|
http://www.abbs.info e-mail:[email protected] ISSN
0582-9879
ACTA BIOCHIMICA et
BIOPHYSICA SINICA 2003, 35(8): 741–746
CN 31-1300/Q |
|
Short Communication |
Analysis
of Rat Electroencephalogram during Slow Wave Sleep and Transition Sleep Using
Wavelet Transform
( Department of Biotechnology,
College of Life Science, Zhejiang University, Hangzhou 310027, China)
Abstract The dynamic features of rat EEGs collected during slow wave
sleep (SWS) and transition sleep (TS) were investigated in both time and
frequency domains using wavelet transform based on multi-resolution signal
decomposition. EEGs of freely moving rats were recorded with implanted
electrodes and then decomposed into four components of δ, θ,
α and β using wavelet transform. The
power and power percentage of each component were calculated as functions of
time. In SWS EEGs, the results showed that there existed as much as 26.2%±7.7% time duration in which the δ power percentage was less than 50%. In
addition, the powers of other three components in small δ
EEGs were significantly larger than those in large δ EEGs. This result revealed a reciprocal
relationship between δ oscillation and spindle
oscillation. Comparatively, the conventional method of FFT based power spectrum
could only show a δ power-dominating (70.6%±6.4%) spectrum of SWS EEGs. In the
non-stationary TS EEG, spindle and non-spindle segments were distinguished
based on the wavelet components of θ
and α, and then the average duration of the spindles was estimated. In
conclusion, the wavelet transform may be useful in developing novel
quantitative time-frequency measures of sleep EEGs as valuable complements of
conventional FFT method to analyze the transient changes in sleep EEGs induced
by physiological, pathological or pharmacological conditions.
Key
words wavelet transform; EEG;
slow wave sleep; transition sleep; FFT power spectrum
Electroencephalogram(EEG) reflects the
integrative activities of synaptic potentials of millions of pyramidal cells in
the cerebral cortex. Its amplitude and rhythm frequency change greatly under
different physiological and pathological conditions. For example, EEG appears
as low-amplitude fast waves during waking state, high-amplitude slow waves
during slow wave sleep (SWS), evident θ
waves during paradoxical sleep (PS), and high amplitude spikes within epileptic
seizure periods. Since the introduction of the fast Fourier transform (FFT) by
Cooley and Tukey in 1965, the FFT power spectral analysis has become the most
common method to quantitate the power distribution in EEG[1－7]. However, this method assumes the
signal to be stationary, not changing with time[1,2]. Therefore, the spectrum
can only show an average power distribution in frequency domain without any
change information in time domain.
In reality, EEG always possesses many
fast changes in transients. To treat it as a stationary signal as in FFT
spectral analysis will neglect those types of information. Especially, during
transition sleep (TS) that defined as a period between SWS sleep and PS
sleep[8,9], EEG is obviously non-stationary since the low amplitude waves and
the high amplitude sleep spindles appear alternately. This type of EEG is not
suitable to be analyzed by FFT spectrum.
In recent years, the wavelet transform
(WT) method for the time-frequency analysis of signal has been developed. Based
on the algorithm of multi-resolution signal decomposition, WT is useful to fast
locate the non-stationary signal simultaneously in frequency and time domains.
It has been applied in the analysis of biomedical signals[10－13] such as noise filtering, data
compression, spike detection, event-related potential evaluation[14] and fetal
electrocortical activity investigation[15－17].
Especially, a lot of work has been done in analysis of epileptiform activity of
EEG[18－22] by using WT methods.
However, few works have been reported on using WT to investigate sleep EEG
signals.
In this paper, the WT method is applied
to reveal the time evolution of different frequency components in EEGs of SWS
sleep and transition sleep, which provided some potential quantitative measures
of sleep EEGs.
1 Methods
1.1 Wavelet transform
Wavelet transform decomposes a signal
into a set of basis functions that are formed from a single prototype wavelet,
called mother wavelet function, by dilations and contractions in scales as well
as shifts in time domain. The wavelet becomes wider under a larger scale and
narrower under a smaller scale to obtain various resolutions on time-scale
plane. Here, the scale corresponds to the frequency in FFT spectrum. The
dilations and contractions of wavelets enable WT to produce both good time
resolutions at high frequencies and good frequency resolutions at low
frequencies, which is especially suitable for analyzing both long-term slow
alterations and short-term quick alterations in EEG. In this paper, we use the
fast WT algorithm of multiresolution signal decomposition[23]. Briefly
speaking, the algorithm repeatedly filters the sampled time sequence x(n) by a
set of paired high-pass and low-pass filters to yield a detail component and an
approximate component on every scale level. Each of the two components occupies
half of the total frequency band on the corresponding scale level with the
detail one in higher half and the approximate one in the lower half. Suppose
cDj,k and cAj,k are the coefficients of the detail component Dj and the
approximate component Aj on the scale level j and the time k, respectively.
Then, Dj and Aj are in the following frequency bands[15,24]:
Dj：[2－(j+1)Fs, 2－jFs](1)
Aj：[0,2－(j+1)Fs]
j=1,2,…,M(2)
where, Fs is the samplinrrg rate. The
original signal x(n) can be represented as the sum of components, namely:
x(n)=D1+A1=D1+D2+A2=…=ΣM[]j=1Dj+AM,
Aj=Aj+1+Dj+1(3)
1.2 EEG recording and processing
Under urethane (Biomedical product of
China) anesthesia (1.25 g/kg i.p.), nine adult Sprague-Dawley rats
(approximately 250 g, both sex, from Laboratory Animal Center in Zhejiang) were
implanted with EEG recording electrodes(made in our laboratory) over the right
frontal cortex, the right occipital cortex, and a ground electrode over the
cerebellum. The electrodes were secured to the skull with dental cement
(Biomedical product of China). Rats were allowed to recover from surgery for a
week before EEG recording[5,7].
EEG signals were amplified with a
low-pass filter of 100 Hz, digitized at 400 Hz by a PowerLab system (AD
Instruments) with 12-bit A/D and then stored into a computer. Three vigilance
states of waking, SWS and PS were recognized by visual inspection of rat
behaviors and the patterns of EEG waves. About 4 min occipital EEG segment was
selected from each rat under SWS sleep. Because there was no obvious TS epochs
in three rats, we collected a total of 17 TS EEG epochs with an average
duration of 15.4 s ± 5.6 s (x±s) from six rats.
These EEG signals were re-sampled with a
lower sampling rate of 128 Hz after they were filtered by an 8th order low-pass
digital Butterworth filter with a cut-off frequency of 30 Hz. Then, Daubechies
10 wavelet function was applied to decompose the EEGs into 4 scale levels and
the following components in corresponding frequency bands were used in further
analyses: δ (A4, 0－4 Hz), θ
(D4, 4－8 Hz), α(D3, 8－16 Hz), β
(D2, 16－32 Hz)[15,24]. Finally, the
time evolution power curve and power percentage curve in each of these
frequency bands were evaluated with overlapping time windows of 0.5 s and 0.125
s shift step. For comparison, FFT based power spectrums were estimated for
every 8 s of SWS EEGs, which resulted in a frequency resolution of 0.125 Hz,
and then averaged over the total 4 min EEG.
2 Results
Fig.1 shows a 16 s segment of SWS EEG and
its power curves of four wavelet components of δ,
θ, α and β.
Obviously, the powers of the components varied with time. At some transients,
the δ waves dominated over the signal;
while at other transients, faster waves dominated. However, the FFT power
spectrum of a 4 min EEG epoch at the same time only displayed that the power in
δ band was significantly higher
than others (Fig.2).
Fig.1 SWS EEG and its power curves of WT components
(A) A 16 s segment of SWS EEG. (B) Power
curve of δ
WT component. (C) Power curve of θ
WT component. (D) Power curve of αWT component. (E) Power
curve of β
WT component.2.1Analysis of SWS EEG
Fig.2 FFT based power spectrum of a 4 min SWS EEG
The histograms of absolute power and
power percentage of the four components calculated from a 4 min SWS EEG are
shown in Fig.3(A) and 3(B). The mean value of δ
power located in the highest position, and those of θ and α
powers located in the middle positions, while that of β power located in the lowest position
[Fig.3(A)]. The situations were similar in the histograms of power percentage
[Fig.3(B)]. These indicated that the mean values were consistent with those of
FFT power spectrum in Fig.2. However, there were cross sections among all of
the four components in both histograms, and the power percentage of δ component ranged from less than 10% to
more than 90% [Fig.3(B)], which meant that at some time the δ power was even smaller than the powers
of the other components.
/
Fig.3 Histograms of powers and power percentages of the WT components
(A)
Histograms of powers of the four WT components computed from the same 4 min SWS
EEG as used in Fig.2. (B) Histograms of power percentages of the four WT
components.
We divided each SWS EEG epoch collected
from all the nine rats into two groups: the large δ segment with the δ power percentage being more than 50%,
the small one with the δ power percentage being less
than 50%. The result showed that totally an average of 73.8%±7.7% of the SWS EEGs belonged to the
large δ segment. Comparison of the
large δ group, the small δ group and the FFT power spectrum
(one-way analysis of variance, ANOVA) showed significant differences among the
powers of the corresponding components in the three groups [F(2, 24) = 7.4–80.0, P<0.01], as well as their power
percentages [F(2, 24) = 71.2–262, P<0.001].
In addition, the results of post hoc
two-tailed paired t-test for the comparisons between each of two power groups
are showed in Fig.4(A). The δ power in large δ group was larger than in small δ group, but the other three components in
large δ group were smaller than in
small δ group. A comparison between
the FFT spectrum group and WT large δ
group showed no significant difference in δ
power, while the other three components in the FFT spectrum were all greater
than those in the WT large δ group. A comparison of the
FFT spectrum with the WT small δ group showed that the δ power was greater and the β power was smaller in the former than in
the latter, while no significant differences existed in the θ and α powers. The situations for the
power percentages [Fig.4(B)] were similar to those for the powers[Fig.4(A)]
except that there were no significant differences between the FFT spectrum
group and the WT large δ group for all of the four
components [Fig.4(B)].
/
Fig.4 Comparisons of the powers and power percentages of SWS EEG of different groups
(A) Comparisons of the powers of SWS EEG
among WT large δ
group, the WT small δ
group and the FFT spectrum group for the four components of δ,
θ, α and β.
(B) Comparisons of the power percentages of SWS EEG among WT large δ
group, the WT small δ
group and the FFT spectrum group for the four components. Values were
represented as mean x±s
(n=9). *P<0.01 vs. the WT small δ
group; #P<0.01 vs. the WT large δ
group; ^ P<0.01 vs. the WT small δ
group.
2.2 Analysis of TS EEG
Transition sleep is a short-lasting EEG
stage following SWS and characterized by high-amplitude spindles superimposing
on a background of low-voltage activity[8,9]. Fig.5 shows a segment of TS EEG
with four WT power components. The histograms of the powers and power
percentages of TS EEG are shown in Fig.6(A) and 6(B) respectively. In both
histograms, except the β component locating in a
lower position, the other three components located in close positions and their
values varied in a relatively large range. Since the power of spindle (7－14 Hz) located mainly in the frequency
band of θ and α, we divided the TS EEG
into spindle and non-spindle segment based on the power sum of the θ and α components. If the power sum was
larger than its average value over the whole TS EEG epoch and the duration
lasted more than 1 s, then the corresponding EEG segment was recognized as a
spindle segment, while the remainder was recognized as non-spindle segments
[Fig.5(F)]. 28 spindles were identified by this algorithm in total 17 EEG
epochs and the average spindle duration was 1.85 s ± 0.74 s.
Fig.5 Transition sleep EEG and power curves of WT components
(A) A segment of transition sleep EEG.
(B) Power curves of δ
WT component. (C) Power curves of θ
WT component. (D) Power curves of α WT component. (E) Power curves of β
WT component. (F) Power sums of θ
and α WT components. The thin line in F indicates the mean value of the power
sum used to identify the spindle periods that are marked out by the bars under
the curve.
Fig.6 Histograms of power and relative percentages of the four WT components of TS EEG
(A) Histograms of powers of the four WT
components calculated from 5 epochs of TS EEG with a total length of 75 s EEG
collected from a representative rat. (B) Histograms of relative power
percentages of the four WT components.
The comparisons of the four WT components
between the spindle and the non-spindle segments by the two-tailed paired
t-test showed that there was no significant difference in the power of δ and β,
while the power of θ and α were significantly
larger in spindle segments than those in non-spindle ones [Fig.7(A)]. In
addition, there were no significant differences in the power percentages of δ and θ
between them, but the α power percentage was larger and the β power percentage was smaller in spindle
segments than in non-spindle segments [Fig.7(B)].
Fig.7 Comparisons of the powers and power percentages of TS EEG of different groups
(A) Comparisons of the powers for WT
components of δ,
θ, α
and β between the spindle segments and the non-spindle
segments in TS EEG. (B) Comparisons of relative power percentages for WT
components of δ,
θ, α and β
of TS EEG. Values were represented as x±s.
* P<0.01 vs. the non-spindle segments.
3 Discussion
FFT based power spectrum indicated that
the δ power percentage in SWS EEG
was 70.6%±6.4% [Fig.4(B)]. However, WT
analysis indicated that the component powers in different frequency bands
varied with time, and the δ power percentage was less
than 50% in more than a quarter of EEG. Moreover, The powers of θ, α and β
components during small δ EEG were significantly larger
than those during large δ EEG. This implied an inverse
relationship between δ oscillation (1－4 Hz) and spindle oscillation (7－14 Hz) that was found in other
studies[7,25,26]. δ oscillation and sleep spindle
are two major parts in SWS EEG. Both of them are related with the
hyperpolarizing potentials in membranes of the thalamocortical neurons, but the
potential levels required by the two oscillations are quite different.
Therefore, it seems that they cannot be generated simultaneously. Intracellular
recordings revealed a mutual exclusivity between spindle and δ oscillations[25]. An inverse
relationship between the two oscillations was also found in human beings[26].
However, by using the FFT based spectral analysis, no clear reciprocal
relationship was seen in rat sleep, because both δ
and spindle activities increased from light SWS sleep to deep SWS sleep[4]. It
might be due to the comparisons were made between relatively long duration of
different sleep stages, such as light SWS and deep SWS, so that the reciprocal
relationship could not be identified. Even though both activities increased
along with the development of SWS sleep, they could still appear alternatively
at transients. This situation was revealed in this paper by the method of WT.
Recently, high temporal resolution in
sleep analysis has made it possible to identify the short-term transition sleep
between the SWS sleep and the PS sleep as an important period[8,9]. Studies in
rats showed that the amount of TS containing sleep sequences was significantly
higher in fast learning rats than in slow learning rats, which suggested that
TS containing sleep sequences were involved in long-term storage of novel
adaptive behavior[27]. However, so far few studies have reported quantitative
methods to analyze the non-stationary EEG signal during TS sleep. In this
paper, the method of wavelet transform proved to be useful to locate the sleep
spindles in TS EEG and to estimate their durations, as well as to analyze the
changes of different EEG components under the periods of spindles and
non-spindles.
In conclusion, the application of WT
method may provide some novel quantitative measures in sleep EEG
investigations, such as the percentage of small or large δ segment in SWS sleeps, the spindle
amount and their durations in TS sleeps, as well as the power distribution of
each WT component. These measures can be used as valuable complements of
conventional FFT method to analyze the changes in sleep EEGs induced by
physiological, pathological or pharmacological effects.
References
1 Bronzino JD.
Quantitative analysis of the EEG-general concepts and animal studies. IEEE
Trans Biomed Eng, 1984, 31(12): 850－856
2 Muthuswamy J, Thakor NV.
Spectral analysis methods for neurological signals. J Neurosci Methods, 1998,
83(1): 1－14
3 Ferri R, Elia M,
Musumeci SA, Pettinato S. The time course of high-frequency bands (15－45 Hz) in all-night spectral analysis of
sleep EEG. Clin Neurophysiol, 2000, 111(7): 1258－1265
4 Bjorvatn B, Fagerland
S, Ursin R. EEG power densities (0.5－20
Hz) in different sleep-wake stages in rats. Physiol Behav, 1998, 63(3): 413－417
5 Ehiers CL, Slawecki CJ.
Effects of chronic ethanol exposure on sleep in rats. Alcohol, 2000, 20(2): 173－179
6 Hansen MK, Krueger JM.
Subdiaphragmatic vagotomy does not block sleep deprivation-induced sleep in
rat. Physiol Behav, 1998, 64(3): 361－365
7 Schwierin B, Achermann
P, Deboer T, Oleksenko A, Borbely AA, Tobler I. Regional differences in the
dynamics of the cortical EEG in the rat after sleep deprivation. Clin
Neurophysiol, 1999, 110(5): 869－875
8 Gottesmann C. The
transition from slow-wave sleep to paradoxical sleep: evolving facts and
concepts of the neurophysiological processes underlying the intermediate stage
of sleep, Neurosci Biobehav Rev, 1996, 20(3): 367－387
9 Piscopo S, Mandile P,
Montagnese P, Cotugno M, Giuditta A, Vescia S. Identification of trains of
sleep sequences in adult rats. Behav Brain Res, 2001, 119(1): 93－101
10 Unser M, Aldroubi A. A review
of wavelet in biomedical applications. Proceedings of the IEEE, 1996, 84: 626－638
11 Figliola A, Serrano E.
Analysis of physiological time series using wavelet transforms. IEEE Eng Med
Biol Mag, 1997, 16(3): 74－79
12 Zhang Z, Kawabata H, Liu ZQ.
Electroencephalogram analysis using fast wavelet transform. Comput Biol Med,
2001, 31(6): 429－440
13 Samar VJ, Bopardikar A, Rao
R, Swartz K. Wavelet analysis of neuroelectric waveforms: a conceptual
tutorial. Brain Lang, 1999, 66(1): 7－60
14 Yordanova J, Kolev V, Rosso
OA, Schurmann M, Sakowitz OW, Ozgoren M, Basar E. Wavelet entropy analysis of
event-related potentials indicates modality-independent theta dominance. J
Neurosci Methods, 2002, 117(1): 99－109
15 Akay M, Akay YM, Cheng P, Szeto
HH. Time-frequency analysis of the electrocortical activity during maturation
using wavelet transform. Biol Cybern, 1994, 71(2): 169－176
16 Akay M, Akay YM, Szeto HH.
The effects of morphine on the relationship between fetal EEG, breathing and
blood pressure signals using fast wavelet transform, Biol Cybern, 1996, 74(4):
367－372
17Akay
M, Akay YM, Cheng P, Szeto HH. Investigating the effects of opioid drugs on
electrocortical activity using wavelet transform. Biol Cybern, 1995, 72(5): 431－437
18 Akin M. Comparison of wavelet
transform and FFT methods in the analysis of EEG signals. J Med Syst, 2002,
26(3): 241－247
19 Schiff SJ, Aldroubi A, Unser
M, Sato S. Fast wavelet transformation of EEG. Electrencephalogr Clin
Neurophysiol, 1994, 91(6): 442－455
20 Sartoretto F, Ermani M.
Automatic detection of epileptiform activity by single-level wavelet analysis.
Clin Neurophysiol, 1999, 110(2): 239－249
21 Uchibori M, Saito K, Yokoyama
S, Sakamoto Y, Suzuki H, Tsuji T, Suzuki K. Foci identification of spike
discharges in the EEGs of sleeping El mice based on the electric field model
and wavelet decomposition of multi monopolar derivations. J Neurosci Methods,
2002, 117(1): 51－63
22 Clark I, Biscay R, Echeverria
M, Virues T. Multiresolution decomposition of non-stationary EEG signals: A
preliminary study. Comput Biol Med, 1995, 25(4): 373－382
23 Mallat SG. A theory for
multiresolution signal decomposition: The wavelet representation. IEEE Trans
Pattern Anal Machine Intell, 1989, 11: 674－693
24 Li D, Magnuson DSK, Jung R.
Non-stationary analysis of extracellular neural activity. Neurocomputing, 2000,
32-33: 1083－1093
25 Steriade M, McCormick DA,
Sejnowski TJ. Thalamocortical oscillation in the sleeping and aroused brain.
Science, 1993, 262(5134): 679－685
26 Dijk DJ, Hayes B, Czeisler
CA. Dynamics of electroencephalographic sleep spindles and slow wave activity
in men——Effect of sleep deprivation.
Brain Res, 1993, 626(1-2): 190－199
27 Mandile P, Vescia S,
Montagnese P, Piscopo S, Cotugno M, Giuditta A. Post-trial sleep sequences
including transition sleep are involved in avoidance learning of adult rats.
Behav Brain Res, 2000, 112(1-2): 23－31.
_____________________________________
Received: February 21, 2003Accepted: May 23, 2003
*Correspondence: Tel, 86-571-87951539; Fax, 86-571-87951358; e-mail, [email protected]