachiasmatic nucleus (SeN) lesioning. Although there have
been several studies of the power spectral or frequency characteristics of the EEG in
the rat (1-3), only one major study (3), to our knowledge, has previously examined rat
EEG in the time domain. Since that study measured zero crossings per 10 s, no specific
Accepted for publication June 1987.
Address correspondence and reprint requests to B. M. Bergmann, Sleep Research Laboratory, 5743 S.
Drexel Avenue, Chicago, IL 60637, U.S.A.
523
524
B. M. BERGMANN ET AL.
information about EEG activity at any wavelength could be obtained. A major advantage of using PAA is that its results are directly comparable to the signal as it is displayed on screen or polygraph paper (all are in the time domain), whereas the results of
analysis in the frequency domain are not always intuitively obvious. A detailed theoretical explanation of how PAA provides a better match to observed characteristics of
human EEG is given by Ktonas and Gosalia (4), and their arguments presumably apply
to rat EEG as well. An extreme example of one of the problems with interpreting
spectral analysis is as follows: If two identical 12-Hz spindles, which are 180 out of
phase, lie within the sampling window, they will be represented in the resulting power
spectrum by power at higher and lower frequencies, but the 12-Hz component will be
canceled by the phase shift. PAA, on the other hand, would report the appropriate
number of waves with wavelengths corresponding to 12 Hz. The power spectrum
would be mathematically correct, but uninformative about the extent of spindling
within the window. In general, the power concentration at "spindle frequencies" will
depend not only on spindle amplitude and total spindle length, but also on phase shifts
between and within spindles in the window.
PAA does have deficiencies. If a wave is complex in shape, the type of PAA used in
this study (zero crossing detection) will be insensitive to the complexity. Thus, if
"alpha-delta" (alpha activity riding on delta waves) were encountered, our method
would be sensitive only to the delta waves, and the alpha activity would go undetected.
Spectral analysis, on the other hand, would typically show frequency components in
both the delta and the alpha portions of the spectrum. In summary, spectral analysis,
because it is a frequency-domain measure, cannot specify incidence and amplitude of
individual waves. PAA cannnot differentiate frequency components because it is in the
time domain. PAA is more appropriate if the EEG is considered to contain a series of
discrete events, e.g., slow waves or spindles, whereas spectral analysis is more appropriate if the EEG is considered to reflect the superimposed continuous output of a
group of oscillators with variable amplitudes but stable, unshifting frequency characteristics. Describing wave shape in the time domain is beyond the scope of this paper.
0
METHODS
Subjects and experimental procedures
Nine male Sprague-Dawley rats weighing 280-450 g were implanted with chronic
recording electrodes under general anesthesia (pentobarbital, ketamine). The suprachiasmatic nuclei were lesioned in four of the rats by passing 1.8 rnA at radio frequency
from a Grass lesion maker separately through each of two stereotaxically positioned 00
insect pins insulated to within 0.4 mm of the tip. With the mouthpiece positioned 5.0
mm above the interaural line, stereotaxic coordinates for the lesions with respect to
bregma were 1.4 mm anterior, ±0.3 mm lateral, and 9.4 mm dorsal (5).
Unilateral cortical EEG was recorded from 3-0 stainless steel jeweler's screws
threaded into holes drilled through the skull at 1 mm posterior and 2.5 mm lateral to
bregma and at 1 mm anterior and 3.5 mm lateral to lambda. Hippocampal theta waves
were recorded from two screws within 1 mm of the skull midline, one 2.5 mm anterior
to bregma and the other midway between lambda and bregma. The electromyogram
(EMG) was recorded from silver plates cemented to the skull under either the temporalis or the nuchal muscle. Leads from all electrodes were soldered to a miniature
nine-pin plug cemented to the skull.
Sleep, Vol. 10, No.6, 1987
PERIOD-AMPLITUDE ANALYSIS OF RAT EEG
525
After surgery, the rats were placed in test cages and allowed to recover for at least 1
week. A recording cable attached to the rat's plug was connected to a commutator on a
counterbalanced boom, permitting unrestricted movement within the recording cage.
Intact rats were recorded on an LD 12: 12 schedule (light = 37 Lux, dark < 1 Lux).
Lesioned rats were maintained in constant dim illumination at 2.8 Lux and recorded for
at least 2 weeks, and their loss of circadian rhythms was verified both by inspection of
"running wheel" -style plots of hourly sleep scores and by statistical test of their periodograms.
When rats showed recovery from surgery, good recordings, and (for SeN rats) confirmed loss of rhythms, they were transferred to a 30 cm x 23 cm x 50 cm high
experimental chamber with an identical recording assembly for several days until continuous monitoring revealed stable sleep stage scores. Then, lateral cortical EEG was
recorded on FM tape for 24 h, starting at lights off for intact rats. Teklad rat chow and
fresh tap water were available ad lib. A white noise generator masked sounds from
outside the recording room.
Recording and stage scoring
Amplification and ink recording of EEG, EMG, and theta activity were made with a
Beckman Type R polygraph, with the low-frequency time constant set at 0.3 s. The
EEG signal was band-pass filtered at 1 and 20 Hz (3 dB, 24 dB/Oct). The theta signal
was passed through a filter centered at 7 Hz (12 dB/Oct). EMG was high-pass filtered
at 22 Hz (12 dB/Oct) and passed through a notch-reject filter at 60 Hz. For automatic
scoring, the filtered signals were rectified and passed to integrators, which reset to zero
each time a preset voltage was reached. Thus, the integrated amplitude of each signal
for a 30-s epoch was represented by the number of resets for that epoch. The reset
counts were stored on disk by a PDP-II computer.
Stage scoring was performed automatically by the Parametric Animal State Scoring
(PASS) system developed in our laboratory (6). This system makes use of the observation that the EEG, theta, and EMG measures for a day's epochs tend to group together
into clusters corresponding to wake, NREM sleep, and paradoxical sleep (PS). Each
day the computer produced frequency distributions of the integrated amplitudes for the
three measures for the 2,880 epochs and selected the modes in the distributions for
each of four clusters: the low-EEG, low-theta, high-EMG cluster (wake); the highEEG, high-theta, low-EMG cluster (high amplitude NREM); the low-EEG, low-theta,
low-EMG cluster (low amplitude NREM); and the low-EEG, high-theta, low-EMG
cluster (PS). Then each epoch was assigned to the cluster (and score) whose mode was
closest to the epoch's EEG, theta, and EMG measures. Low-voltage NREM appears
primarily at sleep onset, after body movements in sleep, and following PS episodes.
For most analyses, low- and high-amplitude NREM were combined as total NREM,
since the two stages normally have similar behavior, response thresholds, and PGO
spike activity (6). A property of PASS that is particularly valuable to this study is that,
although within-sleep distinctions are based primarily on EEG and theta differences,
sleep versus wake is scored primarily by EMG differences, thus providing a degree of
independence between these scores and the EEG measures.
Period-amplitude analysis
The filtered EEG signal was recorded on a Hewlett Packard model 3900 FM tape
recorder along with an epoch identification signal. Tapes were played back through a
Kron-Hite Model 3700 band-pass filter set at 0.2-20 Hz, 3 dB, 24 dB/Oct (real time)
Sleep, Vol. 10, No.6, 1987
526
B. M. BERGMANN E1 AL.
into an 8-bit AID converter attached to a PDP 11 computer, which sampled at 500 Hz
(real iime). Temporal resolution was thus 2 ms, and amplitude resolution was 0.4% fun
scale. The digitized signal was reconverted to an analog display, and gain was adjusted
until the highest waves in NREM were near clipping. This approach maximized amplitude resolution of the AID conversion at the expense of an amplitude calibration. An
assembly language program performed the PAA at twice real time.
The program detected and measured half-waves, defined as in previous PAA (4,7) as
the portion of the EEG signal lying between successive zero crossings. Starting at a
zero crossing, the program would count the number of samples (timing) and sum the
absolute values of these samples until the next zero crossing was reached. The
summed amplitude would then be divided by the number of samples to give the mean
amplitude for the half-wave. This procedure gave an amplitude measure that was independent of wavelength, and since it represented the amplitude of a square wave having
the same area as the wave measured, to some extent it was also independent of wave
shape. It also meant that waves were treated as objects, i.e., a long wave would contribute the same amount to amplitude statistics as a short wave. Half-waves lasting
more than 250 samples (500 ms) were rejected. Otherwise, half-waves were sorted into
bins according to wavelength, so that a total number of waves and a total of the mean
amplitudes was kept for each wavelength category. When the epoch identification and
timing signal indicated the end of an epoch, the epoch was matched with its sleep
score, and the number of waves and total amplitude for each wavelength category were
added to the sum for that category for that sleep score.
The choice of EEG filtering was a compromise between removing non-EEG signals
(noise) and distortion of the EEG and encompassed the range of frequencies normally
examined in rat sleep EEG recordings. Thus the "zero" in the definition of half-waves
corresponds to the zero position of a pen used for EEG tracings, and the sum of the
lengths of the half-waves in an epoch corresponds to the length of the epoch (30 s).
This broad-band analysis is in contrast to the procedure of filtering for a narrow band
within the EEG and then detecting zero crossings within the filtered output. Such a
procedure has several problems. First, it requires a priori selection of frequency
ranges, rather than their post hoc determination. Second, the positioning and filtering
characteristics of the low-frequency (high-pass) filter will strongly influence the definition of "zero" for zero crossing, i.e., results will depend strongly on the specific filter
used. This problem is part of a more general problem of distortion of waves by narrowband filters by removing their low- and high-frequency components and (for analog
filters) phase-shifting some of the remaining components. In the extreme, the filter
output will approximate the frequency component of the EEG at the filter's center
frequency. Then, since there will always be some power at that frequency, "waves"
will be measured whenever the amplitude exceeds the detection threshold of the instruments or an arbitrary threshold set by the experimenter, whether or not they correspond to visually observed waveforms. Such problems are not encountered in broadband analysis.
Initially, the wavelength categories corresponded to the sampling times, i.e., there
were 250 categories corresponding to wavelengths, from 1 sample (2 ms) to 250
samples (500 ms) per half-wave. Examination of these data showed that most of the
waves were concentrated at the shorter wavelengths, between 40 and 130 ms, and that
there was no obvious clustering of data within subgroups of wavelengths within sleep
stages. We therefore decided to group wavelengths into categories corresponding apSleep, Vol. 10, No.6, 1987
PERIOD-AMPLITUDE ANALYSIS OF RAT EEG
527
proximately to frequencies between 1 and 16 Hz, using this conversion formula: frequency equals the reciprocal of twice the half-wave length. Between 1 and 5 Hz the
categories were 0.5 Hz wide. Between 5 and 16 Hz categories were 1 Hz wide. The
small amount of data above 16 Hz, where frequency resolution was poor, was discarded. This approach has two advantages. First, it produces very wide categories at
long wavelengths, where there were relatively few data, and narrow categories at the
high concentration of data at short wavelengths, thus allowing closer inspection of the
more interesting portions of the data. Second, it conforms to the common practice in
sleep research (e.g., 10) of referring to wavelengths by their corresponding frequencies. The approach also has two drawbacks. It requires the use of terms to describe the data such as "frequency" and "bandwidth" that technically should be reserved to frequency-domain analyses. Also, care must be taken in combining data,
since operations that are linear in frequency will be nonlinear in wavelength, and vice
versa.
Histology
SCN rats were killed with an anesthetic overdose followed by intracardiac perfusion
of saline, then 10% formalin. Brains were extracted and stored in 35% sucrose/lO%
formalin solution and later sliced in 60-f.1m sections with a freezing microtome. Sections corresponding to the SCN and the lesions were mounted and stained with cresyl
violet.
RESULTS
Intact rats
Sleep in the intact rats has been described in a previous article (8) and is shown
graphically in a companion article to this study (9). Briefly, the rats showed a more or
less diurnal square wave pattern of sleep with NREM at 28.3%, PS at 4.1%, and wake
at 67.1% of total time in the dark and 68.3,11.7, and 20.0%, respectively in the light.
Figure lA shows the wave incidence-average number of full waves per minute or
half waves per 30-s epoch-as a function offrequency for 24 h for the intact rats during
wake, PS, and NREM sleep. (A more correct label than "wave incidence" would be
"wave density," because each incidence value has been divided by its bandwidth, the
reciprocal of its shortest wavelength minus the reciprocal of its longest wavelength, to
produce a bandwidth-independent value.) The functions are smooth and unimodal,
with PS shifted slightly toward shorter wavelengths than wake, and NREM shifted
strongly toward longer wavelengths. Waves in the 1-4-Hz region represent 32.5% of
NREM wave incidence, 24.9% of PS incidence, and 28.5% of wake incidence, for a
difference of 15.9% between NREM and wake, 28.0% between NREM and PS (both p
< 0.001 two-tailed t), and 9.7% between PS and wake (p < 0.02). Within NREM, as
EEG amplitude increases, the average shift toward longer wavelengths increases.
NREM with EEG near wake level (low-voltage NREM) shows no shift from wake.
Amplitude per wave as a function of frequency (Fig. IB) was calculated for each
wavelength category in each sleep category by dividing its amplitude sum by its wave
sum and, for each rat, dividing by the total measured amplitude, giving a result that is
independent of bandwidth and gain. Amplitude per wave varied smoothly, with a single
broad mode in all three stages except for a small blip at 1 Hz in wake, owing in part to
extremely low wave incidence (i.e., a small n in the divisor) at 1 Hz and in part to the
greater likelihood of artifacts in wake. Amplitude measures < 1.5 Hz are reduced ~ 15%
Sleep. Vol. 10, No.6, 1987
B. M. BERGMANN ET AL.
528
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FIG. 1. Mean electroencephalographic wavelength and wave amplitude distributions, averaged over 24 h,
within NREM sleep, paradoxical sleep, and wake. A: Wave incidence in intact rats (average number of full
waves per minute, half waves per 30-s epoch) in each state, corrected for bin width. B: Average amplitude per
wave in intact rats (divided by overall average wave amplitude). C: Wave incidence in suprachiasmatic
nucleus (SCN)-lesioned rats. D: Amplitude per wave in SCN-lesioned rats. Vertical bars represent standard
deviations. See text for measurement and calculation details.
because of filtering. NREM amplitude averaged 160-191 % of wake amplitude, with the
greatest increases at 1.5-3 Hz and the smallest at 4.5-7 Hz. NREM amplitude ranged
from 193% of PS at 1 Hz down to 131% at 16 Hz. Neither comparison is completely
independent of the scoring system, since high-voltage EEG was more likely to be
scored as NREM than wake or PS. PS amplitude varied from 98% of wake below 5 Hz
(excluding 1 Hz) gradually upward to 130% of wake amplitude at 16 Hz.
To find if there was any diurnal variation in these measures, the data were reexamined in 2-h blocks. Figure 2A shows the average percent variation from the mean of the
five rats in each of the 19 wavebands for wave incidence. Incidence (Fig. 2A) varied
most at the extreme frequencies, with the number of waves below 4 Hz varying as a
group -180° out of phase with the waves above 5 Hz, which also varied as a group.
The variation had a strong diurnal component, with the slowest waves most numerous
around light onset, and the fastest waves most numerous around light offset. The 4-5Hz region showed no sign of a 12- or 24-h rhythm; it varied, on average, <1.3% over
the 24 h. The shape of the variation has implications for models of how the EEG and
variations in the EEG are generated (see Discussion).
Diurnal variation in amplitude in NREM (Fig. 2B) was similar to variation in wave
distribution, with two exceptions. First, although there was a near-sinusoidal variation
Sleep, Vol. 10. No.6, 1987
TABLE 1. Acrophase a of rhythms by least-squares cosine fit
Slow waves b
Wake
PS
NREM
~
~
C
Fast waves d
Incidence
Amplitude/wave
Incidence
Amplitude/wave
Incidence
Amplitude/wave
5
6,8 ± 2.43
6,8
(6.4-7,3)
2.40 ± 0,15
5
6,1 ± 2,93
7,5
(7,1-7,8)
3,7 ± 0,18
5
\2,1 ± 0,92
12,1
(11.7-12.4)
6,5 ± ,30
5
\8,0 ± 4,06
17,2
(16,0-18,5)
0,51 ± 0,08
3
20,5 ± 3,54
20,2
(18,6-21.8)
0,56 ± 0,12
5
10.4 ± 1.82
10.4
(9,7-11.0)
9,0 ± 0.44
4
\6,0 ± 1.56
\6,1
(15,2-16,9)
4, ± 0,52
5
\5,7 ± 4,02
14,0
(12.4-15,6)
4,71 ± 0,99
4
19,5 ± 5,07
19,2
(17.4-21.1)
0,35 ± 0,08
5
21.3 ± 4,07
22,1
(21.4-22,8)
0,75 ± 0,07
5
22,7 ± 2.40
22,6
(22,1-23,2)
4,08 ± 0,31
5
17,2 ± 4,67
17,7
(14,9-20,6)
3,28 ± 1.25
5
23,7 ± 0,56
23,7
(23,3-0,1)
19,5 ± 1.13
5
19.4 ± 1.13
19,2
(18.4-20,0)
0,86 ± 0,09
5
18,9 ± 1.62
19,1
(18,8-19,4)
0,67 ± 0,10
4
8,0 ± 0,33
8,5
(7.4-9,3)
1.59 ± 0,21
Acrophase (ACR) given in hours: hour 00,0, dark onset; hour 12,00, light onset. One hour represents a phase shift of 15 degrees,
b Slow waves include 1-4 Hz for NREM, 1.5-3,5 Hz for wake and PS,
C Midrange includes 3,5-6 Hz for Wand P, No NREM midrange band was observed,
d Fast waves include 5-16 Hz for NREM, 9-16 Hz for wake PS,
eN, number of rats with cosine fits significantly different from 0 amplitude (p < 0,05) and with acrophase specified (p < 0,05) within 6
h, Mean acrophase (ACR) is based only on these rats,
i Acrophase calculated from group data (mean of hourly values of all 5 rats; see text for further explanation), The 95% confidence
limits and amplitude measures are based on group data,
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Group ACR
95% confidence
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Group ACR
95% confidence
Amplitude + SO
Midrange
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B. M. BERGMANN ET AL.
530
B. NREM
WAVE INCIDENCE
A. NREM
AMPLITUDE/WAVE
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FIG. 2. A: Percentage change from 24-h mean for EEG wave incidence in intact rats in NREM sleep (double
plotted) for each of 19 frequency (wavelength-I) categories. Frequency values are for low end of category;
e.g., 1.5 represents 1.5-2 Hz. B: Percentage change from 24-h mean amplitude per wave in NREM sleep. C:
Percentage change from 24-h mean wave incidence in paradoxical sleep. 0: Percentage change from 24-h
mean amplitude per wave in PS. E: Percentage change from 24-h mean wave incidence in wake. F: Percentage change from 24-h mean amplitude per wave in wake.
Sleep. Vol. /0. No.6, 1987
PERIOD-AMPLITUDE ANALYSIS OF RAT EEG
531
in amplitude below 4 Hz, which approximated the variation in wave incidence, for high
frequencies amplitude was diminished just before light offset, then enhanced afterward
to produce an abrupt upward transition of amplitude and an offset in phase from the
wave incidence distribution. Second, there was some overlap between the high- and
low-frequency rhythms, as indicated by the extension of the elevation at light offset to
wavelengths below 4 Hz, and a "bump" in the short wave (above S Hz) distribution at
light onset (Fig. 2B).
Rhythms in wake (Fig. 2E and F) were more complicated. As might be expected,
they were considerably lower in amplitUde than the NREM rhythm, and because there
was so little activity near 1 Hz, those values were too erratic to plot. The wave incidence distribution showed signs of three overlapping rhythms: a l.S-3-Hz rhythm
peaking in mid-dark phase, a 3.S-6-Hz rhythm peaking early in the light phase, and a
9-16-Hz rhythm peaking at light offset. Amplitude per wave was generally highest in
the light for all frequencies, with stronger rhythms at higher frequencies. As with
NREM, there was a dip just before lights-off and ajump just afterward.
Like wake, PS had few waves near 1 Hz, and thus the results for that frequency are
too erratic to plot (Fig. 2C and D). Nevertheless, a rhythm in wave incidence below 3.S
Hz can be distinguished, which peaks early in the dark period, and there appear to be
regions of waves acting in concert between 4 and 6 Hz and above 8 Hz. PS amplitude
per wave measures varied together across all frequencies, with the largest diurnal variation at the highest frequencies and a peak late in the light period.
Table 1 provides some quantification of the rhythms visually assessed from Fig. 2.
The data for the table were compiled as follows. If wave incidence for a group of
bandwidths from Fig. 2 appeared to vary in concert, then incidence was combined
across these bands, as described in Methods, to produce a single value for each 2-h
block. Then a cosine curve was fitted by least-squares to the values for the 12 blocks to
find the amplitude and acrophase (ACR-the phase of the fitted cosine wave with
respect to time zero = light offset) of the 24-h sinusoidal component of the diurnal
rhythm of the group bandwidth. The amplitudes for the same group bands were also
combined as described in Methods, and their 24-h cosine fits were similarly calculated.
A rat was considered to have a significant 24-h cosine fit if the amplitude of the fit was
greater than zero at p < O.OS and the ACR was specified within 6 h (90°) at p > 0.9S.
The mean ACRs and their standard deviations were calculated from these significant
values. Additionally, a cosine was fitted to the group mean block values of all five rats
to give the group ACR, its 9S% confidence limits, and an amplitude value for each
waveband incidence and amplitude. As can be seen from the individual and group
cosine fits from Table 1, the group ACRs are strongly representative of those from the
individual rats. There was, however, large variance across individual rats in some PS
measures, as might be expected from the small degree of variation in PS EEG and the
relatively small number of PS epochs. As a result, there is no significant difference
between the PS midrange and fast wave incidence ACRs based on the individual rats'
values (pair t = 1.17, df = 4), although the corresponding group acrophase difference
is highly significant (p < O.OOS, t = 4.01, df = 9). As can be seen from the table, all
other differences in incidence acrophase are highly significant by either approach, thus
supporting the initial waveband selection to the extent that each waveband contains
waves with different diurnal characteristics from the other bands.
In general, the PS and wake acrophases roughly corresponded. Amplitude acrophases for all ranges were in middle to late lights-on. Slow wave incidence acrophases
Sleep, Vol. 10, No.6, 1987
532
B. M. BERGMANN ET AL.
were in middle dark, ~ 1800 out of phase with amplitude. Midrange incidence was ~60°
advanced, in eariy iights-on. Fast wave incidence was approximateiy in phase with
amplitude.
NREM also had similar ACRs for both fast and slow amplitudes per wave, but the
ACRs occurred in the last half of the light period, ~ 1800 out of phase with those of
wake and PS amplitude. In the four rats with significant ACRs for both, the slow wave
amplitude ACR was significantly delayed compared with the fast (p < 0.05, two-tailed
paired t, df "" 3). Similarly, although the slow wave incidence ACR was near the slow
amplitude ACR, they were also significantly different from each other (p < 0.05, df =
4), with incidence always lagging amplitude. Note that the peak values of slow wave
incidence'and amplitude (Fig. 2A and B) occurred identically at light onset, i.e., the
differences in acrophase (Table 1) represent differences in the shape of the diurnal
rhythms, not necessarily differences in peaks or troughs, since the cosine fit takes into
account all 12 points in estimating phase. Fast wave incidence was ~ 1800 out of phase
with slow wave incidence.
SCN-lesioned rats
Examination of the brain sections showed complete bilateral destruction of the SCN
in two rats, all but the rostral third of the SCN on one side destroyed in a third, and all
but a few bilateral rostral sections of the SCN destroyed in the fourth. This lesion was
judged to be ~70% complete. Despite these differences, all four rats failed to generate
free-running sleep-wake rhythms in constant dim light, at least during the 2-3 weeks
recorded. Periodogram analysis for periods between 21 and 30 h showed no rhythmic
components above noise level. Sleep over the 24 h has been described in a previous
article (8) and is shown graphically in a companion article (9). NREM occupied 56.1 %,
PS 7.8%, and wake 36.1% of the time.
A comparison of Fig. IA and C shows that there were two major differences in wave
incidence across frequencies between SCN-Iesioned rats and intact rats. First, within
SCN rats there were almost identical distributions for wake, PS, and NREM; NREM
actually had 0.7% fewer 1-4-Hz waves than PS (NS by two-tailed t) and 5.4% fewer
waves than wake (NS). Second, there was a shift to shorter wavelengths for all three
states; SCN rats had 56% fewer 1-4-Hz waves than intact rats in NREM, 43% fewer in
PS, and 46% fewer in wake (all p < 0.001, two-tailed t, df = 7). Wave incidence in the
1-1.5-Hz range was <0.1 per epoch for NREM and PS and 0.2 per epoch for wake.
The amplitude per wave distribution for SeN rats (Fig. ID) was also markedly different from that of intact rats (Fig. IB). Whereas amplitude in all states was consistently relatively high up to about 6 Hz, then declined progressively at higher frequencies in intact rats, for SCN rats, amplitudes in all states were highest in the 6-8Hz range and declined progressively at both higher and lower frequencies-except for
a peak at 1 Hz, ,which will be discussed below. The combined wave incidence and
amplitude data indicate that compared with intact rats, SCN rats showed not only
fewer of the slowest waves, but relatively low amplitudes of the slow waves that occurred.
As was the case with wake in intact rats, the elevated amplitude values at 1 Hz are
artifactual, the consequence of the very small number of waves at that wavelength (for
some hours there were no waves for any rat) and the tendency for artifact sources to
have large low frequency components. The smooth decline of the amplitude values
above 1 Hz with decreasing frequency argues that otherwise the signal-to-noise ratio
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PERIOD-AMPLITUDE ANALYSIS OF RAT EEG
533
was so high as to make the contribution of artifact negligible. This conclusion agrees
with the impression given by the clean polygraph tracings and the frequency distributions of EEG amplitude, which did not have the outliers characteristic of artifact.
DISCUSSION
NREM wave characteristics
The overall distribution of wave incidence and amplitude in NREM (Fig. lA and B)
revealed no discrete grouping of waves into "slow waves," "spindles," or any other
subset. Of course, the lateral positioning of the EEG electrodes used in the analysis
meant that we did not observe one obvious subset of waveforms seen in the rat-hippocampal theta. Neither did we analyze for complex waveforms such as the repetition
of wave shapes seen in spindles. It was only when we examined the diurnal variations
in our measures that subsets of waves appeared.
The diurnal variation in NREM EEG activity below 4 Hz has been described previously in our laboratory (1) and elsewhere (3). Our current data show that both wave
incidence and amplitude in the 1-4-Hz waveband vary in concert across the diurnal
cycle, thus giving support to the concept that these waves together constitute the
"slow wave" band in the rat, which, as we will discuss, may be equivalent to the
human "delta" band. However, the extension of the amplitude rhythm above 4 Hz
(Fig. 2B) suggests a wider bandwidth for slow waves.
As NREM wave incidence below 4 Hz decreased, incidence above 5 Hz increased,
and vice versa. This result is not surprising, since when there are more slow waves in
an epoch, there is less time for faster activity. However, it does require that the fast
waves behave in a fairly monolithic manner; if there were large shifts in incidence
between moderate and extremely fast waves, these shifts could produce changes in fast
wave incidence independent of slow wave incidence, such as the pattern seen in wake.
If it is assumed that both the waves above 5 Hz and the waves below 4 Hz behave as
monolithic fast and slow groups, as suggested in Fig. 2A and B, then one can model the
generation of the diurnal amplitude and incidence cycles. Three such models are a
"switching" model, a "summation" model, and a "shift" model.
The "switching" model posits a broad-band slow wave generator and a broad-band
fast wave generator whose outputs alternate; i.e., when the slow wave generator is
switched on, the fast generator is turned off, and vice versa. The region around 4.5 Hz
with low diurnal variation in incidence would presumably correspond to the point of
equal density of the fast and slow generator outputs. Although the incidence offast and
slow waves would not be independent, both could be independent of their respective
amplitudes. We show in a companion article (9) that large changes of incidence can
occur with little change in amplitude.
A "summation" model posits a slow generator and fast generator whose continuous
outputs are summed to form the variable portion of EEG. As the amplitude of the slow
generator output increases relative to the fast output, zero crossing PAA detects more
and slower slow waves, and vice versa. If, as is suggested by Fig. 2B, the changes in
fast amplitude are small, slow wave incidence and amplitude will be correlated, as is
indicated in Fig. 2A and B. (The correlation is not perfect, as is shown by the significant difference in slow incidence and amplitude ACRs.) The summation model does
not readily explain the flat region in incidence variation around 4.5 Hz. Assuming there
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B. M. BERGMANN ET AL.
is not rapid variation in the frequencies of the generator outputs, this model is more
suitable for spectral analysis than zero crossing PAA.
The "shift" model posits a single generator whose wave incidence distribution has
the shape shown in Fig. lA, but the overall distribution shifts between longer and
shorter across the diurnal cycle. The large percentage changes occur where the absolute density is small, so that a relatively small number of waves shifted in or out of the
waveband has a proportionally large effect. The flat region in incidence at 4.5 Hz could
represent a point where changes in incidence due to overall distribution shift were
canceled by changes due to the discrete time (the epoch length) for waves to occur. The
major problem with this model is the different amplitude rhythms of the fast and slow
waves where a single generator should produce just one. An addition to the model that
would mitigate this problem would be a wavelength-dependent lights-off masking effect
to produce the abrupt increase that is particularly apparent at the shortest wavelengths.
This addition would remove any advantage of parsimony of the shift model over the
other two.
Each of the models has some explanatory value for our results, and it is quite possible that all three processes-switching, summation, and shifting-occur. Each
model leads to testable hypotheses. The "shift" hypothesis could be tested by measurements in constant light, which would remove any masking effect. One could test
the validity of the "switching" model versus "summation" by performing PAA with
half-waves defined between adjacent negative and positive peaks. The "switching"
model would predict similar results for this method and the method used here, whereas
the "summing" model would predict vastly different results.
PS and wake wave characteristics
For wake and PS, there was a reciprocal relationship between 1.5-3-Hz wave incidence and 3.5-6-Hz incidence. In general, 1.5-3-Hz wave incidence was higher in the
dark than in the light for both PS and wake, whereas the 3.5-6-Hz waves had the
opposite relationship. Presumably, the generator of the 3.5-6-Hz waves played no detectable role in the diurnal rhythms of NREM. If the generator of the 1.5-3-Hz waves
is the same as the slow wave generator of NREM, and if slow waves reflect a recovery
process, one might conclude that some recovery occurs within waking and PS when
the rat is in the dark (mostly waking) portion of the diurnal cycle. However, the amplitude of the slow waves is in a trough during this time, so that amplitUde could not also
be reflecting recovery. The reversed phase of slow wave incidence from amplitUde also
eliminates the "summation" model as an explanation for the reciprocity between slow
and midrange waves. For both wake and PS, there appears to be some common source
of amplitude modulation for all wavelengths.
EEG and rat sleep scoring
The wave incidence and amplitude profiles for wake, PS, (Fig. IA and B) and lowvoltage NREM (not shown) are nearly identical, so to distinguish sleep states by lateral
EEG alone would require more sophisticated analysis than the PAA performed here.
Hippocampal theta, EMG, and/or other electrophysiological measures would more
readily make the distinction. AmplitUde does provide confirmation of NREM sleep: a
high amplitUde at any EEG wavelength indicates NREM, but a low amplitude does not
exclude NREM (6). Our analysis of the diurnal variation of wave incidence indicates
. that a similar situation obtains with slow waves: a high slow wave incidence indicates
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PERIOD-AMPLITUDE ANALYSIS OF RAT EEG
535
NREM, but a low incidence does not exclude it. In normal rats, there is no significant
difference between wake and NREM incidence near the start of lights-off. In SCN rats,
slow wave incidence has practically no value in indicating any state. Because a large
proportion of NREM sleep does not contain relatively high slow wave incidence, we
reiterate the proposal from our initial work (1) that the term "slow wave sleep" be
used to describe that portion of a rat's NREM sleep where slow wave incidence is
high, rather than NREM sleep as a whole.
It could be argued that we can arbitrarily define NREM in any electrophysiological
terms that are convenient, so that, for example, NREM sleep would occur when the
EEG was "significantly" above wake level, rather than as defined by our PASS scoring
system. However, this definition would result in loss of the correspondence between
NREM electrophysiology and NREM behavior that is characteristic of PASS (see
Methods); i.e., there would be significant time periods where the rat was in behavioral
NREM but not in electrophysiological NREM (6).
EEG in SeN lesioned rats
The most striking features of the SeN rat data were the reduced slow wave incidence and amplitude in all states, compared with intact rats. Histology results did not
reveal any large-scale cortical damage, nor is it likely that the reduced lighting, could
have produced so profound a change compared to intact rats. Since the slow wave
incidence in NREM (and wake and PS as well) was below the diurnal minimum of
intact rats, the reduction is not likely to be due to the oscillator getting "stuck" by the
lesion in the dark-onset (minimum slow wave) position nor to the lack of a "slow wave
need" buildup over a diurnal wake period, although the latter could contribute.
The result may be explained in terms of either the "summation" or "switching"
models by incapacitation of the slow generator. The 1.5-3-Hz generator in wake and
PS would be assumed to be the same as the NREM slow generator, so all three states
would be similarly affected. However, as we report in a companion paper (9), when we
sleep-deprived these rats for 24-h, we found that the SCN rats were still capable of
slow wave production during recovery.
Rat EEG versus human EEG
There are several parallels between the slow and fast wave groups in rat NREM and
the delta (Stage 3 and 4) and fast wave (stage 2) episodes in human NREM: Like
human delta, the rat slow waves had the highest incidence and amplitude at the beginning of the diurnal sleep period, and decreased in both parameters as the period progressed. Nap data in humans suggests that the same situation obtains for the waking
period; i.e., as the wake period progresses, both delta as measured by stages 3 and 4
and rat NREM slow wave measures increase. Similarly, fast activity as measured by
stage 2 has a time course in the sleep period like rat NREM fast wave incidence, with
maximal values at the end of the sleep period. In both humans and rats there are relatively small changes in fast amplitude through the sleep period. At a more basic level,
our rats' slow waves increased as EEG amplitude increased, as in humans, and the
low-voltage faster EEG that typified wake, PS, and low-voltage NREM in the rat bears
a strong similarity to the low-voltage fast EEG of human wake, REM sleep, and stage 1
sleep.
Rat EEG differed from human EEG in that we found less differentiation in the rat
EEG. Close examination of short periods of rat EEG did not reveal long sequences of
fast or slow waves seen in human stage 2 and stage 4 sleep, but rather short intermixed
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B. M. BERGMANN ET AL.
bursts lasting a few seconds. There seemed to be less amplitude differentiation between the fast and siow waves than in humans, with fairiy iarge numbers of siow waves
appearing at waking level, and fast waves of comparable amplitude to the largest slow
waves. This lack of differentiation is also reflected on a larger scale in the rats' polyphasic sleep pattern and flatter diurnal rhythms and may reflect the rats' lower level of
cortical differentiation.
The paucity and low amplitude of slow waves in SeN rats is most similar to the
diminution and disappearance of slow waves in the EEG of aged humans (7), who also
exhibit lowered diurnal sleep-wake rhythm amplitude. (Other researchers (10) report
that the number of slow waves is undiminished in aging, but their use of narrow-band
filtering may mean that their "waves" do not conform to the definition used in this
paper.)
Acknowledgment: The authors would like to thank Cathy Jones, Carol Chien, and David
Bowen for their able technical assistance. This research was submitted by Ralph Mistlberger in
partial fulfillment of the requirements for the Ph.D. degree at the University of Chicago and has
previously been reported in abstract form. Support was provided by NIMH grants MH4151 and
MH18428 to Allan Rechtschaffen and Canadian NSERC and FCAC fellowships to Ralph Mistlberger.
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