18-01-2013, 02:49 PM
Non-linear analysis of EEG signals at various
sleep stages
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Introduction
Non-linear dynamical analysis has emerged as a
novel method for the study of complex systems
in the past few decades. The non-linear analysis
method is effectively applied to electroencephalogram
(EEG) to study the dynamics of the complex
underlying behavior [1]. The growth of this method
as a tool for mental health evaluation mainly rests
∗ Corresponding author.
E-mail address: aru[at]np.edu.sg (R. Acharya U.).
on the non-invasive nature of EEG. The approach
is based on the principles of non-linear dynamics
and deterministic chaos that involves the characterization
of the system attractors with its invariant
parameters. This method is far more superior to the
traditional linear methods such as the Fourier transforms
and power spectral analysis [2]. Yet, since the
EEG signal is non-stationary and noisy, all such studies
should be carried out with care and caution [3].
Analysis of sleep EEGs is a very important research
branch of medicine, because of its clinical applications
(such as diagnosis of schizophrenia) and in
brain dynamics research.
0169-2607/$ — see front matter © 2005 Elsevier Ireland Ltd. All rights reserved.
Sleep is not a uniform state, but is characterized
by a cyclic alternating pattern of non-rapid
eye movement (REM) and REM sleep [4—9]. Non-
REM sleep encompasses the deeper stages of sleep
(sleep stages 1 and 2, and slow wave sleep with
sleep stages 3 and 4), whereas REM sleep is a highly
activated state of the brain accompanied by dreaming.
Sleep patterns in humans undergo a marked
change from birth to old age.
In sleep 0 (awake) stage, the patient’s eyes are
open and the EEG is rapidly varying. The voltage
is low and the ‘‘beta waves’’ are prominent. Eyes
move very slowly, the EEG frequency will be 6—8 Hz
and alpha waves are more predominant in the sleep
1 (drowsiness) stage. Sleep 2 stage is the light sleep
state, where the eye movements stop and our brain
waves become slower. Special waves ‘K-complexes’
and sleep spindles begin to appear. In this state,
EEG amplitude is medium and EEG frequency is
4—7 Hz. In stage 3 (deep sleep), extremely slow
brain waves called delta waves begin to appear,
interspersed with smaller, faster waves. EEG signal
will have the frequency 1—3 Hz and amplitude
will be high. By stage 4 (deep sleep, slow wave
sleep), the brain produces delta waves. It is very
difficult to wake someone during stages 3 and 4,
which together are called deep sleep. In stage 4,
the amplitude of EEG will be high, but the frequency
will be less than 2 Hz. The subject’s eyes
move rapidly along with the occasional muscular
twitches in sleep 5 (REM) stage. Theta wave is more
predominant in this sleep stage.
The importance of the biological time-series
analysis, which exhibits typically complex dynamics,
has long been recognized in the area of
non-linear analysis. Several features of these
approaches have been proposed to detect the
hidden important dynamical properties of the
physiological phenomenon. The analysis of these
biological signals is complicated due to its highly
irregular and non-stationary property. The nonlinear
dynamical techniques are based on the
concept of chaos and it has been applied to many
areas including the areas of medicine and biology.
The theory of chaos has been used to detect some
cardiac arrhythmia such as ventricular fibrillation
[10]. Efforts have been made in determining
non-linear parameters like correlation dimension
for pathological signals and it has been shown
that they are useful indicators of pathologies.
Non-linear dynamics theory opens new window
for understanding behavior of EEG. EEG models
were proposed by Freeman [11] for neocortical
dynamics. The technique has been extended
here to identify the abnormalities of different
types. In analysis of EEG data, different chaotic
measures such as correlation dimension, Lyapunov
exponent and entropy are used in recent literature
Baumgaurt-Schmitt et al. have used neural network
to classify the various sleep stages by extracting
the features from the genetic algorithms [18].
Recently, the polysomnography of a healthy male
subject was analyzed by evaluating the correlation
dimensions. The correlation dimensions decreased
from the ‘awake’ stage to sleep stages 1—3 and
increased during rapid eye movement sleep. In each
sleep cycle, the correlation dimensions decrease
for slow wave sleep, and increase for REM sleep
[19,20]. Fell et al. have calculated the first Lyapunovexponents
(L1) for different sleep EEG signal
in 15 healthy subjects corresponding to the sleep
stages 1—4 and REM. And they found statistically
significant differences between the values of L1 for
different sleep stages [21]. Fell et al. have studied
the sleep stages using the spectral analysis and nonlinear
techniques [22,23]. They concluded that nonlinear
measures yield additional information, which
improves the ability to discriminate sleep stages.
Recently, Dingli et al. have shown the spectral analysis
technique for the detection of cortical activity
changes in sleep apnoea subjects. The most consistent
significant change is the decrease in theta
power, during NREM sleep is either associated with
an increase in high frequencies (alpha and sigma)
or delta increase [24]. In this work, we study the six
different types of sleep signals using the non-linear
parameters, namely correlation dimension (CD),
Hurst exponent (H), approximate entropy (ApEn),
largest Lyapunoventropy (LLE), fractal dimension
(FD), phase space plot and recurrence plots (RP).
Methodology
Subjects
The EEG data for analysis were obtained from the
Sleep-EDF Database available from the PhysioBank,
a data resource. The recordings were obtained from
Caucasian males and females (21—35 years old)
without any medication. The recordings were taken
for 24 h from eight subjects. Sleep EEG for 80 h
is extracted from the recordings and sampled at
100 Hz. The sleep stages are coded according to
Rechtschaffen and Kales based on Fpz-Cz/Pz-Oz
EEG [25]. In this work, the maximum available samples
for different sleep states were taken from the
PhysioBank, except for sleep state 0, where 1500
samples were selected. This sample size is sufficient
for accurate analysis and gives better sample
sizes distribution across the various sleep states.
Non-linear analysis of EEG signals at various sleep stages 39
In sleep 1 state, 800 samples (maximum available),
1000 samples in sleep 2—4 state and in sleep 5 state
900 samples (maximum available) were extracted
from PhysioBank for our study.
Phase space plot
In this approach, a phase space plot is obtained
with the X-axis representing the EEG sample x(k),
and the Y-axis representing the EEG sample after
a delay x(k + T). The delay interval T is calculated
using the minimal mutual information technique
[26,27]. It has been observed that the patterns
emerging on the screen can be correlated to the
various sleep states.