In order to discriminate nonlinear deterministic from linear stochastic dynamics we propose the measure x. This measure is based on the calculation of the coarse grained flow average for both the original and an ensemble of surrogate time series. x was extracted from intracranial EEG recordings of seizure free intervals
performed in two patients with focal epilepsy. Our findings suggest that x can possibly contribute to localize and delineate the primary epileptogenic area.

Rationale: Recent studies have provided evidence for essential nonlinearity in intracranial EEG recordings of patients with temporal lobe epilepsy. However, a quantitative distinction between stochasticity and determinism in brain electrical activity is still lacking. For this purpose we applied a combination of two algorithms derived from the theory of nonlinear dynamics allowing to distinguish between linear-stochastic and nonlinear-deterministic dynamical processes.
Methods: The methods of local flow in phase space and surrogate data were used to estimate the fraction of nonlinear determinism (x) in EEG timeseries. At present 80 interictal EEG re-cordings (mean duration: 30 min) of 22 patients with unilateral mesial temporal lobe epilepsy as proven by postoperative complete seizure control were analyzed. Using a moving-window technique ? was extracted from successive EEG epochs of each recording site. In order to evaluate the lateralizing power of this measure an index I_L:=(x_foc-x_nonfoc)/(x_foc+x_nonfoc) was calculated for all recording sites.
Results: Maximum values of I_L were found to be restricted to the primary epileptogenic area. With an increasing distance from this area I_L was less pronounced at adjacent recordings sites and even unspecific at remote recording sites.
Conclusion: These findings indicate that extracting the fraction of nonlinear determinism provides additional information for the lateralization and localization of the primary epileptogenic area  without the necessity of observing seizure activity. Further investigations should include focus localization in neocortical epilepsies as well as testing the predictability of imminent seizure activity.

Rationale: The application of methods derived from the theory of nonlinear dynamical systems has shown to provide useful information in characterizing the spatio-temporal dynamics of the epileptic process. In this framework we have demonstrated (Epilepsia, Suppl. 1998; 39(6):206) that extracting the fraction of nonlinear determinism (x) from the EEG lateralizes the primary epileptogenic area in patients with mesial temporal lobe epilepsy. We now applied this technique to more complicated cases of neocortical lesional epilepsy (NLE).
Methods: The measure x- aiming at quantifying the occurence of nonlinear deterministic dynamics in the EEG - was determined combining the methods of coarse grained flow average and surrogate data. Using a moving window technique we analyzed interictal EEG recordings of eight patients subjected to invasive presurgial evalutation employing subdural grid electrodes.
Results: In those patients who achieved complete seizure control after extended lesionectomy (N=4) maximum values of x were confined to recording sites covering the resected area. In contrast, no correspondence between maximum values of  x and resection area was established in patients with post-operatively persisting seizures (N=4).
Discussion: Despite the small number of cases investigated so far findings indicate that extracting x can contribute to an interictal localization of the primary epileptogenic area in NLE patients. The more widespread spatial distribution of x in patients with persisting seizures might indicate the possible existence of additional foci not indentified by other methods of the presurgical evaluation.

Rationale: Recent studies indicate that methods derived from the theory of nonlinear dynamical systems extract useful information from the EEG for a spatio-temporal characterization of the epileptogenic process. In previous studies we have shown that increased values of the fraction of nonlinear determinism (x) allow the interictal localization of the primary epileptogenic area in patients with focal epilepsies of different cerebral origins. Here we investigate whether temporal changes of x calculated from EEG recordings within the focal area are related to an impending seizure.
Methods: The measure x which is based upon a combination of the methods of coarse grained flow average and surrogate time series, aims at a discrimination of nonlinear deterministic and linear stochastic dynamics. Intracranial EEG recordings of up to now ten patients with focal epilepsies were analyzed. Using a moving window technique, x was calculated from recordings of twelve seizures (pre-seizure recording time at least 20 min.) and from recordings during the interictal state (30-120 min. per patient). Values of x were averaged over recording sites covering the focal area (as confirmed by post-operative complete seizure control) and temporal changes were analyzed.
Results: When compared to average values obtained for the interictal state, x exihibited increased values prior to seven out of twelve seizures while decreased values were found for the remaining seizures. In addition, we observed short- and long-term increases were observed throughout the interictal state which were not followed by a seizure.
Conclusion: Data suggest that a prediction of epileptic seizures based solely on the measure x is possible only at a week degree of specificity and sensitivity. Further studies will be necessary to investigate whether a combination with other measures derived from the theory of nonlinear dynamical systems might.

Introduction: Recent studies indicate that application of methods derived from the theory of nonlinear dynamical systems to the EEG provides information useful for a spatio-temporal characterization of the epileptogenic process. We have shown previously that increased values of the fraction of nonlinear determinism (x) allows focus localization in mesial temporal lobe and neocortical epilepsies during the interictal state. While these analyses were based solely on signals recorded during the awake state, we now investigate the influence of different sleep stages on the discriminative power of x for focus localization.
Rationale: The measure x which is based upon a combination of the methods of coarse grained flow average and surrogate time series, aims to discriminate between nonlinear deterministic and linear stochastic dynamics. Using a moving window technique, we calculated x for continuos intracranial all night EEG recordings from five patients with postoperatively confirmed unilateral focal epilepsies. Sleep stages were classified according to Rechtschaffen and Kales using additional surface EEG recordings. Hence, results were averaged for each patient and each sleep stage.
Results: In all cases, x values calculated from both recordings from within and contralateral to the primary epileptogenic area were found to increase with depth of sleep. In four cases this increase was found to be most prominent for those x values calculated for signals recorded within the focal hemisphere. In one case, however, both absolute values and increase of x for the nonfocal hemisphere exceeded values from the focal hemisphere. In four out of five cases, discriminative power of the measure x to localize the primary epileptogenic area increased with sleep depth.
Conclusion: The fraction of nonlinear determinism appears to be sensitive towards both physiological processes such as sleep and pathological processes such as epilepsy. Nevertheless, data suggest that in terms of focus localization information rendered by x-analysis of sleep EEG recordings might be superior to the analysis of recordings during the awake state.

Rationale: A number of studies indicate that the application of measures derived from the theory of nonlinear deterministic dynamical systems allows localization of epileptic foci from interictal intracranial EEG recordings. In order to determine whether these results are specifically caused by nonlinear deterministic components we now investigate if measures that were developed for the characterization of linear dynamical systems allow the extraction of similar information from the EEG.
Methods: In our analysis we compared the performance of a number of nonlinear and linear measures regarding the discriminative power for the side of the focal hemisphere. As nonlinear measures we used the neuronal complexity loss and the fraction of nonlinear determinism. As linear measures we used spectral power in different frequency bands (d,J,a, and b, statistical moments of higher order (skewness and kurtosis) and the decay time of the autocorrelation function. All measures were calculated from interictal intracranial EEG recordings from 25 patients with unilateral mesial temporal lobe epilepsy. Average duration of each recording was 84 min per patient.
Results: The highest discriminative power was obtained for the fraction of nonlinear determinism and the neuronal complexity loss. All linear measures proved to be less specific for the focal hemisphere. Among the linear measures, the d-band power and the decay time of the autocorrelation function yet showed a high discriminative power, whereas the statistical moments turned out to be quite unspecific for the epileptogenic hemisphere.
Conclusion: The higher performance of nonlinear measures suggests that the epileptogenic process comprises nonlinear deterministic components. Nonetheless, both linear and nonlinear measures can contribute valuable information to the lateralization of the focal hemisphere without the necessity of observing actual seizure activity.

The theory of deterministic chaos addresses simple deterministic dynamics in which nonlinearity gives rise to complex temporal behavior. Although biological neuronal networks such as the brain are highly complicated, a number of studies provide growing evidence that nonlinear time series analysis of brain electrical activity in patients with epilepsy is capable of providing potentially useful diagnostic information. In the present study, this analysis framework was extended by introducing a new measure x, designed to discriminate between nonlinear deterministic and linear stochastic dynamics. For the evaluation of its discriminative power, x was extracted from intracranial multi-channel EEGs recorded during the interictal state in 25 patients with unilateral mesial temporal lobe epilepsy. Strong indications of nonlinear determinism were found in recordings from within the epileptogenic zone, while EEG signals from other sites mainly resembled linear stochastic dynamics. In all investigated cases, this differentiation allowed to retrospectively determine the side of the epileptogenic zone in full agreement with results of the presurgical workup.

Rationale: Nonlinear time series analyses provide increasing evidence for nonlinearity in EEG time series of epilepsy patients, rendering additional information about the spatio-temporal dynamics of the epileptogenic process. Most analysis techniques require stationarity of the time series under investigation and it is often objected that the inherent nonstationary character of brain electrical activity might result in spurious detection on nonlinearity. To examine this objection, we quantify different degrees of nonstationarity and relate our findings to tests for nonlinearity. Methods: 1000 EEG segments recorded intracranially in patients with focal epilepsies and covering different interictal, ictal, pre- and postictal states were analyzed. To quantify nonstationarity and to describe dynamical changes in the EEG we used the recurrence of points in the reconstructed state space. EEG time series were tested for evidence of nonlinearity by combining different nonlinear measures with surrogate data tests.
Results: EEG segments from all states exhibited nonlinearity for all degrees of nonstationarity including approximate stationarity. Conclusion: Since no general relationship could be established between nonstationarity and nonlinearity, the aforementioned objection could clearly be rejected. Moreover, we hypothesize that characteristic time scales of nonstationarity in brain electric activity might even contribute to an improved understanding of the epileptogenic process.

We compare dynamical properties of brain electrical activity from different recording regions and from different physiological and pathological brain states. Using the nonlinear prediction error and an estimate of an effective correlation dimension in combination with the method of iterative amplitude adjusted surrogate data we analyze sets of electroencephalographic (EEG) time series: surface EEG recordings from healthy volunteers with eyes closed and eyes open, intracranial EEG recordings from epilepsy patients during the seizure free interval from within and from outside the seizure generating area as well as intracranial EEG recordings of epileptic seizures. As a pre-analysis step an inclusion criterion of weak stationarity was applied. Surface EEG recordings with eyes open were compatible with the surrogates' null hypothesis of a Gaussian linear stochastic process. Strongest indications of nonlinear deterministic dynamics were found for seizure activity. Results of the other sets were found to be in between these two extremes.

We propose a measure for nonstationarity which is based on the analysis of distributions of temporal distances of neighboring vectors in state space. As an extension of previous techniques our method does not require a partitioning of the time series. Moreover, the deviation of mean recurrence times from frequency distributions that would be expected under stationary conditions allows us to estimate the statistical significance of the method.

Rationale: An important issue in epileptology is whether specific features can be extracted from the EEG that are predictive of an impending seizure. Much research has been done on this topic lately, and different univariate measures from nonlinear time-series analyses have been used. In this study we use a bivariate measure to determine the phase synchronization in intracranial EEG recordings from up to now 15 patients suffering from different types of focal epilepsy. We evaluate the merit of this measure to distinguish between interictal and preictal states.
Methods: Using a moving-window technique an average of 10 EEG segments per patient recorded from bilateral intrahippocampal depth electrodes were analyzed. Instantaneous phases of the EEG signals were determined by means of the Hilbert Transformation and the mean phase coherence was used as a measure for phase synchronization. Phase coherence values of adjacent electrode contacts were evaluated in terms of level and variation for interictal and preictal recordings.
Results: In the majority of the patients analyzed, distinct differences between interictal and preictal states were revealed. In contrast to interictal states which were characterized by high and constant values of the mean phase coherence, low values were observed before an impending seizure. In most cases, these states of decreased synchronization started hours before the actual seizures.
Conclusion: Findings indicate that the analysis of phase synchronization might offer the possibility of distinguishing a preictal from an interictal state thus rendering helpful information for an actual prediction of seizures. Specific changes in brain dynamics traced by the mean phase coherence appear to be different from those traced by other measures, possibly making measures for phase synchronization a valuable addition to EEG analysis techniques.

Application of nonlinear time-series analyses to the EEG have been shown to be useful in gathering spatio-temporal information about the epileptogenic process. In this study we use the mean phase coherence as a measure for phase synchronization between EEG signals recorded simultaneously from different regions within the brain. Taking advantage of the bivariate nature of this measure we examine long-term shifts in synchronization prior to seizures and their dependence on the position of the recording sites within the brain.
For a group of 10 patients suffering from temporo-mesial epilepsy, a total of 13 seizures recorded from intra-hippocampal depth electrodes each equipped with 10 recording sites were analyzed and compared to a number of interictal recordings. Using a moving-window technique, the mean phase coherence as a measure for phase synchronization was determined for all possible combinations of recording sites in each hemisphere resulting in triangular synchronization matrices.
For those patients that showed a preictal drop in synchronization prior to seizure onset, this drop was found to exhibit a characteristic depencence on the respective recording sites in almost all of the cases. In particular, a characteristic gap in synchronization along the axis of the intrahippocampal electrodes was observed.
Findings indicate that regions of the brain that are normally highly synchronized are separated into two independently synchronized regions prior to seizure onset. This phenomenon might be related to the concept of the inhibitory surrounding demarcating the epileptic focus from the surrounding regions of the brain. Therefore further analysis of the spatial characteristics of phase synchronization might lead to more insight into the nature of the epileptogenic process.

Rationale: An important issue in epileptology is the question whether epileptic seizures can be anticipated. Recent studies have shown that certain measures derived from the theory of nonlinear time series analysis are to some extend capable of extracting information from the EEG that allows the definition of a preictal state and its distinction from the interictal state. In particular, we have shown a significant loss of phase synchronization to be a characteristic feature of the preictal state. In this study we evaluate the merit of the cross correlation function as a linear measure to distinguish between interictal and preictal states.
Methods: 23 EEG recordings containing spontaneously occurring seizures were selected from 16 patients suffering from different types of focal epilepsy. In addition, 61 EEG recordings from the interictal state were selected from the same group of patients to serve as controls and reference states. Data were recorded from bilateral intrahippocampal depth electrodes and were analyzed using a moving-window technique. As a measure for synchronization/similarity, the maximum of the normalized cross correlation function was used. Cross correlation values of adjacent electrode contacts were evaluated and the criterion for the detection of a preictal state was defined as a drop of the time profiles below the interictal mean by more than 3 standard deviations.
Results: In 19 out of the 23 seizure recordings, a preictal state could successfully be detected. In terms of patients, preictal state detection was successful in 13 out of the 16 patients. In all of the interictal recordings there was not a single false positive detection. Duration of detected preictal states ranged from several minutes to more than 3 hours.
Conclusion: Findings indicate that apart from measures derived from the theory of nonlinear time series analysis, linear measures such as the well-known cross correlation function appear to be capable of distinguishing preictal from interictal states thus rendering helpful information with regard to an actual prediction or even prevention of seizures.

Rationale: Recent studies have shown nonlinear EEG analysis to be useful for detecting pre/interictal and permanent changes of neuronal synchronization in epilepsy patients. We were interested whether characteristic changes of EEG power, synchronization, and complexity can also be found in the focal EEG during amygdala kindling in rats, a model of human temporal lobe epilepsy. The advantage of this model was the possibility to record at various stages before and after complex partial and generalized seizures during the stepwise progression of epileptogenesis.
Methods: Eight female Wistar rats were implanted with two chronic stimulation/recording electrodes into the right basolateral amygdala. After two weeks, the rats were daily stimulated (500 µA, 1 ms pulses, 50 Hz for 1 s) which elicited initially limbic focal and subsequently secondary generalized seizures. The EEG of the amygdala was recorded versus an indifferent screw electrode in the contralateral parietal bone for 30 min before and after each seizure. Using a moving-window approach, spectral power, complexity (measured by an effective correlation dimension), and synchronization (measured by the mean phase coherence) were determined.
Results: The immediate effect of the kindling in most animals was an increase in synchronization. Evaluation of the chronic progression of kindling after a period of nine days revealed for the EEG recordings after kindling significant increase in power and decrease in complexity while for the EEG recordings before kindling an increase in synchronization was the only significant effect.
Conclusion: Findings indicate that different measures from nonlinear time series analysis provide supplementary information about different states of neuronal synchronization during kindling. In particular temporary and permanent effects characterizing the progression of epileptogenesis can be distinguished.

RATIONALE: One of the most important questions in epileptology is whether specific features can be extracted from time series of brain electrical activity that are predictive of an impending seizure. To this aim, we have investigated and compared the performance of three recently proposed and two established measures, all of them quantifying spatio-temporal variations of interdependence between different areas of the human brain.
METHODS: Intracranial multichannel EEG recorded pre-ictally in patients with mesial temporal lobe epilepsy were probed for early indicators of imminent seizure activity. Long-lasting interictal EEG recordings were used to serve as controls. The applied interdependence measures comprised symmetric (cross-correlation C and mutual information M) as well as non-symmetric measures (nonlinear interdependences S and H and transfer entropy T).
RESULTS: The measures yielded different degrees of performance in characterizing the temporal variability of interdependences in EEGs recorded shortly before and hours away from an epileptic seizure. Due to their asymmetric character three of the measures provided additional information about the direction of interdependence and were especially suitable to analyze spatio-temporal interactions between the primary epileptogenic area and other parts of the brain.
CONCLUSIONS: The analysis of seizure generating patterns using bivariate time series analysis techniques offers a promising approach to the anticipation of epileptic seizures. The new interdependence measures proved useful in gathering additional information about features of brain electrical activity predictive of an impending seizure. This might lead to an deeper insight into mechanisms of ctogenesis and offer new possibilities for therapeutic intervention.

Characterizing Nonstationarities in the EEG of Epilepsy Patients

RATIONALE: Linear and nonlinear time series analyses are gaining an increasing relevance in characterizing the EEG and in understanding the epileptogenic process. The inherent nonstationarity in EEG time series, however, forces almost all analysis techniques to be applied in a moving window fashion using a window length short enough to approximate quasi-stationarity. Here we investigate whether the quantification of nonstationarity on large time scales allows further insight into the epileptogenic process.
METHODS: To quantify nonstationarity we examine long-term changes of EEG dynamics by comparing the recurrence of points in a reconstructed state space to the statistical behavior of recurrence in time series of stationary processes. We apply this technique to intracranial EEG recordings from patients with mesial temporal lobe epilepsy.
RESULTS: Even on a time scale of several minutes, the majority of EEG time series recorded outside the epileptogenic area can be regarded as stationary except for statistical fluctuations. In contrast, EEG time series recorded within the epileptogenic area exhibit a higher degree of nonstationarity even in the absence of high-amplitude epileptiform potentials.
CONCLUSIONS: Our data suggest that the epileptogenic process leads to an increase in nonstationarity in EEG time series. Characterizing nonstationarity can reveal additional information about the epileptogenic process and thus might be valuable for a further improvement of the presurgical evaluation.

On the influence of nonstationarity of the EEG on the capability of nonlinear surrogate measures to characterize the spatial distribution of the epileptogenic process.
Rationale: In a previous study we compared different techniques from linear and nonlinear time series analysis in an application to intracranial EEG recordings of the seizure free interval of patients with mesial temporal lobe epilepsy (MTLE) (Epilepsia 2001, 42, Suppl. 7, 98). It was demonstrated that particularly nonlinear time series analysis measures in combination with the method of surrogates (termed NST techniques) allowed a correct lateralization of the focal hemisphere in a high percentage of cases. However, NST techniques implicitly assume stationarity of the investigated dynamics, a pre-requisite not fulfilled for neuronal dynamics. Consequently, many periods of EEG recordings exhibit nonstationary features, while other periods appear to be stationary. The aim of the present study was therefore to elucidate the influence of nonstationarity on the discriminative power of NST techniques for the focal hemisphere in MTLE patients.
Methods: Our retrospective out-of-sample study was based on intracranial EEG recordings of the seizure-free interval of 38 patients with unilateral MTLE. Using a moving window technique on average 116 minutes per patient were analyzed. In a first step a criterion for weak stationarity was applied in order to separate the EEG into stationary and nonstationary segments. For all segments a set of surrogate time series was generated using an iterative amplitude adjusted technique. Three measures from nonlinear time series analysis (coarse grained flow average, prediction error, and an estimate of the correlation dimension) were calculated from both the original EEG time series and the corresponding set of surrogate time series. The differences between these values (EEG and the surrogates' mean values) were used as NST measures. The subsequent evaluation was carried for all segments and solely based on stationary segments.
Results: Based on all segments a correct localization could be established for 35 out of 38 cases for the NST measures based on the coarse grained flow average and the correlation dimension, and in 33 cases for the prediction error. For the individual patients the portion of segments that were classified as nonstationary ranged from 15% to 40%. Nonetheless, based solely on the remaining stationary segments still 34 cases were correctly lateralized for the coarse grained flow average and the correlation dimension, while the performance of the NST measure based on the prediction error did not change at all.
Conclusions: In agreement with recent studies our results indicate that NST measures can contribute valuable information to the lateralization of the focal hemisphere without the necessity of observing actual seizure activity. Furthermore, the discriminative power of NST techniques for the focal hemisphere is not related to the influence of nonstationarity of the EEG as tested here.

RATIONALE: In a number of recent studies, the concept of phase synchronization has been applied to EEGs for description of spatiotemporal dynamics of the epileptic brain. We compare two different phase synchronization analyzes techniques on a theoretical basis. Subsequently the ability of both measures to lateralize the focal hemisphere in patients with mesial temporal lobe epilepsy (MTLE) is investigated.
METHODS: Fifty five interictal artifact-free EEG recordings were selected from 23 MTLE patients. Data were recorded using chronically implanted intrahippocampal depth electrodes each equipped with 10 contacts. We applied two phase synchronization analyzes techniques that are based on two different approaches for extraction of the instantaneous phase, namely the Hilbert and the wavelet transform. We calculate the wavelet transform using complex demeaned Morlet wavelet. For each time and scale the instantaneous phase of the EEG was defined as the argument of the corresponding complex wavelet coefficient. Lateralization of the focal hemisphere was done by comparing the degree of synchronization for ipsi- and contralateral hemispheres after averaging over time and over all combinations of channels for the respective side.
RESULTS: Based on theoretical considerations we show the close relation of the phases defined from Hilbert and wavelet transforms. These phases are identical if prefiltering of the EEG signal is applied before the calculation of the Hilbert transform. The filter characteristics should correspond to the wavelet mother function. Using the Hilbert phase synchronization, we could correctly lateralize the focal hemisphere in 18 of the 23 patients. A better discrimination was achieved by means of wavelet phase synchronization for the scales of the wavelet corresponding to the beta frequency range (20 correct cases).
CONCLUSIONS: The comparison shows good performance of both phase synchronization analyzes techniques for focus lateralization in MTLE. The better discrimination achieved by the wavelet phase synchronization analyzes technique can be explained by its ability to extract more specific information for different frequency ranges. The techniques described in this study might render additional information helpful for an improvement of the presurgical evaluation of MTLE patients.

RATIONALE: In the rapidly developing field of seizure prediction more and more interest is directed towards the question of how to quantify the performance of measures applied to the EEG in seperating pre-ictal from inter-ictal states. In this study we compare two different concepts to address this point. Both evaluations are based on the extraction of characteristic features (e.g. positive and negative deviations from a given reference level) derived from time profiles of bivariate measures. While the first approach is aiming at a statistical seperation of the pre-ictal from the inter-ictal states, the second one is an algorithmic approach defining alarms and evaluating their distribution relative to the times of seizure onset in terms of sensitivity and specificity. For the latter approach a new way of weighting sensitivity and specificity to get one overall measure of performance is introduced.
METHODS: We analyzed continuous intracranial multichannel EEG recorded from patients suffering from unilateral mesial temporal lobe epilepsy (MTLE). In the first step a number of bivariate measures (e.g. cross correlation) were calculated applying a moving window technique. Secondly, from the resulting time profiles we extracted and parametrized characteristic features (e.g. positive and negative deviations from a given reference level). Using on the one hand a statistical and on the other hand an algorithmic approach the performances of the different measures were evaluated automatically.
RESULTS: Within the statistical as well as within the algorithmic approach the different bivariate measures yielded different degrees of performance in distinguishing pre-ictal from inter-ictal states. For the latter approach different ways of weighting sensitivity and specificity to get one overall measure of performance were compared. As a solution to the problem of how to define sensitivity and specificity for continuous long-time recordings we propose the use of the prediction horizon as a common time unit to get a proper normalized measure of performance (similar to the discrete case of diagnostic tests where the natural unit is the single patient).
CONCLUSIONS: While the statistical approach is free of parameters and therefore acts as an unbiased criterion for the distinguishability of the two different states, the algorithmic approach offers the possibility to adjust certain parameters. However, as with the parameters of the single measures much care has to be taken to avoid in-sample optimization. Also, for this approach a proper weighting of sensitivity and specificity seems to be of high importance for an unbiased judgement of the performance of any measure.

RATIONALE: Previous studies have demonstrated the relevance of a number of nonlinear time series analysis techniques for the spatiotemporal characterization of the epileptogenic process. Almost all of these techniques require the system under investigation to be stationary. For the dynamical system brain, however, this is far from being the case. EEG recordings of several tens of seconds length, nevertheless are usually regarded as approximately stationary. On longer observation times (segmentation size) of the EEG, however, the statistical significance of an analysis technique should be improved almost always. We here investigate an enlarged observation time of EEG segments up to minutes. We compare the distribution and thus the significance of nonlinear measures of the EEG, covering different states for different observation times. Furthermore, we estimate the nonstationarity of the observed EEG segments and exclude all segments which are significantly nonstationary.
METHODS: EEG segments recorded intracranially in patients with focal epilepsies and covering different states: interictal, preictal, ictal and postictal were analyzed. The EEG segments were enlarged starting with 23.6 s up to 94.4 s corresponding to 4096 data points and 16384 data points respectively. Short segments were included in longer ones. Analysis techniques comprised nonlinear measures for complexity, determinism and nonlinearity, using iterative amplitude adjusted surrogate data for each segment. Nonstationarity was quantified by measuring the loss of recurrence in reconstructed state space.
RESULTS: Some epochs within long nonstationary segments appear stationary. On the other hand, even segments which are nonstationary appear stationary when they are enlarged. For most measures, the distributions of the estimated values show a deviation between EEG segments from preictal and interictal states. This deviation enlarged with increasing observation time, particularly for measures employing surrogate data.
CONCLUSIONS: Results suggest that most measures show an increased performance in characterizing and discriminating EEG time series under control of stationarity if the observation time was enlarged. Moreover, we hypothize that investigating nonstationarity at characteristic time scales might improve the understanding of the spatiotemporal ictogenic process.

RATIONALE: The EEG can be regarded as a mixture of electrical potentials that originate from distinct sources. Independent component analysis (ICA) is a recently developed method that allows to decompose multivariate signals into their statistically most independent components. This preprocessing step might enhance features that are not available with other methods, by suppressing irrelevant components. We investigate the ability of this technique to improve focus localization in patients with mesial temporal lobe epilepsy (MTLE).
METHODS: We applied ICA on intracranial artifact free EEG recordings of the seizure free interval of 18 patients with unilaterial MTLE. Two different ICA-algorithms were used to decompose the EEG. Subsequently, the mean phase coherence, a well established measure of phase synchronization, was calculated for all channel combinations of both the original EEG and the independent components. Focus lateralization was done by comparing the degree of synchronization for the two hemispheres after averaging over time.
RESULTS: Higher values of the mean phase coherence were found predominantely for the focal hemisphere for both the original EEG and independent components.For a high percentage of patients it was possible to get a correct lateralization of the focal hemisphere. Although in general lower values of the mean phase coherence were found for the independent components, still a higher discriminartive power for the focal hemisphere was obtained from this method.
CONCLUSIONS: Lower values of the mean phase coherence found for the independent components indicate that ICA allows to decrease linear correlations that are known to increase values of synchronization measures. Furthermore, our results indicate that ICA can be helpfull to further improve the capability of the mean phase coherence to lateralize the focal area.

RATIONALE: An important issue in epileptology is the question whether epileptic seizures can be anticipated. Recent studies have shown that certain measures derived from the theory of nonlinear time series analysis are to some extend capable of extracting information from the EEG that allows the characterization of a pre-ictal state and its distinction from the interictal state. In particular, we have shown a significant loss of phase synchronization to be a characteristic feature of the pre-ictal state. In the present study we investigate some problems and pitfalls that can arise when applying an anticipation technique based on this pre-ictal drop in phase synchronization to the EEG recorded continuously over several days.
METHODS: Showing exemplary segments of the synchronization profiles calculated from the continuous EEG recordings from our patients, we first describe characteristic features of the pre-ictal state and try to distinguish this state from the interictal state. We put a particular emphasis on phenomena occurring during sleep. These segments are then compared to the entire profiles, which in turn are scanned for correlation to changes in AED level and vigilance states during this period of time. Finally, the possible influence of a priori knowledge such as best channel selection is examined.
RESULTS: Examination of sleep phases revealed an increase in phase synchronization during slow-wave sleep (as determined by elevated delta power). Furthermore, certain epochs of distinct anticorrelation appeared to occur predominantly during sleep. Regarding the entire recording length, there appears to be an influence of AED levels on the general level of phase synchronization. All of the above phenomena are likely to result in a decrease in sensitivity and/or specificity of an anticipation technique. In addition, the performance of such an algorithm seems to heavily rely on the a priori knowledge of a best channel combination.
CONCLUSIONS: Findings indicate that a number of phenomena, namely slow-wave sleep, anticorrelation epochs, AED levels and selection of channels may have a strong influence on phase synchronization levels and predictive performance, respectively, that needs to be taken into account when designing an algorithm for seizure anticipation.

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last change: 09/01/03 by Ralph G. Andrzejak