Proceedings of 2013 IEEE Conference on Information and Communication Technologies (ICT 2013)
Fuzzy Lyapunov exponent based onset detection of the Epileptic Seizures N. Arunkumar, K. Ramkumar, S. Hema, A. Nithya, Poornima Prakash, V. Kirthika Department of Electronics and Instrumentation Engineering SASTRA UNIVERSITY Thanjavur, India
[email protected] Abstract – Various algorithms have been proposed for the detection of onset of epilepsy. Here we have used the Rosenstein algorithm to calculate the Largest Lyapunov exponent of the given Electroencephalogram (EEG) signal. We have combined this algorithm with fuzzy-rule based system. A fuzzy interference system is employed to detect the normal and the onset of epilepsy. Keywords: Fuzzy logic, epilepsy, Largest Lyapunov Exponent.
I.
INTRODUCTION
Electroencephalogram (EEG) was discovered in 1930 [10] and this rGcords the electrical activity of the brain. The recording is done using surface electrodes placed at the scalp of the head. This is recorded from different positions of the scalp. Hence it can also be used for recording the abnormal electrical patterns arising in the brain. One such abnormal pattern is called as epilepsy. It is said that about 50 million people in the world have epilepsy. One who has this problem is not received well in the society. Epilepsy is the neurological disorder. This is characterized by the sudden occurrence of seizures in some portion of the brain [13]. These seizures come as episodic but occur as temporary events. They are understood as abnormal and excessive discharges from the brain. Epilepsy may lead to severe injuries as they get onset randomly for a person and if one is driving or swimming, it can lead to fatal injuries or even death, as one may even lose consciousness during epilepsy. Hence if an alarm system can be designed to monitor the patient for the onset of epilepsy, it can be used to give an alarm to alert the patients [14]. Many methods have been employed in the past [1, 2, 4] for detecting the onset of the seizure. Seizure termination was identified using sample entropy [4]. In our previous work, we have also employed approximate entropy (ApEn) [3] for detecting the onset of epilepsy [19]. In this work, we have used lyapunov exponent and fuzzy logic as a tool to detect onset and termination of epileptic seizure automatically without any manual monitoring of doctors.
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II.
METHODS AND MATERIALS
In this section, we describe the methods that we have employed for the automatic detection of the onset of epileptic seizures. A. Data The EEG data for this work was collected from the Department of Neuromedicine, Thanjavur Medical College Hospital, Thanjavur. The dataset contains two types, i.e., normal EEG, normal EEG followed by the onset of epileptic seizures. A total of 200 such data were collected and considered for analysis in this work. The EEG was recorded using a neuroscan machine named Neuromax from Medicaid systems at 256 samples per second. Each data is acquired for 32 seconds. B. Largest Lyapnunov Exponent (LLE):: Largest Lyapunov Exponent (LLE) measures the sensitive dependence on the initial conditions [17]. It measures the chaos of the signal quantitatively. Wolf et al was the one who proposed the first algorithm for calculating the Largest Lyapunov Exponent [13]. The disadvantage of this is that it is sensitive to noises. And it is also unreliable for small sets of data. Due to the disadvantages of Wolf algorithm , we have moved on to the Rosenstein algorithm which is fast, easy to implement and robust to changes in relation to the following quantities: embedding dimension, time delay, divergence of nearest trajectories, noise level and size of data set [13]. Hence we are using Rosenstein algorithm in this work to identify the LLE. C. LLE Calculation: In general, the presence of repetitive patterns in a time series make it more predictable than the one without repetitive patterns. LLE is utilized to characterize this dynamics in electroencephalogram time series. The normal EEG is random in nature i.e., no repetitive patterns whereas epileptic signal has almost repetitive patterns. When there is chaos in the signal, it is characterized by Largest Lyapunov Exponent [15]. The calculation of LLE is given as below: First step is the reconstruction of dynamic attractor from a single time series.
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Proceedings of 2013 IEEE Conference on Information and Communication Technologies (ICT 2013) The reconstructed trajectory is denoted as X. It is a M×m matrix in which each row is a phase-space vector. ܺ ൌ ሾܺଵ ܺଶ ǥܺெ ሿ்
….(1)
where ܺ is the state of the dynamic system at the discrete time i. Each ܺ is given as ܺ ൌ ሾݔ ݔା ǥ ǤǤݔାሺିଵሻ ሿ , where J is the reconstruction delay and m is the embedding dimension. The relation between m, M, J and N is given as M = N-(m-1) J
….(2)
After the reconstruction of dynamics the nearest neighbor of each point of trajectory is located. The nearest neighbor, ܺÉ , is found by searching for the point that minimizes the difference for the particular reference point, ܺǤ This can be expressed as follows,
݀ ሺͲሻ ൌ ೕ ܺ צ െ ܺ צ
….(3)
Where ݀ ሺͲሻ is the initial distance from the point j to its nearest neighbor. The lyapunov exponent is calculated as , ଵ
ଵ
ሺெିሻ
ௗ ሺሻ
ߣଵ ሺ݅ ሻ ൌ Ǥ௱௧ . ሺெିሻ σୀ ݈݊ ௗ ೕሺሻ ….(4) ೕ
Where t is the sampling period,݀ ሺ݅ሻ is the pair of nearest neighbors and i is the discrete time steps. D. LLE for normal EEG and epileptic EEG: The positive value of LLE indicates the chaotic nature of the signal [20]. There is a significant variation in the value of LLE which is calculated from the EEG signal of epileptic patients than from the EEG signal of healthy volunteers [20]. For calculating the LLE in this work, we chose embedding dimension as 3 and time delay (lag) as 1. The LLE values are plotted against the total number of samples. It is found from the graph that the value of LLE is almost less than 10 for non-epileptic EEG signal and greater than 10 for epileptic signal (fig.1). E. Fuzzy Rule-Based Decision Making: The largest lyapunov exponent values of the EEG signal are given as input to the fuzzy interference system (FIS). The threshold parameter is set as 10. The input variables are normalized into the interval [0 15] for fuzzification. The trapezoidal membership functions were assigned to input and output variables of the fuzzy system [14]. Three membership functions or fuzzy sets are assigned as input such as LOW (‘L’) for LLE10 and MEDIUM (‘M’) for 9< LLE< 11.
978-1-4673-5758-6/13/$31.00 © 2013 IEEE
Here we have used Sugeno fuzzy model for generating fuzzy rules. The ‘If Then’ rules which are framed for the fuzzy system to detect the onset are as follows, (1) If the input is L then the output is 0. (2) If the input is M then the output is 0.5. (3) If the input is H then the output is 1. The signal is given as input using Adaptive Neuro Fuzzy Interference system (Anfis). Using the rules given above, three levels of outputs are generated. The output will be ‘0’ for the input fuzzy set ‘L’ (fig.2). This shows that the signal is normal and free from epileptic seizure. The output will be ‘1’ for the input fuzzy set ‘H’ (fig.3). This indicates that the signal has epileptic seizures., whereas the output will be ‘0.5’ for the input fuzzy set ‘M’ (fig.4) which shows the seizure onset. II.
RESULTS AND DISCUSSION
The LLE is calculated for every 46 samples of an EEG signal and plotted against the total number of samples (8000). From the Fig (1), it is found that the LLE value for the onset of epileptic seizure is 10 (below 10 as normal and above 10 as epilepsy).These values are kept as a threshold value for the fuzzy interference system. Fig (1) shows the plot of EEG signal with seizure against LLE. Fig (2) shows the output of fuzzy interference system for normal condition i.e., output as 0 (L). Fig (3) shows the output of fuzzy system for epileptic seizure i.e., output as 1 (H) and Fig (4) shows the output of the fuzzy system for onset of epileptic seizure i.e., output as 0.5 (M). III.
CONCLUSION
In this paper, we presented a method to detect the onset of seizure using fuzzy interference system. We focused in designing an alarm system to alert the patient at the seizure onset using adaptive fuzzy logic system.The overall accuracy achieved is 94%. REFERENCES [1] U. Rajendra Acharya, Filippo Molinarib, S. Vinitha Sreec, Subhagata Chattopadhyayd, Kwan-Hoong Nge,f, Jasjit S. Suri, “Automated diagnosis of epileptic EEG using entropies”, Biomedical Signal Processing and Control, 2012, pp. 401-408. [2] Truong Quang Dang Khoa, Nguyen Thi Minh Huong, and Vo Van Toi , “Detecting Epileptic Seizure from Scalp EEG Using Lyapunov Spectrum”, Computational and Mathematical Methods in Medicine Volume 2012 (2012), Article ID 847686, [3] Pincus, S.,. Approximate entropy (ApEn) as a complexity measure. Chaos 5, 1995, 110–117.
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Proceedings of 2013 IEEE Conference on Information and Communication Technologies (ICT 2013) [4] Abdulhamit Subasi ,” Application of adaptive neuro-fuzzy inference system for epileptic seizure detection using wavelet feature extraction”, Department of Electrical and Electronics Engineering, Kahramanmaras Sutcu Imam University, Kahramanmaraú, Turkey, computers in biology and medicine37(2007)227-244. [5] N. Arunkumar, V.S. Balaji, Subhasree, Vellanki Rathna lihitha, Sharmila, Sivakama sundari, “Automatic detection of epileptic seizures using independent component analysis”, IEEE International Conference on Advances in Engineering, Science and Management, Vol. 1, pp. 556-558 [6] N. Arunkumar, Mohamed Sirajudeen, Approximate Entropy Based Ayurvedic Pulse Diagnosis for Diabetics - A Case Study, IEEE. [7] N. Arunkumar, S. Jayalalitha, Adarsh Venugopal, Dinesh S, Dinesh Sekar, Sample Entropy based Ayurvedic Pulse Diagnosis for Diabetics, IEEE International Conference on Advances in Engineering, Science and Management, Vol. 2, pp. 65-66 [8] N. Arunkumar, S. Jayalalitha, Adarsh Venugopal, Dinesh S, Dinesh Sekar, Automatic Identification of Acute Arthristis from Ayurvedic Wrist Pulses, IEEE 2012 International conference on Electronics Computer Technology, Vol. 1, pp. 506-508 [9] Krystal AD, Zaidman C, Greenside HS, Weiner RD, Coffey CE, “The largest Lyapunov exponent of the EEG during ECT seizures as a measure of ECT seizure adequacy”, Electroencephalogr Clin Neurophysiol. 1997 Dec;103(6):599-606. [10] Swiderski,B,Osowski.S , Rysz. A,” Lyapunov exponent of EEG signal for epileptic seizure characterization” , Circuit Theory and Design, 2005. Proceedings of the 2005 European Conference on 28 Aug.-2 Sept. 2005 [11] James. C.J,Jones. R.D, Bones. P.J, Carroll. G.J, “Spatial analysis of multi-channel EEG recordings through a fuzzy-rule based system in the detection of epileptiform events”, Engineering in Medicine and Biology Society, 1998. Proceedings of the 20th Annual International Conference of the IEEE,29 Oct-1 Nov 1998.
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Proceedings of 2013 IEEE Conference on Information and Communication Technologies (ICT 2013)
Fig.1. EEG signal with epileptic seizure and its corresponding Largest Lyapunov exponent(LLE) value plot.
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Proceedings of 2013 IEEE Conference on Information and Communication Technologies (ICT 2013)
Fig. 2. Output is ‘0’ for ‘L’ fuzzy set (i.e. the LLE value is less than 10)
Fig.3. Output is ‘1’ for ‘H’ fuzzy set (i.e. for LLE greater than 10).
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Proceedings of 2013 IEEE Conference on Information and Communication Technologies (ICT 2013)
Fig. 4 Output is ‘0.5’ for ‘M’ fuzzy set (i.e. for LLE value between 9 & 11)
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