Diagnosis of epilepsy from interictal EEGs based on chaotic and wavelet transformation

Abstract

In this study, we have reinvestigated the chaotic features and sub-band energies of EEG and its ability for aiding neurologists in detecting epileptic seizures. The study was done on the EEG of ictal and interictal phases of epileptic patients and of normal subjects. The EEG was decomposed using discrete wavelet transform to obtain various sub-bands and the chaotic features like correlation dimension and largest Lyapunov exponent were extracted. The analysis results clearly show that the correlation dimension and largest Lyapunov exponent have their lowest value during seizure activity, higher for interictal and even higher values for normal EEG. These values strongly suggest that interictal phase EEG of an epileptic patient is less complex and more predictable compared to normal EEG. Chaotic features extracted are potential parameters for automated diagnosis of epilepsy. Support vector machine (SVM) classifier was implemented based on both sub-band energies and chaotic features extracted from EEG. Classification performance parameters of SVM classifier based on sub-band decomposed energies and chaotic features were calculated.

Full text

Diagnosis of epilepsy from interictal EEGs based on chaotic
and wavelet transformation
Jisu Elsa Jacob
1
•Vijith Vijayakumar Sreelatha
1
•Thomas Iype
2
•
Gopakumar Kuttappan Nair
3
•Doris George Yohannan
4
Received: 31 May 2016 / Accepted: 15 July 2016 / Published online: 2 August 2016
Springer Science+Business Media New York 2016
Abstract In this study, we have reinvestigated the chaotic
features and sub-band energies of EEG and its ability for
aiding neurologists in detecting epileptic seizures. The
study was done on the EEG of ictal and interictal phases of
epileptic patients and of normal subjects. The EEG was
decomposed using discrete wavelet transform to obtain
various sub-bands and the chaotic features like correlation
dimension and largest Lyapunov exponent were extracted.
The analysis results clearly show that the correlation
dimension and largest Lyapunov exponent have their lowest
value during seizure activity, higher for interictal and even
higher values for normal EEG. These values strongly sug-
gest that interictal phase EEG of an epileptic patient is less
complex and more predictable compared to normal EEG.
Chaotic features extracted are potential parameters for
automated diagnosis of epilepsy. Support vector machine
(SVM) classifier was implemented based on both sub-band
energies and chaotic features extracted from EEG. Classi-
fication performance parameters of SVM classifier based on
sub-band decomposed energies and chaotic features were
calculated.
Keywords Correlation dimension Discrete wavelet
transform Electroencephalogram Epilepsy Ictal 
Interictal Largest Lyapunov exponent
1 Introduction
EEG clearly sketches working of brain and contains valu-
able information relating to the neuro-physiological state of
the patient. It is a non invasive technique that can be used
extensively for the diagnosis of various pathological con-
ditions of the brain. Presently EEG is analysed only by
visual inspection and linear method of analysis with which
only subtle information can be extracted. Brain being a
highly dynamic and non linear system can be analysed in a
better way by chaotic analysis.
Seizure is an event in which there is excessive and
abnormal firing of the neurons in the cortex of the brain.
Seizures can occur due to many causes—ranging from
pathologies in the brain, imbalance in blood electrolytes,
extreme temperature to infections or toxins affecting the
brain. We generally say that these are ‘provoked’ type of
seizures. Epilepsy is a specific condition in which a patient
suffers from recurrent and unprovoked seizures. If an
epileptic patient suffers from an attack of a seizure, he is
said to be in an ‘ictal’ phase. The time period in which the
patient does not have a seizure is referred to as an ‘inter-
ictal’ period. The duration of an interictal period depends
upon the frequency of seizures, type of epilepsy and is
quite variable from patient to patient [1].
Discrete wavelet transform has been widely used in
biomedical signals as they are non stationary. The major
&Vijith Vijayakumar Sreelatha
vijith729@gmail.com
1
Department of Electronics and Communication Engineering,
Sree Chitra Thirunal College of Engineering,
Thiruvananthapuram, Kerala, India
2
Government Medical College, Thiruvananthapuram, Kerala,
India
3
Department of ECE, TKM College of Engineering, Kollam,
Kerala, India
4
Department of Anatomy, Sree Gokulam Medical College and
Research Foundation, Venjaramoodu, Thiruvananthapuram,
Kerala, India
123
Analog Integr Circ Sig Process (2016) 89:131–138
DOI 10.1007/s10470-016-0810-5

advantage of discrete wavelet transform is that both time
and frequency information can be extracted from it. The
mother wavelet taken for this study is Daubechies wavelet
and it has been used for the sub band decomposition.
Chaotic features measure the complexity and chaoticity of
the brain dynamics. Our study aims at understanding the
non linear dynamics of EEG during the ictal and interictal
phase of epilepsy.
2 Materials and methods
For conducting the wavelet analysis and chaotic analysis,
EEG data has been taken from Government Medical College
Thiruvananthapuram, Kerala. EEG data of epileptic patients
during their ictal and interictal phase has been obtained and
compared with that of normal healthy subjects. We con-
ducted this study on 10 epileptic patients. The diagnosis of
epilepsy was made by consultant neurologists. We obtained
10 ictal phase EEG epochs and 10 interictal phase EEG
epochs from each of the 10 epilepsy patients. We compared
the data with a control group of 20 normal individuals. EEG
was taken for them for evaluation of syncope and was found
to be normal. 5 epochs of EEG was obtained for each normal
patient. All epochs were selected by consultant neurologists
by identifying artifact free regions. Each EEG epoch has
6000 sampling points covering 12 seconds with sampling
frequency 500 Hz. Cases with age more that 50 years and
age less than 20 years were excluded. Cases with neuro-
logical diagnosis other than epilepsy were excluded. All
EEG signals were recorded with 128 channel amplifier sys-
tem and 12 bit A/D resolution with spectral bandwidth of
0.5–80 Hz for the acquisition system. The average reference
montage was selected for all the EEG data used in this study.
Figure 1shows three sample EEG epochs of Ictal EEG,
Interictal EEG and Normal EEG.
All the analysis related to this work were done using
MATLAB R2013a which is a high level technical com-
puting software and used extensively in the field of signal
processing, numerical integration and many other appli-
cation fields.
3 Methodology
The methodology used in this work consist of three steps
(1) EEG is decomposed into its sub-bands delta, theta,
alpha and beta using wavelet transform and their energies
are calculated (2) Chaotic features Correlation dimension
(CD) and largest Lyapunov exponent (LLE) are calculated
for normal and epileptic EEG (3) SVM classifier is
implemented based on chaotic features as well as energies
of EEG sub-bands and classifier performance is evaluated.
3.1 Discrete wavelet transform (DWT)
Fourier transform is being employed for the EEG analysis to
get spectral information but their time domain information is
also relevant for its analysis. Multi-resolution analysis like
Fig. 1 a Ictal EEG, bInterictal EEG, cNormal EEG
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123

wavelet transform gives a time frequency representation of
the signal [2]. DWT of a time series signal like EEG is
obtained by passing it through a series of high pass and low
pass filters. The advantage for DWT is the low computation
time and ease of implementation considering the samples to
be passed through a low pass filter of impulse response of
g[n] and a high pass filter of impulse h[n] [3].
Ylow n½¼xn½gn½¼X
1
k¼1
xk½gnk½ ð1Þ
Yhigh n½¼xn½hn½¼ X
1
k¼1
xk½hnk½ ð2Þ
This low pass filter output is again passed through a set
of high pass and low pass filter thus downsampling it by 2.
Then the filter outputs are
Ylow n½¼xn½gn½¼X
1
k¼1
xk½g2nk½ ð3Þ
Yhigh n½¼xn½hn½¼ X
1
k¼1
xk½h2nþ1k½ð4Þ
When the EEG signal is decomposed by 6-level discrete
wavelet transform as shown in Fig. 2the various sub-bands
can be obtained [4]. Delta sub-band less than 4 Hz (A
6
),
theta from 4 to 7 Hz (D
6
), alpha from 8 to 13 Hz (D
5
), beta
from 13 to 30 Hz (D
4
) and gamma greater than 30 Hz (D
3
)
are obtained as shown in Fig. 3.
3.2 Chaotic analysis
All physiological signals are non stationary and cannot be
analysed completely by the classical time-domain analysis
or frequency-domain techniques. Many studies have
proved promising results for the chaotic analysis of such
signals.
The EEG signal can be represented as a time series
vector x[n] ={x
1
,x
2
……….x
N
} recorded at various time
instants where N is the total numbers of data points and the
subscripts are indicating the time instants of the data point.
Phase space reconstruction, being the first step in chaotic
analysis of time-series, is done using Taken’s method [5].
The one-dimensional EEG time series x (n) is viewed in an
m- dimensional Euclidean space as,
XmnðÞ¼xnðÞ;xnþsðÞ;...;xnþm1ðÞsðÞ½ð5Þ
where sis the time delay and m is the embedding dimen-
sion. An important property of dissipative deterministic
dynamical systems is that, if the system is observed for a
long time, the trajectory will converge to a subspace of the
total state space. This subspace is a geometrical object
which is called the attractor of the system. It is called
attractor since it ‘attracts’ trajectories from all possible
initial conditions. The strange or chaotic attractor is a very
complex object with fractal geometry as shown in Fig. 4.
The dynamics corresponding to a strange attractor is called
deterministic chaos.
Fig. 2 Structure of wavelet
decomposition
Analog Integr Circ Sig Process (2016) 89:131–138 133
123

3.2.1 Correlation dimension
Nonlinear systems gravitate towards the specific regions in
phase that is known as attractors. The attractor states the
response of the system as the time progress. The attractor has
two main properties complexity and chaoticity. Complexity
is a measure of geometrical properties of the attractor and is
characterized by the magnitude of attractor dimension which
need not an integer value. Complexity of the system corre-
sponds to the correlation dimension (CD) of the system.
Fractal dimension can be measured using correlation
dimension. Brain, being a non-linear system can be assessed
in this manner using its signal EEG. The pattern of neuronal
firing is less organized and has greater complexity for normal
healthy subjects. The complexity value decreases when the
signal goes from normal to epileptic seizure. That means the
value of CD generally decreases during this period.
Natarajan et al. [6] states that minimum embedding dimen-
sion should be greater than CD for any chaotic attractor.
False nearest neighbour (FNN) method is used to choose
the appropriate embedding dimension. If the embedding
dimension m is sufficiently high (more than twice the
dimension of the systems attractor), the series of recon-
structed vectors constitute an ‘equivalent attractor’. The
method of estimating the embedding dimension from the
phase space patterns proposed by Grassberger et al. [7]is
followed in this work. The probability of two points on the
trajectory that are separated by a distance r indicates the
correlation integral function C(r). Our values support this
as the minimum embedding dimension is identified as 10
and time delay is 1. Figures 5and 6show the computation
of correlation integral and correlation dimension.
Correlation integral C(r)
CðrÞ¼ 1
N2X
N
x¼1
X
N
y¼1;x6¼1
hrXxXy



 ð6Þ
Fig. 3 Various EEG sub-bands after discrete wavelet transform
Fig. 4 Chaotic attractor
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123

CD ¼lim
r!0
log CðrÞ
logðrÞð7Þ
where N is the number of data points in phase space, r is
the radial distance around each reference point X
i
,X
x
,X
y
is
the points of the trajectory in the phase space, His the
Heaviside function.
3.2.2 Largest Lyapunov exponent
Largest Lyapunov exponent corresponds to chaoticity of a
system. Lyapunov exponent kmeasures the rate at which the
trajectories separate from one another. LLE (k
max
)ofthe
attractor is a measure of the convergence or divergence of
nearby trajectories in phase space. It provides a quantitative
and qualitative characterization of dynamical behaviour of the
system. For diverging trajectory, system has more than one
positive Lyapunov exponents, then the future state of the
system with an uncertain initial condition cannot be predicted.
This type of system is known as chaotic. A positive Lyapunov
exponent effectively represents a loss of system information
[8]. For converging trajectories, the corresponding Lyapunov
exponents are negative. A zero exponent means that orbits
maintain their relative positions and they are on stable attrac-
tors. Finally, a positive exponent implies the orbits are on a
chaotic attractor. An embedding dimension of 10 and a delay
of 1 is used for calculating LLE. The algorithm proposed by
Wolf et al. [9] is used to extract LLE from EEG data.
Consider two EEG data points X
0
and X
0
?dx
0
each of
which will generate an orbit in that space using some
system of equations and the separation between the two
orbits will be a function of time. Sensitive dependence can
arise only in some portions of a system, this separation is
also a function of the location of the initial value and has
the form dx(X
0
,t). In a system with attracting fixed points
or attracting periodic points dx(X
0
,t) diminishes asymp-
totically with time. For chaotic points, the function dx(X
0
,t)
will behave erratically. Thus it is useful to study the mean
exponential rate of divergence of two initially close orbits
using the formulae,
k¼lim
t!1
1
tln jdxX
0;tðÞj
jdX0jð8Þ
3.3 Classification with support vector machine
(SVM)
In binary classification, support vector machine is one of the
commonly employed supervised learning models. For pat-
tern classification, SVM is a powerful tool and it is based on
the statistical learning theory and structural risk minimisa-
tion. The algorithm involves training with feature vectors X
i
of signals of two different classes for normal and interictal to
learn a decision boundary that separates these two classes.
Once the decision boundary is learned, the SVM algorithm
determines the class membership of a newly observed fea-
ture vector X
i
based on which side of the boundary the
vector falls. Classifier performance can be analysed by the
computation of sensitivity, specificity and accuracy [10].
Sensitivity Number of true positives/the total number of
interictal segments labelled by the trained neurologist. True
positive represents an interictal segment that is identified
by the EEG experts and correctly detected as ‘interictal’ by
the algorithm.
SN ¼TP
TP þFN 100 ð9Þ
Specificity Number of true negatives/the total number of
normal segments labelled by the trained neurologist. True
negative represents a segment labelled as normal both by
the algorithm and by the trained neurologist.
SP ¼TN
TN þFP 100 ð10Þ
Accuracy Number of correctly identified segments/total
number of segments.
AC ¼TP þTN
TP þTN þFP þFN 100 ð11Þ
True positive (TP) and True negative (TN) represents
the total number of correctly detected true positive events
and true negative events. The False positive (FP) and False
negative (FN) represents the total number of erroneously
positive events and erroneously negative events.
Fig. 5 Correlation integral v/s normalized distance
Fig. 6 Estimation of correlation dimension
Analog Integr Circ Sig Process (2016) 89:131–138 135
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4 Results and discussion
4.1 Wavelet analysis
Discrete wavelet analysis was performed on the data. EEG
epochs of both normal and epileptic patients were decom-
posed into sub-bands namely delta, theta, alpha and gamma
using DWT. Here as the sampling rate is 500 Hz, maximum
frequency is taken to be 250 Hz. Therefore 6-level decom-
position is carried out using dB2 as the mother wavelet [4].
Based on the results obtained, we can say that wavelet
transform has good resolution and high performance for
visualization of the epilepsy and it can be used in clinical
research area. Here, we are emphasising the relevance of
decreased values of energy for the different sub-bands in
interictal EEGs compared to normal EEG. As interictal
Fig. 7 Box plot representing energy distribution in delta band for
ictal, interictal and normal EEG
Fig. 8 Box plot representing energy distribution in theta band for
ictal, interictal and normal EEG
Fig. 9 Box plot representing energy distribution in alpha band for
ictal, interictal and normal EEG
Fig. 10 Box plot representing energy distribution in beta band for
ictal, interictal and normal EEG
Fig. 11 Box plot representing distribution of CD in ictal, interictal
and normal EEG
136 Analog Integr Circ Sig Process (2016) 89:131–138
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phase of an epileptic person is the seizure free period, these
decreased values can be greatly utilized for the diagnosis of
epilepsy. The result clearly shows that for all sub-bands,
interictal EEG has lower value compared to that of normal
EEG. Most of the related works have compared these
features for normal and ictal cases. So this result clearly
gives a new path for the automated diagnosis of epilepsy
and is emphasising the values corresponding to interictal
phase (Figs. 7,8,9and 10).
4.2 Chaotic analysis
Chaotic analysis was performed on EEG epochs of normal
subjects and epileptic patients and features were extracted.
These results convey the information that the complexity of
EEG and of brain dynamics is higher in the normal healthy
condition of a person. The values of CD and LLE were
calculated in Adeli et al. [11] from epileptic EEG available
in the data base of University of Bonn. It reported similar
results for CD but in case of LLE interictal had lower value
compared to ictal. In this work, both correlation dimension
and largest Lyapunov exponent were computed and were
found to be the lowest for ictal phase, higher for interictal
and even higher for normal healthy subjects (Figs. 11 and
12).
We have implemented an SVM classifier for the diag-
nosis of epilepsy from EEG signal during the interictal
state. The details of data set provided for training and
testing of the classifier is provided in Table 1. The features
utilized for classification with SVM include both the rela-
tive energies of sub-bands (delta, theta, alpha and beta) and
chaotic features CD and LLE. These features were used to
train the SVM classifier to classify the epileptic and normal
persons. The greatest advantage is that both the sub-band
energies and chaotic features can be utilised for this clas-
sification. Table 2shows the sensitivity, specificity and
accuracy values for classification based on both chaotic
features and energies of EEG sub-bands.
5 Conclusion
This work tried to compute the chaotic features as well as
the sub-band energies for ictal, interictal and normal EEG
and to classify them using SVM based on these extracted
features. Results show that the complexity, unpredictability
and randomness of brain activity reduce considerably in an
epileptic patient compared to a normal healthy subject.
This work may be extended for the diagnosis of other
pathological conditions. Here, we are emphasising the
relevance of decreased values of chaotic features and sub-
band energies in interictal EEG. Most of the works in the
field have compared these features for normal and ictal
cases. As interictal phase of an epileptic person is the
seizure free period, all these values can be greatly utilized
for the diagnosis of epilepsy.
Acknowledgments The authors are thankful to the authority of
Government Medical College, Thiruvananthapuram, Kerala for giv-
ing access to their epileptic EEG database. We are also thankful to the
neurologists and EEG technicians for the helpful discussions and for
clearing our queries related to this work.
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Fig. 12 Box plot representing distribution of LLE in ictal, interictal
and normal EEG
Table 1 Data set for training and testing
Interictal Normal Total
Training 50 50 100
Testing 50 50 100
Table 2 Classification performance based on EEG sub-band energies
and chaotic features
Based on EEG sub-band
energies
Based on chaotic
features
Sensitivity
(%)
90 100
Specificity
(%)
88 100
Accuracy
(%)
91 100
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Jisu Elsa Jacob received her
B.Tech degree in Electronics
and Communication Engineer-
ing from T.K.M College of
Engineering, Kollam and
M.Tech degree in Electronics
from Cochin University of Sci-
ence and Technology. She is
currently working as Assistant
Professor in Department of
Electronics and Communication
Engineering in Sree Chitra
Thirunal College of Engineer-
ing, Thiruvananthapuram. She
is currently pursuing her Ph.D.
in biomedical signal processing from University of Kerala.
Vijith Vijayakumar Sreelatha
received his B.Tech degree in
Electronics and Communication
Engineering from University of
Kerala. He is currently pursuing
his M.Tech degree in Signal
Processing from Sree Chitra
Thirunal College of Engineer-
ing, Thiruvananthapuram. His
area of interest is biomedical
signal processing and non linear
analysis.
Thomas Iype received his MD
(General Medicine) from Medi-
cal College Kottayam, Gandhiji
University in October 1988, DM
(Neurology) from Medical Col-
lege, Trivandrum, University of
Kerala in September 1991 and
MRCP (UK) Royal College of
Physicians London in 2000. He
has got a teaching experience of
35 years. He has set up Neu-
rology services for the first time
in Government Medical Col-
lege, Thrissur in 2006 and
organized upgradation of Neu-
rology department in Government Medical College, Thiruvanantha-
puram. He published extensively in many national, international
journals/conferences and author of many neurology related books. He
received state best doctor award in 2011 (Medical education cate-
gory), Government of Kerala. He is currently the Professor and Head
of the Department of Neurology, Government Medical College,
Thiruvananthapuram.
Gopakumar Kuttappan Nair
received his Ph.D. (Faculty of
Engineering and Technology) in
Chaos Theory and Applications
from University of Kerala
(2012). He is currently working
as Professor & Head, Depart-
ment of ECE, TKM College of
Engineering, Kollam, Kerala.
He is the member of Indian
Society for Technical Education
(ISTE), fellow of Institute of
Electronics & Telecommunica-
tion Engineering (IETE) and
The Institution of Engineers
India (IEI). He published many papers in International Journals,
International Proceedings and National Proceedings and also authored
several text book in engineering.
Doris George Yohannan is
currently working as Assistant
Professor of Anatomy in Sree
Gokulam Medical College and
Research Foundation, Thiru-
vananthapuram, Kerala. He
received his MBBS degree and
MD degree in Anatomy from
Government Medical College,
Thiruvananthapuram. He has
published in national and inter-
national journals of anatomy
and his field of interest is
neuroanatomy.
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