Characteristic nonlinearities of the 3/s ictal electroencephalogram identified by nonlinear autoregressive analysis

We describe a method for the characterization of electroencephalographic (EEG) signals based on a model which features nonlinear feedback. The characteristic EEG fingerprints obtained through this approach display the time-course of nonlinear interactions, rather than aspects susceptible to standard spectral analysis. Fingerprints of seizure discharges in six patients (five with typical absence seizures, one with complex partial seizures) revealed significant nonlinear interactions. The timing and pattern of these interactions correlated closely with the seizure type. Nonlinear autoregressive (NLAR) analysis is compared with other nonlinear dynamical measures that have been applied to the EEG.     

An autoregressive method for the measurement of synchronization of interictal and ictal EEG signals

We propose a new measure of synchronization of multichannel ictal and interictal EEG signals. The measure is based on the residual covariance matrix of a multichannel autoregressive model. A major advantage of this measure is its ability to be interpreted both in the framework of stochastic and deterministic models. A preliminary analysis of EEG data from three patients using this measure documents the expected increased synchronization during ictal periods but also reveals that increased synchrony persists for prolonged periods (up to 2 h or more) in the postictal period. Received: 20 July 1997 / Accepted in revised form: 26 January 1999     

Topographic analysis of dimension estimates of EEG and filtered rhythms in epileptic patients with complex partial seizures

Nonlinear dynamic properties were analyzed on the EEG and filtered rhythms recorded from healthy subjects and epileptic patients with complex partial seizures. Estimates of correlation dimensions of control EEG, interictal EEG and ictal EEG were calculated. The values were demonstrated on topograms. The delta (0.5–4 Hz), theta (4–8 Hz), alpha (8–13 Hz), beta (13–30 Hz) and gamma (30–40 Hz) components were obtained and considered as signals from the cortex. Corresponding surrogate data was produced. Firstly, the influence of sampling parameters on the calculation was tested. The dimension estimates of the signals from the frontal, temporal, parietal and occipital regions were computed and compared with the results of surrogate data. In the control subjects, the estimates between the EEG and surrogate data did not differ (P > 0.05). The interictal EEG from the frontal region and occipital region, as well as its theta component from the frontal region, and temporal region, showed obviously low dimensions (P < 0.01). The ictal EEG exhibited significantly low-dimension estimates across the scalp. All filtered rhythms from the temporal region yielded lower results than those of the surrogate data (P < 0.01). The dimension estimates of the EEG and filtered components markedly changed when the neurological state varied. For each neurological state, the dimension estimates were not uniform among the EEG and frequency components. The signal with a different frequency range and in a different neurological state showed a different dimension estimate. Furthermore, the theta and alpha components demonstrated the same estimates not only within each neurological state, but also among the different states. These results indicate that the theta and alpha components may be caused by similar dynamic processes. We conclude that the brain function underlying the ictal EEG has a simple mechanism. Several heterogeneous dynamic systems play important roles in the generation of EEG. Received: 10 December 1999 / Accepted in revised form: 8 May 2000     

Relevance of nonlinear lumped-parameter models in the analysis of depth-EEG epileptic signals

In the field of epilepsy, the analysis of stereoelectroencephalographic (SEEG, intra-cerebral recording) signals with signal processing methods can help to better identify the epileptogenic zone, the area of the brain responsible for triggering seizures, and to better understand its organization. In order to evaluate these methods and to physiologically interpret the results they provide, we developed a model able to produce EEG signals from “organized” networks of neural populations. Starting from a neurophysiologically relevant model initially proposed by Lopes Da Silva et al. [Lopes da Silva FH, Hoek A, Smith H, Zetterberg LH (1974) Kybernetic 15: 27–37] and recently re-designed by Jansen et al. [Jansen BH, Zouridakis G, Brandt ME (1993) Biol Cybern 68: 275–283] the present study demonstrates that this model can be extended to generate spontaneous EEG signals from multiple coupled neural populations. Model parameters related to excitation, inhibition and coupling are then altered to produce epileptiform EEG signals. Results show that the qualitative behavior of the model is realistic; simulated signals resemble those recorded from different brain structures for both interictal and ictal activities. Possible exploitation of simulations in signal processing is illustrated through one example; statistical couplings between both simulated signals and real SEEG signals are estimated using nonlinear regression. Results are compared and show that, through the model, real SEEG signals can be interpreted with the aid of signal processing methods. Received: 3 January 2000 / Accepted: 24 March 2000     

Analysis of Epileptic Discharges from Implanted Subdural Electrodes in Patients with Sturge-Weber Syndrome

ObjectiveAlmost two-thirds of patients with Sturge-Weber syndrome (SWS) have epilepsy, and half of them require surgery for it. However, it is well known that scalp electroencephalography (EEG) does not demonstrate unequivocal epileptic discharges in patients with SWS. Therefore, we analyzed interictal and ictal discharges from intracranial subdural EEG recordings in patients treated surgically for SWS to elucidate epileptogenicity in this disorder.MethodsFive intractable epileptic patients with SWS who were implanted with subdural electrodes for presurgical evaluation were enrolled in this study. We examined the following seizure parameters: seizure onset zone (SOZ), propagation speed of seizure discharges, and seizure duration by visual inspection. Additionally, power spectrogram analysis on some frequency bands at SOZ was performed from 60 s before the visually detected seizure onset using the EEG Complex Demodulation Method (CDM).ResultsWe obtained 21 seizures from five patients for evaluation, and all seizures initiated from the cortex under the leptomeningeal angioma. Most of the patients presented with motionless staring and respiratory distress as seizure symptoms. The average seizure propagation speed and duration were 3.1 ± 3.6 cm/min and 19.4 ± 33.6 min, respectively. Significant power spectrogram changes at the SOZ were detected at 10–30 Hz from 15 s before seizure onset, and at 30–80 Hz from 5 s before seizure onset.SignificanceIn patients with SWS, seizures initiate from the cortex under the leptomeningeal angioma, and seizure propagation is slow and persists for a longer period. CDM indicated beta to low gamma-ranged seizure discharges starting from shortly before the visually detected seizure onset. Our ECoG findings indicate that ischemia is a principal mechanism underlying ictogenesis and epileptogenesis in SWS.     

Multiway analysis of epilepsy tensors

MOTIVATION: The success or failure of an epilepsy surgery depends greatly on the localization of epileptic focus (origin of a seizure). We address the problem of identification of a seizure origin through an analysis of ictal electroencephalogram (EEG), which is proven to be an effective standard in epileptic focus localization. SUMMARY: With a goal of developing an automated and robust way of visual analysis of large amounts of EEG data, we propose a novel approach based on multiway models to study epilepsy seizure structure. Our contributions are 3-fold. First, we construct an Epilepsy Tensor with three modes, i.e. time samples, scales and electrodes, through wavelet analysis of multi-channel ictal EEG. Second, we demonstrate that multiway analysis techniques, in particular parallel factor analysis (PARAFAC), provide promising results in modeling the complex structure of an epilepsy seizure, localizing a seizure origin and extracting artifacts. Third, we introduce an approach for removing artifacts using multilinear subspace analysis and discuss its merits and drawbacks. RESULTS: Ictal EEG analysis of 10 seizures from 7 patients are included in this study. Our results for 8 seizures match with clinical observations in terms of seizure origin and extracted artifacts. On the other hand, for 2 of the seizures, seizure localization is not achieved using an initial trial of PARAFAC modeling. In these cases, first, we apply an artifact removal method and subsequently apply the PARAFAC model on the epilepsy tensor from which potential artifacts have been removed. This method successfully identifies the seizure origin in both cases.     

Surrogate data analysis of sleep electroencephalograms reveals evidence for nonlinearity

 We tested the hypothesis of whether sleep electroencephalographic (EEG) signals of different time windows (164 s, 82 s, 41 s and 20.5 s) are in accordance with linear stochastic models. For this purpose we analyzed the all-night sleep electroencephalogram of a healthy subject and corresponding Gaussian-rescaled phase randomized surrogates with a battery of five nonlinear measures. The following nonlinear measures were implemented: largest Lyapunov exponent L1, correlation dimension D2, and the Green-Savit measures δ2, δ4 and δ6. The hypothesis of linear stochastic data was rejected with high statistical significance. L1 and D2 yielded the most pronounced effects, while the Green-Savit measures were only partially successful in differentiating EEG epochs from the phase randomized surrogates. For L1 and D2 the efficiency of distinguishing EEG signals from linear stochastic data decreased with shortening of the time window. Altogether, our results indicate that EEG signals exhibit nonlinear elements and cannot completely be described by linear stochastic models. Received: 21 December 1995/Accepted in revised form: 19 March 1996     

Complexity of Multi-Channel Electroencephalogram Signal Analysis in Childhood Absence Epilepsy

Absence epilepsy is an important epileptic syndrome in children. Multiscale entropy (MSE), an entropy-based method to measure dynamic complexity at multiple temporal scales, is helpful to disclose the information of brain connectivity. This study investigated the complexity of electroencephalogram (EEG) signals using MSE in children with absence epilepsy. In this research, EEG signals from 19 channels of the entire brain in 21 children aged 5-12 years with absence epilepsy were analyzed. The EEG signals of pre-ictal (before seizure) and ictal states (during seizure) were analyzed by sample entropy (SamEn) and MSE methods. Variations of complexity index (CI), which was calculated from MSE, from the pre-ictal to the ictal states were also analyzed. The entropy values in the pre-ictal state were significantly higher than those in the ictal state. The MSE revealed more differences in analysis compared to the SamEn. The occurrence of absence seizures decreased the CI in all channels. Changes in CI were also significantly greater in the frontal and central parts of the brain, indicating fronto-central cortical involvement of “cortico-thalamo-cortical network” in the occurrence of generalized spike and wave discharges during absence seizures. Moreover, higher sampling frequency was more sensitive in detecting functional changes in the ictal state. There was significantly higher correlation in ictal states in the same patient in different seizures but there were great differences in CI among different patients, indicating that CI changes were consistent in different absence seizures in the same patient but not from patient to patient. This implies that the brain stays in a homogeneous activation state during the absence seizures. In conclusion, MSE analysis is better than SamEn analysis to analyze complexity of EEG, and CI can be used to investigate the functional brain changes during absence seizures.     

Application of a dissimilarity index of EEG and its sub-bands on prediction of induced epileptic seizures from rat's EEG signals

ObjectiveEpileptic seizures are defined as manifest of excessive and hyper-synchronous activity of neurons in the cerebral cortex that cause frequent malfunction of the human central nervous system. Therefore, finding precursors and predictors of epileptic seizure is of utmost clinical relevance to reduce the epileptic seizure induced nervous system malfunction consequences. Researchers for this purpose may even guide us to a deep understanding of the seizure generating mechanisms. The goal of this paper is to predict epileptic seizures in epileptic rats.MethodsSeizures were induced in rats using pentylenetetrazole (PTZ) model. EEG signals in interictal, preictal, ictal and postictal periods were then recorded and analyzed to predict epileptic seizures. Epileptic seizures were predicted by calculating an index in consecutive windows of EEG signal and comparing the index with a threshold. In this work, a newly proposed dissimilarity index called Bhattacharyya Based Dissimilarity Index (BBDI), dynamical similarity index and fuzzy similarity index were investigated.ResultsBBDI, dynamical similarity index and fuzzy similarity index were examined on case and control groups and compared to each other. The results show that BBDI outperforms dynamical and fuzzy similarity indices. In order to improve the results, EEG sub-bands were also analyzed. The best result achieved when the proposed dissimilarity index was applied on Delta sub-band that predicts epileptic seizures in all rats with a mean of 299.5 s.ConclusionThe dissimilarity of neural network activity between reference window and present window of EEG signal has a significant increase prior to an epileptic seizure and the proposed dissimilarity index (BBDI) can reveal this variation to predict epileptic seizures. In addition, analyzing EEG sub-bands results in more accurate information about constituent neuronal activities underlying the EEG since certain changes in EEG signal may be amplified when each sub-band is analyzed separately.SignificanceThis paper presents application of a dissimilarity index (BBDI) on EEG signals and its sub-bands to predict PTZ-induced epileptic seizures in rats. Based on the results of this work, BBDI will predict epileptic seizures more accurately and more reliably compared to current indices that increases epileptic patient comfort and improves patient outcomes.     

Nonlinearity in normal human EEG: cycles,temporal asymmetry,nonstationarity and randomness,not chaos

Two-hour vigilance and sleep electroencephalogram (EEG) recordings from five healthy volunteers were analyzed using a method for identifying nonlinearity and chaos which combines the redundancy–linear redundancy approach with the surrogate data technique. A nonlinear component in the EEG was detected, however, inconsistent with the hypothesis of low-dimensional chaos. A possibility that a temporally asymmetric process may underlie or influence the EEG dynamics was indicated. A process that merges nonstationary nonlinear deterministic oscillations with randomness is proposed for an explanation of observed properties of the analyzed EEG signals. Taking these results into consideration, the use of dimensional and related chaos-based algorithms in quantitative EEG analysis is critically discussed. Received: 25 September 1994 / Accepted in revised form: 10 July 1996     

Nonlinear EEG analysis based on a neural mass model

The well-known neural mass model described by Lopes da Silva et al. (1976) and Zetterberg et al. (1978) is fitted to actual EEG data. This is achieved by reformulating the original set of integral equations as a continuous-discrete state space model. The local linearization approach is then used to discretize the state equation and to construct a nonlinear Kalman filter. On this basis, a maximum likelihood procedure is used for estimating the model parameters for several EEG recordings. The analysis of the noise-free differential equations of the estimated models suggests that there are two different types of alpha rhythms: those with a point attractor and others with a limit cycle attractor. These attractors are also found by means of a nonlinear time series analysis of the EEG recordings. We conclude that the Hopf bifurcation described by Zetterberg et al. (1978) is present in actual brain dynamics. Received: 11 August 1997 / Accepted in revised form: 20 April 1999     

Fractal dimension of electroencephalographic time series and underlying brain processes

 Fractal dimension has been proposed as a useful measure for the characterization of electrophysiological time series. This paper investigates what the pointwise dimension of electroencephalographic (EEG) time series can reveal about underlying neuronal generators. The following theoretical assumptions concerning brain function were made (i) within the cortex, strongly coupled neural assemblies exist which oscillate at certain frequencies when they are active, (ii) several such assemblies can oscillate at a time, and (iii) activity flow between assemblies is minimal. If these assumptions are made, cortical activity can be considered as the weighted sum of a finite number of oscillations (plus noise). It is shown that the correlation dimension of finite time series generated by multiple oscillators increases monotonically with the number of oscillators. Furthermore, it is shown that a reliable estimate of the pointwise dimension of the raw EEG signal can be calculated from a time series as short as a few seconds. These results indicate that (i) The pointwise dimension of the EEG allows conclusions regarding the number of independently oscillating networks in the cortex, and (ii) a reliable estimate of the pointwise dimension of the EEG is possible on the basis of short raw signals. Received: 1 September 1994/Accepted in revised form: 16 May 1995     

Nonlinear dynamics of the EEG separated by independent component analysis after sound and light stimulation

 The electroencephalogram (EEG) is a multiscaled signal consisting of several time-series components each with different dominant frequency ranges and different origins. Nonlinear measures of the EEG reflect the complexity of the overall EEG, but not of each component in it. The aim of this study is to examine effect of the sound and light (SL) stimulation on the complexity of each component of the EEG. We used independent component analysis to obtain independent components of the EEG. The first positive Lyapunov exponent (L1) was estimated as a nonlinear measure of complexity. Twelve subjects were administered photic and auditory stimuli with a frequency of 10 Hz, which corresponded to the alpha frequency of the EEG, by a sound and light entrainment device. We compared the L1 values of the EEGs and their independent components between baseline and after the SL stimulation. We detected that the L1 values of the EEG decreased after the SL stimulation in all channels except C3 and F4, indicating that the complexity of the EEG decreased. We showed that alpha components increased in proportion but decreased in complexity after the SL stimulation. The beta independent components were found to decrease in proportion and complexity. These results suggest that decreased complexity of the EEG after the SL stimulation may be principally caused by decreased complexity and increased proportion of the alpha independent components. We showed also that theta components increased in complexity after the SL stimulation. We propose that nonlinear dynamical analysis combined with independent component analysis may be helpful in understanding the temporal characteristics of the EEG, which cannot be detected by conventional linear or nonlinear methods. Received: 12 March 2001 / Accepted in revised form: 27 November 2001     

Widespread EEG Changes Precede Focal Seizures

The process by which the brain transitions into an epileptic seizure is unknown. In this study, we investigated whether the transition to seizure is associated with changes in brain dynamics detectable in the wideband EEG, and whether differences exist across underlying pathologies. Depth electrode ictal EEG recordings from 40 consecutive patients with pharmacoresistant lesional focal epilepsy were low-pass filtered at 500 Hz and sampled at 2,000 Hz. Predefined EEG sections were selected immediately before (immediate preictal), and 30 seconds before the earliest EEG sign suggestive of seizure activity (baseline). Spectral analysis, visual inspection and discrete wavelet transform were used to detect standard (delta, theta, alpha, beta and gamma) and high-frequency bands (ripples and fast ripples). At the group level, each EEG frequency band activity increased significantly from baseline to the immediate preictal section, mostly in a progressive manner and independently of any modification in the state of vigilance. Preictal increases in each frequency band activity were widespread, being observed in the seizure-onset zone and lesional tissue, as well as in remote regions. These changes occurred in all the investigated pathologies (mesial temporal atrophy/sclerosis, local/regional cortical atrophy, and malformations of cortical development), but were more pronounced in mesial temporal atrophy/sclerosis. Our findings indicate that a brain state change with distinctive features, in the form of unidirectional changes across the entire EEG bandwidth, occurs immediately prior to seizure onset. We postulate that these changes might reflect a facilitating state of the brain which enables a susceptible region to generate seizures.     

Estimating short-run and long-run interaction mechanisms in interictal state

We address the issue of analyzing electroencephalogram (EEG) from seizure patients in order to test, model and determine the statistical properties that distinguish between EEG states (interictal, pre-ictal, ictal) by introducing a new class of time series analysis methods. In the present study: firstly, we employ statistical methods to determine the non-stationary behavior of focal interictal epileptiform series within very short time intervals; secondly, for such intervals that are deemed non-stationary we suggest the concept of Autoregressive Integrated Moving Average (ARIMA) process modelling, well known in time series analysis. We finally address the queries of causal relationships between epileptic states and between brain areas during epileptiform activity. We estimate the interaction between different EEG series (channels) in short time intervals by performing Granger-causality analysis and also estimate such interaction in long time intervals by employing Cointegration analysis, both analysis methods are well-known in econometrics. Here we find: first, that the causal relationship between neuronal assemblies can be identified according to the duration and the direction of their possible mutual influences; second, that although the estimated bidirectional causality in short time intervals yields that the neuronal ensembles positively affect each other, in long time intervals neither of them is affected (increasing amplitudes) from this relationship. Moreover, Cointegration analysis of the EEG series enables us to identify whether there is a causal link from the interictal state to ictal state.     

Eigenspace Time Frequency Based Features for Accurate Seizure Detection from EEG Data

Background

Epilepsy is a neurological disorder that affects over 2% of the world population. Epilepsy patients suffer from recurring seizures that can be very harmful. The unpredictability of seizures is a major concern for medical practitioners because uncontrollable seizures can lead to sudden death and morbidity. A system that could warn patients and doctors alike about the impending seizure event would dramatically enhance the quality of life for patients.

The prediction of EEG signals using a feedback-structured adaptive rational function filter

 In this article, we present a feedback-structured adaptive rational function filter based on a recursive modified Gram-Schmidt algorithm and apply it to the prediction of an EEG signal that has nonlinear and nonstationary characteristics. For the evaluation of the prediction performance, the proposed filter is compared with other methods, where a single-step prediction and a multi-step prediction are considered for a short-term prediction, and the prediction performance is assessed in normalized mean square error. The experimental results show that the proposed filter shows better performance than other methods considered for the short-term prediction of EEG signals. Received: 22 September 1998 / Accepted in revised form: 29 February 2000     

一种改进的近似熵——样品熵及其在颞叶癫痫患者脑电信号分析中的应用

采用了近似熵(approximately entropy,ApEn)和它的改进算法,即样品熵(sample entropy,SampEn)分析了8位颞叶癫痫患者和10位健康人员的短程脑电信号。在计算过程中使用了两种滑动窗口和5个不同的过滤标准r。结果显示颞叶癫痫患者组脑电信号的熵值显著低于健康组,而且患者癫痫病灶所在的脑半球的复杂度远远小于非癫痫病灶的脑半球。小的滑动窗口能更多地反映与癫痫发作相关的细节。对于1秒的滑动窗口,过滤标准r不能小于时间序列标准差的0．15％;而对于4秒的滑动窗口,则过滤标准r不能小于时间序列标准差的10％。研究结果表明,在短程脑电信号的非线性分析中,样品熵是一种比近似熵更为可靠的非线性分析方法。颞叶癫痫患者脑电信号的熵值低于健康人员,这可能表明脑电活动的非线性程度的降低是由于神经信号在大脑内的传递受到了阻碍或者损坏,使得神经信号成了相对孤立的信息源。     

Dynamic Imaging of Coherent Sources Reveals Different Network Connectivity Underlying the Generation and Perpetuation of Epileptic Seizures

The concept of focal epilepsies includes a seizure origin in brain regions with hyper synchronous activity (epileptogenic zone and seizure onset zone) and a complex epileptic network of different brain areas involved in the generation, propagation, and modulation of seizures. The purpose of this work was to study functional and effective connectivity between regions involved in networks of epileptic seizures. The beginning and middle part of focal seizures from ictal surface EEG data were analyzed using dynamic imaging of coherent sources (DICS), an inverse solution in the frequency domain which describes neuronal networks and coherences of oscillatory brain activities. The information flow (effective connectivity) between coherent sources was investigated using the renormalized partial directed coherence (RPDC) method. In 8/11 patients, the first and second source of epileptic activity as found by DICS were concordant with the operative resection site; these patients became seizure free after epilepsy surgery. In the remaining 3 patients, the results of DICS / RPDC calculations and the resection site were discordant; these patients had a poorer post-operative outcome. The first sources as found by DICS were located predominantly in cortical structures; subsequent sources included some subcortical structures: thalamus, Nucl. Subthalamicus and cerebellum. DICS seems to be a powerful tool to define the seizure onset zone and the epileptic networks involved. Seizure generation seems to be related to the propagation of epileptic activity from the primary source in the seizure onset zone, and maintenance of seizures is attributed to the perpetuation of epileptic activity between nodes in the epileptic network. Despite of these promising results, this proof of principle study needs further confirmation prior to the use of the described methods in the clinical praxis.     

Nonlinear analysis of EEG signals: Surrogate data analysis

ObjectivesThe electroencephalogram (EEG) signal contains information about the state and condition of the brain. The aim of the study is to conduct a nonlinear analysis of the EEG signals and to compare the differences in the nonlinear characteristics of the EEG during normal state and the epileptic state.DataThe EEG data used for this study – which consisted of epileptic EEG and normal EEG – were obtained from the EEG database available with the Bonn University, Germany.ResultsThe attractors seen in normal and epileptic human brain dynamics were studied and compared. Surrogate data analyses were conducted on two nonlinear measures, namely the largest Lyapunov exponent and the correlation dimension, to test the hypothesis whether EEG signals were in accordance with linear stochastic models.DiscussionsThe existence of deterministic chaos in brain activity is confirmed by the existence of a chaotic attractor; also, saturation of the correlation dimension towards a definite value is the manifestation of a deterministic dynamics. Also a reduction is observed between the dimensionalities of the brain attractors from normal state to the epileptic state. The evaluation of the largest Lyapunov exponent also confirms the lowering of complexity during an episode of seizure.ConclusionIn case of Lyapunov exponent of EEG data, the change due to surrogating is small suggesting that it is not representing the system complexity properly but there is a marked change in the case of correlation dimension value due to surrogating.