Investigation of non-linear properties of multichannel ... - Laurent Pezard

and Duke, 1992; Elbert et al., 1994; Rey and Guillemant,. 1997). The clinical ..... cerebral dynamics is different than that observed in the case of PD. A number of ...
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Clinical Neurophysiology 112 (2001) 38±45

Investigation of non-linear properties of multichannel EEG in the early stages of Parkinson's disease Laurent Pezard a, Robert Jech b, EvzÏen RuÊzÏicÏka b,* a

Laboratoire de Neurosciences Comportementales, Universite Rene Descartes, 45 rue des Saints-PeÁres, F-75270 Paris Cedex 06, France b Clinic of Neurology, Charles University, KaterÏinska 30, CZ-120 00 Praha 2, Czech Republic Accepted 25 October 2000

Abstract Objectives: Modi®cations of brain activity in the early stages of Parkinson's disease (PD) are dif®cult to detect using electroencephalography (EEG) signals and are often biased by l-DOPA treatment. We compare here the performances of both linear and non-linear methods in differentiating EEG of l-DOPA naive PD patients from that of control subjects. Methods: Resting multichannel EEG (20 electrodes, 30 s epochs) of 9 patients with PD in Hoehn and Yahr stages 1±2 (4 women, 5 men, mean age 54.3 years, range 48±63 years) were compared with those of 9 control subjects (7 women, two men, mean age 51.3 years, range 43± 61 years). The following measurements were computed: u-, a- and b-band relative powers constituted the linear indices; localized entropy, slope asymmetry and number of non-linear EEG segments constituted the non-linear indices. Results: In the case of linear quanti®cation, only a decrease in the b-band was observed for patients. Signi®cant non-linear structures were observed in our EEG data. Non-linear quanti®ers demonstrate an increase in entropy and in the number of non-linear EEG segments for the patients. Conclusions: Changes in EEG dynamics observed here in l-DOPA naive PD patients may represent early signs of cortical dysfunction produced by subcortical dopamine depletion. q 2001 Elsevier Science Ireland Ltd. All rights reserved. Keywords: Parkinson's disease; EEG; Spectral analysis; Non-linear dynamics; Entropy; Surrogate data

1. Introduction Parkinson's disease (PD) is characterized by a motor disorder caused by nigrostriatal dopaminergic de®ciency. However, the presence of cognitive de®cits in PD also suggests disturbances on cortical and subcortico-cortical levels (Dubois et al., 1991). Indeed, as demonstrated by Javoy-Agid and Agid (1980), the ascendant mesocortical dopamine system may be affected as well. Electroencephalography (EEG) is generally used to depict brain electrical activity re¯ecting the functional state of cortical layers and their subcortical driving structures. A number of studies showed EEG abnormalities in PD patients, most commonly represented by a generalized slowing of EEG activity (de Weerd et al., 1990; Soikkeli et al., 1991; Neufeld et al., 1994). However, studies usually included patients in advanced stages of the disease where non-dopaminergic lesions supposedly contribute to general

* Corresponding author. Tel./fax: 1420-2-24-91-69-80. E-mail address: [email protected] (E. RuÊzÏicÏka).

motor and non-motor dysfunction (Agid et al., 1987; Pillon et al., 1989). l-DOPA treatment may be another source of bias as demonstrated by studies of event-related potential modi®cations induced by dopaminergic treatment (RuÊzÏicÏka and El Massioui, 1993). Our aim was to verify if patients in the early stages of PD and before the introduction of l-DOPA treatment show any electrophysiological indices of brain dysfunction. To achieve this goal, we used both classical EEG spectral analysis and numerical methods based on non-linear dynamics. Spectral analysis and non-linear analysis are different ways of dealing with EEG apparent complexity. The former belongs to the theory of random process and, in that case, the EEG signal is generally considered as a linear stochastic process. The latter belongs to dynamical systems theory and, thus, EEG complexity is viewed as the result of nonlinear deterministic dynamics (possibly a `chaotic' process). These two approaches gather each other when dealing with the problem of signals characterized by a continuous spectrum (Berge et al., 1986) such as commonly observed in EEG. In fact, this continuous spectrum may be either related

1388-2457/01/$ - see front matter q 2001 Elsevier Science Ireland Ltd. All rights reserved. PII: S13 88-2457(00)0051 2-5

CLINPH 2000614

L. Pezard et al. / Clinical Neurophysiology 112 (2001) 38±45

to a quasi-periodic signal with a high (possibly in®nite) number of frequencies or to an aperiodic signal. If the signal is indeed aperiodic, it may have been generated by a nonlinear deterministic system with a low number of degrees of freedom. Therefore, the existence of low-dimensional nonlinear systems with complex aperiodic behaviors demonstrates the possibility of a deterministic approach for problems which were previously only statistically tractable. In the case of EEG, such a perspective may imply more parsimonious models to account for EEG complexity. The application of non-linear analysis EEG considers the brain as a physical dynamical system (McKenna et al., 1994). The putative importance of non-linear analysis has been previously emphasized (Jansen, 1991; Pritchard et al., 1994; Micheloyannis et al., 1998) and reviewed (Pritchard and Duke, 1992; Elbert et al., 1994; Rey and Guillemant, 1997). The clinical importance of non-linear indices has been investigated in several neurological and psychiatric conditions such as Creutzfeld±Jacob disease (Babloyantz and Destexhe, 1988; Stam et al., 1997), Alzheimer's disease (Pritchard et al., 1991; Pezard et al., 1998; Jelles et al., 1999), depression (Nandrino et al., 1994; Pezard et al., 1996b; Thomasson et al., 2000), schizophrenia (Roschke et al., 1995) and epilepsy (Babloyantz and Destexhe, 1986; Martinerie et al., 1998; Lehnertz et al., 2000a). For books on the topic, see BasËar (1990), Duke and Pritchard (1991), Jansen and Brandt (1993), and Lehnertz et al. (2000b). Few studies have investigated the non-linear dynamics of EEG in PD (Stam et al., 1994, 1995). Their results mainly showed speci®c patterns of dysfunction in dementia and PD on the basis of indices computed for the global brain electrical activity. Our study completes those previous ®ndings (1) by computing linear and non-linear electrode-related indices and (2) by studying l-DOPA naive patients in the ®rst stages of the disease.

2. Methods 2.1. Subjects After approval by the local ethics committee (General Faculty Hospital, Prague), we studied 9 patients with PD (4 women, 5 men, mean age 54.3 years, range 48±63 years) meeting the criteria for the diagnosis of idiopathic PD (Ward and Gibb, 1990). The mean duration of PD was 3 years (range 1±6 years); 3 patients were in Hoehn and Yahr stage 1, 3 were in stage 1.5, and 3 were in stage 2. We included only l-DOPA naive patients; 7 of them were taking selegiline (5±10 mg), 6 were taking amantadine (200±300 mg), one was taking biperiden (2 mg), one was taking benztropine (6 mg), one was taking alprazolam (0.25 mg), one was taking piracetam (1200 mg) and one patient was without medication. Nine subjects (7 women, two men, mean age 51.3 years,


range 43±61 years) with no history or symptoms of neurological or mental illness served as controls. The scores for the Mini-Mental-Status examination were within normal limits (28±30) in all patients and control subjects. Informed consent was obtained from all the subjects. 2.2. EEG recordings EEG was recorded by a multichannel apparatus Brainscope q (M&I Ltd., Czech Republic) using 20 Ag-AgCl electrodes set on the scalp according to the 10±20 International Electrode Placement System (Jasper, 1958) (including the Oz electrode but not the Fpz one) referenced to the linked mastoids. The EEG signal was digitized on 16 bits using a 1 kHz frequency per channel and then bandpass ®ltered between 0.5 and 70 Hz. In order to eliminate ocular artifacts, vertical and horizontal eye movements were simultaneously recorded. All subjects were examined in the supine position during an eyes closed condition in a quiet and dimly shielded room. For each subject, 30 s of multichannel EEG signals free of signs of impaired wakefulness, ocular movements and other artifacts were selected for analysis. 2.3. Analysis of the EEG data 2.3.1. Segmentation of the EEC signals Each 30 s multichannel EEG signal was divided into 29 segments of 1024 ms. The EEG segments were notch ®ltered to eliminate 50 Hz artifacts. 2.3.2. Linear analysis Linear analysis is based on the assumption that the linear components (e.g. mean, autocorrelation, power spectrum) are suf®cient to describe a signal. In particular, for spectral analysis, it is assumed that frequency bands are independent and can be studied separately. Our linear analysis is based on this standard assumption used in EEG quanti®cation. The power spectrum of each multichannel EEG segment was computed on the basis of a Fast Fourier Transform of the data. For each channel, the total power in each spectrum was calculated by summing all components and the powers in u-, a- and b-bands were calculated by summing components in bands from 4 to 8, 8 to 12 and 12 to 30 Hz, respectively. The power in each band was divided by the total power to provide u-, a- and b-band relative powers which were used as our linear measurements. 2.3.3. Non-linear analysis General principle. In non-linear analysis, a different assumption is made, namely that some non-linear deterministic structures are present in the data. Non-linear indices are thus computed from the data. We choose here two electrode-related measurements: slope asymmetry and local entropy (to be described below). Since linear properties may be responsible for the results of non-linear analysis,


L. Pezard et al. / Clinical Neurophysiology 112 (2001) 38±45

the non-linear measurements have to be statistically validated. Surrogate data which share the same linear characteristics with the raw data are constructed (to be described below). Non-linear measurements are computed for those surrogate data. A statistical procedure allows us to test whether the measurements obtained from the raw data differ from those obtained from the surrogate data. In that case, non-linear structures are evidenced and, consequently, linear characteristics are not suf®cient for a reliable description of the data. On the contrary, if measurements obtained from surrogate data do not differ from those obtained from raw data, either no non-linear structure exists in the data or some drawbacks prevent its characterization. Time series slope asymmetry. The concept of slope asymmetry is derived from the fact that time series generated from linear processes (such as sine waves) appear statistically the same whether the data are viewed as running forward or backward in time. By contrast, nonlinear systems generally have distinct rise and fall times. For such systems, this measure captures the difference between the rise times (upward part) and fall times (downward part) of the oscillations in a dynamical system. One of the simplest ways to measure slope asymmetry is by the skewness (third statistical moment) of differences between successive samples (Ehlers et al., 1998) P …x 2 xi21 †3 Slope asymmetry ˆ ÿP i 3=2 …xi 2 xi21 †2 Non-linear forecasting and local entropy. Local entropy measures the loss of predictability of the EEG dynamics. It is computed using numerical methods based on the principles of non-linear dynamics: trajectory reconstruction and non-linear forecasting (detailed descriptions can be found in Pezard et al., 1994, 1996a). 1. The set of 1024 samples recorded over 20 electrodes is considered as a set of 1024 vectors in a 20-dimensional space. This ®rst step constitutes a multichannel reconstruction procedure transforming the time series into a multidimensional trajectory representing the evolution of brain activity (for a discussion of the validity of reconstruction methods in the context of EEG, see Pezard et al., 1999; Pritchard, 1999). 2. The reconstructed trajectory was characterized using a non-linear forecasting method. It permits one to obtain quanti®ers of the brain activity related to each recording site. Namely, a local linear model (Sugihara and May, 1990) is used to forecast the evolution of the vectors in the 20-dimensional space several time steps ahead. To avoid correlation artifacts, vectors closer than 20 time steps to the vector to be predicted were discarded from the prediction model (Theiler, 1986). The decrease of the correlation coef®cient between the observed values and the predicted ones constitutes a prediction curve. This

curve is used to compute an entropy index (K) (Wales, 1991). The prediction curves obtained for each electrode permit the computation of local entropies (Ki for electrode i). A high entropy corresponds to a rapidly decreasing predictability. Surrogate data testing. In order to ensure the presence of non-linear structures in the brain dynamics, we proceeded to a surrogate data test. Namely, multivariate linearly correlated noises that share the same linear characteristics (in particular the power spectrum and phase relations) with the observed signals were generated (Prichard and Theiler, 1994). Non-linear indices (slope asymmetry and Ki) are computed for the surrogate signals and for the observed signals. In this study, two successive steps were followed. 1. Firstly, non-linearities were analyzed at a coarse level using only one multivariate surrogate time series for each EEG segment and the presence of signi®cant nonlinearity was thus tested at the level of the entire set of EEG data. 2. Secondly, a set of 39 multivariate surrogate data was generated for each EEG segment. This procedure allows one to test the presence of non-linearity at the ®ne level of individual EEG segment. This second step was performed using the non-linear indices for which signi®cant global non-linearities were observed. If the index computed for the set of surrogate data signi®cantly differs from that of the observed signals, it can be concluded that a non-linear process is involved in the generation of the observed EEG segment. In order to control possible false rejections of the linearity assumption, we constructed arti®cial random multichannel time series as follows (Rombouts et al., 1995) xk;t ˆ 0:9…xk;t21 1 1:05…xk;t21 2 xk;t22 † 1 e 1 0:015xk21;t † where xk,t is the amplitude value of channel k at time t (here k ˆ 1, ¼, 20 and t ˆ 1, ¼, 1024) and e is independently distributed discrete noise. A set of 261 (9 £ 29) such linearly correlated noises was generated and divided into 9 sets of 29 individual multichannel time series to mimic a group of 9 subjects each associated with 29 EEG segments. These data were analyzed in the second step described above using the same procedure as the EEG data. They thus allow us to estimate the level of spurious rejections of the linearity assumption. 2.4. Statistical analysis of the EEG quanti®ers Each patient was characterized by the averaged values computed over the 29 EEG segments of u-, a- and b-band relative powers for the linear measurements and of slope asymmetry, local entropy (Ki) and the number of non-linear segments for the non-linear measurements.

L. Pezard et al. / Clinical Neurophysiology 112 (2001) 38±45

Analyses of variance were used to test the effect of the group factor (two levels, controls and patients) and of the electrode factor (20 levels) for the linear measurements (u-, a- and b-band relative powers). In the ®rst step of nonlinear analysis, an analysis of variance with 3 factors: type of data (two levels, raw and surrogate), group (two levels, controls and patients) and electrode (20 levels), was used to characterize their effects on local entropy (Ki) and slope asymmetry. In the case of the measurement where a signi®cant effect of the type of data was found, this index was used in the second step of our non-linear analysis. In the second step of the non-linear analysis, a ®rst stage consists of testing the presence of false positive non-linearity in our EEG data. For that purpose, we analyzed two 2 £ 2 contingency tables (Conover, 1999) comparing frequencies of linearity assumption rejection for either controls versus random data or PD patients versus random data. Since signi®cant rejections of the linearity assumption were observed (see Section 3), an analysis of variance was used to test the effect of the group factor (two levels, controls and patients) and of the electrode factor (20 levels) for the number of non-linear segments obtained for EEG data.


Fig. 1. Relative powers of u-, a- and b-band of EEG rhythms for controls and PD patients averaged over the 20 electrodes. Standard errors are represented with vertical lines. *P , 0:001.

3. Results 3.2. Non-linear analysis

3.1. Linear analysis The results of spectral analysis are summed up in Table 1 for statistical analysis and in Fig. 1 for the difference between groups. The decrease of the b-band relative power in the patients is the only signi®cant difference between controls and patients observed for linear measurements. The heterogeneity of brain activity is assessed by the signi®cant effect of the electrode factor observed for the 3 rhythms. No interaction between group and electrode factors was observed, which does not permit one to search for localized effects. Table 1 Results of the analysis of variance for the u-, a- and b-band relative powers Effect


F value

P value

u -band Group Electrode Group £ electrode

1 19 19

3.416 6.115 0.273

0.066 ,0.001 0.999

a -band Group Electrode Group £ electrode

1 19 19

2.444 1.642 0.067

0.119 0.045 1.000

b -band Group Electrode Group £ electrode

1 19 19

13.720 2.812 0.154

,0.001 ,0.001 0.999

3.2.1. First step: coarse analysis The statistical results are summed up in Table 2. The slope asymmetry index detects non-linear structures (see Fig. 2), but does not depict any difference between groups or electrodes. The local entropy index does not detect any non-linear structures but shows a signi®cant increase of entropy for patients (see Fig. 3) and an effect of the elecTable 2 Results of the analysis of variance for the non-linear measurements in the coarse step (raw versus surrogate data) Effect


F value

P value

Local entropy Type Group Electrode Type £ group Type £ electrode Group £ electrode Type £ group £ electrode

1 1 19 1 19 19 19

0.382 9.597 4.779 0.003 0.004 0.359 0.004

0.537 0.002 ,0.001 0.958 1.000 0.995 1.000

Slope asymmetry Type Group Electrode Type £ group Type £ electrode Group £ electrode Type £ group £ electrode

1 1 19 1 19 19 19

11.999 1.015 0.703 1.419 0.732 0.594 0.805

,0.001 0.314 0.817 0.234 0.787 0.912 0.703


L. Pezard et al. / Clinical Neurophysiology 112 (2001) 38±45 Table 3 Results of the analysis of variance for the number of EEG segments where signi®cant non-linear structures were found in the ®ne step of the non-linear analysis

Fig. 2. Difference between raw and surrogate data shown by slope asymmetry (S. A. £ 10 24) averaged over the 20 electrodes for both groups. Standard errors are represented with vertical lines. *P , 0:001.

trode factor. Nevertheless, the absence of signi®cant interaction does not permit one to test for localized effects. 3.2.2. Second step: ®ne analysis On the basis of the results obtained in the ®rst step, the ®ne analysis was performed using the slope asymmetry index. The frequencies of the linearity assumption rejection were compared between EEG data (controls and PD patients) and arti®cial multichannel random data. The frequency of rejection of the linearity assumption is signi®-

Fig. 3. Local entropy (kKl in s 21) for controls and PD patients averaged over the 20 electrodes. Standard errors are represented with vertical lines. *P , 0:01.



F value

P value

Group Electrode Group £ electrode

1 19 19

5.641 1.269 0.453

0.018 0.202 0.978

cantly higher than the level of spurious rejections for both groups (T12 ˆ 107:5, P , 0:001 for controls; T12 ˆ 204:3, P , 0:001 for PD patients). Signi®cant non-linear structures were thus detected in our EEG data at the level of individual EEG segments. The effect of the notch ®lter on the frequency of linearity assumption rejection was tested using the same procedure in the case of the control group. No signi®cant difference between notch-®ltered and unnotch-®ltered data was observed (T12 ˆ 0:88, P . 0:75). The effect of the notch-®lter on the non-linearity level can thus be dismissed. The statistical results obtained for the comparison between EEG data in controls and PD patients are summed up in Table 3. The number of EEG segments where signi®cant non-linear structure was found is higher in PD patients than in controls (see Fig. 4). Nevertheless, non-linear structure does not vary with electrode.

4. Discussion PD is known as a predominantly motor disorder produced by dopaminergic de®ciency in the basal ganglia. However, non-motor impairment including cognitive dysfunction has frequently been observed in the early stages of PD (Cooper et al., 1991). Electrophysiological methods can help to investigate various non-motor aspects of the disease independently from basic motor impairment; for example, event-related potentials allow one to study the speed of cognitive processing in speci®c tasks (see RuÊzÏicÏka and El

Fig. 4. Number of non-linear EEG-segments (# Seg.) averaged over the 20 electrodes. Standard errors are represented with vertical lines. *P , 0:05.

L. Pezard et al. / Clinical Neurophysiology 112 (2001) 38±45

Massioui, 1993, for review). Furthermore, EEG analysis (linear and non-linear methods) depicts more global indices of brain function that can re¯ect disturbed subcortico-cortical mechanisms in patients with advanced PD and/or dementia (de Weerd et al., 1990; Stam et al., 1994, 1995; Pezard et al., 1998). The goal of our study was to search for such electrophysiological indices in less advanced cases of PD. With that in mind, we examined both linear and nonlinear EEG characteristics in a group of non-demented patients in the early stages of PD without l-DOPA medication. With regard to the linear EEG indices, we observed a decrease in the relative power of the b-band in PD patients compared to controls. The a- and u-band relative powers were not signi®cantly different from controls. On the contrary, in previous studies in more advanced stages of PD accompanied with cognitive decline, generalized slowing of EEG was observed with an increase in d- and u-band (de Weerd et al., 1990; Soikkeli et al., 1991). Therefore, we may hypothesize that the isolated diminution of b-band power represents the earliest linear EEG marker of initial cortical or subcortico-cortical dysfunction in PD. The linear indices are not suf®cient to fully describe the complexity of brain activity since the comparison between slope asymmetry of raw EEG signals and surrogate data showed the presence of signi®cant non-linear structures in the EEG of both PD patients and controls. Employing our two non-linear indices (slope asymmetry and entropy) to study the difference between PD patients and controls, we observed that the EEG of PD patients is characterized by a higher presence of non-linear EEG segments and by a higher entropy. High entropy means that the quality of prediction of EEG dynamics decreases more rapidly in PD patients than in controls. Thus, the local linear model used to forecast the time-evolution of EEG is better in the case of controls than in PD patients. In other words, the 20-dimensional trajectory of PD patients contains more non-linear structures than that of the controls. This result suggests that with the trajectory reconstruction, less non-linear structure is lost in PD patients than in controls (Hegger et al., 1998). Since it has been shown that the amount of detected non-linearity decreases with the augmentation of dimension (Lachaux et al., 1997), we can hypothesize that PD would be associated with brain dynamics of a lower dimension than that of controls as previously reported (Stam et al., 1994). The modi®cations of brain dynamics in early stages of PD were observed only at a global level without any signi®cant localization for both linear and non-linear indices. Nevertheless, linear indices (u-, a- and b-band relative powers) and entropy index depicted a signi®cant effect of the electrode factor whereas slope asymmetry does not. Spectral indices and entropy are thus more speci®c than slope asymmetry in dealing with spatial heterogeneity of brain functioning. An increase in non-linear structure was observed here for


EEG data in PD patients compared to controls. We checked the validity of these results for group comparisons. Namely, we investigated possible spurious detection of non-linear structure and show that the number of EEG segments where non-linear structures were detected is above the level of false detection. Thus, variations in this number of EEG segments can be considered as signi®cant for the comparison between controls and PD patients, although the level of non-linear segments remains low (between 1 and 2%, i.e. similar to the results observed for alpha rhythm in healthy volunteers by Stam et al. (1999)). Nevertheless, our ®ndings are contrary to those obtained in studies of Alzheimer's disease (Jelles et al., 1999) or of ethanol intake (Ehlers et al., 1998) where a reduction of non-linear structures in EEG data compared to controls was reported. We assume that the effect of ethanol and Alzheimer's disease on cerebral dynamics is different than that observed in the case of PD. A number of previous PD studies were done in chronically treated patients in whom the effects of disease chronicity and possible dementia might in¯uence the results. In an attempt to avoid such a confusion, we included in the present study only non-demented patients in early stages of PD without l-DOPA treatment. However, since nonlinear EEG measures may be sensitive to medication effects (Wackermann et al., 1993; Pezard et al., 1998), possible in¯uences of other drugs have to be considered. Most of our patients were receiving a combination of drugs with putative neuroprotective and/or weak symptomatic effects (selegiline, amantadine). Nevertheless, these drugs do not appear to signi®cantly in¯uence either cognition or electrophysiological indices in early stages of PD (Gelenberg et al., 1989; Dalrymple-Alford et al., 1995; Ziemann et al., 1997). Our results are thus more probably related to disease effects than to medication effects. In conclusion, the reduced power of b-band and the increase of entropy and the number of non-linear EEG segments may represent the early signs of subcortico-cortical dysfunction in PD. Studies following the disease progression and treatment effects might be able to demonstrate if it is namely the impairment of the dopaminergic system in PD that causes this modi®cation of brain dynamics. Acknowledgements The study was partly supported by Charles University (project CEZ J13/98 111100001) and by the Scienti®c Service of the French Embassy in Prague. The authors are thankful to Dr J. Roth and Dr P. Mecir who kindly referred two patients and to O. KucÏerova for her technical assistance with EEG recordings. L.P. gratefully acknowledges fruitful discussions with J. Martinerie and I. Rivals. The comments of anonymous reviewers on a previous version of the manuscript allowed us to improve this article.


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