Non-linear time series analysis of intracranial EEG recordings in patients with epilepsy--an overview

A scalable platform for acquisition of high-fidelity human intracranial EEG with minimal clinical burden

Human neuroscience research has been significantly advanced by neuroelectrophysiological studies from people with refractory epilepsy-the only routine clinical intervention that acquires multi-day, multi-electrode human intracranial electroencephalography (iEEG). While a sampling rate below 2 kHz is sufficient for manual iEEG review by epileptologists, computational methods and research studies may benefit from higher resolution, which requires significant technical development. At adult and pediatric Stanford hospitals, research ports of commercial clinical acquisition systems were configured to collect 10 kHz iEEG of up to 256 electrodes simultaneously with the clinical data. The research digital stream was designed to be acquired post-digitization, resulting in no loss in clinical signal quality. This novel framework implements a near-invisible research platform to facilitate the secure, routine collection of high-resolution iEEG that minimizes research hardware footprint and clinical workflow interference. The addition of a pocket-sized router in the patient room enabled an encrypted tunnel to securely transmit research-quality iEEG across hospital networks to a research computer within the hospital server room, where data was coded, de-identified, and uploaded to cloud storage. Every eligible patient undergoing iEEG clinical evaluation at both hospitals since September 2017 has been recruited; participant recruitment is ongoing. Over 350+ terabytes (representing 1000+ days) of neuroelectrophysiology were recorded across 200+ participants of diverse demographics. To our knowledge, this is the first report of such a research integration within a hospital setting. It is a promising approach to promoting equitable participant enrollment and building comprehensive data repositories with consistent, high-fidelity specifications towards new discoveries in human neuroscience.

Fractal Phototherapy in Maximizing Retina and Brain Plasticity

The neuroplasticity potential is reduced with aging and impairs during neurodegenerative diseases and brain and visual system injuries. This limits the brain's capacity to repair the structure and dynamics of its activity after lesions. Maximization of neuroplasticity is necessary to provide the maximal CNS response to therapeutic intervention and adaptive reorganization of neuronal networks in patients with degenerative pathology and traumatic injury to restore the functional activity of the brain and retina.Considering the fractal geometry and dynamics of the healthy brain and the loss of fractality in neurodegenerative pathology, we suggest that the application of self-similar visual signals with a fractal temporal structure in the stimulation therapy can reactivate the adaptive neuroplasticity and enhance the effectiveness of neurorehabilitation. This proposition was tested in the recent studies. Patients with glaucoma had a statistically significant positive effect of fractal photic therapy on light sensitivity and the perimetric MD index, which shows that methods of fractal stimulation can be a novel nonpharmacological approach to neuroprotective therapy and neurorehabilitation. In healthy rabbits, it was demonstrated that a long-term course of photostimulation with fractal signals does not harm the electroretinogram (ERG) and retina structure. Rabbits with modeled retinal atrophy showed better dynamics of the ERG restoration during daily stimulation therapy for a week in comparison with the controls. Positive changes in the retinal function can indirectly suggest the activation of its adaptive plasticity and the high potential of stimulation therapy with fractal visual stimuli in a nonpharmacological neurorehabilitation, which requires further study.

Physiological and pathological neuronal connectivity in the living human brain based on intracranial EEG signals: the current state of research

Over the past decades, studies of human brain networks have received growing attention as the assessment and modelling of connectivity in the brain is a topic of high impact with potential application in the understanding of human brain organization under both physiological as well as various pathological conditions. Under specific diagnostic settings, human neuronal signal can be obtained from intracranial EEG (iEEG) recording in epilepsy patients that allows gaining insight into the functional organisation of living human brain. There are two approaches to assess brain connectivity in the iEEG-based signal: evaluation of spontaneous neuronal oscillations during ongoing physiological and pathological brain activity, and analysis of the electrophysiological cortico-cortical neuronal responses, evoked by single pulse electrical stimulation (SPES). Both methods have their own advantages and limitations. The paper outlines available methodological approaches and provides an overview of current findings in studies of physiological and pathological human brain networks, based on intracranial EEG recordings.

Chaotic and stochastic dynamics of epileptiform-like activities in sclerotic hippocampus resected from patients with pharmacoresistant epilepsy

The types of epileptiform activity occurring in the sclerotic hippocampus with highest incidence are interictal-like events (II) and periodic ictal spiking (PIS). These activities are classified according to their event rates, but it is still unclear if these rate differences are consequences of underlying physiological mechanisms. Identifying new and more specific information related to these two activities may bring insights to a better understanding about the epileptogenic process and new diagnosis. We applied Poincaré map analysis and Recurrence Quantification Analysis (RQA) onto 35 in vitro electrophysiological signals recorded from slices of 12 hippocampal tissues surgically resected from patients with pharmacoresistant temporal lobe epilepsy. These analyzes showed that the II activity is related to chaotic dynamics, whereas the PIS activity is related to deterministic periodic dynamics. Additionally, it indicates that their different rates are consequence of different endogenous dynamics. Finally, by using two computational models we were able to simulate the transition between II and PIS activities. The RQA was applied to different periods of these simulations to compare the recurrences between artificial and real signals, showing that different ranges of regularity-chaoticity can be directly associated with the generation of PIS and II activities.

Temporal lobe epilepsy (TLE) is the most prevalent type of epilepsy in adults and hippocampal sclerosis is the major pathophysiological substrate of pharmaco-refractory TLE. Different patterns of epileptiform-like activity have been described in human hippocampal sclerosis, but the standard analysis applied to characterize the activities usually do not consider the nonlinear features that epileptiform patterns exhibit. Here, using Poincaré map and Recurrence Quantitative Analysis we characterized the most prevalent type of epileptiform-like activities—interictal-like events (II) and periodic ictal spiking (PIS), recorded in vitro from resected hippocampi of pharmacoresistant patients with TLE—according to their levels of stochasticity, chaoticity and determinism. The II activities showed to be more chaotic with complex rhythmicity than PIS activities. The nonlinear dynamic differences between II and PIS leads us to conjecture that they are expressions of different seizure susceptibility. We also identified that each hippocampal subfield expresses II and PIS activities in a specific and different way. Finally, from the modulation of internal parameters of two computational models, we show the conversion of one type of activity into the other, showing how specific neuron networks synchronize over time, leading to II and PIS activities and then into a generalized seizure.

EEG based cognitive task classification using multifractal detrended fluctuation analysis

Locating cognitive task states by measuring changes in electrocortical activity due to various attentional and sensory-motor changes, has been in research interest since last few decades. In this paper, different cognitive states while performing various attentional and visuo-motor coordination tasks, are classified using electroencephalogram (EEG) signal. A non-linear time-series method, multifractal detrended fluctuation analysis (MFDFA) , is applied on respective EEG signal for features. Using MFDFA based features a multinomial classification is achieved. Nine channel EEG signal was recorded for 38 young volunteers (age: 25 ± 5 years, 30 male and 8 female), during six consecutive tasks. First three tasks are related to increasing levels of selective focus vision; next three are reflex and response based computer tasks. Total of 90 features (ten features from each of nine channel) were extracted from Hurst and singularity exponents of MFDFA on EEG signals. After feature selection, a multinomial classifier of six classes using two methods: support vector machine (SVM) and decision tree classifier (DTC). An accuracy of 96.84% using SVM and 92.49% using DTC was achieved.

Alcoholic EEG signal classification with Correlation Dimension based distance metrics approach and Modified Adaboost classification

The basic function of the brain is severely affected by alcoholism. For the easy depiction and assessment of the mental condition of a human brain, Electroencephalography (EEG) signals are highly useful as it can record and measure the electrical activities of the brain much to the satisfaction of doctors and researchers. Utilizing the standard conventional techniques is quite hectic to derive the useful information as these signals are highly non-linear and non-stationary in nature. While recording the EEG signals, the activities of the neurons are recorded from various scalp regions which has varied characteristics and has a very low magnitude. Therefore, human interpretation of such signals is very difficult and consumes a lot of time. Hence, with the advent of Computer Aided Diagnosis (CAD) Techniques, identifying the normal versus alcoholic EEG signals has been of great utility in the medical field. In this work, we perform the initial clustering of the alcoholic EEG signals by means of using Correlation Dimension (CD) for easy feature extraction and then the suitable features are selected in it by means of employing various distance metrics like correlation distance, city block distance, cosine distance and chebyshev distance. Proceeding in such a methodology aids and assures that a good discrimination could be achieved between normal and alcoholic EEG signals using non-linear features. Finally, classification is then carried out with the suitable classifiers chosen such as Adaboost.RT classifier, the proposed Modified Adaboost.RT classifier by means of introducing Ridge and Lasso based soft thresholding technique, Random Forest with bootstrap resampling technique, Artificial Neural Networks (ANN) such as Radial Basis Functions (RBF) and Multi-Layer Perceptron (MLP), Support Vector Machine (SVM) with Linear, Polynomial and RBF Kernel, Naïve Bayesian Classifier (NBC), K-means classifier, and K Nearest Neighbor (KNN) Classifier and the results are analyzed. Results report a comparatively high classification accuracy of about 98.99% when correlation distance metrics are utilized with CD and the proposed Modified Adaboost.RT classifier using Ridge based soft thresholding technique.

Big data to smart data in Alzheimer's disease: The brain health modeling initiative to foster actionable knowledge

Massive investment and technological advances in the collection of extensive and longitudinal information on thousands of Alzheimer patients results in large amounts of data. These "big-data" databases can potentially advance CNS research and drug development. However, although necessary, they are not sufficient, and we posit that they must be matched with analytical methods that go beyond retrospective data-driven associations with various clinical phenotypes. Although these empirically derived associations can generate novel and useful hypotheses, they need to be organically integrated in a quantitative understanding of the pathology that can be actionable for drug discovery and development. We argue that mechanism-based modeling and simulation approaches, where existing domain knowledge is formally integrated using complexity science and quantitative systems pharmacology can be combined with data-driven analytics to generate predictive actionable knowledge for drug discovery programs, target validation, and optimization of clinical development.

Phase Response Synchronization in Neuronal Population with Time-Varying Coupling Strength

We present the dynamic model of global coupled neuronal population subject to external stimulus by the use of phase sensitivity function. We investigate the effect of time-varying coupling strength on the synchronized phase response of neural population subjected to external harmonic stimulus. For a time-periodic coupling strength, we found that the stimulus with increasing intensity or frequency can reinforce the phase response synchronization in neuronal population of the weakly coupled neural oscillators, and the neuronal population with stronger coupling strength has good adaptability to stimulus. When we consider the dynamics of coupling strength, we found that a strong stimulus can quickly cause the synchronization in the neuronal population, the degree of synchronization grows with the increasing stimulus intensity, and the period of synchronized oscillation induced by external stimulation is related to stimulus frequency.

Dynamics of directional coupling underlying spike-wave discharges

PURPOSE

Spike and wave discharges (SWDs), generated within cortico-thalamo-cortical networks, are the electroencephalographic biomarker of absence epilepsy. The current work aims to identify mechanisms of SWD initiation, maintenance and termination by the analyses of dynamics and directionality of mutual interactions between the neocortex and various functionally different thalamic nuclei.

METHODS

Local-field potential recordings of 16 male Wistar Albino Glaxo from Rijswijk (WAG/Rij) rats, equipped with electrodes targeting layer 4-6 of the somatosensory cortex, rostral and caudal reticular thalamic nuclei (rRTN and cRTN), ventro-posteromedial (VPM), anterior (ATN) and posterior (PO) thalamic nuclei, were obtained. 3s epochs prior to SWD onset, after SWD onset, prior to SWD offset and after SWD offset were analyzed with newly developed time-variant adapted nonlinear Granger causality.

RESULTS

A gradual increase in coupling toward SWD onset between cortico-cortical pairs appears as early as 2s preictally. Next first unidirectional increase in coupling is noticed in a restricted number of cortico-thalamic and thalamo-cortical channel pairs, which turn into bidirectional coupling approaching SWD onset, and a gradual increase of intrathalamic coupling. Seizure onset is characterized by a coupling decrease for more than a second in a majority of channel pairs, only the cortex kept driving the cRTN. Intrathalamically the cRTN drives the PO, VPM and ATN. Most channel pairs no longer show differences in coupling with baseline during SWD maintenance, a major exception is the unidirectional coupling between cortex and cRTN. Toward the end of SWDs, more and more channel pairs show an increase in often bidirectional coupling, this increase suddenly vanishes at SWD offset.

CONCLUSION

The initiation of SWD is due to a gradual increase in intracortical coupling, followed by a selective increase in first unidirectional and later bidirectional coupling between the cortex and thalamus and also intrathalamically. Once the network is oscillating, coupling decreases in most of the channel pairs, although the cortex keeps its influence on the cRTN. The SWD is dampened by a gradual increase in coupling strength and in the number of channel pairs that influence each other; the latter might represent an endogenous brake of SWDs.

Fractality of sensations and the brain health: the theory linking neurodegenerative disorder with distortion of spatial and temporal scale-invariance and fractal complexity of the visible world

The theory that ties normal functioning and pathology of the brain and visual system with the spatial-temporal structure of the visual and other sensory stimuli is described for the first time in the present study. The deficit of fractal complexity of environmental influences can lead to the distortion of fractal complexity in the visual pathways of the brain and abnormalities of development or aging. The use of fractal light stimuli and fractal stimuli of other modalities can help to restore the functions of the brain, particularly in the elderly and in patients with neurodegenerative disorders or amblyopia. Non-linear dynamics of these physiological processes have a strong base of evidence, which is seen in the impaired fractal regulation of rhythmic activity in aged and diseased brains. From birth to old age, we live in a non-linear world, in which objects and processes with the properties of fractality and non-linearity surround us. Against this background, the evolution of man took place and all periods of life unfolded. Works of art created by man may also have fractal properties. The positive influence of music on cognitive functions is well-known. Insufficiency of sensory experience is believed to play a crucial role in the pathogenesis of amblyopia and age-dependent diseases. The brain is very plastic in its early development, and the plasticity decreases throughout life. However, several studies showed the possibility to reactivate the adult's neuroplasticity in a variety of ways. We propose that a non-linear structure of sensory information on many spatial and temporal scales is crucial to the brain health and fractal regulation of physiological rhythms. Theoretical substantiation of the author's theory is presented. Possible applications and the future research that can experimentally confirm or refute the theoretical concept are considered.

Kernel Collaborative Representation-Based Automatic Seizure Detection in Intracranial EEG

Automatic seizure detection is of great significance in the monitoring and diagnosis of epilepsy. In this study, a novel method is proposed for automatic seizure detection in intracranial electroencephalogram (iEEG) recordings based on kernel collaborative representation (KCR). Firstly, the EEG recordings are divided into 4s epochs, and then wavelet decomposition with five scales is performed. After that, detail signals at scales 3, 4 and 5 are selected to be sparsely coded over the training sets using KCR. In KCR, l2-minimization replaces l1-minimization and the sparse coefficients are computed with regularized least square (RLS), and a kernel function is utilized to improve the separability between seizure and nonseizure signals. The reconstructed residuals of each EEG epoch associated with seizure and nonseizure training samples are compared and EEG epochs are categorized as the class that minimizes the reconstructed residual. At last, a multi-decision rule is applied to obtain the final detection decision. In total, 595 h of iEEG recordings from 21 patients with 87 seizures are employed to evaluate the system. The average sensitivity of 94.41%, specificity of 96.97%, and false detection rate of 0.26/h are achieved. The seizure detection system based on KCR yields both a high sensitivity and a low false detection rate for long-term EEG.

Tracking slow modulations in synaptic gain using dynamic causal modelling: validation in epilepsy

In this work we propose a proof of principle that dynamic causal modelling can identify plausible mechanisms at the synaptic level underlying brain state changes over a timescale of seconds. As a benchmark example for validation we used intracranial electroencephalographic signals in a human subject. These data were used to infer the (effective connectivity) architecture of synaptic connections among neural populations assumed to generate seizure activity. Dynamic causal modelling allowed us to quantify empirical changes in spectral activity in terms of a trajectory in parameter space — identifying key synaptic parameters or connections that cause observed signals. Using recordings from three seizures in one patient, we considered a network of two sources (within and just outside the putative ictal zone). Bayesian model selection was used to identify the intrinsic (within-source) and extrinsic (between-source) connectivity. Having established the underlying architecture, we were able to track the evolution of key connectivity parameters (e.g., inhibitory connections to superficial pyramidal cells) and test specific hypotheses about the synaptic mechanisms involved in ictogenesis. Our key finding was that intrinsic synaptic changes were sufficient to explain seizure onset, where these changes showed dissociable time courses over several seconds. Crucially, these changes spoke to an increase in the sensitivity of principal cells to intrinsic inhibitory afferents and a transient loss of excitatory–inhibitory balance.

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We propose a framework to characterise slow dynamical changes in the brain.

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Dynamical causal modelling finds the most likely connectivity among two brain areas.

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The synaptic weights defining these connections are tracked in time.

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We analyse brain activity of an epileptic subject, at the focus and just outside it.

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We point to modulations of synaptic connections as responsible of the seizure.

Epileptic neuronal networks: methods of identification and clinical relevance

The main objective of this paper is to examine evidence for the concept that epileptic activity should be envisaged in terms of functional connectivity and dynamics of neuronal networks. Basic concepts regarding structure and dynamics of neuronal networks are briefly described. Particular attention is given to approaches that are derived, or related, to the concept of causality, as formulated by Granger. Linear and non-linear methodologies aiming at characterizing the dynamics of neuronal networks applied to EEG/MEG and combined EEG/fMRI signals in epilepsy are critically reviewed. The relevance of functional dynamical analysis of neuronal networks with respect to clinical queries in focal cortical dysplasias, temporal lobe epilepsies, and "generalized" epilepsies is emphasized. In the light of the concepts of epileptic neuronal networks, and recent experimental findings, the dichotomic classification in focal and generalized epilepsy is re-evaluated. It is proposed that so-called "generalized epilepsies," such as absence seizures, are actually fast spreading epilepsies, the onset of which can be tracked down to particular neuronal networks using appropriate network analysis. Finally new approaches to delineate epileptogenic networks are discussed.

NONLINEAR ANALYSIS OF PHYSIOLOGICAL SIGNALS: A REVIEW

This paper reviews various nonlinear analysis methods for physiological signals. The assessment is based on a discussion of chaos-inspired methods, such as fractal dimension (FD), correlation dimension (D2), largest Lyapunov exponet (LLE), Renyi's entropy (REN), Shannon spectral entropy (SEN), and approximate entropy (ApEn). We document that these methods are used to extract discriminative features from electroencephalograph (EEG) and heart rate variability (HRV) signals by reviewing the relevant scientific literature. EEG features can be used to support the diagnosis of epilepsy and HRV features can be used to support the diagnosis of cardiovascular diseases as well as diabetes. Documenting the widespread use of these and other nonlinear methods supports our thesis that the study of feature extraction methods, based on the chaos theory, is an important subject which has been gaining more and significance in biomedical engineering. We adopt the position that pursuing research in the field of biomedical engineering is ultimately a progmatic activity, where it is necessary to engage in features that work. In this case, the nonlinear features are working well, even if we do not have conclusive evidence that the underlying physiological phenomena are indeed chaotic.

MULTISCALE ENTROPY ANALYSIS OF EEG RECORDINGS IN EPILEPTIC RATS

In this study, we investigate multiscale entropy (MSE) as a tool to evaluate the dynamic characteristics of electroencephalogram (EEG) during seizure-free, pre-seizure and seizure state, respectively, in epileptic rats. The results show that MSE method is able to reveal that EEG signals are more complex in seizure-free state than in seizure state, and can successfully distinguish among different seizure states. The classification ability of the MSE measures is tested using the linear discriminant analysis (LDA). Test results confirm that the classification accuracy of MSE method is superior to traditional single-scale entropy method. MSE method has potential in classifying the epileptic EEG signals.

Tackling EEG signal classification with least squares support vector machines: a sensitivity analysis study

The electroencephalogram (EEG) signal captures the electrical activity of the brain and is an important source of information for studying neurological disorders. The proper analysis of this biological signal plays an important role in the domain of brain-computer interface, which aims at the construction of communication channels between human brain and computers. In this paper, we investigate the application of least squares support vector machines (LS-SVM) to the task of epilepsy diagnosis through automatic EEG signal classification. More specifically, we present a sensitivity analysis study by means of which the performance levels exhibited by standard and least squares SVM classifiers are contrasted, taking into account the setting of the kernel function and of its parameter value. Results of experiments conducted over different types of features extracted from a benchmark EEG signal dataset evidence that the sensitivity profiles of the kernel machines are qualitatively similar, both showing notable performance in terms of accuracy and generalization. In addition, the performance accomplished by optimally configured LS-SVM models is also quantitatively contrasted with that obtained by related approaches for the same dataset.

From intracerebral EEG signals to brain connectivity: identification of epileptogenic networks in partial epilepsy

Epilepsy is a complex neurological disorder characterized by recurring seizures. In 30% of patients, seizures are insufficiently reduced by anti-epileptic drugs. In the case where seizures originate from a relatively circumscribed region of the brain, epilepsy is said to be partial and surgery can be indicated. The success of epilepsy surgery depends on the accurate localization and delineation of the epileptogenic zone (which often involves several structures), responsible for seizures. It requires a comprehensive pre-surgical evaluation of patients that includes not only imaging data but also long-term monitoring of electrophysiological signals (scalp and intracerebral EEG). During the past decades, considerable effort has been devoted to the development of signal analysis techniques aimed at characterizing the functional connectivity among spatially distributed regions over interictal (outside seizures) or ictal (during seizures) periods from EEG data. Most of these methods rely on the measurement of statistical couplings among signals recorded from distinct brain sites. However, methods differ with respect to underlying theoretical principles (mostly coming from the field of statistics or the field of non-linear physics). The objectives of this paper are: (i) to provide an brief overview of methods aimed at characterizing functional brain connectivity from electrophysiological data, (ii) to provide concrete application examples in the context of drug-refractory partial epilepsies, and iii) to highlight some key points emerging from results obtained both on real intracerebral EEG signals and on signals simulated from physiologically plausible models in which the underlying connectivity patterns are known a priori (ground truth).

Research on the relation of EEG signal chaos characteristics with high-level intelligence activity of human brain

Using phase space reconstruct technique from one-dimensional and multi-dimensional time series and the quantitative criterion rule of system chaos, and combining the neural network; analyses, computations and sort are conducted on electroencephalogram (EEG) signals of five kinds of human consciousness activities (relaxation, mental arithmetic of multiplication, mental composition of a letter, visualizing a 3-dimensional object being revolved about an axis, and visualizing numbers being written or erased on a blackboard). Through comparative studies on the determinacy, the phase graph, the power spectra, the approximate entropy, the correlation dimension and the Lyapunov exponent of EEG signals of 5 kinds of consciousness activities, the following conclusions are shown: (1) The statistic results of the deterministic computation indicate that chaos characteristic may lie in human consciousness activities, and central tendency measure (CTM) is consistent with phase graph, so it can be used as a division way of EEG attractor. (2) The analyses of power spectra show that ideology of single subject is almost identical but the frequency channels of different consciousness activities have slight difference. (3) The approximate entropy between different subjects exist discrepancy. Under the same conditions, the larger the approximate entropy of subject is, the better the subject's innovation is. (4) The results of the correlation dimension and the Lyapunov exponent indicate that activities of human brain exist in attractors with fractional dimensions. (5) Nonlinear quantitative criterion rule, which unites the neural network, can classify different kinds of consciousness activities well. In this paper, the results of classification indicate that the consciousness activity of arithmetic has better differentiation degree than that of abstract.

Stimulation-based anticipation and control of state transitions in the epileptic brain

We focus on the implications that the underlying neuronal dynamics might have on the possibility of anticipating seizures and designing an effective paradigm for their control. Transitions into seizures can be caused by parameter changes in the dynamic state or by interstate transitions as occur in multi-attractor systems; in the latter case, only a weak statistical prognosis of the seizure risk can be achieved. Nevertheless, we claim that by applying a suitable perturbation to the system, such as electrical stimulation, relevant features of the system's state may be detected and the risk of an impending seizure estimated. Furthermore, if these features are detected early, transitions into seizures may be blocked. On the basis of generic and realistic computer models we explore the concept of acute seizure control through state-dependent feedback stimulation. We show that in some classes of dynamic transitions, this can be achieved with a relatively limited amount of stimulation.

Learning-rate-dependent clustering and self-development in a network of coupled phase oscillators

We investigate the role of the learning rate in a Kuramoto Model of coupled phase oscillators in which the coupling coefficients dynamically vary according to a Hebbian learning rule. According to the Hebbian theory, a synapse between two neurons is strengthened if they are simultaneously coactive. Two stable synchronized clusters in antiphase emerge when the learning rate is larger than a critical value. In such a fast learning scenario, the network eventually constructs itself into an all-to-all coupled structure, regardless of initial conditions in connectivity. In contrast, when learning is slower than this critical value, only a single synchronized cluster can develop. Extending our analysis, we explore whether self-development of neuronal networks can be achieved through an interaction between spontaneous neural synchronization and Hebbian learning. We find that self-development of such neural systems is impossible if learning is too slow. Finally, we demonstrate that similar to the acquisition and consolidation of long-term memory, this network is capable of generating and remembering stable patterns.

Spatial analysis of intracerebral electroencephalographic signals in the time and frequency domain: identification of epileptogenic networks in partial epilepsy

Electroencephalography (EEG) occupies an important place for studying human brain activity in general, and epileptic processes in particular, with appropriate time resolution. Scalp EEG or intracerebral EEG signals recorded in patients with drug-resistant partial epilepsy convey important information about epileptogenic networks that must be localized and understood prior to subsequent therapeutic procedures. However, this information, often subtle, is 'hidden' in the signals. It is precisely the role of signal processing to extract this information and to put it into a 'coherent and interpretable picture' that can participate in the therapeutic strategy. Nowadays, the panel of available methods is very wide depending on the objectives such as, for instance, the detection of transient epileptiform events, the detection and/or prediction of seizures, the recognition and/or the classification of EEG patterns, the localization of epileptic neuronal sources, the characterization of neural synchrony, the determination of functional connectivity, among others. The intent of this paper is to focus on a specific category of methods providing relevant information about epileptogenic networks from the analysis of spatial properties of EEG signals in the time and frequency domain. These methods apply to either interictal or ictal recordings and share the common objective of localizing the subsets of brain structures involved in both types of paroxysmal activity. Most of these methods were developed by our group and are routinely used during pre-surgical evaluation. Examples are detailed. Results, as well as limitations of the methods, are also discussed.

Epilepsy and nonlinear dynamics

This overview summarizes findings obtained from analyzing electroencephalographic (EEG) recordings from epilepsy patients with methods from the theory of nonlinear dynamical systems. The last two decades have shown that nonlinear time series analysis techniques allow an improved characterization of epileptic brain states and help to gain deeper insights into the spatial and temporal dynamics of the epileptic process. Nonlinear EEG analyses can help to improve the evaluation of patients prior to neurosurgery, and with an unequivocal identification of precursors of seizures, they can be of great value in the development of seizure warning and prevention techniques.

Transition to seizures in the isolated immature mouse hippocampus: a switch from dominant phasic inhibition to dominant phasic excitation

The neural dynamics and mechanisms responsible for the transition from the interictal to the ictal state (seizures) are unresolved questions in epilepsy. It has been suggested that a shift from inhibitory to excitatory GABAergic drive can promote seizure generation. In this study, we utilized an experimental model of temporal lobe epilepsy which produces recurrent seizure-like events in the isolated immature mouse hippocampus (P8-16), perfused with low magnesium ACSF, to investigate the cellular dynamics of seizure transition. Whole-cell and perforated patch recordings from CA1 pyramidal cells and from fast- and non-fast-spiking interneurons in the CA1 stratum oriens hippocampal region showed a change in intracellular signal integration during the transition period, starting with dominant phasic inhibitory synaptic input, followed by dominant phasic excitation prior to a seizure. Efflux of bicarbonate ions through the GABA A receptor did not fully account for this excitation and GABAergic excitation via reversed IPSPs was also excluded as the prime mechanism generating the dominant excitation, since somatic and dendritic GABA A responses to externally applied muscimol remained hyperpolarizing throughout the transition period. In addition, abolishing EPSPs in a single neuron by intracellularly injected QX222, revealed that inhibitory synaptic drive was maintained throughout the entire transition period. We suggest that rather than a major shift from inhibitory to excitatory GABAergic drive prior to seizure onset, there is a change in the interaction between afferent synaptic inhibition, and afferent and intrinsic excitatory processes in pyramidal neurons and interneurons, with maintained inhibition and increasing, entrained 'overpowering' excitation during the transition to seizure.

Differentiation of MEG activity in multiple sclerosis patients with the use of nonlinear analysis

The aim of this study is to investigate if there is any nonlinearity in the magnetoencephalographic recordings of patients with multiple sclerosis in comparison with controls in order to find out the differences in the mechanisms underlying their brain waves. Five multiple sclerosis patients and five controls were included in this study. Chaotic activity of multiple sclerosis patients is lower than in the normal brain. Nonlinear analysis may offer fertile perspectives for understanding the features of patients with multiple sclerosis.

Hypnotic abreaction releases chaotic patterns of electrodermal activity during dissociation

Chaotic transitions emerge in a wide variety of cognitive phenomena and may possibly be linked to specific changes during development of mental disorders. There are several hypotheses that link the dissociation to critical chaotic shifts with the resulting self-organization of behavioral patterns during critical periods. In 2 patients, hypnotic revivification of dissociated trauma along with measurement of bilateral electrodermal activity (EDA) for therapeutic and research purposes was performed. Nonlinear data analysis of EDA records shows a difference between degree of chaos in hypnotic relaxed state before revivification of the trauma and dissociated state after reliving the traumatic memory. Results suggest that the dissociated state after revivification of the trauma is significantly more chaotic than the state during the hypnotic relaxation before the event. Findings of this study suggest a possible role of neural chaos in the processing of the dissociated traumatic memory during hypnotic revivification.

Comparison of two estimators of time-frequency interdependencies between nonstationary signals: application to epileptic EEG

Numerous works have been dedicated to the development of signal processing methods aimed at measuring the degree of association between EEG signals. This interdependency parameter is often used to characterize the functional coupling between different brain structures or regions during either normal or pathological processes. In this paper we focus on the time-frequency characterization of interdependencies between nonstationary signals. Particularly, we propose a novel estimator based on the cross correlation of narrow band filtered signals. In a simulation framework, results show that this estimator may exhibit higher statistical performances (bias and variance) compared to a more classical estimator based on the coherence function. On real data (intracerebral EEG signals), they show that this estimator enhances the readability of the time-frequency representation of the relationship and can thus improve the interpretation of nonstationary interdependencies in EEG signals. Finally, we illustrate the importance of characterizing the relationship in both time and frequency domains by comparing with frequency-independent methods (linear and nonlinear).

Multiclass support vector machines for EEG-signals classification

In this paper, we proposed the multiclass support vector machine (SVM) with the error-correcting output codes for the multiclass electroencephalogram (EEG) signals classification problem. The probabilistic neural network (PNN) and multilayer perceptron neural network were also tested and benchmarked for their performance on the classification of the EEG signals. Decision making was performed in two stages: feature extraction by computing the wavelet coefficients and the Lyapunov exponents and classification using the classifiers trained on the extracted features. The purpose was to determine an optimum classification scheme for this problem and also to infer clues about the extracted features. Our research demonstrated that the wavelet coefficients and the Lyapunov exponents are the features which well represent the EEG signals and the multiclass SVM and PNN trained on these features achieved high classification accuracies.

Epileptic seizure detection from ECoG using recurrence time statistics

A recurrence time statistics T1 is defined and used as a feature extraction method for seizure detection. The preliminary data shows that during seizure T1 generates a peak and this peak clearly distinguishes the seizure state from background activity. When applied to multi-channel ECoG recordings, the spatial-temporal signature of T1 can be clearly observed to discriminate seizures. The T1 feature was used for automated seizure detection on two sets of long term monitoring ECoG data. The detection probability reached 97% with a 0.29 per hour average false alarm rate.

A complete strategy for patient un-specific detection of epileptic seizures using crude estimations of entropy

This paper outlines a complete strategy for patient un-specific detection of epileptic seizures on scalp data. Using a crude estimation of entropy and contextual information derived from methods employed by human experts, a true positive classification rate of 94% was achieved on 125 seizures, 22 different patients and over 500 hours of EEG recordings. False positives remain low enough for this algorithm to be clinically applicable. This paper outlines the strategy, providing justification and exploration on the estimation of entropy using low number of data samples.

Quantitative evaluation of linear and nonlinear methods characterizing interdependencies between brain signals

Brain functional connectivity can be characterized by the temporal evolution of correlation between signals recorded from spatially-distributed regions. It is aimed at explaining how different brain areas interact within networks involved during normal (as in cognitive tasks) or pathological (as in epilepsy) situations. Numerous techniques were introduced for assessing this connectivity. Recently, some efforts were made to compare methods performances but mainly qualitatively and for a special application. In this paper, we go further and propose a comprehensive comparison of different classes of methods (linear and nonlinear regressions, phase synchronization, and generalized synchronization) based on various simulation models. For this purpose, quantitative criteria are used: in addition to mean square error under null hypothesis (independence between two signals) and mean variance computed over all values of coupling degree in each model, we provide a criterion for comparing performances. Results show that the performances of the compared methods are highly dependent on the hypothesis regarding the underlying model for the generation of the signals. Moreover, none of them outperforms the others in all cases and the performance hierarchy is model dependent.

Analysis of EEG background activity in Alzheimer's disease patients with Lempel–Ziv complexity and central tendency measure

In this study we have investigated the electroencephalogram (EEG) background activity in patients with Alzheimer's disease (AD) using non-linear analysis methods. We calculated the Lempel-Ziv (LZ) complexity - applying two different sequence conversion methods - and the central tendency measure (CTM) of the EEG in 11 AD patients and 11 age-matched control subjects. CTM quantifies the degree of variability, while LZ complexity reflects the arising rate of new patterns along with the EEG time series. We did not find significant differences between AD patients and control subjects' EEGs with CTM. On the other hand, AD patients had significantly lower LZ complexity values (p<0.01) at electrodes P3 and O1 with a two-symbol sequence conversion, and P3, P4, O1 and T5 using three symbols. Our results show a decreased complexity of EEG patterns in AD patients. In addition, we obtained 90.9% sensitivity and 72.7% specificity at O1, and 72.7% sensitivity and 90.9% specificity at P3 and P4. These findings suggest that LZ complexity may contribute to increase the insight into brain dysfunction in AD in ways which are not possible with more classical and conventional statistical methods.

Classification of epilepsy types through global network analysis of scalp electroencephalograms

Epilepsy is a dynamic disease in which self-organization and emergent structures occur dynamically at multiple levels of neuronal integration. Therefore, the transient relationship within multichannel electroencephalograms (EEGs) is crucial for understanding epileptic processes. In this paper, we show that the global relationship within multichannel EEGs provides us with more useful information in classifying two different epilepsy types than pairwise relationships such as cross correlation. To demonstrate this, we determine the global network structure within channels of the scalp EEG based on the minimum spanning tree method. The topological dissimilarity of the network structures from different types of temporal lobe epilepsy is described in the form of the divergence rate and is computed for 11 patients with left (LTLE) and right temporal lobe epilepsy (RTLE). We find that patients with LTLE and RTLE exhibit different large scale network structures, which emerge at the epoch immediately before the seizure onset, not in the preceding epochs. Our results suggest that patients with the two different epilepsy types display distinct large scale dynamical networks with characteristic epileptic network structures.

Layer IV of the primary somatosensory cortex has the highest complexity under anesthesia and cortical complexity is modulated by specific thalamic inputs

The system complexity, as calculated from correlation dimension, embedded in each layer and its modulation by specific inputs and general excitatory state are not yet known. The aims of present study were to estimate the system complexity across the cortical layers by analyzing intracortical EEG signals using a nonlinear analytical method, and to identify how layer-related complexity varies with the alteration of thalamic input and brain state. Male Sprague-Dawley rats were anesthetized under l% halothane. Sixteen channels of evoked or spontaneous EEG signals were recorded simultaneously across the six cortical layers in the somatosensory cortex with a single Michigan probe. The system complexity was assessed by computing correlation dimension, D(2), based on the Nonlinear Time Series Analysis data analysis program. Cortical layer IV exhibited a D(2) value, 3.24, that was significantly higher than that of the other cortical layers. The D(2) values in layers IV and II/III were significantly reduced after reversible deactivation of the ventral posterior lateral thalamic nucleus. D(2) decreased with increases in administered halothane concentration from 0.75% to 2.0%, particularly in layer IV. The present findings suggest that cortical layer IV maintains a higher complexity than the other layers and that the complexity of the mid-cortical layers is subject to regulation from specific thalamic inputs and more sensitive to changes in the general state of brain excitation.

Fuzzy similarity index for discrimination of EEG signals

In this study, a new approach based on the computation of fuzzy similarity index was presented for discrimination of electroencephalogram (EEG) signals. The EEG, a highly complex signal, is one of the most common sources of information used to study brain function and neurological disorders. The analyzed EEG signals were consisted of five sets (set A-healthy volunteer, eyes open; set B-healthy volunteer, eyes closed; set C-seizure-free intervals of five patients from hippocampal formation of opposite hemisphere; set D-seizure-free intervals of five patients from epileptogenic zone; set E-epileptic seizure segments). The EEG signals were considered as chaotic signals and this consideration was tested successfully by the computation of Lyapunov exponents. The computed Lyapunov exponents were used to represent the EEG signals. The aim of the study is discriminating the EEG signals by the combination of Lyapunov exponents and fuzzy similarity index. Toward achieving this aim, fuzzy sets were obtained from the feature sets (Lyapunov exponents) of the signals under study. The results demonstrated that the similarity between the fuzzy sets of the studied signals indicated the variabilities in the EEG signals. Thus, the fuzzy similarity index could discriminate the healthy EEG segments (sets A and B) and the other three types of segments (sets C, D, and E) recorded from epileptic patients.

Efficient unsupervised algorithms for the detection of seizures in continuous EEG recordings from rats after brain injury

Long-term EEG monitoring in chronically epileptic animals produces very large EEG data files which require efficient algorithms to differentiate interictal spikes and seizures from normal brain activity, noise, and, artifact. We compared four methods for seizure detection based on (1) EEG power as computed using amplitude squared (the power method), (2) the sum of the distances between consecutive data points (the coastline method), (3) automated spike frequency and duration detection (the spike frequency method), and (4) data range autocorrelation combined with spike frequency (the autocorrelation method). These methods were used to analyze a randomly selected test set of 13 days of continuous EEG data in which 75 seizures were imbedded. The EEG recordings were from eight different rats representing two different models of chronic epilepsy (five kainate-treated and three hypoxic-ischemic). The EEG power method had a positive predictive value (PPV, or true positives divided by the sum of true positives and false positives) of 18% and a sensitivity (true positives divided by the sum of true positives and false negatives) of 95%, the coastline method had a PPV of 78% and sensitivity of 99.59, the spike frequency method had a PPV of 78% and a sensitivity of 95%, and the autocorrelation method yielded a PPV of 96% and a sensitivity of 100%. It is possible to detect seizures automatically in a prolonged EEG recording using computationally efficient unsupervised algorithms. Both the quality of the EEG and the analysis method employed affect PPV and sensitivity.

Distribution of Spatial Complexity of EEG in Idiopathic Generalized Epilepsy and Its Change After Chronic Valproate Therapy

The objective of this study was to investigate the global and regional spatial synchrony of the EEG background activity, and to assess the effect of chronic valproate therapy on spatial synchrony. 15 idiopathic generalized epilepsy (IGE) patients were examined and compared to 16 normal controls. Resting EEG with 19 channels was investigated before and during chronic administration of valproate (VPA). Omega, a single-valued measure of spatial covariance complexity, was calculated to assess the degree of spatial synchrony of EEG. Furthermore, a new parameter was defined to characterize the distribution of spatial synchrony (Antero-Posterior Complexity Ratio, APCR). Global Omega complexity was significantly lower in IGE compared to controls, while regional complexity showed significant differences only in the anterior region: the IGE group showed lower complexity. APCR was significantly lower in IGE. VPA therapy (1) lowered the global complexity, (2) increased regional complexity in the anterior region, but decreased it in the posterior region, and (3) increased APCR. In IGE lower complexity, i.e. enhanced spatial synchrony, was found, especially in the anterior cortical area. VPA modified the distribution of spatial synchrony in IGE patients towards that of normal controls, although the effect is not identical with full normalization of cortical bioelectric activity. Whether the observed change of spatial synchrony distribution may reflect the normalizing effect of valproate on the brain state is worth further investigation.

Time-frequency characterization of interdependencies in nonstationary signals: application to epileptic EEG

For the past decades, numerous works have been dedicated to the development of signal processing methods aimed at measuring the degree of association between electroencephalographic (EEG) signals. This interdependency parameter, which may be defined in various ways, is often used to characterize a functional coupling between different brain structures or regions during either normal or pathological processes. In this paper, we focus on the time-frequency characterization of the interdependency between signals. Particularly, we propose a novel estimator of the linear relationship between nonstationary signals based on the cross correlation of narrow band filtered signals. This estimator is compared to a more classical estimator based on the coherence function. In a simulation framework, results show that it may exhibit better statistical performances (bias and variance or mean square error) when a priori knowledge about time delay between signals is available. On real data (intracerebral EEG signals), results show that this estimator may also enhance the readability of the time-frequency representation of relationship and, thus, can improve the interpretation of nonstationary interdependencies in EEG signals. Finally, we illustrate the importance of characterizing the relationship in both time and frequency domains by comparing with frequency-independent methods (linear and nonlinear).