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Non-linear EEG analysis in children with epilepsy and electrical status epilepticus during slow-wave sleep (ESES)
Clinical Neurophysiology 112 (2001) 2274–2280 www.elsevier.com/locate/clinph
Non-linear EEG analysis in children with epilepsy and electrical status epilepticus during slow-wave sleep (ESES) Raffaele Ferri a,b,*, Maurizio Elia b, Sebastiano A. Musumeci b, Cornelis J. Stam c a
b
Sleep Research Center, Oasi Institute, Via Conte Ruggero 73, 94018 Troina, Italy Department of Neurology, Oasi Institute for Research on Mental Retardation and Brain Aging (IRCCS), Troina, Italy c Department of Clinical Neurophysiology, University Medical Center, Amsterdam, The Netherlands Accepted 10 September 2001
Abstract Objective: The objective of this work was to study the non-linear aspects of electroencephalography (EEG) in children with epilepsy and electrical status epilepticus during slow-wave sleep (ESES). Methods: In this study, we recorded the sleep EEG in 5 subjects with ESES (4 males and one female, aged 6.5–10 years) who were also mentally retarded and affected by cerebral palsy (3 subjects) and hydrocephalus (two subjects). The signals were sampled at 128 Hz and stored on hard disk. All the subsequent computational steps were performed on EEG epochs (4096 data points) selected from wakefulness and non-rapid eye movement (non-REM) (with ESES) or REM sleep. The dynamic properties of the EEG were assessed by means of the nonlinear cross prediction (NLCP) test which uses 3 different ‘model’ time series in order to predict non-linearly the original data set (Pred, Ama and Tir). Pred is a measure of the predictability of the time series and Ama and Tir are measures of asymmetry, indicating non-linear structure. Moreover, the correlation dimension (D2) was estimated by means of the algorithm by Grassberger and Procaccia (1983) for the epochs showing non-linear nature. Results: The NLCP test provided evidence of significant non-linear dynamics in all epochs of non-REM sleep, when ESES was evident. Only during this stage, the possible presence of low-dimensional chaos could also be suspected (average D2 ¼ 4:02; range 3.16–6.21). EEG without ESES could not be distinguished from linearly filtered noise. Conclusions: The results of the present study seem to indicate that subjects with ESES show a profound modification of their EEG dynamics with the occurrence, during sleep, of long periods characterized by non-linear dynamics and, probably, low-dimensional chaotic structure able to modify in a substantial way their brain functioning during sleep. q 2001 Elsevier Science Ireland Ltd. All rights reserved. Keywords: Encephalopathy with electrical status epilepticus during slow-wave sleep; Epilepsy; Sleep; Electroencephalography; Non-linear dynamics; Nonlinear cross prediction; Chaos; Correlation dimension
1. Introduction Encephalopathy with electrical status epilepticus during slow-wave sleep (ESES) syndrome is a condition characterized by continuous spikes and waves occurring during sleep and epilepsy, with onset at around 4–5 years of age and a generally favorable course, with disappearance at around 10–15 years of age (Tassinari et al., 1977, 2000). The persistence of this particular electroencephalographic (EEG) condition during sleep is accompanied by the appearance of complex and severe neurological impairment involving language, learning capabilities and psychomotor development. When psychomotor development is abnormal prior to the occurrence of ESES, a worsening of mental capabil* Corresponding author. Tel.: 1 39-935-936111; fax: 139-935-653327. E-mail address: [email protected] (R. Ferri).
ities is almost always detectable after the appearance of seizures and continuous spikes and waves during sleep (Tassinari et al., 1977, 2000). The peculiar sleep EEG pattern of ESES corresponds to the term ‘continuous spikes and waves during sleep’ adopted by the Commission on Classification and Terminology of the International League Against Epilepsy (1989) and, probably, ESES syndrome includes the so-called acquired aphasia or Landau–Kleffner syndrome (Landau and Klefner, 1957; Giovanardi Rossi et al., 1999; Tassinari et al., 2000). One way to gain a better understanding of the pathophysiological processes underlying a phenomenon like ESES, is by the use of concepts and analytical tools derived from the theory of non-linear dynamical systems (‘chaos theory’). In this approach, the essential features of the dynamical system underlying the EEG are reconstructed by representing the
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system as a trajectory in its state space (Takens, 1981). This trajectory is assumed to converge to a limit set which is called the attractor of the system. The attractor of the system is a geometrical object which can be characterized by measures such as the correlation dimension D2 (complexity or degrees of freedom of the system) or the Kolmogorov entropy (unpredictability or irregularity of the system dynamics). To validate this approach, it is important to know whether the system generating a time series is high dimensional and stochastic, or low dimensional and nonlinear; however, also non-linear stochastic systems and linear low-dimensional processes can be characterized. Non-linear dynamics can be demonstrated with the method of surrogate data (Pijn et al., 1991; Theiler et al., 1992) or with tests that look for asymmetries in the data (Diks et al., 1995; Stam et al., 1998). Application of non-linear time series analysis to EEG has shown that non-epileptic EEG usually reflects mostly high dimensional, stochastic dynamics (Pritchard et al., 1995; Rombouts et al., 1995). This is true for normal background activity as well as irregular slow waves (Stam and Pritchard, 1999). So far, highly non-linear dynamics has only been demonstrated in a small number of EEG phenomena such as frontal intermittent rhythmic delta activity (FIRDA) (Stam and Pritchard, 1999), periodic discharges (Stam et al., 1999) and epileptic seizure activity (Pijn et al., 1991, 1997). In particular, non-linear dynamics may be a sensitive indicator for impending seizures allowing their prediction 11–20 min ahead (Lehnertz and Elger, 1998; Le van Quyen et al., 2001). Thus, knowledge of the dynamics underlying an EEG phenomenon can lead to clinical applications such as automatic detection or predictions of seizures. The present study was undertaken to study the dynamics underlying ESES. The hypothesis was that ESES, like other types of epileptic EEG activity described in the literature, would reflect highly non-linear and possibly low-dimensional dynamics, whereas non-ESES sleep and wakefulness EEG would correspond with linear stochastic dynamics. We used the non-linear cross prediction (NLCP) algorithm as a robust indicator of non-linear dynamics because this method avoids some of the bias that may affect phase randomized surrogate data (Stam et al., 1998). Only when the NLCP
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method clearly showed non-linear dynamics, an attempt was made to compute the correlation dimension of the EEG. 2. Materials and methods 2.1. Subjects In this study, we recorded sleep EEG in 5 subjects with ESES (4 males and one female, aged 6.5–10 years) who were also mentally retarded. Their clinical characteristics are reported in Table 1. 2.2. Experimental protocol and recording procedure All subjects slept in the laboratory for an adaptation night (23.00–7.00 h); during the following night, all subjects underwent polysomnographic investigation, which included EEG (6 bipolar channels), electrooculogram (EOG) and electromyogram (EMG) of the submentalis muscle. Signals were sampled at 128 Hz (8-bit A/D precision) and stored on hard disk; the C3–T3 or C4–T4 derivations were used for all the subsequent computational steps which were performed on EEG epochs (4096 data points) selected from quiet wakefulness preceding sleep onset, non-rapid eye movement (REM) sleep (with ESES) and REM sleep (without ESES). For each of these stages, 6–8 artifact-free epochs were selected. 2.3. Non-linear measures 2.3.1. NLCP test The dynamical properties of the EEG were assessed by means of the software developed at Department of Neurology and Clinical Neurophysiology, Leyenburg Hospital, The Hague, The Netherlands (DIGEEG2) which computes NLCP test introduced by Stam et al. (1998). This test uses 3 different ‘model’ time series in order to predict non-linearly the original data set. The first is the original data set itself (Pred), the second is an amplitude inverted copy of the original time series (Ama) and the third is a time reversed copy (Tir). With this test it is possible to reject the null hypothesis that the original time series is linearly
Table 1 Clinical characteristics of the patients included in this study a Subject Sex/age Etiology, neurologic examination
Seizure type AEDs
1
M/6.5
CPS
2 3 4 5
M/9.0 M/9.3 M/9.8 F/10.0
Hypoxic-ischemic encephalopathy, tetraplegia Porencephaly, right hemiplegia Hydrocephalus, normal Hydrocephalus, tetraplegia Porencephaly, right hemiplegia
CPS CPS AA CPS
EEG during wakefulness
VPA, ESM, HC
Right parietal–temporal–occipital SW; left frontal–central–temporal SW VPA, ESM, LTG, CLB Left temporal–occipital SW VPA, ESM, CLB, HC Left temporal–occipital SW PB, CBZ Right temporal–occipital SW VPA, CLB, GVG, ESM, HC Left frontal–central–temporal SW
a CPS, complex partial seizures; AA, atypical absences; AEDs, antiepileptic drugs; PB, Phenobarbital; CBZ, carbamazepine; VPA, valproic acid; CLB, clobazam; GVG, g-vynil-GABA; ESM, ethosuximide; HC, hydrocortisone; ACTH, adrenocorticotropic hormone; LTG, lamotrigine; SW, spike and wave complexes.
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filtered Gaussian white noise, when predictability using the amplitude inverted copy (Ama) is worse than that using the original data set (Pred). Moreover, when predictability using the time reversed model (Tir) is worse than that of the original model itself, the hypothesis that the time series represents a static, non-linear transform of an underlying linearly filtered Gaussian white noise can also be rejected. Pred is the prediction horizon (expressed in ms) for which the normalized prediction error first exceeds 0.75. The Ama and Tir are the differences (in ms) between the prediction time for the prediction based upon the time series and its inverted/reversed copy. If one takes the average Ama and Tir of the group, then the 95% confidence interval can be computed; if this 95% confidence interval does not overlap with zero, there is significant amplitude or time asymmetry (at the group level) and thus an indication of non-linearity.
mal activity appeared fragmented and less continuous, occupying less than 25% of the tracing. In this stage, focal discharges could be recognized. On awakening, ESES disappeared abruptly. Fig. 1 shows, as an example, the EEG recorded in one of our ESES patients during wakefulness, ESES and REM sleep. Fig. 2 shows the results of the NLCP test applied to all the EEG epochs selected for this study. In the left graph, the results of the calculation of Pred are shown (group average and 95% confidence intervals); this parameter shows slightly different values in the 3 conditions considered (wakefulness, ESES and REM sleep), but these differences were not statistically significant.
2.3.2. Correlation dimension The lower limit of D2 was determined, for all individual profiles, by reconstructing the state vector on the basis of time delay embedding (Takens, 1981), with time delays chosen on the basis of the individual zero-crossing of the autocorrelation function and then by means of the method by Grassberger and Procaccia (1983) for embedding dimensions up to 16. The logarithm of the correlation integral was then plotted against log (r). The estimate of D2 was obtained when a clear-cut plateau was found in this plot, the plateau did not change with increasing embedding dimension, i.e. it showed saturation and the plot was different from that obtained with the corresponding surrogate data set (see below). More details on the mathematical aspects of the calculation of the lower limit of D2 can be found in one of our previous papers (Ferri et al., 1996). In the calculation of D2, in order to avoid the effect of the eventual correlation between adjacent data points, the Theiler correction was introduced with a value of 4 times the delay chosen (Theiler, 1986). In order to further exclude the possibility that filtered white noise could account for the results, the so-called ‘surrogate data’ method was utilized (Theiler et al., 1992; Rapp et al., 1993): an artificial signal was then obtained, for each data set, by calculating its Fourier transform, randomizing the phase and then calculating the inverse Fourier transform; in this way, the power spectra of the original and artificial data sets were identical. Finally, D2 for the surrogate time series was calculated. 3. Results In all subjects, the typical sleep EEG pattern of ESES was found: as soon as the patients fell asleep, continuous bilateral and diffuse spike and wave or polyspike and wave complexes, at 1.5–2.5 Hz, appeared and persisted through all the non-REM sleep stages. During REM sleep, paroxys-
Fig. 1. EEG recorded in one patient with ESES during wakefulness (top), ESES (middle) and REM sleep (bottom).
R. Ferri et al. / Clinical Neurophysiology 112 (2001) 2274–2280
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Fig. 2. Results of the NLCP test applied to the EEG epochs selected for this study. In the left graph the results of the calculation of Pred are shown, the middle graph shows the results of the calculation of Ama and the right graph reports the results of the calculation of Tir. All values are shown as group average and (histogram); the bars indicate the 95% confidence intervals.
In the same figure, the middle graph shows the results of the calculation of Ama (group average and 95% confidence intervals) and the right graph reports the same for Tir. In both cases, only during ESES the values obtained were high and their 95% confidence interval not overlapping with zero (null hypothesis rejected). Moreover, the differences observed between the different states were also statistically significant ðP , 0:0224Þ. For this reason, all the subsequent calculations were performed only on EEG epochs recorded during ESES. Fig. 3 shows, as an example, the initial 8 s of one ESES epoch (top, left); on the right, also the bidimensional phase–space graph (lag ¼ 10) of the whole 4096 data point (32 s) epoch, corresponding to the time series on the left, is shown. Moreover, the graph for the calculation of the NLCP test in the same ESES epoch (bottom, left) is displayed together with, on the right side, the plot of the logarithm of the correlation integral (D2) versus log (r). In this figure, it is possible to note that the phase–space, graph tends to show an attractor. Fig. 4 shows, on the contrary, the initial 8 s of the surrogate time series corresponding to the ESES epoch shown in Fig. 3 (top, left); on the right, also the bidimensional phase–space graph (lag ¼ 10) of the whole 4096 data-point (32 s) epoch, corresponding to the time series on the left, is shown. Moreover, the graph of the calculation of the NLCP test in the same surrogate data set (bottom, left) is displayed together with, on the right side, the plot of the logarithm of the correlation integral (D2) versus log (r). In this figure, it is possible to note that in the phase–space no attractor is recognizable. In this example, the two plots of the logarithm of the correlation integral against log (r) reported in Figs. 3 and
4 and obtained for the real and for the surrogate data sets, respectively, are clearly different; it is also easy to see that a plateau (with saturation) is present only on the plot corresponding to the real signal recorded during ESES. As shown in the example reported in Figs. 3 and 4, the subsequent estimation of D2 allowed us to recognize a clearcut plateau in the plot of the logarithm of the correlation integral against log (r) in 27 out of the 32 ESES EEG epochs analyzed and a group average value of 4.02 (range 3.16– 6.21) was found. In all cases, these plots were clearly different from those obtained from surrogate data sets in which no plateau or saturation was observed.
4. Discussion The present study was undertaken to study the nature of the dynamics underlying ESES. The results obtained clearly confirm the original hypothesis: ESES, like other types of epileptic EEG activity described in the literature, seem to reflect highly non-linear and possibly low-dimensional dynamics, whereas non-ESES sleep and wakefulness EEG seem to correspond with linear stochastic dynamics. In a recent study in normal subjects (Ferri et al., 2001) we have shown that, during sleep, highly non-linear dynamics can be observed only during short (few seconds) epochs of sleep stage 2 and slow-wave sleep, coincident with the A1 phase of the so-called cyclic alternating pattern (Terzano et al., 1988); however, in the same study no information on the dimensionality could be obtained because of the shortness of the same epochs. Most of the EEG recorded during sleep shows only minimal evidence of non-linear structure
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Fig. 3. Initial 8 s of one ESES epoch (top, left); on the right, also the bidimensional phase–space graph (lag ¼ 10) of the whole 4096 data-point (32 s) epoch, corresponding to the time series on the left, is shown. Moreover, the graph of the calculation of the NLCP test in the same ESES epoch (bottom, left) is displayed together with, on the right side, the plot of the logarithm of the correlation integral (D2) versus log (r).
(Achermann et al., 1994). In this respect, normal sleep EEG resembles normal background activity during the awake state (Pritchard et al., 1995; Rombouts et al., 1995). Thus, the results of the present study seem to indicate that patients with ESES show a profound modification of their sleep EEG structure, in comparison with that of normal subjects, with the presence of long lasting highly non-linear and possibly low-dimensional dynamics. Nonlinear dynamics is a necessary, but not a sufficient condition for low dimensional chaotic dynamics. There is general agreement that the EEG during epileptic seizures reflects highly non-linear dynamics, but whether it really is an example of chaos remains the subject of controversy (Theiler, 1995; Pijn et al., 1997). A further argument for the presence of low-dimensional structure in the ESES data is the clear plateau in the plot of D2 versus log (r); moreover, this plateau saturates with increasing embedding dimension up to 16. Similar results were reported for EEG recorded during a temporal lobe seizure (Pijn et al., 1997). These findings are consistent with a hypothesis of
low-dimensional chaos, although a more modest explanation in terms of periodical dynamics with dynamical noise cannot be excluded. Our study was not aimed at discovering changes in dynamical structure of the EEG preceding the onset of ESES; however, it must be noticed that non-linear dynamics were not found in the quiet wakefulness preceding sleep, in our subjects; on the contrary, as already reported Section 1, other authors have shown the possibility that non-linear dynamics may be detected 11–20 min before the onset of epileptic seizures (Lehnertz and Elger, 1998; Le van Quyen et al., 2001). It is now accepted that different important neuropsychological cognitive processes take place during sleep, such as memory consolidation, forgetting, stimulation of brain maturation, etc. (Giuditta, 1994; Jouvet, 1998). The profound changes in brain dynamics we found in ESES might be considered to be able to disrupt normal brain functioning during sleep of these patients and to be one of the possible mechanisms of their cognitive deficits.
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Fig. 4. Initial 8 s of the surrogate time series corresponding to the ESES epoch shown in Fig. 3 (top, left); on the right, also the bidimensional phase–space graph (lag ¼ 10) of the whole 4096 data-point (32 s) epoch, corresponding to the time series on the left, is shown. Moreover, the graph of the calculation of the NLCP test in the same surrogate data set (bottom, left) is displayed together with, on the right side, the plot of the logarithm of the correlation integral (D2) versus log (r).
There is little doubt that a causal relationship exists between the occurrence of ESES and the onset of neuropsychological impairment or worsening of a previously impaired psychomotor development (as in our subjects). This view is supported by different considerations: (a) a close time relationship is evident between ESES and psychomotor impairment (De Marco, 1988; Tassinari et al., 2000); (b) the duration of ESES is important in determining the final neuropsychological outcome (Rousselle and Revol, 1995) and (c) there is a strict association between neuropsychological function impairment and locus of the interictal focal epileptiform abnormalities ( Rousselle and Revol, 1995; Tassinari et al., 1995, 2000; Neville et al., 1998; Veggiotti et al., 1999). It is important to underline that our group was composed of patients with cerebral palsy or hydrocephalus, abnormal EEG during wakefulness (see Table 1) and ESES. Even though these patients had a clearly symptomatic form of ESES, a favorable outcome was observed at follow-up with the recovery of the psychomotor status which preceded the ESES; that this outcome is relatively independent of the
etiology of ESES has already been shown (Guerrini et al., 1998). However, notwithstanding its peculiar neurophysiologic mechanisms, the analysis of the non-linear structure of EEG during ESES yields results similar to those obtained for other ictal patterns (Pijn et al., 1997), as stated above. This fact points to one evident problem with one-dimensional measures, such as D2: the possibility of characterizing a complex pattern by means of a single measure, mostly in applications where data reduction can be of practical use such as epilepsy and sleep, seems to be attractive; on the contrary, D2 does not seem to be very helpful in differentiating the type of seizures if it always maps onto the same small region of the scale. For this reason, new approaches and improvements of this technique seem to be necessary and, in the near future, a further insight into the analysis of the normal and pathological EEG structure might be achieved by means of the extension of the analysis to the globality of information gained by multichannel EEG recordings (Pijn et al., 1991; Wackermann, 1999).
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Non-linear EEG analysis in children with epilepsy and electrical status epilepticus during slow-wave sleep (ESES) Raffaele Ferri a,b,*, Maurizio Elia b, Sebastiano A. Musumeci b, Cornelis J. Stam c a
b
Sleep Research Center, Oasi Institute, Via Conte Ruggero 73, 94018 Troina, Italy Department of Neurology, Oasi Institute for Research on Mental Retardation and Brain Aging (IRCCS), Troina, Italy c Department of Clinical Neurophysiology, University Medical Center, Amsterdam, The Netherlands Accepted 10 September 2001
Abstract Objective: The objective of this work was to study the non-linear aspects of electroencephalography (EEG) in children with epilepsy and electrical status epilepticus during slow-wave sleep (ESES). Methods: In this study, we recorded the sleep EEG in 5 subjects with ESES (4 males and one female, aged 6.5–10 years) who were also mentally retarded and affected by cerebral palsy (3 subjects) and hydrocephalus (two subjects). The signals were sampled at 128 Hz and stored on hard disk. All the subsequent computational steps were performed on EEG epochs (4096 data points) selected from wakefulness and non-rapid eye movement (non-REM) (with ESES) or REM sleep. The dynamic properties of the EEG were assessed by means of the nonlinear cross prediction (NLCP) test which uses 3 different ‘model’ time series in order to predict non-linearly the original data set (Pred, Ama and Tir). Pred is a measure of the predictability of the time series and Ama and Tir are measures of asymmetry, indicating non-linear structure. Moreover, the correlation dimension (D2) was estimated by means of the algorithm by Grassberger and Procaccia (1983) for the epochs showing non-linear nature. Results: The NLCP test provided evidence of significant non-linear dynamics in all epochs of non-REM sleep, when ESES was evident. Only during this stage, the possible presence of low-dimensional chaos could also be suspected (average D2 ¼ 4:02; range 3.16–6.21). EEG without ESES could not be distinguished from linearly filtered noise. Conclusions: The results of the present study seem to indicate that subjects with ESES show a profound modification of their EEG dynamics with the occurrence, during sleep, of long periods characterized by non-linear dynamics and, probably, low-dimensional chaotic structure able to modify in a substantial way their brain functioning during sleep. q 2001 Elsevier Science Ireland Ltd. All rights reserved. Keywords: Encephalopathy with electrical status epilepticus during slow-wave sleep; Epilepsy; Sleep; Electroencephalography; Non-linear dynamics; Nonlinear cross prediction; Chaos; Correlation dimension
1. Introduction Encephalopathy with electrical status epilepticus during slow-wave sleep (ESES) syndrome is a condition characterized by continuous spikes and waves occurring during sleep and epilepsy, with onset at around 4–5 years of age and a generally favorable course, with disappearance at around 10–15 years of age (Tassinari et al., 1977, 2000). The persistence of this particular electroencephalographic (EEG) condition during sleep is accompanied by the appearance of complex and severe neurological impairment involving language, learning capabilities and psychomotor development. When psychomotor development is abnormal prior to the occurrence of ESES, a worsening of mental capabil* Corresponding author. Tel.: 1 39-935-936111; fax: 139-935-653327. E-mail address: [email protected] (R. Ferri).
ities is almost always detectable after the appearance of seizures and continuous spikes and waves during sleep (Tassinari et al., 1977, 2000). The peculiar sleep EEG pattern of ESES corresponds to the term ‘continuous spikes and waves during sleep’ adopted by the Commission on Classification and Terminology of the International League Against Epilepsy (1989) and, probably, ESES syndrome includes the so-called acquired aphasia or Landau–Kleffner syndrome (Landau and Klefner, 1957; Giovanardi Rossi et al., 1999; Tassinari et al., 2000). One way to gain a better understanding of the pathophysiological processes underlying a phenomenon like ESES, is by the use of concepts and analytical tools derived from the theory of non-linear dynamical systems (‘chaos theory’). In this approach, the essential features of the dynamical system underlying the EEG are reconstructed by representing the
1388-2457/01/$ - see front matter q 2001 Elsevier Science Ireland Ltd. All rights reserved. PII: S13 88- 2457(01)0067 6-9
CLINPH 2001633
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system as a trajectory in its state space (Takens, 1981). This trajectory is assumed to converge to a limit set which is called the attractor of the system. The attractor of the system is a geometrical object which can be characterized by measures such as the correlation dimension D2 (complexity or degrees of freedom of the system) or the Kolmogorov entropy (unpredictability or irregularity of the system dynamics). To validate this approach, it is important to know whether the system generating a time series is high dimensional and stochastic, or low dimensional and nonlinear; however, also non-linear stochastic systems and linear low-dimensional processes can be characterized. Non-linear dynamics can be demonstrated with the method of surrogate data (Pijn et al., 1991; Theiler et al., 1992) or with tests that look for asymmetries in the data (Diks et al., 1995; Stam et al., 1998). Application of non-linear time series analysis to EEG has shown that non-epileptic EEG usually reflects mostly high dimensional, stochastic dynamics (Pritchard et al., 1995; Rombouts et al., 1995). This is true for normal background activity as well as irregular slow waves (Stam and Pritchard, 1999). So far, highly non-linear dynamics has only been demonstrated in a small number of EEG phenomena such as frontal intermittent rhythmic delta activity (FIRDA) (Stam and Pritchard, 1999), periodic discharges (Stam et al., 1999) and epileptic seizure activity (Pijn et al., 1991, 1997). In particular, non-linear dynamics may be a sensitive indicator for impending seizures allowing their prediction 11–20 min ahead (Lehnertz and Elger, 1998; Le van Quyen et al., 2001). Thus, knowledge of the dynamics underlying an EEG phenomenon can lead to clinical applications such as automatic detection or predictions of seizures. The present study was undertaken to study the dynamics underlying ESES. The hypothesis was that ESES, like other types of epileptic EEG activity described in the literature, would reflect highly non-linear and possibly low-dimensional dynamics, whereas non-ESES sleep and wakefulness EEG would correspond with linear stochastic dynamics. We used the non-linear cross prediction (NLCP) algorithm as a robust indicator of non-linear dynamics because this method avoids some of the bias that may affect phase randomized surrogate data (Stam et al., 1998). Only when the NLCP
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method clearly showed non-linear dynamics, an attempt was made to compute the correlation dimension of the EEG. 2. Materials and methods 2.1. Subjects In this study, we recorded sleep EEG in 5 subjects with ESES (4 males and one female, aged 6.5–10 years) who were also mentally retarded. Their clinical characteristics are reported in Table 1. 2.2. Experimental protocol and recording procedure All subjects slept in the laboratory for an adaptation night (23.00–7.00 h); during the following night, all subjects underwent polysomnographic investigation, which included EEG (6 bipolar channels), electrooculogram (EOG) and electromyogram (EMG) of the submentalis muscle. Signals were sampled at 128 Hz (8-bit A/D precision) and stored on hard disk; the C3–T3 or C4–T4 derivations were used for all the subsequent computational steps which were performed on EEG epochs (4096 data points) selected from quiet wakefulness preceding sleep onset, non-rapid eye movement (REM) sleep (with ESES) and REM sleep (without ESES). For each of these stages, 6–8 artifact-free epochs were selected. 2.3. Non-linear measures 2.3.1. NLCP test The dynamical properties of the EEG were assessed by means of the software developed at Department of Neurology and Clinical Neurophysiology, Leyenburg Hospital, The Hague, The Netherlands (DIGEEG2) which computes NLCP test introduced by Stam et al. (1998). This test uses 3 different ‘model’ time series in order to predict non-linearly the original data set. The first is the original data set itself (Pred), the second is an amplitude inverted copy of the original time series (Ama) and the third is a time reversed copy (Tir). With this test it is possible to reject the null hypothesis that the original time series is linearly
Table 1 Clinical characteristics of the patients included in this study a Subject Sex/age Etiology, neurologic examination
Seizure type AEDs
1
M/6.5
CPS
2 3 4 5
M/9.0 M/9.3 M/9.8 F/10.0
Hypoxic-ischemic encephalopathy, tetraplegia Porencephaly, right hemiplegia Hydrocephalus, normal Hydrocephalus, tetraplegia Porencephaly, right hemiplegia
CPS CPS AA CPS
EEG during wakefulness
VPA, ESM, HC
Right parietal–temporal–occipital SW; left frontal–central–temporal SW VPA, ESM, LTG, CLB Left temporal–occipital SW VPA, ESM, CLB, HC Left temporal–occipital SW PB, CBZ Right temporal–occipital SW VPA, CLB, GVG, ESM, HC Left frontal–central–temporal SW
a CPS, complex partial seizures; AA, atypical absences; AEDs, antiepileptic drugs; PB, Phenobarbital; CBZ, carbamazepine; VPA, valproic acid; CLB, clobazam; GVG, g-vynil-GABA; ESM, ethosuximide; HC, hydrocortisone; ACTH, adrenocorticotropic hormone; LTG, lamotrigine; SW, spike and wave complexes.
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filtered Gaussian white noise, when predictability using the amplitude inverted copy (Ama) is worse than that using the original data set (Pred). Moreover, when predictability using the time reversed model (Tir) is worse than that of the original model itself, the hypothesis that the time series represents a static, non-linear transform of an underlying linearly filtered Gaussian white noise can also be rejected. Pred is the prediction horizon (expressed in ms) for which the normalized prediction error first exceeds 0.75. The Ama and Tir are the differences (in ms) between the prediction time for the prediction based upon the time series and its inverted/reversed copy. If one takes the average Ama and Tir of the group, then the 95% confidence interval can be computed; if this 95% confidence interval does not overlap with zero, there is significant amplitude or time asymmetry (at the group level) and thus an indication of non-linearity.
mal activity appeared fragmented and less continuous, occupying less than 25% of the tracing. In this stage, focal discharges could be recognized. On awakening, ESES disappeared abruptly. Fig. 1 shows, as an example, the EEG recorded in one of our ESES patients during wakefulness, ESES and REM sleep. Fig. 2 shows the results of the NLCP test applied to all the EEG epochs selected for this study. In the left graph, the results of the calculation of Pred are shown (group average and 95% confidence intervals); this parameter shows slightly different values in the 3 conditions considered (wakefulness, ESES and REM sleep), but these differences were not statistically significant.
2.3.2. Correlation dimension The lower limit of D2 was determined, for all individual profiles, by reconstructing the state vector on the basis of time delay embedding (Takens, 1981), with time delays chosen on the basis of the individual zero-crossing of the autocorrelation function and then by means of the method by Grassberger and Procaccia (1983) for embedding dimensions up to 16. The logarithm of the correlation integral was then plotted against log (r). The estimate of D2 was obtained when a clear-cut plateau was found in this plot, the plateau did not change with increasing embedding dimension, i.e. it showed saturation and the plot was different from that obtained with the corresponding surrogate data set (see below). More details on the mathematical aspects of the calculation of the lower limit of D2 can be found in one of our previous papers (Ferri et al., 1996). In the calculation of D2, in order to avoid the effect of the eventual correlation between adjacent data points, the Theiler correction was introduced with a value of 4 times the delay chosen (Theiler, 1986). In order to further exclude the possibility that filtered white noise could account for the results, the so-called ‘surrogate data’ method was utilized (Theiler et al., 1992; Rapp et al., 1993): an artificial signal was then obtained, for each data set, by calculating its Fourier transform, randomizing the phase and then calculating the inverse Fourier transform; in this way, the power spectra of the original and artificial data sets were identical. Finally, D2 for the surrogate time series was calculated. 3. Results In all subjects, the typical sleep EEG pattern of ESES was found: as soon as the patients fell asleep, continuous bilateral and diffuse spike and wave or polyspike and wave complexes, at 1.5–2.5 Hz, appeared and persisted through all the non-REM sleep stages. During REM sleep, paroxys-
Fig. 1. EEG recorded in one patient with ESES during wakefulness (top), ESES (middle) and REM sleep (bottom).
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Fig. 2. Results of the NLCP test applied to the EEG epochs selected for this study. In the left graph the results of the calculation of Pred are shown, the middle graph shows the results of the calculation of Ama and the right graph reports the results of the calculation of Tir. All values are shown as group average and (histogram); the bars indicate the 95% confidence intervals.
In the same figure, the middle graph shows the results of the calculation of Ama (group average and 95% confidence intervals) and the right graph reports the same for Tir. In both cases, only during ESES the values obtained were high and their 95% confidence interval not overlapping with zero (null hypothesis rejected). Moreover, the differences observed between the different states were also statistically significant ðP , 0:0224Þ. For this reason, all the subsequent calculations were performed only on EEG epochs recorded during ESES. Fig. 3 shows, as an example, the initial 8 s of one ESES epoch (top, left); on the right, also the bidimensional phase–space graph (lag ¼ 10) of the whole 4096 data point (32 s) epoch, corresponding to the time series on the left, is shown. Moreover, the graph for the calculation of the NLCP test in the same ESES epoch (bottom, left) is displayed together with, on the right side, the plot of the logarithm of the correlation integral (D2) versus log (r). In this figure, it is possible to note that the phase–space, graph tends to show an attractor. Fig. 4 shows, on the contrary, the initial 8 s of the surrogate time series corresponding to the ESES epoch shown in Fig. 3 (top, left); on the right, also the bidimensional phase–space graph (lag ¼ 10) of the whole 4096 data-point (32 s) epoch, corresponding to the time series on the left, is shown. Moreover, the graph of the calculation of the NLCP test in the same surrogate data set (bottom, left) is displayed together with, on the right side, the plot of the logarithm of the correlation integral (D2) versus log (r). In this figure, it is possible to note that in the phase–space no attractor is recognizable. In this example, the two plots of the logarithm of the correlation integral against log (r) reported in Figs. 3 and
4 and obtained for the real and for the surrogate data sets, respectively, are clearly different; it is also easy to see that a plateau (with saturation) is present only on the plot corresponding to the real signal recorded during ESES. As shown in the example reported in Figs. 3 and 4, the subsequent estimation of D2 allowed us to recognize a clearcut plateau in the plot of the logarithm of the correlation integral against log (r) in 27 out of the 32 ESES EEG epochs analyzed and a group average value of 4.02 (range 3.16– 6.21) was found. In all cases, these plots were clearly different from those obtained from surrogate data sets in which no plateau or saturation was observed.
4. Discussion The present study was undertaken to study the nature of the dynamics underlying ESES. The results obtained clearly confirm the original hypothesis: ESES, like other types of epileptic EEG activity described in the literature, seem to reflect highly non-linear and possibly low-dimensional dynamics, whereas non-ESES sleep and wakefulness EEG seem to correspond with linear stochastic dynamics. In a recent study in normal subjects (Ferri et al., 2001) we have shown that, during sleep, highly non-linear dynamics can be observed only during short (few seconds) epochs of sleep stage 2 and slow-wave sleep, coincident with the A1 phase of the so-called cyclic alternating pattern (Terzano et al., 1988); however, in the same study no information on the dimensionality could be obtained because of the shortness of the same epochs. Most of the EEG recorded during sleep shows only minimal evidence of non-linear structure
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Fig. 3. Initial 8 s of one ESES epoch (top, left); on the right, also the bidimensional phase–space graph (lag ¼ 10) of the whole 4096 data-point (32 s) epoch, corresponding to the time series on the left, is shown. Moreover, the graph of the calculation of the NLCP test in the same ESES epoch (bottom, left) is displayed together with, on the right side, the plot of the logarithm of the correlation integral (D2) versus log (r).
(Achermann et al., 1994). In this respect, normal sleep EEG resembles normal background activity during the awake state (Pritchard et al., 1995; Rombouts et al., 1995). Thus, the results of the present study seem to indicate that patients with ESES show a profound modification of their sleep EEG structure, in comparison with that of normal subjects, with the presence of long lasting highly non-linear and possibly low-dimensional dynamics. Nonlinear dynamics is a necessary, but not a sufficient condition for low dimensional chaotic dynamics. There is general agreement that the EEG during epileptic seizures reflects highly non-linear dynamics, but whether it really is an example of chaos remains the subject of controversy (Theiler, 1995; Pijn et al., 1997). A further argument for the presence of low-dimensional structure in the ESES data is the clear plateau in the plot of D2 versus log (r); moreover, this plateau saturates with increasing embedding dimension up to 16. Similar results were reported for EEG recorded during a temporal lobe seizure (Pijn et al., 1997). These findings are consistent with a hypothesis of
low-dimensional chaos, although a more modest explanation in terms of periodical dynamics with dynamical noise cannot be excluded. Our study was not aimed at discovering changes in dynamical structure of the EEG preceding the onset of ESES; however, it must be noticed that non-linear dynamics were not found in the quiet wakefulness preceding sleep, in our subjects; on the contrary, as already reported Section 1, other authors have shown the possibility that non-linear dynamics may be detected 11–20 min before the onset of epileptic seizures (Lehnertz and Elger, 1998; Le van Quyen et al., 2001). It is now accepted that different important neuropsychological cognitive processes take place during sleep, such as memory consolidation, forgetting, stimulation of brain maturation, etc. (Giuditta, 1994; Jouvet, 1998). The profound changes in brain dynamics we found in ESES might be considered to be able to disrupt normal brain functioning during sleep of these patients and to be one of the possible mechanisms of their cognitive deficits.
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Fig. 4. Initial 8 s of the surrogate time series corresponding to the ESES epoch shown in Fig. 3 (top, left); on the right, also the bidimensional phase–space graph (lag ¼ 10) of the whole 4096 data-point (32 s) epoch, corresponding to the time series on the left, is shown. Moreover, the graph of the calculation of the NLCP test in the same surrogate data set (bottom, left) is displayed together with, on the right side, the plot of the logarithm of the correlation integral (D2) versus log (r).
There is little doubt that a causal relationship exists between the occurrence of ESES and the onset of neuropsychological impairment or worsening of a previously impaired psychomotor development (as in our subjects). This view is supported by different considerations: (a) a close time relationship is evident between ESES and psychomotor impairment (De Marco, 1988; Tassinari et al., 2000); (b) the duration of ESES is important in determining the final neuropsychological outcome (Rousselle and Revol, 1995) and (c) there is a strict association between neuropsychological function impairment and locus of the interictal focal epileptiform abnormalities ( Rousselle and Revol, 1995; Tassinari et al., 1995, 2000; Neville et al., 1998; Veggiotti et al., 1999). It is important to underline that our group was composed of patients with cerebral palsy or hydrocephalus, abnormal EEG during wakefulness (see Table 1) and ESES. Even though these patients had a clearly symptomatic form of ESES, a favorable outcome was observed at follow-up with the recovery of the psychomotor status which preceded the ESES; that this outcome is relatively independent of the
etiology of ESES has already been shown (Guerrini et al., 1998). However, notwithstanding its peculiar neurophysiologic mechanisms, the analysis of the non-linear structure of EEG during ESES yields results similar to those obtained for other ictal patterns (Pijn et al., 1997), as stated above. This fact points to one evident problem with one-dimensional measures, such as D2: the possibility of characterizing a complex pattern by means of a single measure, mostly in applications where data reduction can be of practical use such as epilepsy and sleep, seems to be attractive; on the contrary, D2 does not seem to be very helpful in differentiating the type of seizures if it always maps onto the same small region of the scale. For this reason, new approaches and improvements of this technique seem to be necessary and, in the near future, a further insight into the analysis of the normal and pathological EEG structure might be achieved by means of the extension of the analysis to the globality of information gained by multichannel EEG recordings (Pijn et al., 1991; Wackermann, 1999).
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