International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
Volume 2, Issue 5, May 2013
ISSN 2319 - 4847
Use Of Recurrence For Detection of Epilepsy
Mohd. Suhaib Kidwai1, Saifur Rahman2
1&2
Department of Electronics & Communication,
Integral University, Lucknow ,India
Abstract
This paper proposes a very simple and user friendly method to determine the occurrence of epilepsy by using the EEG
signals.The mathematical concept of recurrence forms the basis for the detection of epileptic seizure ,and the tool used is
MATLAB.MATLAB allows the user to efficiently design an algorithm and execute a program so as to detect the level of
synchronism between the signals from various channels of an EEG machine.
Keyword: Introduction,Theory,Epileptic seizure,Recurrence
1. Introduction:
About 1% of the world’s population is suffering from epilepsy .In this scenario it becomes important to device a
method for efficient detection of epilepsy or epileptic fits,because the efficient and timely detection can only lead to the
timely treatment of any disease.
In this work I had use the mathematical concept of recurrence and a factor called synchronization index to determine
the occurrence of epileptic seizure.
2. Theory:
Epilepsy is a common term that incorporates different types of seizures. Epilepsy is characterized by unprovoked,
recurring seizures that disturb the nervous system. Seizures or convulsions are temporary alterations in brain functions
due to abnormal electrical activity of a group of brain cells that present with apparent clinical symptoms and findings .
Epilepsy may be caused by a number of unrelated conditions, including damage resulting from high fever, stroke,
toxicity, or electrolyte imbalances.
The disease epilepsy is characterized by a sudden and recurrent malfunction of the brain that is termed “seizure.”
Epileptic seizures reflect the clinical signs of an excessive and hyper synchronous activity of neurons in the brain .
Approximately one in every 100 persons will experience a seizure at some time in their life .
Epilepsy can be segregated into two broad categories namely idiopathic epilepsy and symptomatic epilepsy. The former
is a kind of epilepsy in which the cause for the epilepsy remains unmarked whereas in the latter case a concrete cause is
identified. The symptomatic epilepsy is typically identified through any one of the subsequent symptoms: stroke,
serious illness in the nervous system, severe damage to the skull and more. In general there are nearly twenty types of
seizures. These types are again divided into two categories namely partial seizures and generalized seizures.[2]
Fig. 1: Coupling of EEG signals taken from channel C3 and F7,during epileptic seizure
Volume 2, Issue 5, May 2013
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International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
Volume 2, Issue 5, May 2013
ISSN 2319 - 4847
During the onset of epileptic seizure all the channels of an EEG machine give the signals which have the high degree
of phase synchronization or coupling.The condition for the epileptic seizure is that all the channels of the EEG from
the patient’s head give the electric signals which have a high degree of synchronisation.
This degree of synchronisation has been measured by using a mathematical parameter known as coupling index ρπ(t).
,where
is the normalised order pattern value.
This
is measured for each signals that are being taken from the different electrode and then the values of
are
plotted against time,the high rising of this
graph shows the instants of high synchronisation between the two
EEG signals taken from two different electrodes placed on the same patient .
So to check the onset of the epileptic seizure ,EEG signals from various channels are compared and the coupling
index
is calculated and plotted between the signals .The high value of
between the
various channels suggests the onset of epileptic seizure[13]
Fig. 2: Flowchart/Algorithm of calculating
using the available EEG data
The above flowchart explains the step by step method of calculating the
and also shows the intermediary
requirements for the calculation and plotting of .The algorithm is briefly explained below:
1. Taking the samples from EEG machine :The samples are taken from different electrodes and processed in such a
manner that the values can be stored in a matrix .The matrix is treated as the input for the MATLAB program which is
made for calculation of
2. Calculation of the order pattern values for the signals taken from different electrode:Once the signal samples are
being taken they are compared with themselves first in the following manner:
Given a dynamical system represented by a one-dimensional time series {x(t)}t the original phase space can be
reconstructed by time delay embedding (t)=(x(t) , x(t +υ) , ..., x(t+(n−1)υ))
We denote these relations as order patterns π and derive the symbol sequence
Similarly
can be calculated for the signal y(t)which is being taken from some other
electrode and whose
values are to be compared with that of x(t).
3. Once the order patterns are formed we will get the matrix of
and
.Next step is to compare every value of
with every value of
using the following condition:
Here ORP means Order Recurrence Plot.This is a plot which will represent the matrix of 0’s and 1’s in a graphical
form.
Hence ORP is a plot of a Boolean matrix R (t, t’) of size MxN, where M, N are the lengths of the order pattern
sequences. Similarly to the CRPs we observe different structures in the ORPs. If there are no dependencies the plot is
dominated by single dots. Strong dependencies yield to diagonal lines
Volume 2, Issue 5, May 2013
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International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
Volume 2, Issue 5, May 2013
ISSN 2319 - 4847
ORP on different time series. (a) Bivariate Gaussian noise, (b) Periodic functions with time-varying amplitudes and
off-sets, but constant period, (c) Periodic functions with decreasing and increasing period, respectively, and (d) Onset of
an epileptic seizure on EEG channels. All plots with embedding dimension n=3.
For short time dependencies we have used a modified form of previous equation as given below:
In this way we focus the study to an area close to the main diagonal. Diagonal lines of figures are transformed to
horizontal lines and it is more convenient to study a longer range in time.
4. Finding the recurrence rate of order patterns:Now when we have ORP next step is to find the recurrence rate of order
patterns using the following formula:
5. Now the final step is to find the coupling index which will be detremined by using the above found parameters.The
values of
will be fed in the following formula:
τmax=25 and τmin=-25 for EEG signals.
This gives 0≤ ρπ≤ 1, where :
ρπ =0 corresponds to no coupling
For each and every step described above ,a separate MATLAB program has been written and then a they are put
together to form a main program which finds the value of
and finally the values of
between the signals from two
channels of an EEG is plotted in MATLAB tool to see the degree of synchronisation between the signals from the two
channels of the EEG [1][3][5].
Likewise signals from all the channels will be used to find the degree of synchronism between them.A high degree of
synchronism between all the channel shows the onset of epileptic seizure.
3. Results:
Here I had take two random channels or electrodes and found the coupling index between them.Their plots are given
below:
X channel is 3
500
0
-500
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Y channel is 27
500
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pie
pie
ro
h (t)
Copling Index roh
0. 01
0. 005
0
0
Volume 2, Issue 5, May 2013
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Time
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4500
5000
5500
(t )
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Page 427
International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
Volume 2, Issue 5, May 2013
ISSN 2319 - 4847
X channel is 3
500
0
-500
0
1000
2000
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6000
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6000
Y channel is 5
200
0
-200
0
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5
10
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pie
roh (t)
500
1000
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3500
pie
x 10
0
2500
Copling Index roh
-3
1
0.5
0
500
1000
1500
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Time
4000
4500
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5500
(t)
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X channel is 1
500
0
-500
0
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6000
Y channel is 7
2000
0
-2000
0
1000
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pie
roh (t)
1
0.5
0
0
500
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Copling Index roh
-3
4000
4500
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5500
(t)
pie
x 10
1000
1500
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2500
Time
3000
3500
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4500
5000
The above drawn curves are the Recurrence plot and the plot showing the variation of coupling
the signals which are taken from various electrodes or channels of EEG.
index
(t) between
Following inferences can be deduced from the above drawn curves:
1. The coupling index between any two channels is increasing with increase in the disturbances in the signals taken
from the different electrodes.
2. During the disturbances the phase of the signals aquires synchronism,and hence the coupling index
is
increasing when the disturbance is increasing.This shows that the signals are higly coupled or synchronised.
3. The graph having random black and white lines is referred as the order recurrence plots and they show the matrix
which is formed after comparing the
,where x and y are the signals taken from different channels
and refers to the immediate neighbors with which a sample is compared.
4. Conclusion:
From the above plots it is evident that their is a significant amount of synchronism between the various channels and
hence it can be termed that the patient(whose data is taken),is suffering from acute epileptic seizure at an instant.
This work paves the way for developing easy and flexible algorithms which can be used to detect the brain related
disorders by taking the EEG samples and finding the degree of synchronism between them by using the mathematical
concept of recurrences.
Moreover since this method is basically programming based and uses the mathematical relation of recurrence ,so this
work can further help the researchers to make a program or develop an algorithm which can use other signals like ECG
and EMG to diagnose other cardiac or muscular disorders.
References:
[1.] MATLAB:An Introduction with applications By Amos Gilat.
[2.] Recurrence plots for the analysis of complex systems ,Norbert Marwan, M. Carme Romano, Marco Thiel, Jürgen
Kurths, Nonlinear Dynamics Group, Institute of Physics, University of Potsdam, Potsdam 14415, Germany.
[3.] Time Series Analysis of Complex Dynamics in Physiology and Medicine Leon Glass and Daniel Kaplan
Department of Physiology, McGill University 3655Drummond Stree Montreal, Qebec Canada H3G 1Y6
November 10, 1992.
[4.] Pikovsky, M. Rosenblum and J. Kurths, Synchronization- A Universal Concept in Nonlinear Sciences, Cambridge
University Press, Cambridge, England, (2001).
[5.] Schafer, M.G. Rosenblum, J. Kurths, and H. H. Abel, Intermittent Lag Synchronization In a Driven System of
Coupled Oscillators, Nature (London) 392, 239 (1998).
Volume 2, Issue 5, May 2013
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International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
Volume 2, Issue 5, May 2013
ISSN 2319 - 4847
[6.] Schafer, M. G. Rosenblum, H. H. Abel, and J. Kurths, Synchronization in the human cardio respiratory system,
Phys. Rev. E 60, 857 (1999).
[7.] Stefanovska, H. Haken, P. V. E. McClintock, M. Hozic ,F. Bajrovic, and S. Ribaric, Reversible Transitions
between Synchronization States of the Cardio respiratory System Phys. Rev. Lett.85, 4831(2000).
[8.] Musizza, A. Stefanovska, P.V. E. McClintock,M. Palus, J. Petrovci, S. Ribaric, and F. F. Bajrovic, Interactions
between cardiac, respiratory and EEG-δ oscillations in rats during anesthesia, J. Physiol. 580, 315 (2007).
[9.] S. J. Schiff, P. So, T. Chang, R. E. Burke, and T. Sauer, Detecting dynamical interdependence and generalized
synchrony through mutual prediction in a neural ensemble, Phys. Rev. E 54, 6708 (1996).
[10.] M. L. van Quyen, J. Martinerie, C. Adam, and F. J. Varela, Nonlinear analyses of interictal EEG map the brain
interdependences in human focal epilepsy, Physica (Amsterdam) 127D, 250 (1999).
[11.] P. Tass, M. G. Rosenblum, J. Weule, J. Kurths, A. Pikovsky, J. Volkmann, A. Schnitzler, and H.J.Freund,
Detection of n:m Phase Locking from Noisy Data: Application to Magnetoencephalography, Phys. Rev. Lett.81,
3291(1998).
[12.] M. Palus, V. Komarek, Z. Hrncır, and K. Sterbova, Synchronization as adjustment of information rates: Detection
from bivariate time series, Phys. Rev. E63, 046211 (2001).
[13.] M. Palus, V. Komarek, Z. Prochazka, Z. Hrncir, and K. Sterbova, Synchronization and Information flow in EEGs
of Epileptic Patients, IEEE Eng. Med. Biol. Mag. 20, 65 (2001).
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[15.] www.encyclopedia.com
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