Use Of Recurrence For Detection of Epilepsy

Transcription

1 Volume 2, Issue 5, May 213 ISSN Use Of Recurrence For Detection of Epilepsy Mohd. Suhaib Kidwai 1, Saifur Rahman 2 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 1 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 213 Page 425

2 Volume 2, Issue 5, May 213 ISSN 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 ρ π.,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 the original phase space can be reconstructed by time delay embedding =(x, 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 ywhich is being taken from some other electrode and whose values are to be compared with that of x. 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 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 213 Page 426

3 Volume 2, Issue 5, May 213 ISSN 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: τ max =25 and τ min =-25 for EEG signals. This gives ρ π 1, where : ρ π = 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: 5-5 X channel is 3 Y channel is roh pie Volume 2, Issue 5, May 213 Page 427

4 Volume 2, Issue 5, May 213 ISSN X channel is 3 Y channel is roh pie.5 1 x X channel is 1 Y channel is roh pie.5 1 x The above drawn curves are the Recurrence plot and the plot showing the variation of coupling index between the signals which are taken from various electrodes or channels of EEG. 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.] 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 1, [4.] Pikovsky, M. Rosenblum and J. Kurths, Synchronization- A Universal Concept in Nonlinear Sciences, Cambridge University Press, Cambridge, England, (21). [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 213 Page 428

5 Volume 2, Issue 5, May 213 ISSN [6.] Schafer, M. G. Rosenblum, H. H. Abel, and J. Kurths, Synchronization in the human cardio respiratory system, Phys. Rev. E 6, 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(2). [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. 58, 315 (27). [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, 678 (1996). [1.] 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, 25 (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, (21). [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. 2, 65 (21). [14.] [15.] Volume 2, Issue 5, May 213 Page 429