Application of wavelet-based similarity analysis to epileptic seizures prediction

Computers in Biology and Medicine 37 (2007) 430 – 437 www.intl.elsevierhealth.com/journals/cobm

Application of wavelet-based similarity analysis to epileptic seizures prediction Gaoxiang Ouyang, Xiaoli Li∗ , Yan Li, Xinping Guan Centre for Networking Control and Bioinformatics (CNCB), Yanshan University, Qinhuangdao, Hebei, 066004, China

Abstract Epileptic seizures prediction is an interesting issue in epileptology, since it can promise a novel approach to control seizures and understand the mechanism of epileptic seizures. In this paper, we describe a new method, called wavelet-based nonlinear similarity index (WNSI), to predict epileptic seizures using EEG recordings in real time. This method combines wavelet techniques and nonlinear dynamics. The test results of EEG recordings of rats and humans show that WNSI can track the hidden dynamical changes of brain electrical activity. Particularly, we found that it can obtain the best performance of seizure prediction at the beta (10–30 Hz) frequency band of EEG signals. A possible reason is suggested from the functional connectivity of the brain. In terms of this study, it is recommended that wavelet technique is very useful to improve the performance of epileptic seizures prediction. 䉷 2006 Elsevier Ltd. All rights reserved. Keywords: Wavelet decomposition; Epileptic seizure; EEG; Similarity; Prediction; Beta wave

1. Introduction During the past decade, it was confirmed that the epileptic seizures could be anticipated prior to their occurrences. The epileptic seizures prediction is becoming an interesting issue for clinical analysis and research of epilepsy. This is because the prediction of epileptic seizures before clinical onset can promise a new diagnostic approach and provide a control sign to avoid a on-coming seizure. On the other hand, the exploration of pre-seizure stage could be helpful to understand the mechanisms underlying epilepsy [1,2]. So far, a number of methods derived from the theory of dynamical systems are proposed to predict epileptic seizures [3–9], to some extent these methods are capable of extracting an informative signal from EEG recordings for epileptic seizures prediction, including nonlinear dynamics and chaos [4,5,10,11], similarity [12–16], phase coherence [17,18] and time domain analysis [19,20], etc. In [21], three typical nonlinear seizure prediction methods were evaluated by using depth EEG recordings, the results show that the existing ∗ Corresponding author.

E-mail address: [email protected] (X. Li). 0010-4825/$ - see front matter 䉷 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.compbiomed.2006.08.010

prediction methods are still not sufficient for clinical applications. It is desirable to develop a new prediction method for the epileptic seizures. In the previous work [16], a nonlinear similarity index (NSI) from a dynamical similarity index (DSI) [12,13] was proposed to predict epileptic seizures. Although the method can obtain a robust feature to predict epileptic seizures from EEG recordings, it is still limited by artefact noises, volume conduction and skull filtering [13]. To overcome the effect of noise on analysis of EEG data, a wavelet transform is applied [20,22–26]. One of the advantages of wavelet transform is that wavelet filtering does not modify the pattern of EEG data, so that the dynamics hidden in EEG data are retained [26]. Another interesting issue is whether or not the wavelet based on pre-processing can further improve the performance of non-linear similarity index to predict epileptic seizures. To answer the above question, this paper addresses a new measure of similarity based on wavelet decomposition to predict epileptic seizures. First, EEG recordings are decomposed into different frequency bands’ oscillations by using a maximal overlap discrete wavelet transform (MODWT) [27]. Then, some frequency bands’ oscillations

G. Ouyang et al. / Computers in Biology and Medicine 37 (2007) 430 – 437

431

EEG (mv)

1000 0 tb

-1000 0

2

tc

4

6

8

10

12

14

16

4

6

8

10

12

14

16

Similarity Index

1 0.8 0.6

NSI B3-WNSI

0.4

B4-WNSI

0.2

B5-WNSI

0 0

2

6 NSI 5 B3-WNSI 4 B4-WNSI 3 B5-WNSI 2 0

2

4

6

8 Time (min)

10

12

14

16

Fig. 1. Top: EEG recordings of experiment rat 8, the tb and tc are injection and seizure time. Middle: The time course of the raw similarity index between the reference window and the moving test windows of 10 s lengths. The similarity indices are around 1 during the interictal phase, and the values of NSI are more oscillatory. A long lasting decrease of similarity during the preictal phase can be observed in all methods. Bottom: The deviations of mean value  during the interictal phase from the smoothed similarity profiles d are depicted in standard deviations using a color scale (changes in the green color of time windows indicate the deviation levels up to 4 S.D.). Such a change can be observed in all similarity indices, but first observed in the B3-WNSI at 9:10 (m:s), which indicates to detect the preictal phase.

are selected to further analyze the dynamic properties of brain electrical activity. Finally, an active suggestion is obtained from the practical tests, i.e. wavelet-based preprocessor is promising to improve the prediction rate of epileptic seizures.

2. EEG recordings 2.1. Rat EEG recordings In this study, 16 adult Sprague–Dawley rats are applied for prediction of epileptic seizures. The rats were anaesthetized with an intraperitioneal (i.p.) injection of Nembutal (sodium pentobarbital, 65 mg/kg of body weight) and mounted in a stereotaxic apparatus. An electrode was placed in epidural space to record the EEG signals from temporal lobe. During the experiments, each rat was initially anaesthetized with a dose of pentobarbital (65 mg/kg, i.p.), whose body temperature was maintained (36.5–37.5 ◦ C) with a blanket covering. The degree of anesthesia was assessed by continuously monitoring the EEG and additional doses of anesthetic were administered at the slightest change towards an awake

pattern (i.e., an increase in the frequency and reduction in the amplitude of the EEG waves). Then, bicuculline i.p. injection was used to induce epileptic seizures. EEG data was recorded through an amplifier with band-pass filter setting of 0.5–100 Hz. The sampling rate is 200 Hz. The details on the experiments can be found in [16]. The seizure onset time is determined by visual identification of a clear electrographic seizure discharge. The earliest EEG change is called the seizure onset time. The interval between the seizure onset time and the injection time is taken as the maximum prediction duration or extended pre-ictal phase. 2.2. Intracranial human EEG recordings In this study, the EEG recordings of four patients are selected from FSPEEG Database (http://www.fdm.unifreiburg.de/groups/timeseries/epi/EEGData/), the patients suffered from medically intractable focal epilepsy. Permission to use the database has been obtained from the Epilepsy Center of the University Hospital of Freiburg, Germany. The epileptic focus is located in neocortical brain structures. The depth of EEG data is very clear and has a high signal-tonoise ratio and fewer artifacts by comparing with scalp EEG

432

G. Ouyang et al. / Computers in Biology and Medicine 37 (2007) 430 – 437

EEG (mv)

1000 0 tb

-1000 0

2

tc

4

6

8

10

12

14

16

4

6

8

10

12

14

16

Similarity Index

1 0.8 0.6

NSI B3-WNSI

0.4

B4-WNSI

0.2

B5-WNSI

0 0

2

6 NSI 5 B3-WNSI 4 B4-WNSI 3 B5-WNSI 2 0

2

4

6

8 Time (min)

10

12

14

16

Fig. 2. Top: EEG recordings of experiment rat 4, the tb and tc are injection and seizure time. Middle: The time course of the raw similarity index between the reference window and the moving test windows of 10 s lengths. The similarity indices are around 1 during the interictal phase, while the similarity indices start to decrease during the preictal phases. Bottom: The deviations of mean value  during the interictal phase from the smoothed similarity profiles d are depicted in standard deviations using a color scale (changes in the green color of time windows indicate the deviation levels up to 4 S.D.). And such a change can be only observed in the B3-WNSI at 10:10 (m:s) and B4-WNSI at 10:20 (m:s) prior to the seizure.

recordings. The EEG data is acquired by using a Neurofile NT digital video EEG system with 128 channels, 256 Hz sampling rate, a 16 bit analogue-to-digital converter. The details of the FSPEEG Database can be found in Ref. [21].

and Lj −1 (S) Vj,t

=



g˜ j,l St−1modN ,

(2)

l=0

3. Method The prediction method of epileptic seizures based on wavelet-based nonlinear similarity index (WNSI) for EEG analysis contains the following three steps. Firstly, a MODWT [27] is applied to decompose EEG data into several sub-oscillations with different frequency bands. Given an EEG data S of the length N, let {hj,l ; l=0, . . . , Lj − 1} and {gj,l ; l = 0, . . . , Lj − 1} be a jth level wavelet filter and a scaling filter; where, Lj = (2j − 1)(L − 1) + 1, and L denotes the width of the initial filter. The corresponding jth level MODWT wavelet and scaling filters are defined by h˜ j,l = hj,l /2j/2 and g˜ j,i = gj,l /2j/2 . The jth level MODWT wavelet and scaling coefficients are N dimensional vectors Wj and Vj , they are [27] Lj −1 (S)

Wj,t =

 l=0

h˜ j,l St−1modN

(1)

where t = 1, . . . , N − 1. After MODWT, the signals energy is equal to a summation of square of wavelet coefficients and square of scaling coefficients, it is written as follows: S2 =

J 

Wj 2 + VJ 2 .

(3)

j =1

The jth level MODWT detail and approximation are defined as follows: Bj ≡ WjT Wj

and

Aj ≡ VjT Vj .

(4)

In contrast to DWT (discrete wavelet transform), the details and approximation of MRA in MODWT are associated with zero phase filters and MODWT has a remarkable nature that the time-shift of details and approximation are consistent with one of input signals [27]. A wavelet function called Daubechies-4 is used in this paper. The MODWT of EEG

G. Ouyang et al. / Computers in Biology and Medicine 37 (2007) 430 – 437

433

Table 1 Anticipation time for the all rat tests Sprague–Dawley rat ID

EPPa (s)

NSI (s)

B3-WNSI (s)

B4-WNSI (s)

B5-WNSI (s)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

326 346 80 171 235 357 280 216 315 152 86 105 160 104 264 121

215 297 40 0 196 222 249 108 215 11 19 False 8 50 40 38

255 327 60 22 216 262 279 158 255 31 39 23 38 80 50 58

225 307 50 12 206 232 259 108 225 11 29 23 8 40 50 28

215 297 50 0 206 222 259 98 215 11 9 3 0 20 0 18

Mean

207.4

134.6

113.3

101.4

106.8

a EPP is the abbreviation for the extended preictal phase, i.e. the interval between the seizure onset time and injection time.

data S can be given by J 

Bj + A J ,

300

(5)

j =1

where Bj and AJ are the details and approximation, respectively. Secondly, a nonlinear similarity measure based on different bands Bj (j = 1, . . . , 5) is addressed to track the hidden dynamic change of brain electrical activity over time. The idea of the NSI is to compare the dynamics between the test series St in a sliding window and the reference series Sref . The reference series should be far from seizures. Mathematical details of the NSI method can be found in [16]. In this paper, the NSI method is used to calculate the similarity index for the details Bj (j = 1, . . . , 5), so five WNSIs  at the each sliding window St can be obtained. Finally, a preictal detection algorithm on the basis of the similarity measure is addressed to predict epileptic seizures. The main procedure of the detection method will be shown in Section 4 through a case study. The details of detection method can be found in [16].

4. Results 4.1. Prediction of rat epileptic seizures To investigate the performance of this method, we compare the results with the NSI method. We did not analyze the neural activities at the B1 (50–100 Hz) and B2 (25–50 HZ) bands corresponding wavelet resolution levels 1 and 2, respectively. High-frequency brain activity is eliminated, since their contributions during ictal seizures are not as strong as

250 Time (s)

S=

350

200 150 100 50 0 EPP

NSI

B3-NSI

B4-NSI

B5-NSI

Fig. 3. The Boxplot of anticipation time of the NSI and WNSI prediction methods (also include extended preictal phase).

one at the middle and low frequencies [28]. In this work, the neural activities at the B3 (12.5–25 Hz), B4 (6–12.5 Hz) and B5 (3–6 Hz) bands are employed for the epileptic seizures prediction. Figs. 1 and 2 show two cases of the prediction of epileptic seizures by using a moving-window technique [29]. EEG signal firstly is divided into segments of 10 s. Then, the WNSI is computed after embedding the EEG segment with a dimension of m = 9, a delay of  = 13, and a radius of r =2 (in units of the standard deviation ) [16]. Finally, three WNSI measures (B3-WNSI, B4-WNSI and B5-WNSI) are obtained over time. In Fig. 1, the similarity profiles between the reference series and test series are plotted. It can be seen that the four similarity indices decrease during the preictal phases. During the interictal phase, the reference window and test windows share the same underlying dynamics, so the value of similarity index is around 1. But that the

434

G. Ouyang et al. / Computers in Biology and Medicine 37 (2007) 430 – 437

Table 2 Result of one-way repeated measure ANOVA ANOVA source of variation

Sums of squares (SS)

Degrees of freedom (DF)

Mean square (MS)

F-test

Treatment Error Subject Total

121704 41958 816414 980076

4 60 15 79

30426 699.3

43.51P < 0.001

similarity indices of NSI are more oscillatory, and the S.D. of  is 0.0248. The S.D. of B3-WNSI, B4-WNSI and B5WNSI is 0.0109, 0.0132 and 0.0157, respectively. Since wavelet transform can effectively eliminate the noise component hidden in the EEG signals, the S.D. of B is smaller than the one of . In other words, B is more insensitive to the change of the position of EEG segment. A simple conclusion can be made that wavelet transform is able to improve the performance of seizures prediction and extend the length of the anticipation time. As can be seen in Fig. 1, the epileptic seizures occur at 11:48 (m:s) after injecting bicuculline, and brain electrical activities begin to tend towards the seizure phase from around 9:10 (m:s). The complexity of the cortical dynamics decreases significantly from a interictal stage to a ictal stage [6,30]. A similar conclusion can be obtained that the similarity index gradually decreases prior to seizures. Analysis of the 16 rats’ EEG recordings show that the similarity index decreases at the preictal phase in 15 rats. Fig. 2 shows another case study. The similarity indices start to decrease during the preictal phases. At the same, the NSI-based similarity indices decrease prior to the seizures, but it cannot sufficiently reach a statistical threshold. The NSI method fails to detect the preictal phase. Since the wavelet decomposition can efficiently eliminate the noise from the initial EEG and obtain a detailed analysis of the EEG, the WNSI method is able to extract more qualitative information about the dynamical and geometrical properties of underlying dynamics. Furthermore, the beta oscillation plays an important role in the long-range neural communication (functional connectivity) [31]. B3-WNSI method can be more accurate to determine the distinctness between the normal and pathological phases, namely the interictal and preictal phase. As can be seen in Fig. 2, the B3-WNSI and B4-WNSI can successfully detect the preictal phase.

4.2. Performance analysis of WNSI Most of the rat tests show there exists a decrease in the similarity indices of B3-WNSI and B4-WNSI prior to the seizures. A best performance of Q=100% is obtained. There is only a false positive detection (the time of first positive detection of PSD prior to the injection time) in the rat 12. The performance Q of NSI and B5-WNSI methods for whole group of rats is equal to 91.9% and 91.1%, respectively, as

Table 3 Result of pair-wise comparisons via Scheffe’s post-hoc test Difference between treatment means

NSI

B3-WNSI

B4-WNSI

B5-WNSI

EPP NSI B3-WNSI B4-WNSI

100.6∗∗

72.8∗∗ 27.8∗∗

94.1∗∗ 6.7 21.3∗

106.0∗∗ 5.4 33.2∗∗ 11.9

∗∗ and ∗ imply that the two treatment level means are statistically different

at the a = 0.01 and a = 0.05 level, respectively.

can be found in Table 1. These results are in agreement with the previous finding [5,6,12] that the temporal and spatial distribution of neural activity start to change several minutes prior to seizures. Anticipation time is defined as the time interval between the first positive detection of PSD and the seizure onset. The above cases show the B3-WNSI can obtain the maximum mean anticipation time (i.e. 134.6 s). The statistical analysis for each anticipation time (include extended preictal phase) is carried out. First, a one-way ANOVA is performed using a standard tool of numerical analysis (Matlab’s ANOVA routine, statistics toolbox) [32]. The results are presented in Fig. 3. It is seen that the anticipation time values of NSI and WNSI are lower than the extended preictal phase, and the anticipation time values of B3-WNSI are higher than ones of NSI, B4-WNSI and B5WNSI. The lower and upper lines of the “box” in Fig. 3 are the 25th and 75th percentiles of the sample, the distance between the top and bottom of the box is the inter quartile range and the line in the middle of the box is the sample median. The “whiskers” (lines extending above and below the box) shows the extent of the rest of the sample. The notches in the boxes are a graphic confidence interval (95%) about the median of a sample. In order to test these observed mean differences statistically, a one-way repeated measure ANOVA is performed for time values of five different measures, as shown in Table 2. It can be seen that the F-test is significant at the P < 0.001 level of probability. Thereby, we suggest the null hypothesis, i.e., no differences among five different measures should be rejected. A Scheffe’s post-hoc test to all pairwise comparisons between the means is shown in Table 3. The extended preictal phase is significantly longer than the

G. Ouyang et al. / Computers in Biology and Medicine 37 (2007) 430 – 437

435

S B3 B4 B5 1

2

3

Similarity Index

1 0.9 0.8 NSI B3-WNSI B4-WNSI B5-WNSI

0.7 0.6 -20

-18

-16

-14

-12

-10

-8

-6

-4

-2

0

2

4 6

NSI 5 B3-WNSI 4 B4-WNSI 3 B5-WNSI 2 -20

-18

-16

-14

-12

-10

-8 -6 Time (min)

-4

-2

0

2

4

Fig. 4. Top: Analysis of the intracranial EEG recordings from patient C. Original EEG segments and its B3, B4, B5 frequency bands with MRA are depicted during the interictal phase (1), during the few minutes before the seizure (2) and during the seizure (3). Middle: The time course of the raw similarity index between the reference window and the moving test windows of 8 s lengths, the grey vertical bar marked represents the interval from seizure onset time to seizure end time. The similarity indices are around 1 during the interictal phase, and the similarity indices start to decrease before the seizure. Bottom: The deviations of mean value  during the interictal phase from the smoothed similarity profiles d are depicted in standard deviations using a color scale (changes in the green color of time windows indicate the deviation levels up to 4 S.D.). Such a change can be observed in all similarity indices.

anticipation time. In addition, the anticipation time based on B3-WNSI is the longest. These performances are based on the fact that wavelet decomposition can view the details of the EEG recordings and overcome the effect of noise; on the other hand the B3 band with wavelet resolution level of 3 (12.5–25 Hz) is at the beta band, the median frequency of this beta band is a typical nature of a epileptic seizure. Therefore, B3-WNSI is the best to detect the preictal phase and gains a longest anticipation time. A seizure prediction method should gain a high percentage of a seizure and obtain a low false positive prediction rate. Winterhalder et al. [33] proposed that the prediction methods may be evaluated with a sensitivity and a specificity. In practice, false positive prediction cannot be prevented. But too many false alarms may result in a negative effect on the epilepsy patients, which will not take further alarms seriously and will be unprepared for a seizure. On the other hand, the epilepsy patients who take all alarms seriously will suffer from a huge psychological stress. In the WNSI

method, wavelet transform eliminates the effect of noise component, so the similarity indices of Wavelet-based NSI are smoother during the interictal phase than those of NSI, the Wavelet-based NSI can obtain a lower false positive prediction rate. In Table 1, there is only a false positive detection during the interictal phase for NSI; but there is not a single false positive detection during the entire EEG recordings for WNSI. WNSI method possesses a lower false positive prediction rate.

4.3. Intracranial human EEG analysis In order to further investigate the performance of this new method, the proposed WNSI method is also applied to analyze the intracranial human EEG recordings of four epilepsy patients. EEG recordings is divided into segments of 8 s by a moving window [29], then the EEG segment is spitted in several sub-oscillations with different frequency bands

436

G. Ouyang et al. / Computers in Biology and Medicine 37 (2007) 430 – 437

10 9 Anticipation time (min)

8 NSI

7 6

B3-WNSI

5 4

B4-WNSI

3 B5-WNSI

2 1 0 1

2 A

1

2 B

1

2 C

3

1

2 D

Seizures Patients

Fig. 5. Anticipation time for all the patients and seizures. The anticipation time of the NSI, B3-WNSI, B4-WNSI and B5-WNSI is 5.95±1.54, 6.98±1.50, 6.30 ± 1.67 and 5.82 ± 1.28 min, respectively.

by using MODWT. The WNSI is computed for each suboscillation with a dimension of m = 9, a delay of  = 13, and a radius of r = 2 (in units of the standard deviation ) [16]. A same procedure is carried out for human EEG data at the B3 (16–32 Hz), B4 (8–16 Hz) and B5 (4–8 Hz) bands corresponding to wavelet resolution levels 3, 4 and 5, respectively. These different bands are independently applied to predict epileptic seizures. Fig. 4 (top) shows the EEG segments S and sub-oscillations at the B3, B4 and B5 frequency bands during the interictal phase (1), during the few minutes prior to the seizure (2) and during the seizure (3). Visual inspections show that sub-oscillations have not an obvious change prior to the seizure. A raw similarity profile between the reference series and test series are plotted at the middle of Fig. 4. It is found that the four similarity indices are around 1 during the interictal phase, while they start to gradually decrease prior to the seizures. In order to track the changes of these dynamics, the preictal detection method that are for animal tests is applied to independently analyze each similarity profiles. Setting detection parameters k = 4 and d = 7, the deviations of mean value  during the interictal phase from the smoothed similarity profiles d are depicted at the bottom of Fig. 4. It can be seen that the method WNSI can successfully detect the preictal phase, in particular the B3-WNSI is the earliest to predict the seizure. Fig. 5 summarizes the results of seizure prediction for four patients. The results show WNSI also can successfully detect the preictal phase. In particular, the B3-WNSI can obtain the maximum mean anticipation time (6.98 ± 1.50 min). This is because the median frequency at the B3 band (16–32) is a typical feature of epileptic seizures. Furthermore, it is known that the beta oscillation is directly related to the long range of neural communication (functional connectivity) [30]. Thus, a possible mechanism of seizure is associated with the beta wave in the neural activity, so that B3-WNSI method can obtain a longest anticipation time.

5. Conclusions To predict epileptic seizures, this paper describes a novel similarity approach based on MODWT to track the hidden dynamic characteristics of EEG data. We find that the similarity indices gradually decrease during the preictal phase. These results support the idea that deterministic non-linear processes are involved in preictal neural reorganization. The developed similarity algorithm based on wavelets can improve the performance of the epileptic seizures prediction. The WNSI method can increase the sensitivity and decrease the false positive rate; and obtain a longer anticipation time than the NSI method. In particular, the B3-WNSI obtains a longest anticipation time. Acknowledgments This work was supported by the National Natural Science Foundation of China (60575012). Authors are grateful for the helpful comments of reviewers to improve this manuscript. References [1] L.D. Iasemidis, Epileptic seizure prediction and control, IEEE Trans. Biomed. Eng. 50 (5) (2003) 548–558. [2] K. Lehnertz, B. Litt, The first international collaborative workshop on seizure prediction: summary and data description, Clin. Neurophysiol. 116 (3) (2005) 493–505. [3] L.D. Iasemidis, J.C. Sackellares, The evolution with time of the spatial distribution of the largest Lyapunov exponent on the human epileptic cortex, in: D. Duke, W. Pritchard (Eds.), Measuring Chaos in the Human Brain, World Scientific, Singapore, 1991, pp. 49–82. [4] K. Lehnertz, C. Elger, Can epileptic seizures be predicted? Evidence from nonlinear time series analysis of brain electrical activity, Phys. Rev. Lett. 80 (1998) 5019–5022.

G. Ouyang et al. / Computers in Biology and Medicine 37 (2007) 430 – 437 [5] J. Martinerie, C. Adam, M. Le Van Quyen, M. Baulac, S. Clemenceau, B. Renault, F. Varela, Epileptic seizures can be anticipated by non-linear analysis, Nat. Med. 4 (1998) 1173–1176. [6] X. Li, G. Ouyang, X. Yao, X. Guan, Dynamical characteristics of pre-epileptic seizures in rats with recurrence quantification analysis, Phys. Lett. A 333 (1–2) (2004) 164–171. [7] X. Li, J. Li, X. Yao, Complexity and synchronization of EEG with parametric modelling, IEEE Workshop on Life Science Data Mining 2004, 1–4 November 2004, Brighton, UK, pp. 34–38. [8] M. Le Van Quyen, J. Soss, V. Navarro, R. Robertson, M. Chavez, M. Baulac, J. Martinerie, Preictal state identification by synchronization changes in long-term intracranial EEG recordings, Clin. Neurophysiol. 116 (3) (2005) 559–568. [9] S. Viglione, G. Walsh, Proceedings: epileptic seizure prediction, Electroencephalogr. Clin. Neurophysiol. 39 (1975) 435–436 (abstract). [10] L.D. Iasemidis, J. Sackellares, H. Zaveri, W. Williams, Phase space topography and the Lyapunov exponent of electrocorticograms in partial seizures, Brain Topogr. 2 (1990) 187–201. [11] C.E. Elger, K. Lehnertz, Seizure prediction by non-linear time series analysis of brain electrical activity, Eur. J. Neurosci. 10 (1998) 786–789. [12] M. Le Van Quyen, J. Martinerie, M. Baulac, F. Varela, Anticipating epileptic seizures in real time by a non-linear analysis of similarity between EEG recordings, Neuro. Report 10 (1999) 2149–2155. [13] M. Le Van Quyen, J. Martinerie, V. Navarro, M. Baulac, F. Varela, Characterizing neurodynamic changes before seizures, J. Clin. Neurophysiol. 18 (2001) 191–208. [14] V. Navarro, J. Martinerie, M. Le Van Quyen, S. Clemenceau, M. Baulac, C. Adam, F. Varela, Seizures anticipation in human neocortical partial epilepsy, Brain 125 (2002) 640–655. [15] X. Li, X. Yao, Application of Fuzzy Similarity to Prediction of Epileptic Seizure Using EEG Signals, Lecture Notes in Artificial Intelligence, vol. 3613, Springer, Berlin, 2005, pp. 645–652. [16] X. Li, G. Ouyang, Nonlinear similarity analysis for epileptic seizures prediction, Nonlinear Anal. Theor. 64 (8) (2006) 1666–1678. [17] F. Mormann, R.G. Andrzejak, T. Kreuz, C. Rieke, P. David, C.E. Elger, K. Lehnertz, Automated detection of a preseizure state based on a decrease in synchronization in intracranial electroencephalogram recordings from epilepsy patients, Phys. Rev. E 67 (2003) 021912: 1-10. [18] F. Mormann, T. Kreuz, R.G. Andrzejak, P. David, K. Lehnertz, C. Elger, Epileptic seizures are preceded by a decrease in synchronization, Epilepsy Res. 53 (2003) 173–185. [19] B. Litt, R. Esteller, J. Echauz, M. D’Alessandro, R. Shor, T. Henry, P. Pennell, C. Epstein, R. Bakay, M. Dichter, G. Vachtsevanos, Epileptic seizures may begin hours in advance of clinical onset: a report of five patients, Neuron 30 (2001) 51–64. [20] S. Gigola, F. Ortiz, C.E. D’Attellis, et al., Prediction of epileptic seizures using accumulated energy in a multiresolution framework, J. Neurosci. Meth. 138 (2004) 107–111. [21] T. Maiwald, M. Winterhalder, A. Aschenbrenner-Scheibe, H.U. Voss, A. Schulze-Bonhage, J. Timmer, Comparison of three nonlinear seizure prediction methods by means of the seizure prediction characteristic, Physica D 194 (2004) 357–368. [22] S. Blanco, C.E. D’Attellis, S.I. Isaacson, O.A. Rosso, R.O. Sirne, Time-frequency analysis of electroencephalogram series. II. Gabor and wavelet transform, Phys. Rev. E 54 (6) (1996) 6661–6672. [23] M. Unser, A. Aldroubi, A review of wavelets in biomedical applications, Proc. IEEE 84 (1996) 626–638. [24] O.A. Rosso, M.L. Mairal, Characterization of time dynamical evolution of electroencephalographic epileptic records, Physica A 312 (2002) 469–504. [25] H. Adeli, Z. Zhou, N. Dadmehr, Analysis of EEG records in an epileptic patient using wavelet transform, J. Neurosci. Meth. 123 (2003) 69–87.

437

[26] O.A. Rossoa, S. Blancoa, A. Rabinowicz, Wavelet analysis of generalized tonic-clonic epileptic seizures, Signal Process. 83 (2003) 1275–1289. [27] Donald B. Percival, Andrew T. Walden, Wavelet methods for time series analysis, Cambridge, 2000, pp. 159–205 (Chapter 5). [28] R. Quian Quiroga, S. Blanco, O.A. Rosso, H. GarcUVa, A. Rabinowicz, Searching for hidden information with Gabor transform in generalized tonic-clonic seizures, Electroenceph. Clin. Neurophysiol. 103 (1997) 434–439. [29] J.S. Barlow, Methods of analysis of nonstationary EEGs with emphasis on segmentation techniques: a comparative review, J. Clin. Neurophysiol. 2 (1985) 267–304. [30] X. Li, P.G. Kapiris, J. Polygiannakis, K.A. Eftaxias, X. Yao, Fractal spectral analysis of pre-epileptic seizures phase: in terms of criticality, J. Neural Eng. 2 (2005) 11–16. [31] A. Schnitzler, J. Gross, Normal and pathological oscillatory communication in the brain, Nat. Rev. Neurosci. 6 (2005) 285–296. [32] R.V. Hogg, J. Ledolter, Engineering Statistics, MacMillan Publishing Company, 1987. [33] M. Winterhalder, T. Maiwald, H.U. Voss, R. AschenbrennerScheibe, J. Timmer, A. Schulze-Bonhagea, The seizure prediction characteristic: a general framework to assess and compare seizure prediction methods, Epilepsy Behav. 4 (3) (2003) 318–325.

Gaoxiang Ouyang received the B.S. degree in Automation and M.S. degrees in Control Theory and Control Engineering from Yanshan University, China in 2002 and 2004, respectively. He is currently working on a Ph.D. in Control Science and Engineering with his research interests including the fields of bio-signal process and analysis, such as EEG, neural model, and dynamics system.

Xiaoli Li received the B.S.E. and M.S.E. degrees from Kun-ming University of Science and Technology, and the Ph.D. degree from Harbin Institute of Technology, China, in 1992, 1995, and 1997, respectively, all in mechanical engineering. From April 1998 to October 2003, he was a Research Fellow of the Department of Manufacturing Engineering, City University of Hong Kong, of the Alexander von Humboldt Foundation at the Institute for Production Engineering and Machine Tools, Hannover University, Germany, a Post doc fellow at the Department of Automation and Computer — Aided Engineering, Chinese University of Hong Kong. In 2002, he was appointed as professor at the Electrical Engineering School, Yanshan University, China. Currently he also works in Cercia, School of Computer Science, University of Birmingham, UK. His main areas of research: Bio-signal analysis; Computational intelligence: Monitoring; Manufacturing system.

Yan Li received the B.S. degree in Automation and M.S. degrees in Control Theory and Control Engineering from Yanshan University, China in 2001 and 2006, respectively. He is currently working on a Ph.D. in Control Science and Engineering with his research interests including the fields of biosignal process and analysis.

Xinping Guan received the B.S. degree in Mathematics from Harbin Normal University, the M.S. degree in Applied Mathematics and the Ph.D. degree in Electrical Engineering from Harbin Institute of Technology, Harbin, China, in 1986, 1991 and 1999, respectively. He is currently a Professor and Dean of the Institute of Electrical Engineering, and director of the Centre for Networking Control and Bioinformatics (CNCB), Yanshan University, Qinhuangdao, China. He has published more than 200 papers in mathematical, technical journals and conferences. He is a Senior Member of IEEE, Reviewer of Mathematic Review of America, Member of the Council of Chinese Automation Committee and Member of the Council of Chinese Artificial Intelligence Committee. His research interests include Signal Processing and Image Processing, robust control and intelligent control of time-delay systems, Control and Synchronization of Nonlinear Dynamic System, and congestion control of networks.