Wavelet Spectral Entropy for Indication of Epileptic Seizure in Extracranial EEG Xiaoli Li Cercia, School of Computer Science, The University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK [email protected]

Abstract. Automated detection of epileptic seizures is very important for an EEG monitoring system. In this paper, a continuous wavelet transform is proposed to calculate the spectrum of scalp EEG data, the entropy and a scaleaveraged wavelet power are extracted to indicate the epileptic seizures by using a moving window technique. The tests of five patients with different seizure types show wavelet spectral entropy and scale-averaged wavelet power are more efficiency than renormalized entropy and Kullback_Leiler (K-L) relative entropy to indicate the epileptic seizures. We suggest that the measures of wavelet spectral entropy and scale-averaged wavelet power should be contained to indicate the epileptic seizures in a new EEG monitoring system. The abstract should summarize the contents of the paper and should contain at least 70 and at most 150 words. It should be set in 9-point font size and should be inset 1.0 cm from the right and left margins. There should be two blank (10-point) lines before and after the abstract. This document is in the required format. Keywords: Epileptic seizure; Wavelet analysis; Spectral entropy; EEG.

1 Introduction It is known that continuous EEG recordings are widely applied to analyze / diagnose epilepsy patients [1], in particular automated detection of the epileptic seizures is very helpful and efficient for epilepsy diagnosis, unlike traditional methods that a trained technician reviews the entire EEG manually. Currently, various methods have been proposed, including linear methods [2], nonlinear methods [3-5], computational intelligence [6] and information theory [7]. The spectral analysis based method still is the most reliable for the detection of epileptic seizures. Since poor frequency resolution of the discrete Fourier transform (DFT), wavelet-based techniques are receiving growing interest given their ability to provide comparable spectral statistics that are local in time. At present, wavelet techniques become one of the most attractive methods to detect epileptic seizures [8-11]. Unfortunately, most of wavelet methods just focus on the energy information in the time frequency domain. In this paper, spectral entropy of neural activity at the time –frequency domain is proposed to indicate the epileptic seizures. Traditionally, the entropy can characterize the degree of randomness of time sequence and quantify the difference between two probability distributions. Generally speaking, entropy is a measure of the uncertainty I. King et al. (Eds.): ICONIP 2006, Part III, LNCS 4234, pp. 66 – 73, 2006. © Springer-Verlag Berlin Heidelberg 2006

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of a random process, or a complexity measure of a dynamical system [12]. In [7,13], renormalized entropy and Kulback-Leibler (K-L) entropy for EEG signals are proposed; it is found that there is a decrease of the renormalized and K-L entropy during the epileptic seizures. The following two disadvantages limit the detection of seizure. The spectral estimation with Fourier transform is possible to result in some of spouse information for a complex nonstationary EEG data. The second disadvantage of the renormalized entropy and K-L relative entropy is needed to determine a reference segment for each case. This paper presents wavelet spectral entropy and scale-averaged wavelet power to indicate the epileptic seizure. The five case studies showed that this method is better to indicate the epileptic seizures than renormalized and K-L entropy in EEG.

2 Methods Wavelet analysis is a powerful tool to analyze EEG data. Projecting a time series into a time–scale space, the dominant modes of variability and its variation over time can be explored [14]. Previous works show Morlet wavelet transform can efficiently represent neural activity [15]. A Morlet wavelet function ψ 0 (t ) is written as

ψ 0 (t ) = π −1 / 4eiω t e −t 0

where

ω0

2

/2

(1)

.

ω0 ≥ 6 , which is an optimal [16]. Given ψ 0 (t ) , a family of

is the wavelet central angle frequency, often

value to adjust the time – frequency resolution wavelet can be generated by a dilation,

ψ s (t ) =

1 ψ 0 (t / s), s ∈ (0,+∞) , s is 2

called scale. Wavelet ψ s (t ) can be taken as a parametric filter that is specified by the scale parameter s; and the duration of its impulse response increases with the increase of s. Continuous wavelet transform (CWT) are performed through the convolution of a parent wavelet function ψ s (t ) with the analyzed signal x(t); it is:

W ( s ,τ ) =

1 * t −τ x(t )ψ s ( )dt . ∫ s s

(2)

where s and τ denote the scale and translation; * denotes complex conjugation. By adjusting the scale s, a series of different frequency components in the signal can be extracted. The factor s is for energy normalization across the different scales. Through wavelet transforms, the information of the time series x(t) is projected on the two dimension space (scale s and translation τ ). Given an EEG time series, X={xn}, n = 0 … N-1, with equal time spacing dt, the continuous wavelet transform of the discrete sequence is defined as the convolution of xn with a scaled and translated version of ψ 0 (t ) ; it is given by

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Ws (n) = ∑ xnψ ' s *( n'=0

(n'− n)dt ). s

(3)

where * denotes the complex conjugate. Changing the wavelet scale s and translating along the localized time index n , a map can be constructed to show the amplitude of any feature versus the scale at a short time. Large values of the map (wavelet coefficients) reflect the combined effect of a large fluctuation of the time series and of a good matching of shape between the series and the wavelet function. If a vertical slice through a wavelet plot is a measure of the local spectrum, the time-averaged wavelet spectrum over a certain period is

Ws 2 ( n ) =

n2

1 na

∑ W (n)

n = n1

2

s

.

(4)

where the index n is arbitrarily assigned to the midpoint of n1 and n2; and na=n2-n1+1 is the number of points averages over. By repeating (4) at each time step, we create a wavelet plot smoothed by a certain window. We define the global time-average of the instantaneous wavelet spectrum as follows:

I (s) = W 2 ( s) =

1 N

N −1

∑ W ( n) n =0

s

2

.

(5)

Where I(s) is called wavelet spectrum, which is the expected value of the global timeaverage of the instantaneous power of Ws(n). The entropy concept is applied to measure the fluctuation of wavelet spectrum, which is called wavelet spectrum entropy. To examine fluctuations in power of a time series over a range of scales (a band), a scale-averaged wavelet power is defined as the weighted sum of the wavelet power spectrum over scales sj1 to sj2:

dd Wn2 = j t Cd

j2

∑

j = j1

Wn ( s j ) sj

2

.

(6)

where, dj is scale step; dt is the time space of the time series; the Cd is scale independence and is a constant for each wavelet function. The scale-averaged wavelet power is a time series of the average variance in a certain frequency band, which can be used to examine modulation of a time series. In the following section, the wavelet spectrum entropy and scale-averaged wavelet power are used to analyze the epileptic EEG signals; these two feature values are taken as the indications of the epileptic seizures simultaneously. These two features contain the change degree and distribution of signal power at the time – scale domain.

3 Results and Discussions The EEG data analyzed in this paper are derived from Dr. Alpo Vaerri (Tampere University of Technology). Sampling frequency of the EEG data is 200 Hz. The data

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is recorded by four bipolor montage, which are located in F8-C4, F7-C3, T6-02, and F5-01. EEG data of five patients with different epileptic seizures were collected by sampling frequency of 200 Hz. EEG of patient 1 contains petit mal epileptic discharges, patient 2’s EEG contains irregular type epileptic discharges, patient 3’s EEG contains three type epileptic discharges, patient 4’s EEG contains epileptic seizures with EMG activity on the EEG, and patient 5’s EEG contains psychometric epileptic seizures. (a) 100 E E G (m v)

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This paper uses wavelet spectrum entropy and scale-averaged wavelet power to indicate the epileptic seizures. An EEG data is divided into consecutive segments of length N=512 with a 50% overlap. Fig. 1 shows an EEG signal of patient 1, a petit mal epileptic seizure occurs at the 30 second. In Fig. 1 (b), K-L relative entropy can indicate the petit mal epileptic seizures occurred at the 30 second, however, the spikes that occurs after 90 second are detected as well. The renormalized entropy cannot give significant indications for these seizures. Fig. 1 (c) shows the wavelet spectrum entropy and scale - averaged wavelet power based on Morlet wavelet that can indicate the seizure at the second of 30. The epileptic seizure occurs at the second 12 is also indicated, unlike the K-L relative entropy and renormalized wavelet spectrum. The scale-averaged wavelet power can basically indicate other petit mal epileptic seizures as well, although it is not clearer than K-L relative entropy. This is due to the fact that the renormalized entropy and K-L relative entropy have a reference segment for the case. If we can select a reference segment well, a good result could be obtained, otherwise the result is so much bad. This selection is not a very easy task in the practical implement because of the variation of cases.

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Fig. 2. (a) EEG recorded from the F8-C4 electrode of patient 2 (irregular type epileptic discharges); (b) Renormalized entropy (solid line) and K-L relative entropy (dot line) calculated with FT; (c) The normalized wavelet spectrum entropy (solid line) and scale-averaged wavelet power (dot line) by using Morlet wavelet transform

Fig. 2 shows the EEG signal of patient 2 with irregular type epileptic seizure. The EEG signal contains two irregular epileptic seizures during the 50-60 and 105-110 second. Fig. 2 (c) shows the normalized wavelet spectrum entropy and scale-averaged wavelet power can indicate these two seizures clearly. However, the renormalized entropy and K-L relative entropy fail to indicate these two seizures in Fig. 2 (b). This is resulted by the selection of the reference segment before running the detection method. EEG of a patient with mixed epileptic seizures is shown in Fig. 3 (a). Most of the seizures of the patient could be indicated with the normalized wavelet spectrum entropy, seeing Fig. 3 (c), but the seizure occurs during 130-140 second. The scaleaveraged wavelet power can indicate these seizures well, like the K-L relative entropy. Renormalized entropy only indicates the a few seizures, however. Fig. 4 shows an epileptic EEG data of patient 4 with EMG activity. The patient occurs EMG activity during the 50-80 and 150-160 second, respectively. Fig. 4 (b) and (c) show the renormalized entropy, K-L relative entropy and normalized wavelet spectrum entropy did not overcome the effect of the EMG activity. However, that scale-averaged wavelet power is able to overcome this effect of the EMG activity, seeing the dot line in Fig. 4 (c), meanwhile the epileptic seizures are indicated completely. Fig. 5 (a) shows the EEG of a patient with psychomotor epileptic seizures. Seeing Fig. 5 (b) and (c), the normalized wavelet spectrum entropy is the best to indicate the seizures among other entropy. It is found that two hidden seizures that occur at the second 20 and 58 could be indicated by the normalized wavelet spectrum entropy (seeing the solid line of Fig. 5 (c)). In this paper, we employ the wavelet spectrum entropy and scale-averaged wavelet power based on the Morlet wavelet transforms to indicate the seizures of five patients. It is found that theses two feature values could indicate the epileptic seizures effectively. Some of hidden seizures could be indicated, but also the effect of EMG

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activity to detection of epileptic seizure could be avoided for scale-averaged wavelet power. It is noticed that the renormalized entropy and K-L relative entropy two methods need a segment of EEG as a reference. In the future work, we will combine the normalized wavelet spectrum entropy and scale-averaged wavelet power to come up with a new detection method of epileptic seizures in extracranial EEG.

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Fig. 5. (a) EEG recorded from the F8-C4 electrode of patient 5 (psychomotoric epileptic seizures); (b) Renormalized entropy (solid line) and K-L relative entropy (dot line) calculated with FT; (c) The normalized wavelet spectrum entropy (solid line) and scale-averaged wavelet power (dot line) by using Morlet wavelet transform

Acknowledgments. The work is supported by Cercia, The Centre of Excellence for Research in Computational Intelligence and Applications, in the School of Computer Science at the University of Birmingham, UK and National Natural Science Foundation of China (60575012).

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