Wavelet analysis of generalized tonic-clonic epileptic seizures

Signal Processing 83 (2003) 1275 – 1289 www.elsevier.com/locate/sigpro

Wavelet analysis of generalized tonic-clonic epileptic seizures Osvaldo A. Rossoa;∗ , Susana Blancoa , Adrian Rabinowiczb a Instituto

de Calculo, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pabellon II, Ciudad Universitaria, 1428 Ciudad de Buenos Aires, Argentina b Departament of Neurology and Epilepsy Program, Instituto de Investigaciones Neurol ogicas Raul Carrea (FLENI), Monta˜neses 2325, 1429 Ciudad de Buenos Aires, Argentina Received 10 July 2000; received in revised form 13 September 2002

Abstract The analysis of generalized tonic-clonic seizures is usually di0cult with quantitative EEG techniques due to muscle artifact. We applied two quanti4ers based on the Wavelet Transform to evaluate 20 seizures from eight consecutive patients admitted for video-EEG monitoring. We studied the relative wavelet energy and the wavelet entropy over time. In 16 events 20 we found signi4cant decremental activity in the relative wavelet energy associated with frequency band 0.8–3:2 Hz (delta activity) at the seizure onset, indicating that the seizure is dominated by medium frequency bands 3.2–12:8 Hz (theta and alpha bands). In 19 events the mean wavelet entropy presents lower values during the ictal period compared to the pre-ictal 20 period, indicating that the associated dynamic is more ordered and simple. Thus the employed tools show good accuracy for detecting changes in the system dynamic. We conclude that this behavior could be induced by frequency tuning in the neuronal activity triggered by an hypothetic epileptic focus. ? 2003 Elsevier Science B.V. All rights reserved. Keywords: Epileptic seizures; EEG; Wavelet; Signal entropy

1. Introduction Synchronous neuronal discharges create rhythmic potential 9uctuations, which can be recorded from the scalp through electroencephalography. The electroencephalogram (EEG) can be roughly de4ned as the mean brain electrical activity measured at di:erent sites of the head. EEG patterns correlated with normal functions and diseases of the central nervous system ∗ Corresponding author. Tel.: +54-11-4576-3375; fax: +54-11-4786-8114. E-mail addresses: [email protected], [email protected] (O.A. Rosso), [email protected] (S. Blanco), alr@9eni. org.ar (A. Rabinowicz).

are de4ned on an empirical basis. The clinical interpretation of EEG attempts to link pathological features (clinical symptomatology) with visual inspection and pattern recognition of EEG. Although this traditional analysis is quite useful, visual inspection of the EEG is subjective and hardly allows any systematization [29]. To overcome this, quantitative EEG analysis (qEEG) introduces objective measures re9ecting the characteristics of the brain activity as well as the associated dynamics. We must remark, however, that these methods have not been developed to substitute traditional EEG visual analysis, but rather to complement it. The concept of ergodicity of the time series, which requires stationarity of the signal, is the common assumption in most traditional methods of signal

0165-1684/03/$ - see front matter ? 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0165-1684(03)00054-9

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analysis. The EEG time series complies with this assumption only for very limited intervals of time and quite often the variation of the signal over time is of primary interest. This is the case for identi4cation of epileptic seizure onset and localization of epileptic associated foci, among others. Processing of information by the brain is re9ected in dynamical changes of electrical activity in time, frequency and space. Therefore, study of this process requires methods which can describe the variation of the signal in time and frequency. An attractive property for these quanti4ers is that they are related with physical properties; therefore their interpretation and the implications of their results is straightforward. As a result, to understand the associated dynamics of the EEG time series, one can study the temporal evolution of these associated quanti4ers and reach conclusions about their behavior under di:erent pathologies and diseases. Very interesting results characterizing the time evolution of EEG associated dynamics have recently been reported by some research groups using quanti4ers based on measurements of nonlinear dynamics applied to EEG epileptic time series provided by depth and cortical electrodes. They analyze the EEG during seizure onset and the background EEG (preand post-ictal), following the temporal evolution of the signal complexity (associated with the measurement of the correlation dimension D2 ) [12,25] and the chaoticness degree (through the largest Lyapunov exponent, max ) [19,20,24]. The main 4ndings from these reports are a reduction of these two quanti4ers during the ictal stage, suggesting that a transition takes place at the seizure onset in the dynamic behavior of the neural network from a complex behavior to a simpler one [30]. Furthermore, some researchers report a signi4cant decrease of these quanti4ers a few minutes before the seizure-onset raising the hypothesis that epileptic seizure could be predicted [19,20,25]. The basic requirement for nonlinear dynamic metric tools (Chaos Theory) to be applied to experimental data is the stationarity of the time series, which suggests the time series is representative of a unique and stable attractor. Also for the evaluation of D2 and max , de4ned as asymptotic properties of the attractor, long time recordings are required. By applying a static measurement of D2 and max to selected portions of

brain electrical activity (EEG time series), satisfying all the mathematical hypothesis requirement, di:erent states can be characterized [2,3,5,7,9]. These metric invariants require the computation of some previous parameters which rapidly degrade with additive noise, often giving vague results (for a review see Elbert et al. [16] and BaHsar [4]). Another group of qEEG methods are based on time-frequency analysis. Recently we introduced two di:erent techniques of qEEG that allow the analysis of the EEG time series in the time-frequency domain. The 4rst is based on the Gabor transform (GT) [6,9–11,33] and the second in the orthogonal discrete wavelet transform (ODWT) [6,8,23,34,36–39,44]. GT is equivalent to wavelet transform (WT) with a 4xed window. These methods, specially ODWT, do not make assumptions about record stationarity (they do not need to reconstruct any attractor of the dynamical system) and they work only with their measurable response, that is the time series. Taking the wavelet transform of the EEG signal as a basic element, we de4ne two quanti4ers: the relative wavelet energy (RWE) and the wavelet entropy (WS). The RWE provides information about the relative energy associated with the di:erent frequency bands present in the EEG and their corresponding degree of importance. WS bring us information about the degree of order/disorder associated with a multi-frequency signal response. In consequence the time evolution of the WS could give information about the dynamics associated with the EEG records [37–39]. A scalp EEG signal is a nonstationary time series that usually presents artifacts due to electrooculogram (EOG), electromyogram (EMG) and electrocardiogram (ECG), among others [29]. Artifacts make the mathematical analysis of scalp EEG signals di0cult. Sometimes artifacts are presented during a few seconds and can be obviated because they obscure only a small portion of the EEG. In other cases, almost the total signal appears obscured by them, and very little information about the underlying brain activity can be extracted. An example of the kind of scalp EEG signals that are obscured by artifacts occurs during epileptic tonic-clonic (TC) seizures [29]. A TC seizure is characterized by violent muscle contractions. Initial massive tonic spasms are

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replaced seconds later by the clonic phase with violent 9exor movements and characteristic rhythmic spasms towards the ending of the seizure. In these seizures, artifacts related to muscle contractions are especially troublesome because they reach very high amplitudes [29]. In fact, not only do they limit the traditional visual analysis to the pre- and post-ictal periods, but they also restrict the application of some mathematical methods. Analysis of brain activity during this type of seizure has been previously performed only in special circumstances, such as in patients treated with curare (an inhibitor of the muscle responses) [17] or by eliminating the high-frequency muscle activity with the use of traditional 4lters [18]. Traditional 4ltering (band-pass 4lters based on Fourier transform), however, has several disadvantages. First, it is almost impossible to separate brain signal from muscle activity. Filtering those frequencies related to muscle artifacts also a:ects the morphology of the remaining ones. Although 4ltering and signal processing have been applied in the case of linear systems, new techniques are required for the analysis of signals generated by nonlinear ones, like electrical brain activity, because traditional 4ltering processes alter the nonlinear metric invariants [27,28,41]. In this setting, we can use the WT for 4ltering those frequencies strongly associated with muscle activity [5,8,37]. One of the advantages of this method over traditional 4ltering is that wavelet 4ltering of some frequency bands does not modify the pattern of the remaining ones, so the dynamics associated with them do not change either. Noisy signals obtained during a TC seizure are usually rejected during visual inspection by the physicians due to the presence of muscle artifacts. These kind of ictal records could not be compared with studies that use qEEG techniques to search for analogies and differences among patients. Our aim with this work is to show that this kind of EEG recording can be rescued for a qEEG analysis, avoiding noise. In particular we report here a qEEG analysis based on ODWT of TC seizures. As we will show, these quanti4ers present an improvement in the qEEG techniques based on GT and supply a direct and adaptive measurements of the dynamical changes. Increase of the statistical signi4cance with respect to our previous work [33] was also observed.

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2. Materials and methods 2.1. Subjects and data recording Twenty TC seizures from 8 epileptic patients admitted for video-EEG monitoring were analyzed. The subjects consisted of 4 males and 4 females, age 30:87 ± 15:27 (mean ± SD; range 6 –51) with a diagnosis of pharmaco-resistant epilepsy and no other accompanying disorders. Informed consent from all the patients were obtained beforehand. Antiepileptic drugs were gradually reduced in order to precipitate seizures. Interictal EEGs, brain MRIs (magnetic resonance imaging), ictal and interictal SPECTs (single photon emitted computer tomography), and psychological tests were also performed. Scalp and sphenoidal electrodes with bimastoideal reference were applied following the 10 –20 international system. Each signal was digitized at 409:6 Hz through a 12 bit A/D converter and 4ltered with an “antialiasing” 8 pole low pass Bessel 4lter, with a cuto: frequency of 50 Hz. Then, the signal was digitally 4ltered with a 1–50 Hz bandwidth 4lter and stored, after decimation, at 102:4 Hz in a PC hard drive. Recordings were done under video control to have an accurate determination of the di:erent stages of the seizure. The di:erent stages of EEG signals were determined by the physician team. O:-line analysis was performed with characterization of semiological features, timing of the onset and de4nition, when possible, of the anatomical focus for each event. Analysis for each event included 60 s of EEG before the seizure onset and 120 s of ictal and post-ictal phases. All 180 s were analyzed at the C4 derivation, this electrode chosen after visual inspection of the EEG as the one with the least number of artifacts. As an example, in Fig. 1 we present a scalp EEG signal corresponding to a TC seizure recorded over the right central region (C4 channel). These EEG data correspond to the EEG number 3 as labeled in Tables 2 and 3. In this record, pre-ictal phase is characterized by a signal of 50 V. The seizure starts at 80 s, with a discharge of slow waves superimposed with low voltage fast activity. This discharge lasted approximately 9 s and with a mean amplitude of 100 V. Afterwards the seizure spreads, making the analysis of the EEG more complicated due to muscle artifacts. It is possible, however to establish the beginning of the clonic

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Fig. 1. Scalp recorded TC seizure, at right central region (EEG record number 3 in Tables 2 and 3). Seizure starts at 80 s and the clonic phase at 125 s. The seizure ends at 155 s.

phase at approximately 125 s and the end of the seizure at 155 s where there is an abrupt decay of the signal amplitude. 2.2. Wavelet transform, relative wavelet energy and wavelet entropy Wavelet analysis is a method which relies on the introduction of an appropriate basis and a characteri-

zation of the signal by the distribution of amplitude in the basis. If the wavelet is required to form a proper orthogonal basis, it has the advantage that an arbitrary function can be uniquely decomposed and the decomposition can be inverted [1,15,26]. The WT gives us a powerful tool to confront very diverse problems in applied sciences or pure mathematics and o:ers a well suited technique to detect and analyze events occurring in di:erent scales.

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The wavelet is a smooth and quickly vanishing oscillating function with good localization in both frequency and time. A wavelet family a; b is the set of elemental functions generated by dilations and translations of a unique admissible mother wavelet (t): 
t−b −1=2 ; (1) a; b (t) = |a| a where a; b ∈ R; a = 0, are the scale and translation parameters respectively, and t is the time. As a increases, the wavelet becomes narrower. Thus, we have a unique analytic pattern and its replicas at di:erent scales and with variable localization in time. The continuous wavelet transform (CWT) of a signal S(t) ∈ L2 (R) is de4ned as the correlation between the function S(t) with the family wavelet a; b for each a and b [1,15,26]: 
 ∞ t−b −1=2 ∗ dt S(t) (W S)(a; b) = |a| a −∞ = S;

a; b :

(2)

For special election of the mother wavelet function (t) and for the discrete set of parameters, aj = 2−j and bj; k = 2−j k, with j; k ∈ Z (the set of integers) the family j; k (t)

= 2j=2 (2j t − k);

j; k ∈ Z;

(3)

constitutes an orthonormal basis of the Hilbert space L2 (R) (the space of real square summable functions) consisting of 4nite-energy signals [1,5,26]. The correlated decimated discrete wavelet transform (DWT) provides a nonredundant representation of the signal and its values constitute the coe0cients in a wavelet series. These wavelet coe0cients provide full information in a simple way and a direct estimation for local energies at the di:erent scales. Moreover, the information can be organized in a multi-resolution manner, giving a hierarchical scheme of nested subspaces in L2 (R). In the present work we employ orthogonal cubic spline functions as mother wavelets. Among several alternatives, cubic spline functions are symmetric and combine, in a suitable proportion, smoothness with numerical advantages and are recommended tool to represent natural signals [42,43]. In the following we assume that the signal is given by the sampled values S ={s0 (n); n=1; : : : ; M }, which

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correspond to a uniform time grid with sampling time ts . For simplicity we suppose that the sampling rate is ts = 1. If the decomposition is carried out over all resolutions levels, N =log2 (M ), the wavelet expansion will be: −1  

S(t) =

j=−N

Cj (k)

j; k (t)

=

−1 

rj (t);

(4)

j=−N

k

where wavelet coe0cients Cj (k) can be interpreted as the local residual errors between successive signal approximations at scales j and j + 1, and rj (t) is the detail signal at scale j. It contains the information of the signal S(t) corresponding with the frequencies 2j−1 !s 6 |!| 6 2j !s . Since the family { j; k (t)} is an orthonormal basis for L2 (R), the concept of energy is linked with the usual notions derived from the Fourier theory. Then, the wavelet coe0cients are given by Cj (k) = S; j; k , the energy at each resolution level j = −1; : : : ; −N , will be the energy of the detail signal  Ej = rj 2 = |Cj (k)|2 (5) k

and the energy at each sampled time k will be E(k) =

−1 

|Cj (k)|2 :

(6)

j=−N

In consequence the total energy can be obtained by   Etot = S 2 = |Cj (k)|2 = Ej : (7) j¡0

k

j¡0

Then, the normalized values, which represent the RWE (j) = Ej =Etot

(8)

for the resolution level j = −1; −2; : : : ; −N , de4ne by scales the probability distribution of the energy. Clearly,  (j) = 1 (9) j¡0

and, the distribution {(j) } can be considered as a time-scale density. It gives a suitable tool for detecting and characterizing speci4c phenomena. The concept of thermodynamic entropy is well known in physics as a measure of the order/disorder

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of a system. Recently, a new measure of entropy de4ned from Fourier power spectrum, the power spectral entropy [13,31], has been applied to the study of brain signals [21,22]. The disadvantages of a spectral entropy de4ned from the Fourier transform (FT) can be partially resolved by using a short-time Fourier transform (STFT). Powell and Percival [31] de4ned a time evolving entropy from STFT by using a Hanning window. With this approach, a FT is applied to time-evolving windows of a few seconds of data re4ned with an appropriate function. Then, the evolution of the frequencies can be followed and the stationary requirement is partially satis4ed by considering the signals to be stationary in the order of a few seconds. Nevertheless, one critical limitation appears when windowing the data due to the Uncertainly Principle [1,15,26]. If the window is too narrow, the frequency resolution will be poor; and if the window is too wide, the time localization will be less precise. This limitation becomes important when the signal has transient components localized in time as in EEGs or evoked potentials. Consequently, a further improvement over the spectral entropy is to de4ne the entropy from the WT [8,36,37]. The Shannon entropy [40] gives a useful criterion for analyzing and comparing probability distribution. It provides a measure of the information contained in any distribution. We de4ne the total WS [8,36,37] as  WS = − (j) log2 [(j) ]: (10) j¡0

The time evolution of the frequency patterns can be followed with an optimal time-frequency resolution. Then, we can think of WS as a measurement of the degree of order/disorder of the signal, so it can provide useful information about the underlying dynamical process associated with the signal. In fact, a very ordered process could be thought of as a periodic mono-frequency signal (signal with a narrow band spectrum). A wavelet representation of such a signal, will be greatly resolved in one unique wavelet resolution level, meaning all RWE will be almost zero except for the wavelet resolution level which includes the representative signal frequency. For this special level the RWE will be almost one and in consequence the total WS will be near zero or present a very low value. On the other hand, a signal generated by a

totally random process could be taken as representative of a very disordered behavior. In this case one can expect that a very large number of frequencies will be necessary to represent such a signal (signals with a broad band spectrum). This kind of signal will have a wavelet representation with signi4cant contributions from all frequency bands considered in their analysis. Moreover, one could expect that all the contributions will be of the same order. Consequently the RWE will be almost equal for all the resolution levels and the WS will take their maximum value. Eqs. (8) and (10) de4ne useful quanti4ers based on ODWT to make a qEEG analysis. In order to study their temporal evolution, we divide the signal under analysis in sliding temporal windows of L data length and for each interval we evaluate the RWE and the WS and assign the obtained value to the middle point of time window. The minimum length of the temporal window will be one including at least one wavelet coe0cient in every scale. EEG spectral analysis is traditionally performed by studying di:erent frequency bands with well-de4ned boundaries, but could have some small variations according to the particular experiment under consideration. Absolute and relative intensities of these bands are usually analyzed and correlated with different pathologies. In this work, we de4ned six frequency bands for an appropriate wavelet analysis in the multiresolution scheme proposed. We denoted these band-resolution levels by Bj (|j| = 1; : : : ; 6). Their frequency limits as well as their correspondence with traditional EEG frequency bands are given in Table 1. One purpose of this work was to analyze the middle and low-frequency brain activity during TC seizures (in a spirit of extending our previous results using quanti4ers based on the GT [33]). One of the main reasons for using a signal separation method based on orthogonal wavelets was to analyze the remaining signal with minimum modi4cations to the associated dynamic. At this point we also refer to Mallat [26] who proved that in a one-dimensional signal denoising process (assuming additive noise and a separation between bands for noise and signals), an orthogonal wavelet based method is better than a method based on Fourier transform, because wavelets do not change the original signal. The main advantage of 4ltering with orthonormal wavelets is that the morphology of the

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Table 1 Frequency boundaries (in Hz) associated with the di:erent resolution Wavelet levels (j) used in the EEG signals analysis according with sample frequency !s = 102:4 Hz. The traditional EEG frequency bands correspond to the following frequencies:  = 0:5–3:5 Hz;  = 3:5–7:5 Hz;  = 7:5–12:5 Hz;  = 12:5–30 Hz and  ¿ 30 Hz

Notation

B1 B2 B3 B4 B5 B6

Wavelet band

EEG band

!min

!max

j

25.6 12.8 6.4 3.2 1.6 0.8

51.2 25.6 12.8 6.4 3.2 1.6

−1 −2 −3 −4 −5 −6

non4ltered frequencies are not a:ected, therefore the dynamics associated with those non4ltered frequencies do not change either. To limit the evaluation of RWE and WS to the middle and low frequencies, we did not take into account the contributions from B1 and B2 bands with wavelet resolution levels j = −1 and −2, respectively, both containing high-frequency artifacts related to muscular activity that blurred the EEG. Although high-frequency brain activity is also eliminated, their contributions during ictal seizures are not as strong as the middle and low frequencies as has been previously shown [14,17,33]. Once the high-frequency artifacts were eliminated, the time evolution of RWE and WS of the remaining signal were analyzed. For this purpose the signal was divided in epochs of lengths of L = 2:5 s each (M = 256 data). 2.3. Plateau criteria Clear decrements in frequency bands B5 and B6 (delta activity, see Table 1) were seen during the seizures. In order to quantify this observation, the mean relative wavelet energy (MRWE) for |j| = 5 and 6 was evaluated in the pre-ictal phase ((j) pre-ictal ) and compared with its mean values in the low-intensity zones (plateaus) observed during the seizure ((j) ictal ). Pre-ictal MRWE was de4ned as the mean value of the RWE in the minute before the seizure, without considering those areas contaminated by artifacts (de4ned by visual inspection of the EEG). During the ictal phase, plateaus were de4ned

;   ;    

according to the following criteria: (1) plateaus must last at least 10 s in order to avoid local variations, (2) the MRWE of the plateau must be less than 0.3 of the MRWE of the pre-ictal phase (!(j) = (j) ictal =(j) pre-ictal ¡ 0:3) and (3) the standard deviation of the plateau MRWE must be less than 0.03 to con4rm low variability (" ¡ 0:03). Although the selection of these criteria is arbitrary, no plateaus were identi4ed in the pre-ictal phase, strongly indicating that the appearance of a plateau in the ictal phase re9ects a dynamical change rather than a function of the analysis.

3. Results Twenty secondarily generalized TC seizure recordings were studied. The mean duration of the seizures was 92:8 s (SD=±5:76 s) with a range (52–160 s). As an example of the analysis performed with the qEEG based on WT, results of one of the seizures is described and then the global 4ndings are summarized. Figs. 2 and 3 display the time evolution of the two quanti4ers: the RWE without electromyographic contributions ((j) for |j| = 3; : : : ; 6), and the total WE corresponding to the 3 min of EEG data displayed in Fig. 1. Both quanti4ers were evaluated in sliding nonoverlapping time windows of length L = 256 data ≡ 2:5 s.

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Fig. 2. RWE time evolution corresponding to EEG signal displayed in Fig. 1, for the frequency bands B3 (full line), B4 (dots line), B5 (dot-dash line) and B6 (dash line). The vertical lines represent the start and end of the epileptic seizure.

Fig. 3. WS time evolution corresponding to EEG signal displayed in Fig. 1. The vertical lines represent the start and end of the seizure. The solid line represents the total WS and the dash line total WS without the contribution of frequency bands B1 and B2 bands.

From Fig. 2, it can be said that the pre-ictal phase is characterized by a signal dominance of low rhythms (pre-ictal: [(5) + (6) ] ∼ 50%). The seizure starts at 80 s with a discharge of slow waves superimposed with low voltage fast activity. This discharge lasts approximately 8 s and produces a marked rise in low-frequency bands (delta activity), which reaches [(5) + (6) ] ∼ 80% of the RWE. From 90 s the low-frequency activity, represented by (5) and (6) ,

decreases abruptly to values lower than 10% and the other frequency bands (theta and alpha activity) alternatively dominate. It can also be observed in Fig. 2 that the start of the clonic phase is correlated with a rise of (4) and after 140 s, when clonic discharges began to stay more separated, (5) rises up again until the end of the seizure, when (6) also increases very quickly and both frequencies bands are dominant. (5) and (6) maintain this behavior throughout the

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Table 2 Mean values and standard deviation of RWE for frequency bands B5 and B6 in the pre-ictal and ictal stage for the 20 EEG records analyzed. With Qt we denoted the width of the plateau (in s) and with ! the plateau dispersion. Bold numbers identify those parameters not satisfying the plateau criteria

Patient

CS CS LP LP LP DLB DLB AS AS AS AS MB MB IV FT FT FT FT JI JI

EEG

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

RWE pre-ictal

RWE ictal

Ratio ictal/pre-ictal

(5)

(6)

Qt (5)

(5)

Qt (6)

(6)

!(5)

!(6)

0:337 ± 0:137 0:228 ± 0:086 0:374 ± 0:108 0:281 ± 0:113 0:207 ± 0:097 0:097 ± 0:070 0:166 ± 0:086 0:204 ± 0:054 0:301 ± 0:118 0:321 ± 0:121 0:194 ± 0:085 0:116 ± 0:042 0:151 ± 0:056 0:130 ± 0:083 0:199 ± 0:116 0:395 ± 0:111 0:368 ± 0:105 0:386 ± 0:116 0:157 ± 0:106 0:167 ± 0:112

0:252 ± 0:152 0:144 ± 0:104 0:112 ± 0:038 0:153 ± 0:108 0:137 ± 0:117 0:038 ± 0:032 0:071 ± 0:049 0:150 ± 0:099 0:166 ± 0:086 0:158 ± 0:110 0:100 ± 0:051 0:096 ± 0:077 0:137 ± 0:118 0:107 ± 0:045 0:090 ± 0:087 0:251 ± 0:185 0:238 ± 0:121 0:213 ± 0:153 0:319 ± 0:211 0:065 ± 0:046

25.0 22.5 25.0 17.5 15.0 20.0 17.5 10.0 15.0 12.5 12.5 12.5 20.0 22.5 12.5 17.5 27.5 17.5 25.0 17.5

0:027 ± 0:011 0:035 ± 0:024 0:018 ± 0:010 0:012 ± 0:006 0:014 ± 0:005 0:012 ± 0:007 0:070 ± 0:020 0:029 ± 0:020 0:076 ± 0:029 0:067 ± 0:029 0:057 ± 0:018 0:124 ± 0:064 0:152 ± 0:077 0:015 ± 0:007 0:060 ± 0:047 0:047 ± 0:019 0:068 ± 0:030 0:022 ± 0:008 0:026 ± 0:011 0:031 ± 0:015

35.0 35.0 37.5 30.0 22.5 32.5 12.5 20.0 20.0 25.0 17.5 27.5 27.5 42.5 12.5 27.5 42.5 42.5 17.5 32.5

0:006 ± 0:004 0:015 ± 0:015 0:003 ± 0:002 0:006 ± 0:005 0:005 ± 0:004 0:004 ± 0:003 0:027 ± 0:009 0:011 ± 0:004 0:022 ± 0:014 0:037 ± 0:021 0:008 ± 0:006 0:008 ± 0:007 0:021 ± 0:018 0:017 ± 0:012 0:021 ± 0:016 0:010 ± 0:006 0:024 ± 0:015 0:011 ± 0:007 0:007 ± 0:002 0:017 ± 0:011

0.080 0.154 0.048 0.043 0.068 0.124 0.422 0.142 0.252 0.209 0.294 1.069 1.007 0.115 0.302 0.119 0.185 0.057 0.166 0.186

0.024 0.104 0.027 0.039 0.036 0.105 0.380 0.073 0.133 0.234 0.080 0.083 0.153 0.159 0.233 0.040 0.101 0.052 0.022 0.262

post-ictal phase. It can be concluded from this example that the seizure was dominated by middle frequency bands (alpha and theta rhythms) with a corresponding abrupt relative decrease of low-frequency bands (delta activity). By applying the criteria explained in the previous section, a plateau of (5) decrement was de4ned between 115 and 140 s, lasting Qt (5) = 25 s, having a very low variability "(5) = 0:018 and also having a very low ictal to pre-ictal RWE ratio, !(5) = 0:048 (see Table 2). In a similar way for (6) a plateau was de4ned between 110 and 147:5 s; Qt (6) = 37:5 s, with variability "(6) = 0:002 and ictal to pre-ictal RWE ratio, !(6) = 0:027. The WS is shown as a function of time in Fig. 3. Time evolution of the WS when all the frequency bands are included is represented with a continuous line and with a dashed line when contributions due to high-frequency bands (B1 and B2 ) are not taken into account. It is interesting to observe the behavior of the WS during the 4rst 10 s from seizure onset; the WS presents increasing values if all wavelet

frequency bands are included, compared with its values in the pre-ictal stage. In the case that the wavelet frequency bands B1 and B2 (bands that contain mainly the muscular activity) are not included, the main value of the WS is comparatively lower than ictal onset. Then, the behavior of the WS following the seizure onset is compatible with an increase in the degree of disorder of the system induced by high-frequency activity. Superimposed low and medium frequency activity has a more ordered behavior. The decreasing values of the WS after 90 s (in both cases, with and without inclusion of high-frequency bands) are indicative that the system presents a tendency to more ordered behavior. This tendency is better appreciated without the muscle activity. This WS behavior is clearly correlated with the “recruitment epileptic rhythm” (RER) described by Gastaut and Broughton [17]. Moreover, note that the WS in the last case takes a minimum value around 125 s in coincidence with the beginning of the clonic phase. After this point, the WS presents increasing values until

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around 145 s where a clear peak in the WS represents the end of the RER, again in concordance with the Gastaut and Broughton description. The second peak in the WS around 155 s indicates the seizure end. We can see that the WS for the post-ictal stage presents almost constant values, comparable to those obtained for the pre-ictal stage (mean ± SD: [WS]pre-ictal = 1:257 ± 0:78; [WS]post-ictal = 1:292 ± 0:76). In summary, one can associate a more robust degree of order to the EEG activity during the ictal than the pre- and post-ictal stages. The mean WS for the pre-ictal stage is de4ned as the mean value of the WS the minute before the seizure started (WSpre-ictal ), without considering those intervals contaminated by muscle artifact. In fact, we considered the same EEG epochs used to characterize the pre-ictal stage with the RWE. For this EEG record (Fig. 1), the pre-ictal phase WS was given (|j|=1···6) by the following values: WSpre-ictal = 1:377 and (|j|=3···6)

WSpre-ictal = 1:257, if all frequency bands are included or if the high-frequency bands are excluded, respectively (see Table 3, EEG number 3). In a similar way, the mean values for the ictal period are (|j|=1···6) (|j|=3···6) WSictal = 1:386 and WSictal = 0:883 (see Table 3, EEG number 3). De4ning % = WSpre-ictal − WSictal , the above results are summarized as % ∼ 0 if all the frequency bands are included and % ¿ 0 if only the medium and low-frequency bands are considered. These results suggest that electrical brain activity during the ictal stage is more ordered than the pre-ictal stage. It is important to realize that this result is compatible with the ones obtained using quanti4ers based on nonlinear dynamical metrics tools [5,7,9]. This behavior is better observed when electromyographic activity (mainly associated with frequency bands B1 and B2 ) is excluded. The cases with % 6 0 (mainly when all frequency bands are included) can be associated with a signi4cant degree of disorder introduced in the measured electrical activity by muscular activity. Tables 2 and 3 summarize the results from all subjects. The MRWE for the low-frequency bands, B5 and B6 ; ((5)  and (6) ) for the pre-ictal and ictal phases and their ratio (!(5) and !(6) ) are shown in Table 2. The time width of the corresponding plateau, Qt (5) and Qt (6) , are also given. It is interesting to note

that the intersection between both plateau is not null for all the analyzed seizures. Moreover, in general the plateau associated with B6 includes that corresponding to B5 . In all 20 cases plateaus were found for B5 and B6 , but for EEG numbers 12, 13 and 15, the plateau for the B5 band was rejected because it did not match the criteria of low dispersion and presented an ictal to pre-ictal ratio ! ¿ 0:3. In seizure 7, the ratio ! for both frequency bands was greater than 0.3, therefore, it was rejected. Thus, considering the whole group, a stereotyped pattern was identi4ed in 16 20 of the cases while applying RWE as qEEG. This pattern was characterized by a signi4cant reduction in the low-frequency activity, bands B5 and B6 (delta activity) during the seizures (!(5) ¡ 0:4, p ¡ 0:02; and !(6) ¡ 0:2, p ¡ 0:0005, using a one-sample T -test), implying that they were dominated by medium frequency, bands B3 and B4 (theta and alpha rhythms), until the end of the seizure when the low-frequency (delta rhythm) activity rose again. Note that these results show an increase in statistical signi4cance compared with similar results obtained in our previous work using quanti4es based on GT [33] (in 18 20 events plateaus were found events the ictal/pre-ictal delta mean relaand, in 14 20 tive intensity ratio is lower than 0.3, see Table 2 of Ref. [33]) . In reference to the WS as a measure of the degree of order/disorder, we can say that the WS presented lower values in the ictal than in the pre-ictal phase. In particular, if all frequency bands are included in the evaluation, the di:erence between these values (% ¿ 0, p = 0:6737, using a one-sample T -test) are positive in 50% of the cases, but the number of positive di:erences increases up to 95% (% ¿ 0; p ¡ 0:0001, using a one-sample T -test) if the high-frequency bands (B1 and B2 ), mainly associated with the electromyographic activity, are excluded. Consequently, we can associate a more ordered behavior to the brain electrical activity during an epileptic seizure. Important points to note are that (1) our results were obtained with scalp recordings and without the use of curare or any 4ltering method, and (2) slight changes in the de4nition of the plateau showed no signi4cant variations in our studies.

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Table 3 Mean values and standard deviation of the total WS in the pre-ictal and ictal stage for the 20 EEG records analyzed. % denoted the di:erence between the mean values in both stages

Patient

CS CS LP LP LP DLB DLB AS AS AS AS MB MB IV FT FT FT FT JI JI

EEG

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Total wavelet entropy |J | = 1 · · · 6

Total wavelet entropy |J | = 3 · · · 6

WSpre-ictal

WSictal

%

WSpre-ictal

WSictal

%

1:315 ± 0:149 1:493 ± 0:086 1:377 ± 0:089 1:403 ± 0:117 1:391 ± 0:082 1:195 ± 0:139 1:347 ± 0:188 1:642 ± 0:091 1:423 ± 0:136 1:414 ± 0:129 1:408 ± 0:086 1:371 ± 0:214 1:480 ± 0:106 1:286 ± 0:138 1:214 ± 0:194 1:342 ± 0:165 1:296 ± 0:083 1:362 ± 0:156 1:531 ± 0:150 1:436 ± 0:149

1:473 ± 0:166 1:428 ± 0:201 1:386 ± 0:166 1:390 ± 0:177 1:369 ± 0:156 1:424 ± 0:172 1:486 ± 0:162 1:526 ± 0:113 1:512 ± 0:148 1:556 ± 0:123 1:412 ± 0:195 1:346 ± 0:227 1:448 ± 0:154 1:408 ± 0:132 1:437 ± 0:276 1:280 ± 0:252 1:326 ± 0:244 1:295 ± 0:220 1:271 ± 0:175 1:222 ± 0:173

−0.158

1:220 ± 0:106 1:244 ± 0:093 1:257 ± 0:078 1:252 ± 0:094 1:220 ± 0:079 1:012 ± 0:124 1:122 ± 0:181 1:212 ± 0:163 1:280 ± 0:124 1:252 ± 0:094 1:180 ± 0:105 1:111 ± 0:222 1:224 ± 0:070 1:091 ± 0:126 1:040 ± 0:151 1:170 ± 0:109 1:190 ± 0:068 1:219 ± 0:133 1:130 ± 0:160 1:113 ± 0:124

1:003 ± 0:259 0:998 ± 0:247 0:883 ± 0:211 0:919 ± 0:237 0:935 ± 0:186 0:887 ± 0:343 1:065 ± 0:208 1:136 ± 0:161 1:056 ± 0:204 1:133 ± 0:166 1:080 ± 0:150 0:999 ± 0:185 1:139 ± 0:119 0:936 ± 0:274 1:152 ± 0:192 1:030 ± 0:206 1:079 ± 0:156 1:015 ± 0:178 0:828 ± 0:232 0:904 ± 0:233

0.217 0.246 0.374 0.333 0.285 0.125 0.057 0.076 0.224 0.119 0.100 0.112 0.085 0.155 −0.112 0.140 0.111 0.204 0.302 0.209

4. Discussion The main 4nding of the present work, using qEEG techniques based on ODWT is that we con4rm and extend our previous results of quanti4ed analysis of scalp TC epileptic records based on the GT [33]. More important is that the limitations of the Gabor Transform are avoided by the introduction of the present methodology of work based on the WT. The GT gives an optimal representation of the EEG in the time-frequency domain. However, one critical limitation arises when choosing the size of the window to be applied due to the Uncertainty Principle [1,15,26]. In fact, frequencies cannot be resolved instantaneously. Furthermore, a wide window will be necessary for slow processes and a narrow window will be more suitable for data involving fast processes. Due to its 4xed window size, the GT is not optimal for analyzing signals having ranges of frequencies. The main advantage of the WT is that the size of the window is variable, being wider when

0.065 −0.009 0.013 0.022 −0.229 −0.139 0.116 −0.089 −0.142 −0.004 0.025 0.032 −0.122 −0.223 0.062 −0.030 0.067 0.260 0.214

studying low frequencies and narrower when studying the high ones. As a result, the time-frequency resolution is automatically adapted, so it becomes an optimal method to analyze signals involving a range of frequencies. Furthermore, due to their adaptive window size, wavelets lack the requirement of signal stationarity. Although the general characteristics of the frequency dynamics during the TC seizures were visible using the GT [33] (evolution of relative energies), by using the WT it was possible to study their evolution with better resolution. In addition, with the introduction of WS, the dynamics associated with the seizure were characterized [37]. The dominance of the medium frequency bands B3 + B4 (the alpha and theta bands) during the initial phases of a TC seizure were in agreement with previous observations using GT to analyze ictal patterns recorded with depth electrodes [6,9–11] as well as in the analysis of TC scalp recorded seizures using quanti4ers based on GT [33]. Moreover, using the

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quanti4ers based on ODWT, plateaus for all the seizures under study were accurately de4ned and con4rmed our previous results [33]. These 4ndings were similar to the ones highlighted by Gastaut and Broughton [17] in curarizated patients and by Darcey and Williamson [14] with depth electrodes. That is, in the 4rst seconds after seizure onset, they found a 10 Hz, “epileptic recruiting rhythm” frequency that declined towards the end of the seizure. In the present work, the main purpose was to analyze the middle and low-frequency brain activity during TC seizures. Therefore, the two highest wavelet frequency bands were eliminated, both mainly containing artifacts related to muscle activity. Brain activity in these bands was also removed, but they do not have relevant contribution in these kinds of seizures [14,17,33]. The mean WS is signi4cantly lower during the ictal stages than during the pre-ictal ones. Taking into account the de4nition of the WS, this result may be associated with a more rhythmical and ordered behavior compatible with a dynamic process of synchronization in the brain activity. The WS gives a measure of the order/disorder of the system in time. The WS, therefore, is a good parameter to detect dynamical changes in the system behavior as well as to quantify them [37–39]. In addition, the WS has the following advantages over the corresponding parameters: (1) spectral entropy, WS is capable of detecting changes in a nonstationary signal due to the localization characteristics of the wavelet transform, (2) contaminating noise (if concentrated mainly in frequency bands separate from the signal of interest), contributions can be easily eliminated, and 4nally and very importantly, (3) chaotic measures such as correlation dimension and Lyapunov exponent, the WS is parameter free and does not require reconstruction of phase space. Electrophysiology of generalized TC seizures has not been well understood. There are many descriptions of the typical pattern of EEG activity which accompanies these seizures but few detailed or quantitative analysis are given. One of the main reasons is that, immediately after these kind of seizure begin, muscle

activity commences leading to artifacts which obscure the EEG data [29]. The description of these data suggest that generalized TC seizure EEG data have a complex evolution in time and there are reports of spatial variation on their manifestation despite their classi4cation as “generalized seizures” [14,17,29]. Yet, until recently there have been no studies which attempt to study and to quantify these complex dynamics. Little information exists to explain the neurophysiology underlying generalized TC seizures. A naive assumption is to believe that there are not variations in the degree to which cortical neurons participate in the generalized tonic-clonic seizures; however, the data that exist do not support this view [29]. These data instead suggest that there are variations in the degree in which cortical neurons participate in the generalized TC seizures in both animal models and in humans [29,35]. Some researchers have suggested that the “epileptic recruiting rhythm” which is manifest in the EEG after seizure onset is a cardinal feature of these epileptic seizures [17,29]. A more precise characterization of the evolution of those frequencies associated to the “epileptic recruiting rhythm” was made on the basis of a “time-scale-frequency” description that employs trigonometric wavelet packets [8]. From that work, it can be inferred that the central frequency associated to the epileptic recruiting rhythm decreases with time [8,32]. One can thus reasonably conjecture that tonic-phase’s spasms are answers to brain oscillations generated with high frequencies that, owing to the fact that muscles cannot contract in such a rapid fashion, muscle-activity gets restricted to tonic contraction until the frequency of brain oscillations becomes slow enough for the muscle to be capable to oscillate in resonance with them [32]. One critical point is the possible distortion due to spatial propagation of the seizure, since data from the C4 electrode was analyzed and the sources of the seizures were mostly in temporal locations (number of patients and source of seizures: 1 right temporal; 3 left temporal; 2 bitemporal; 2 nonlocalized—see Table 1 of our previous work [33]). In order to overcome this, quanti4ers based on ODWT were also applied to T 3 and T 4 electrodes, obtaining similar results to the ones reported with C4 electrode. That is even though these electrodes present more artifact, compared with C4, the “recruitment epileptic rhythm” was observed,

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as well as decreased WS values for the ictal stage compared with pre-ictal one. For a quantitative analysis of the observed behavior in these two electrodes (T 3 and T 4) the above introduced quanti4ers based on ODWT were evaluated with the same thresholds. The number of cases for which the imposed constraints for the quanti4ers are satis4ed is similar for C3. This implies that the method is transportable to di:erent electrodes. Some variation in the numerical values for the di:erent quanti4ers was observed; it is reasonable to assume that the di:erent positions could provide additional information. Having EEG records at di:erent places, a multichannel analysis should give more reliable results. The problem with the present set of data is inhomogeneity in the seizure localization, which invalidates multichannel analysis using an ANOVA test. New data are being collected in order to solve this problem. Further research with quanti4ers based on ODWT to study the spatial propagation of di:erent rhythm during a seizure is in progress. Another interesting point to note is that although the grouping in frequency bands implies a loss of frequency resolution, it can be more useful than a study of single frequencies or peaks, due to the relations between frequency bands and functions or sources of the brain. In this context, the RWE allows a fast interpretation of several minutes of frequency variations in single display, sometimes di0cult to perform with traditional scalp EEG. 5. Conclusion Two quantitative parameters de4ned from the Wavelet Transform are applied to the analysis of EEG signals. The 4rst parameter, the Relative Wavelet Energy gives an accurate description of the time evolution of the EEG rhythms, and the second, the Wavelet Entropy allows us to characterize the time evolution of the dynamics associated with the EEG records. The analysis showed marked decreases of the low-frequency bands (3.2–0:8 Hz), delta bands, during the seizure due to the dominance of the medium frequency bands (12.8–3:2 Hz), alpha and theta bands, at this stage. Darcey and Williamson [14] also obtained similar patterns analyzing seizures recorded with depth electrodes (recordings nearly free of artifacts). This fact reinforces the idea that the results

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obtained with scalp electrodes were not a spurious e:ect of muscle activity, or consequence of signal separation employed methods. The WS provides new information about EEG signals in comparison with the information obtained by using frequency analysis or other standard methods. A signi4cant decay in the WS due to middle and low frequencies was observed at the beginning and during the ictal stage, indicating a more rhythmic and ordered behavior compatible with a dynamic process of synchronization in the brain activity. This behavior may be thought of as induced by one hypothetical epileptic focus. The use of these quanti4ers based on time-frequency, together with the clinical patient history and the visual assessment of the EEG, can contribute to the identi4cation of the source of epileptic seizures and to a better understanding of its dynamics. Certainly, the use of these quanti4ers is not intended to replace conventional EEG analysis, but rather to complement it and also to provide further insights into the underlying mechanisms of ictal patterns. Therefore, the epileptic recruiting rhythm quanti4cation is useful for characterization of the genesis and spreading of this type of seizure. In this context we consider that the wavelets quanti4ers introduced in the present work and their evaluation on the di:erent channels (multichannel analysis), could be very useful for developing models, as well as elucidated a number of aspects of the spatio-temporal dynamics of the generalized tonic-clonic seizure EEG data that had not previously been appreciated. Moreover, we consider that the information obtained throughout the wavelets coe0cients of a multichannel analysis could be used to study channel and frequency band interactions, giving in consequence very useful information about the brain dynamics associated with this kind of seizure. Acknowledgements This work was partially supported by the Consejo Nacional de Investigaciones CientUV4cas y TUecnicas (CONICET, Argentina), PEI 0003/97, PEI 0004/97, PIP 0029/98 and FundaciUon Alberto J. Roemmers (Argentina). We are very grateful to Prof. Dr. E. BaHsar and the International O0ce of BMBF (ARG-4-G0A-6A), Germany, for their kind hospitality at Institute of Physiology, Medical University LWubeck, Germany, where

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