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Time dependencies in the occurrences of epileptic seizures
Abstract
A new method of analysis, developed within the framework of nonlinear dynamics, is applied to patient recorded time series of the occurrence of epileptic seizures. These data exhibit broad band spectra and generally have no obvious structure. The goal is to detect hidden internal dependencies in the data without making any restrictive assumptions, such as linearity, about the structure of the underlying system. The basis of our approach is a conditional probabilistic analysis in a phase space reconstructed from the original data. The data, recorded from patients with intractable epilepsy over a period of 1-3 years, consist of the times of occurrences of hundreds of partial complex seizures. Although the epileptic events appear to occur independently, we show that the epileptic process is not consistent with the rules of a homogeneous Poisson process or generally with a random (IID) process. More specifically, our analysis reveals dependencies of the occurrence of seizures on the occurrence of preceding seizures. These dependencies can be detected in the interseizure interval data sets as well as in the rate of seizures per time period. We modeled patient's inaccuracy in recording seizure events by the addition of uniform white noise and found that the detected dependencies are persistent after addition of noise with standard deviation as great as 1/3 of the standard deviation of the original data set. A linear autoregressive analysis fails to capture these dependencies or produces spurious ones in most of the cases.
... EEG-based research works on seizure detection adopt commonly one of the these two major approaches [2]: 1) examination of the morphology and topography of waveforms in interictal stage to find events (markers) or changes in neuronal activity that may be precursors to seizures [10], and 2) analysis of the nonlinear spatiotemporal patterns of EEG signals to distinguish seizure-free state from seizure state [11]. ...
... In addition, results of recent investigations [2] indicate that in some cases, EEG subbands delta (0-4 Hz), theta (4-8 Hz), alpha (8)(9)(10)(11)(12), beta (13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30), and gamma (30-60 Hz) may yield more accurate information about constituent neuronal activities underlying the EEG, and consequently, certain changes in the EEGs that are not evident in the original full-spectrum EEG may be amplified when each subband is analyzed separately. ...
... In the second level of decomposition, the a1 component was further decomposed into higher resolution components, d2 (15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30) and lower resolution components, a2 (0-15 Hz). Following this process, after four levels of decomposition, the components retained are a4 (0-4 Hz), d4 (4-8 Hz), d3 (8)(9)(10)(11)(12)(13)(14)(15), d2 (15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30), and d1 (30-60 Hz). Reconstructions of these five components using the inverse wavelet transform approximately correspond to the five physiological EEG subbands delta, theta, alpha, beta, and gamma (see Fig. 2). ...
This study presents applying recurrence quantification analysis (RQA) on EEG recordings and their subbands: delta, theta, alpha, beta, and gamma for epileptic seizure detection. RQA is adopted since it does not require assumptions about stationarity, length of signal, and noise. The decomposition of the original EEG into its five constituent subbands helps better identification of the dynamical system of EEG signal. This leads to better classification of the database into three groups: Healthy subjects, epileptic subjects during a seizure-free interval (Interictal) and epileptic subjects during a seizure course (Ictal). The proposed algorithm is applied to an epileptic EEG dataset provided by Dr. R. Andrzejak of the Epilepsy Center, University of Bonn, Bonn, Germany. Combination of RQA-based measures of the original signal and its subbands results in an overall accuracy of 98.67% that indicates high accuracy of the proposed method.
... Studies in seizure prediction vary in their theoretical approaches, validation of results, and amount of data analyzed. EEG-based seizure detection and prediction methods are mostly based on two approaches: firstly, examination of the waveforms in the seizure-free EEG to find markers or changes in neuronal activity such as spikes which may be precursors to seizures; secondly, analysis of the nonlinear spatiotemporal evolution of the EEG signals to find a governing rule as the system moves from a seizure-free to seizure state [11]. Recurrence quantification analysis [12] and similarity index methods [13] are among the second approach. ...
... Based on the recent studies, EEG signals are multivariate time series caused by highly nonlinear, dynamic and multidimensional systems [22]. One of the approaches for analyzing epileptic EEG signals is to analyze the nonlinear spatiotemporal evolution of the EEG signals to find a governing rule as the system moves from a seizure-free to seizure state [11]. Dynamic systems can be described by a set of states and transition rules, which specify how the system may proceed from one state to another. ...
... In the second level of decomposition, the a1 component was further decomposed into higher resolution components, d2 (15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30) and lower resolution components, a2 (0-15 Hz). Following this process, after four levels of decomposition, the components retained were a4 (0-4 Hz), d4 (4-8 Hz), d3 (8)(9)(10)(11)(12)(13)(14)(15), d2 (15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30), and d1 (30-60 Hz). Reconstructions of these five components using the inverse wavelet transform approximately correspond to the five physiological EEG subbands delta, theta, alpha, beta, and gamma [8]. ...
Epileptic 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.
... Next to no exploration has been done independently to think about the impacts of these individual procedures. EEG range is typically decayed into five EEG sub-groups range: delta (0-4 Hz), theta (4-8 Hz), alpha (8)(9)(10)(11)(12), beta (13-30 Hz), and gamma (30-60 Hz). There is no persuading legitimization that whole EEG range ought to be viable delegate of cerebrum elements than the individual recurrence sub-groups. ...
... Figure measurable and morphological features for independent 1-D detail coefficients and estimation coefficient for EEG flag informational collection when wavelet deterioration. A noteworthy deficiency of existing seizure location calculations is their low exactness bringing about high missed recognition and false alert rates [10]. A strong strategy is a key to exact seizure identification and expectation. ...
Epilepsy is one of the neurological issues causing interminable irregular electrical release in the mind. The electroencephalogram (EEG) has developed as a critical instrument in the cerebrum movement checking for epilepsy conclusion. Hereditary Algorithms (GA) and Neural Networks (NN) have a place with developmental processing that attempt to estimating the neurological issue, for example, epilepsy. In this paper EEG signals broke down for multi resolution sub-band by wavelet disintegration. Wavelet procedure is executed for investigation of EEG and delta, theta, alpha, beta, and gamma sub-groups of EEG. Different features like AR coefficients, control range thickness, entropy and factual features extraction alongside morphological features. The system received to break down three distinctive dataset of EEG signals: 1) Healthy Person; 2) Epileptic Patients amid a without seizure period (interictal or pre-seizure);3) Epileptic Patients amid seizure event (ictal). After feature extraction objective is to enhance the precision of classification. Received GA for feature enhancement alongside multi-layer backpropogation ANN classifier by assessed preparing execution and characterization correctness’s and results reasoned that proposed diagnostic delicate instruments has successfully grouping EEG signals.
... 1) Analysis of EEG signal to find distinguishable features between ictal and non-ictal perids [5]. 2) Analysis of EEG signals to extract distinguishable features between normal, interictal and ictal periods [6]. The proposed work deals with the second problem. ...
... The next step is to identify discriminating features of EEG signals in normal, and ictal classes. Different researchers used different features from time domain, frequency domain, time-frequency domain and/or combination these in different works [1][2][3][4][5][6][7][8][9][10]. Before extracting features it is important to identify least number of features which can discriminate different states (here normal and ictal) of brain with the best performance and low computational complexity and time. ...
The proposed automatic seizure detection algorithm is based on two statistical features in time domain. Classifier used to classify normal and epileptic seizure EEG signals is a linear one. Mean and Minimum value of energy per epoch are used as features for classification. The algorithm was tested on CHB-MIT pediatrics EEG database on three subjects. The classifier was trained with at least 60% of seizures and remaining seizures were given for testing. The performance of algorithm obtained are pretty good with average detection accuracy of 99.81%, sensitivity 100%. and specificity 99.81%. Since there is no transformation from one domain to the other, the computational complexity and computational time required are less as compared to the other works.
... If the phase space is of p dimensions, we can estimate theoretically up to p-1 dependence indices. Applications of these methods are discussed by Wu et al. (43), Iasemidis et al. (44), and Savit and Green (41,42). ...
... The most striking nonlinearities were observed in the signals generated by the epileptogenic focus and in the signals recorded from anatomical regions that generated interictal spikes. Further evidence that nonlinear deterministic processes underlie the occurrence of seizures was obtained by analyzing the time intervals between individual seizures, using the 8 j measures (44). Taken together, these studies suggest that seizures are generated by deterministic nonlinear chaotic systems; thus, the occurrence of epileptic seizures may represent the intermittent phase transitions characteristic of such systems. ...
Recently, interest has turned to the mathematical concept of chaos as an explanation for a variety of complex processes in nature. Chaotic systems, among other characteristics, can produce what appears to be random output. Another property of chaotic systems is that they may exhibit abrupt intermittent transitions between highly ordered and disordered states. Because of this property, it is hypothesized that epilepsy may be an example of chaos. In this review, some of the basic concepts of nonlinear dynamics and chaos are illustrated. Mathematical techniques developed to study the properties of nonlinear dynamical systems are outlined. Finally, the results of applying these techniques to the study of human epilepsy are discussed. The application of these powerful and novel mathematical techniques to analysis of the electroencephalogram has provided new insights into the epileptogenic process and may have considerable utility in the diagnosis and treatment of epilepsy.
... /fneur. . (4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17), the first prospective seizure prediction algorithm running real-time on continuous EEG data was developed by Iasemidis et al. (18). Non-linear features of the EEG, such as the largest Lyapunov exponent and phase changes in the state space, were extracted over time to identify dynamical spatial entrainment changes in the preictal period between critical brain sites. ...
The recurrent and unpredictable nature of seizures can lead to unintentional injuries and even death. The rapid development of electroencephalogram (EEG) and Artificial Intelligence (AI) technologies has made it possible to predict seizures in real-time through brain-machine interfaces (BCI), allowing advanced intervention. To date, there is still much room for improvement in predictive seizure models constructed by EEG using machine learning (ML) and deep learning (DL). But, the most critical issue is how to improve the performance and generalization of the model, which involves some confusing conceptual and methodological issues. This review focuses on analyzing several factors affecting the performance of seizure prediction models, focusing on the aspects of post-processing, seizure occurrence period (SOP), seizure prediction horizon (SPH), and algorithms. Furthermore, this study presents some new directions and suggestions for building high-performance prediction models in the future. We aimed to clarify the concept for future research in related fields and improve the performance of prediction models to provide a theoretical basis for future applications of wearable seizure detection devices.
... In order to discover the events or variations in neuronal action like spikes [5], the analysis of the waveforms in the preictal EEG has been carried out which might be the originators to seizures. 2) In order to discover a governing rule, the examination of the nonlinear spatio-temporal evolution of the EEG signals is executed since the system moves from a state where it is seizure-free towards a seizure state [6]. By means of a wavelet pre-processing,a specific work has been stated correspondingly by using the artificial neural networks [7] on behalf of the prediction of seizure [8]. ...
Using the study of EEG signals, the diagnosis of the brain disorders can be done. By means of a fuzzy KNN classifier, the epileptic seizures existence in EEG signalscan be detected by an effective method which is offered in this paper. Because ofthe abnormal electrical act of a collection of brain cells which is calledseizure, a disease named Epilepsy is caused as a result of temporary fluctuation in brain functions. The performance of the analysis is carried out in 3steps. Forthe EEG signal decompositionwithin delta, theta, alpha, beta and gamma sub bands, usage of biorthogonal discrete wavelet transform is carried out in the initial step. Fromevery sub band, the statistical characteristics are taken out in the succeeding step and the EEG signal classification i.e. epileptic seizure which occurs or not has been performedby fuzzy KNN classifier in the last step. On behalf of two various groups of EEG signals, thistechnique is applicable: 1) Healthy (Normal) EEG dataset; 2) epileptic datasetin the course of a seizure interval. The presence of epileptic seizure in EEG signals can be effectively detected using the proposed methodwhich is presented in the experimental results andmoreoveranacceptable precision is presented in detection.
... An affirmative answer to this question was obtained in a number of studies showing decreased values of correlation dimension in interictal EEGs preceding epileptic seizures (56). Others described that a decrease of the value of the largest Lyapunov exponent occurring simultaneously in a number of EEG channels appears to precede an epileptic seizure (57,58). In yet other studies, a method based on the correlation dimension and surrogate signals was reported to anticipate seizures several minutes before seizure onset (59). ...
Purpose:
The occurrence of abnormal dynamics in a physiological system can become manifest as a sudden qualitative change in the behavior of characteristic physiologic variables. We assume that this is what happens in the brain with regard to epilepsy. We consider that neuronal networks involved in epilepsy possess multistable dynamics (i.e., they may display several dynamic states). To illustrate this concept, we may assume, for simplicity, that at least two states are possible: an interictal one characterized by a normal, apparently random, steady-state of ongoing activity, and another one that is characterized by the paroxysmal occurrence of a synchronous oscillations (seizure).
Methods:
By using the terminology of the mathematics of nonlinear systems, we can say that such a bistable system has two attractors, to which the trajectories describing the system's output converge, depending on initial conditions and on the system's parameters. In phase-space, the basins of attraction corresponding to the two states are separated by what is called a "separatrix." We propose, schematically, that the transition between the normal ongoing and the seizure activity can take place according to three basic models: Model I: In certain epileptic brains (e.g., in absence seizures of idiopathic primary generalized epilepsies), the distance between "normal steady-state" and "paroxysmal" attractors is very small in contrast to that of a normal brain (possibly due to genetic and/or developmental factors). In the former, discrete random fluctuations of some variables can be sufficient for the occurrence of a transition to the paroxysmal state. In this case, such seizures are not predictable. Model II and model III: In other kinds of epileptic brains (e.g., limbic cortex epilepsies), the distance between "normal steady-state" and "paroxysmal" attractors is, in general, rather large, such that random fluctuations, of themselves, are commonly not capable of triggering a seizure. However, in these brains, neuronal networks have abnormal features characterized by unstable parameters that are very vulnerable to the influence of endogenous (model II) and/or exogenous (model III) factors. In these cases, these critical parameters may gradually change with time, in such a way that the attractor can deform either gradually or suddenly, with the consequence that the distance between the basin of attraction of the normal state and the separatrix tends to zero. This can lead, eventually, to a transition to a seizure.
Results:
The changes of the system's dynamics preceding a seizure in these models either may be detectable in the EEG and thus the route to the seizure may be predictable, or may be unobservable by using only measurements of the dynamical state. It is thinkable, however, that in some cases, changes in the excitability state of the underlying networks may be uncovered by using appropriate stimuli configurations before changes in the dynamics of the ongoing EEG activity are evident. A typical example of model III that we discuss here is photosensitive epilepsy.
Conclusions:
We present an overview of these basic models, based on neurophysiologic recordings combined with signal analysis and on simulations performed by using computational models of neuronal networks. We pay especial attention to recent model studies and to novel experimental results obtained while analyzing EEG features preceding limbic seizures and during intermittent photic stimulation that precedes the transition to paroxysmal epileptic activity.
... where y i (d 0 ) and y j (d 0 ) are i th and j th lagged phase locations with a sphere centred at any one of them with radius . Following determination of optimum lag and MED, CD was computed by Taken's estimator considering radius ( ) as 10% of the size of lagged phase space [5]. ...
In Brain Computer Interfacing (BCI), speech imagery is still at nascent stage of development. There are few studies reported considering mostly vowels or monosyllabic words. However, language specific vowels or words made it harder to standardise the whole analysis of electroencephalography (EEG) while distinguishing between them. Through this study, we have explored significance of chaos parameters for different imagined vowels chosen from International Phonetic Alphabets (IPA). The vowels were categorised into two categories, namely, soft vowels and diphthongs. Chaos analysis at EEG subband levels were evaluated. We have also reported significant contrasts between spatiotemporal distributions with chaos analysis for activation of different brain regions in imagining vowels.
... where y i (d 0 ) and y j (d 0 ) are i th and j th lagged phase locations with a sphere centred at any one of them with radius . Following determination of optimum lag and MED, CD is computed by Taken's estimator considering radius ( ) as 10% of the size of lagged phase space [21]. ...
A stable grasp is attained through appropriate hand preshaping and precise fingertip forces. Here, we have proposed a method to decode grasp patterns from motor imagery and subsequent fingertip force estimation model with a slippage avoidance strategy. We have developed a feature-based classification of electroencephalography (EEG) associated with imagination of the grasping postures. Chaotic behaviour of EEG for different grasping patterns has been utilised to capture the dynamics of associated motor activities. We have computed correlation dimension (CD) as the feature and classified with "one against one" multiclass support vector machine (SVM) to discriminate between different grasping patterns. The result of the analysis showed varying classification accuracies at different subband levels. Broad categories of grasping patterns, namely, power grasp and precision grasp, were classified at a 96.0% accuracy rate in the alpha subband. Furthermore, power grasp subtypes were classified with an accuracy of 97.2% in the upper beta subband, whereas precision grasp subtypes showed relatively lower 75.0% accuracy in the alpha subband. Following assessment of fingertip force distributions while grasping, a nonlinear autoregressive (NAR) model with proper prediction of fingertip forces was proposed for each grasp pattern. A slippage detection strategy has been incorporated with automatic recalibration of the regripping force. Intention of each grasp pattern associated with corresponding fingertip force model was virtualised in this work. This integrated system can be utilised as the control strategy for prosthetic hand in the future. The model to virtualise motor imagery based fingertip force prediction with inherent slippage correction for different grasp types ᅟ.
... 20 As the true underlying conditional probability distribution is unknown, our specification of emission distribution depends on several considerations: (1) seizure count data is empirically overdispersed relative to that expected under a generic Poisson process, with the variance exceeding the mean; 21,22 and (2) seizure occurrence patterns exhibit dependence over time. 23,24 To account for these considerations, we employ a zero-inflated Poisson (ZIP) process for the seizure emission distribution. Seizure count data is often zeroinflated, i.e. patients often exhibit prolonged periods during which no seizures are observed, producing a larger number of zeros than expected under a simple Poisson process. ...
Objective: A fundamental challenge in treating epilepsy is that changes in observed seizure frequencies do not necessarily reflect changes in underlying seizure risk. Rather, changes in seizure frequency may occur due to probabilistic variation around
an underlying seizure risk state caused by normal fluctuations from natural history, leading to seizure unpredictability and potentially suboptimal medication adjustments in epilepsy management. However, no rigorous statistical approach exists to systematically distinguish expected changes in seizure frequency due to natural variability from changes in underlying seizure risk.
Methods: Using data from SeizureTracker.com, a patient-reported seizure diary tool containing over 1.2 million recorded seizures across 8 years, a novel epilepsy seizure risk assessment tool (EpiSAT) employing a Bayesian mixed-effects hidden Markov model for zero-inflated count data was developed to estimate changes in underlying
seizure risk using patient-reported seizure diary and clinical measurement data. Accuracy for correctly assessing underlying seizure risk was evaluated through a simulation comparison. Implications for the natural history of tuberous sclerosis complex (TSC) were assessed using data from SeizureTracker.com.
Results: EpiSAT led to significant improvement in seizure risk assessment compared to traditional approaches relying solely on observed seizure frequencies. Applied to TSC, four underlying seizure risk states were identified. The expected duration of each state was <12 months, providing a data-driven estimate of the amount of time a person with TSC would be expected to remain at the same seizure risk level according to the natural course of epilepsy.
Significance: We propose a novel Bayesian statistical approach for evaluating seizure risk on an individual patient level using patient-reported seizure diaries , which allows for the incorporation of external clinical variables to assess impact on seizure risk. This tool may improve the ability to distinguish true changes in seizure risk from natural variations in seizure frequency in clinical practice. Incorporation of systematic statistical approaches into antiepileptic drug (AED) management may help improve understanding of seizure
unpredictability as well as timing of treatment interventions for people with epilepsy.
... Although seizures traditionally have been considered to be unpredictable events, there is increasing evidence that seizure may, in fact, be predictable. Iasemidis et al. (1994) demonstrated that seizures occur in a time-dependent fashion, indicating that the underlying processes are deterministic. Intracranial electroencephalograph (EEG) signals recorded from patients with refractory temporal lobe epilepsy appear to have properties that are characteristic of chaotic systems since: (1) they are non-linear (Casdagli et al., 1996(Casdagli et al., , 1997; (2) they have a non-integer (fractal) dimension (Grassberger and Procaccia, 1983;Babloyantz, 1988); (3) there is at least one positive Lyapunov exponent (Abarbanel et al., 1993;Iasemidis et al., 1990). ...
... Through the method of delays described by Packard [31] and Takens [32] sampling of a single observable over time can approximate the position (state) of the system in a space spanned by the system variables related to this observable. Sampling with the method of delays can be used to reconstruct a multidimensional state space from a single-channel EEG signal [33][34][35][36]. In such an embedding, each state is represented in the state space by a vector X(t) whose components are the delayed versions of the original single-channel EEG time series u(t), that is, XðtÞ ¼ ½uðtÞ, uðt À Þ, . . . ...
... Clustering patterns, in which one seizure appears to increase the likelihood of subsequent seizures, are also encountered frequently in clinical practice. Despite these observations, analyses of long-term seizure patterns based on patient-reported seizure counts (seizure diary) have yielded inconsistent findings (Binnie et al., 1984;Milton et al., 1987;Albert, 1991;Balish et al., 1991;Tauboll et al., 1991;Iasemidis et al., 1994;Bauer and Burr, 2001;Lee and No, 2005;Hall et al., 2009). Although some authors conclude that the timing of seizure recurrence is random, others hypothesize that seizures occur in a probabilistic nonlinear fashion. ...
This resource addresses the disorders presenting in children, adolescents and adults which may be mistaken for epilepsy or which are associated with epilepsy and can develop into or out of epileptic seizures. It features case reports and tables (especially those which address the differential diagnosis of epilepsy and the disorders discussed), and covers anxiety/hyperventilation attacks, psychogenic nonepileptic seizures, epileptic and nonepileptic encephalopathies, autism, autoimmune encephalopathies, Tourette's Syndrome, transient ischemic attacks, transient global amnesia, myoclonus, alcohol-related seizures, hyperekplexia and dyskinesia, stereotypical behaviors, organic personality disorder and episodic dyscontrol syndrome.
... Some authors have applied concepts from dynamic systems theory, including that of self-organizing criticality to study inter-seizure intervals 5 . Other authors have noted more variability in seizure frequency than would be expected if their distribution followed a simple Poisson model, with overdispersion in series of seizure counts [6][7][8][9][10][11] . ...
Objective:
We report on a quantitative analysis of data from a study that acquired continuous long-term ambulatory human electroencephalography (EEG) data over extended periods. The objectives were to examine the seizure duration and interseizure interval (ISI), their relationship to each other, and the effect of these features on the clinical manifestation of events.
Methods:
Chronic ambulatory intracranial EEG data acquired for the purpose of seizure prediction were analyzed and annotated. A detection algorithm identified potential seizure activity, which was manually confirmed. Events were classified as clinically corroborated, electroencephalographically identical but not clinically corroborated, or subclinical. K-means cluster analysis supplemented by finite mixture modeling was used to locate groupings of seizure duration and ISI.
Results:
Quantitative analyses confirmed well-resolved groups of seizure duration and ISIs, which were either mono-modal or multimodal, and highly subject specific. Subjects with a single population of seizures were linked to improved seizure prediction outcomes. There was a complex relationship between clinically manifest seizures, seizure duration, and interval.
Significance:
These data represent the first opportunity to reliably investigate the statistics of seizure occurrence in a realistic, long-term setting. The presence of distinct duration groups implies that the evolution of seizures follows a predetermined course. Patterns of seizure activity showed considerable variation between individuals, but were highly predictable within individuals. This finding indicates seizure dynamics are characterized by subject-specific time scales; therefore, temporal distributions of seizures should also be interpreted on an individual level. Identification of duration and interval subgroups may provide a new avenue for improving seizure prediction.
... In the 1990s, with the emergence of analytical methods derived from the theory of complex nonlinear systems, a number of studies appeared with the same purpose. One of the first to report a method able to detect specific changes in the intracranial EEG preceding a seizure was the group of Iasemidis, Sackellares, and collaborators [16]- [19], who showed evidence for the convergence (entrainment) of phases and values of the maximum rate of generation of information (maximum Lyapunov exponent) from multichannel intracranial and scalp EEG recordings several minutes prior to a seizure. Also, an important contribution in this context was given in a number of studies showing decreased values of correlation dimension in interictal EEGs preceding epileptic seizures recorded intracranially [22]. ...
DOI: 10.1177/0271678X15618219
Studies in rodents suggest that flumazenil is a P-glycoprotein substrate at the blood-brain barrier. This study aimed to assess whether [11C]flumazenil is a P-glycoprotein substrate in humans and to what extent increased P-glycoprotein function in epilepsy may confound interpretation of clinical [11C]flumazenil studies used to assess gamma-aminobutyric acid A receptors. Nine drug-resistant patients with epilepsy and mesial temporal sclerosis were scanned twice using [11C]flumazenil before and after partial P-glycoprotein blockade with tariquidar. Volume of distribution, nondisplaceable binding potential, and the ratio of rate constants of [11C]flumazenil transport across the blood-brain barrier (K1/k2) were derived for whole brain and several regions. All parameters were compared between pre- and post-tariquidar scans. Regional results were compared between mesial temporal sclerosis and contralateral sides. Tariquidar significantly increased global K1/k2 (+23%) and volume of distribution (+10%), but not nondisplaceable binding potential. At the mesial temporal sclerosis side volume of distribution and nondisplaceable binding potential were lower in hippocampus (both ∼-19%) and amygdala (both ∼-16%), but K1/k2 did not differ, suggesting that only regional gamma-aminobutyric acid A receptor density is altered in epilepsy. In conclusion, although [11C]flumazenil appears to be a (weak) P-glycoprotein substrate in humans, this does not seem to affect its role as a tracer for assessing gamma-aminobutyric acid A receptor density.
... Though cycles of seizure activity associated with biological rhythms (circadian and menstrual) have long been recognized, Poisson processes have been felt to describe the pattern of seizure occurrence, with departures perhaps explained by external factors (Milton et al., 1987). Many authors have noted more variability in seizure frequency than would be expected if their distribution followed a simple Poisson model, with overdispersion in series of seizure counts (Balish et al., 1991;Greenwood and Yule, 1920;Hopkins et al., 1985;Iasemidis et al., 1994;Taubøll et al., 1991). ...
The pattern of epileptic seizures is often considered unpredictable, and the interval between events without correlation. A number of studies have examined the possibility that seizure activity respects a power-law relationship, both in terms of event magnitude and inter-event intervals. Such relationships are found in a variety of natural and manmade systems, such as earthquakes or Internet traffic, and describe the relationship between the magnitude of an event and the number of events. We postulated that human inter-seizure intervals would follow a power law relationship, and furthermore that evidence for the existence of a long memory process could be established in this relationship. We performed a post-hoc analysis, studying 8 patients who had long-term (up to 2 years) ambulatory intracranial EEG data recorded as part of the assessment of a novel seizure prediction device. We demonstrated that a power law relationship could be established in these patients (β =-1.5). In 5 out of the 6 subjects whose data was sufficiently stationary for analysis, we found evidence of long memory between epileptic events. This memory spans time scales from 30 minutes to 40 days. The estimated Hurst exponents range from 0.51-0.77±0.01. This finding may provide evidence of phasetransitions underlying the dynamics of epilepsy. © 2014 Cook, Varsavsky, Himes, Leyde, Berkovic, O_brien and Mareels.
... After the seizure, brain dynamics revert to a more disordered state in which previously entrained cortical areas become disentrained (postictal state). The epileptic brain repeats this series of state transitions intermittently, at seemingly irregular but, in fact, time-dependent intervals [15], [16]. This implies that the transition into seizures is not a random process. ...
... Several methods are reported in the literature for extracting quantitative features from EEG signals. Iasemidis and Sackellares [12] applied nonlinear dynamical techniques methods based upon the principal Lyapunov exponent for predicting seizures. Lehnertz and Elger et al. [13] employed nonlinear dynamics to larger datasets, greater numbers of patients for seizure prediction. ...
Features are the crucial basis for detection, classification and regression tasks in biomedical signal processing and are one of the key elements in the data analysis process. The objective of this work is to conduct a preliminary evaluation identify appropriate specific features from a large set of candidate features for predicting seizures. The main implication of this work is to design a Parameter Selective based CAD system, so the authors have laid emphasis on selection of relevant features which are less related, balanced and converge to best solution. These promising, prominent, statistically analyzed features are used for classification of brain signals into ictal and normal conditions. Experimental results show that the resulting attributes when used for classification results in 100% classification accuracy with CSFV, 99.5% with RSFVand 98.5% classification with SFV with MLPNN as classifier. The net increase in percentage classification accuracy is 1.5% with MLPNN, 2% with SVM and 1.8% with KNN with CSFV when compared to efficiency obtained with SFV.
... Several methods are reported in the literature for extracting quantitative features from EEG signals. Iasemidis and Sackellares [12] applied nonlinear dynamical techniques methods based upon the principal Lyapunov exponent for predicting seizures. Lehnertz and Elger et al.[13] employed nonlinear dynamics to larger datasets, greater numbers of patients for seizure prediction. ...
Features are the crucial basis for detection, classification and regression tasks in biomedical signal processing and are one of the key elements in the data analysis process. The objective of this work is to conduct a preliminary evaluation identify appropriate specific features from a large set of candidate features for predicting seizures. The main implication of this work is to design a Parameter Selective based CAD system, so the authors have laid emphasis on selection of relevant features which are less related, balanced and converge to best solution. These promising, prominent, statistically analyzed features are used for classification of brain signals into ictal and normal conditions. Experimental results show that the resulting attributes when used for classification results in 100 % classification accuracy with CSFV, 99.5% with RSFVand 98.5% classification with SFV with MLPNN as classifier. The net increase in percentage classification accuracy is 1.5% with MLPNN, 2% with SVM and 1.8% with KNN with CSFV when compared to efficiency obtained with SFV.
... Much of the previous studies [28, 35-40, 77, 82] in epilepsy have focused on analyzing the temporal changes associated with brain's non linear dynamics. Feature descriptors such as system's complexity or the short-term Lyapunov exponents [35][36][37][38][39][40] Earlier, we derived the SOM-SI measure to define mutual interactions among various nodes in a spatially coupled multi-dimensional system. The affinity matrix representation of the SOM-SI at every time window (of length 10 seconds) provides information on the interactions among all the possible pairs of nodes in a graph. ...
... The symptoms of epileptic seizure which is a rapid synchronous and recurring discharge of brain cells is dependant on the place of origin of the seizure and the stretch of the seizure (Tzallas et al., 2007). They have discovered that the pattern of seizure repetition is arbitrary and takes the form of a uniform Poisson distribution in 50% of the cases for most of the patients with multiple seizures using traditional statistical analyses and assuming that the mean of the seizure rate is constant (Iasemidisa et al., 1994). In several cases, epilepsy can be treated successfully, and several patients are in fact under regular medication (Protopopescu et al., 2001). ...
Epilepsy seizure is the result of the transient and unexpected electrical disturbance of the brain signal. The detection of epilepsy is only possible by analysing the normal and abnormal changes of brain electrical signal. The detection of epilepsy, which includes EEG recordings for the spikes and seizures, is very time consuming, especially in the case of long recordings. In this paper, an Artificial Intelligence (AI) based epilepsy detection technique is proposed. The technique is the combination of Multi-Wavelet Transform (MWT) and Artificial Neural Network (ANN). MWT is a technique based on wavelet theory, which is used to extract the features of EEG signal. The irregularity of EEG signal is measured by using the propose Improved Approximate Entropy (IApE). ANN is an AI that used to detect the type of EEG signal. The proposed technique is implemented, tested and the sensitivity, specificity, accuracy, precision response of IApE and ApE are compared.
... After the seizure (postictal state), brain dynamics revert to a more disordered state in which previously entrained (synchronized) cortical areas become disentrained (desynchronized). The epileptic brain repeats this series of state transitions intermittently, at seemingly irregular but, in fact, time-dependent intervals (Iasemidis et al. 1994;Olson et al. 1989). This implies that the transition into seizures is not a random process. ...
Epilepsy is one of the most common disorders of the nervous system. The progressive entrainment between an epileptogenic focus and normal brain areas results to transitions of the brain from chaotic to less chaotic spatiotemporal states, the epileptic seizures. The entrainment between two brain sites can be quantified by the T-index from the measures of chaos (e.g., Lyapunov exponents) of the electrical activity (EEG) of the brain. By applying the optimization theory, in particular quadratic zero-one programming, we were able to select the most entrained brain sites 10 minutes before seizures and subsequently follow their entrainment over 2 hours before seizures. In five patients with 3–24 seizures, we found that over 90% of the seizures are predictable by the optimal selection of electrode sites. This procedure, which is applied to epilepsy research for the first time, shows the possibility of prediction of epileptic seizures well in advance (19.8 to 42.9 minutes) of their occurrence.
... Department of Biomedical Engg.Trident Academy of Technology Bhubaneswar,Odisha bk.bme.rajanikant@gmail.com inspected by trained neurophysiologist for detecting epileptic seizures[3] or other abnormalities if present. This information is then used for proper clinical diagnosis and then accordingly various therapies, medications or surgical treatments are administered to the subjects. ...
Feature extraction and classification of biosignals is an important issue in development of disease diagnostic expert system (DDES). In this paper we propose a simple method for EEG classification based on Fourier features. Parameters like energy, entropy, power, and kurtosis were considered for discrimination of various categories of EEG signals. After calculating the above mentioned parameters of the discussed signals, we found that without going for rigorous time-frequency domain analysis, only frequency based analysis is well suitable to classify various EEG signals.
... Through the method of delays described by Packard et al. (1980) and Takens (1981), sampling of a single observable over time can approximate the position (state) of the system in a space spanned by the system variables related to this observable. Sampling with the method of delays can be used to reconstruct a multidimensional state space from a singlechannel EEG signal (Babloyantz and Destexhe, 1986;Casdagli et al., 1996;Iasemidis et al., 1993Iasemidis et al., , 1994. In such an embedding, each state is represented in the state space by a vector X(t) whose components are the delayed versions of the original single-channel EEG time series u(t), that is, ...
The ability to predict epileptic seizures well prior to their clinical onset provides promise for new diagnostic applications
and novel approaches to seizure control. Several groups of investigators have reported that it may be possible to predict
seizures based on the quantitative analysis of EEG signal characteristics. The objective of this chapter is first to report
an automated seizure warning algorithm, and second to compare its performance with other, theoretically sound, statistical
algorithms. The proposed automated seizure prediction algorithm (ASPA) consists of an optimization method for the selection
of critical cortical sites using measures from nonlinear dynamics, and a novel method for the detection of preictal transitions
using adaptive transition thresholds according to the current state of dynamical interactions among brain sites. Continuous
long-term (mean 210 hours per patient) intracranial EEG recordings obtained from ten patients with intractable epilepsy (total
of 130 recorded seizures) were analyzed to test the proposed algorithm. For each patient, the prediction ROC (receiver operating
characteristic) curve, generated from ASPA, was compared with the ones from periodic and random prediction schemes. The results
showed that the performance of ASPA is significantly superior to each naïve prediction method used (p-value < 0.05). This
suggests that the proposed nonlinear dynamical analysis of EEG contains relevant information to prospectively predict an impending
seizure, and thus has potential to be useful in clinical applications.
... Through the method of delays described by Packard [31] and Takens [32] sampling of a single observable over time can approximate the position (state) of the system in a space spanned by the system variables related to this observable. Sampling with the method of delays can be used to reconstruct a multidimensional state space from a single-channel EEG signal [33][34][35][36]. In such an embedding, each state is represented in the state space by a vector X(t) whose components are the delayed versions of the original single-channel EEG time series u(t), that is, XðtÞ ¼ ½uðtÞ, uðt À Þ, . . . ...
The phenomenon of epilepsy, one of the most common neurological disorders, constitutes a unique opportunity to study the dynamics of spatiotemporal state transitions in real, complex, nonlinear dynamical systems. We previously demonstrated that measures of chaos and angular frequency obtained from electroencephalographic (EEG) signals generated by critical sites in the cerebral cortex converge progressively (dynamical entrainment) from the asymptomatic interictal state to the ictal state (seizure) [L.D. Iasemidis, P. Pardalos, J.C. Sackellares and D.-S. Shiau (2001). Quadratic binary programming and dynamical system approach to determine the predictability of epileptic seizures. J. Combinatorial Optimization, 5, 9–26; L.D. Iasemidis, D.-S. Shiau, P.M. Pardalos and J.C. Sackellares (2002). Phase entrainment and predictability of epileptic seizures. In: P.M. Pardalos and J. Principe (Eds.), Biocomputing, pp. 59–84. Kluwer Academic Publishers]. This observation suggests the possibility of developing algorithms to predict seizures. One of the central points of those investigations was the application of optimization theory, specifically quadratic zero-one programming, for the selection of the cortical sites that exhibit preictal dynamical entrainment. In this study we present results from the application of this methodology to the prediction of epileptic seizures. Analysis of continuous, long-term (18–140 h), multielectrode EEG recordings from 5 patients resulted in the prediction of 88% of the impending 50 seizures, on average about 83 min prior to seizure onset, with an average false warning rate of one every 5.26 h. These results suggest that this seizure prediction algorithm performs well enough to be used in diagnostic and therapeutic applications in epileptic patients. Similar algorithms may be useful for certain spatiotemporal state transitions in other physical and biological systems.
... This qualifies the proposed scheme as random but renders it irrelevant and biased as an evaluation tool for epileptic seizure prediction. In particular, (a) EEG and seizure occurrences constitute nonstationary time series and depend on the evolving state of the patient (e.g. level of antiepileptic drug, vigilance, sensory inputs, etc.), (b) inter-seizure intervals are not exponentially distributed, (c) seizure occurrences are not independent from each other (e.g., see Iasemidis et al., 1994) and recall the well-known medical fact of seizure clustering), (d) the dependence of features d used in the developed statistic may be time dependent. We have shown in Chaovalitwongse et al. (2005) that this is indeed the case. ...
... 3(c ). Seizure clustering has commonly been documented in epilepsy studies (Iasemidis, Olson, Savit, & Sackellares, 1994; Milton, Gotman, Remillard, & Andermann, 1987). Comparing the SLE and inter-SLE α values of the Rett MeCP2- deficient mouse model to various epilepsies in Suffczynski et al. (2006) revealed a strong resemblance to absence epilepsy, in particular, the greatest resemblance was to the GAERS (Genetic Absence Epilepsy Rats from Strasbourg) (Marescaux & Vergnes, 1995). ...
Rett syndrome is a neurodevelopmental disorder caused by mutations in the X-linked gene encoding methyl-CpG-binding protein 2 (MECP2). Spontaneous recurrent discharge episodes are displayed in Rett-related seizures as in other types of epilepsies. The aim of this paper is to investigate the seizure-like event (SLE) and inter-SLE states in a female MeCP2-deficient mouse model of Rett syndrome and compare them to those found in other spontaneous recurrent epilepsy models. The study was performed on a small population of female MeCP2-deficient mice using telemetric local field potential (LFP) recordings over a 24 h period. Durations of SLEs and inter-SLEs were extracted using a rule-based automated SLE detection system for both daytime and nighttime, as well as high and low power levels of the delta frequency range (0.5-4 Hz) of the recorded LFPs. The results suggest SLE occurrences are not influenced by circadian rhythms, but had a significantly greater association with delta power. Investigating inter-SLE and SLE states by fitting duration histograms to the gamma distribution showed that SLE initiation and termination were associated with random and deterministic mechanisms, respectively. These findings when compared to reported studies on epilepsy suggest that Rett-related seizures share many similarities with absence epilepsy.
Seizures are a disruption of normal brain activity present across a vast range of species and conditions. We introduce an organizing principle that leads to the first objective Taxonomy of Seizure Dynamics (TSD) based on bifurcation theory. The ‘dynamotype’ of a seizure is the dynamic composition that defines its observable characteristics, including how it starts, evolves and ends. Analyzing over 2000 focal-onset seizures from multiple centers, we find evidence of all 16 dynamotypes predicted in TSD. We demonstrate that patients’ dynamotypes evolve during their lifetime and display complex but systematic variations including hierarchy (certain types are more common), non-bijectivity (a patient may display multiple types) and pairing preference (multiple types may occur during one seizure). TSD provides a way to stratify patients in complement to present clinical classifications, a language to describe the most critical features of seizure dynamics, and a framework to guide future research focused on dynamical properties.
Seizures are a disruption of normal brain activity present across a vast range of species and conditions. We introduce an organizing principle that leads to the first objective Taxonomy of Seizure Dynamics (TSD) based on bifurcation theory. The ‘dynamotype’ of a seizure is the dynamic composition that defines its observable characteristics, including how it starts, evolves and ends. Analyzing over 2000 focal-onset seizures from multiple centers, we find evidence of all 16 dynamotypes predicted in TSD. We demonstrate that patients’ dynamotypes evolve during their lifetime and display complex but systematic variations including hierarchy (certain types are more common), non-bijectivity (a patient may display multiple types) and pairing preference (multiple types may occur during one seizure). TSD provides a way to stratify patients in complement to present clinical classifications, a language to describe the most critical features of seizure dynamics, and a framework to guide future research focused on dynamical properties.
Seizures are a disruption of normal brain activity present across a vast range of species and conditions. We introduce an organizing principle that leads to the first objective Taxonomy of Seizure Dynamics (TSD) based on bifurcation theory. The ‘dynamotype’ of a seizure is the dynamic composition that defines its observable characteristics, including how it starts, evolves and ends. Analyzing over 2000 focal-onset seizures from multiple centers, we find evidence of all 16 dynamotypes predicted in TSD. We demonstrate that patients’ dynamotypes evolve during their lifetime and display complex but systematic variations including hierarchy (certain types are more common), non-bijectivity (a patient may display multiple types) and pairing preference (multiple types may occur during one seizure). TSD provides a way to stratify patients in complement to present clinical classifications, a language to describe the most critical features of seizure dynamics, and a framework to guide future research focused on dynamical properties.
The electroencephalography (EEG) is a way to study the individual’s electrical activity of the brain. It is non-invasive technique to analyze brain signals which help to identify that either signals are showing normal or abnormal activity of the brain i.e. Different emotional states and mental diseases. The signals of EEG are non-stationary means the frequency of signals changes over time. To study these non-stationary signals, wavelet transform is used to classify the EEG segment for seven different subjects. In the proposed work, three-dimensional global wavelet spectrum (GWS) are applied on seven EEG datasets to compare the results of different mental states of a person.
Keywords: EEG, global wavelet spectrum
The electroencephalography (EEG) is a way to study the individual’s electrical activity of the brain. It is non-invasive technique to analyze brain signals which help to identify that either signals are showing normal or abnormal activity of the brain i.e. Different emotional states and mental diseases. The signals of EEG are non-stationary means the frequency of signals changes over time. To study these non-stationary signals, wavelet transform is used to classify EEG segment for seven different subjects. In the proposed work, three dimensional global wavelet spectrum (GWS) are applied on seven EEG datasets to compare the results of different mental states of a person.
Objectives
This study elucidated the temporal recurrence patterns of syncope in patients with frequent vasovagal syncope (VVS).
Background
Understanding the temporal distribution of fainting spells in syncope patients may illuminate biological processes and inform decision making.
Methods
Patients from the POST 2 (Prevention of Syncope Trial 2) were included; all had VVS and fainted ≥4 times in the study year, providing ≥3 interevent intervals (IEIs). Only fainting spells separated by ≥1 day were included. IEI distributions were analyzed using Poisson modeling and cumulative sum distributions.
Results
Twenty-four patients (5 males, 19 females; mean 33 years of age) had a total of 286 syncopal events and 262 IEIs, with a median 6 IEI. They resembled excluded subjects in age and sex but fainted more often in their lives (median: 57 vs. 13 fainting spells, respectively; p < 0.0001) and in the previous year (median: 23 vs. 3 fainting spells, respectively; p < 0.0001). Subjects had a median IEI duration of 8 (interquartile range: 4 to 19) days. The IEI distributions were fit well by Poisson models with a median r² of 0.94 (95% confidence interval: 0.91 to 0.97). The patients’ Poisson rate constant frequencies were 7 to 263 fainting spells/year with a median rate of 19 fainting spells/year. The modal syncope frequency was 10 to 15 fainting spells per year. Seven patients had biexponential distributions, and many patients fainted in clusters.
Conclusions
Patients with frequent VVS have fainting spells that occur randomly in time. Clusters of syncope occur, and in this population, there is a central tendency to 10 to 15 fainting spells per year. This provides a quantitative measure of frequency and predictability that may afford individualized treatment goals.
Epileptic seizure prediction has steadily evolved from its conception in the 1970s, to proof-of-principle experiments in the late 1980s and 1990s, to its current place as an area of vigorous, clinical and laboratory investigation. As a step toward practical implementation of this technology in humans, we present an individualized method for selecting electroencephalogram (EEG) features and electrode locations for seizure prediction focused on precursors that occur within ten minutes of electrographic seizure onset. This method applies an intelligent genetic search process to EEG signals simultaneously collected from multiple intracranial electrode contacts and multiple quantitative features derived from these signals. The algorithm is trained on a series of baseline and preseizure records and then validated on other, previously unseen data using split sample validation techniques. The performance of this method is demonstrated on multiday recordings obtained from four patients implanted with intracranial electrodes during evaluation for epilepsy surgery. An average probability of prediction (or block sensitivity) of 62.5% was achieved in this group, with an average block false positive (FP) rate of 0.2775 FP predictions/h, corresponding to 90.47% specificity. These findings are presented as an example of a method for training, testing and validating a seizure prediction system on data from individual patients. Given the heterogeneity of epilepsy, it is likely that methods of this type will be required to configure intelligent devices for treating epilepsy to each individual's neurophysiology prior to clinical deployment.
Electroencephalogram is a pathological phenomena that has chaotic properties and characterized as a nearly random signal as the neurons are theoretically highly non linear. The non-linear analysis method is effectively applied to electroencephalogram signals to study the dynamics of the complex underlying behavior. Analyzing EEG signals with the aid of nonlinear dynamics takes the advantage of requiring much lower quantity of data. The objective of our research is to analyze the acquired EEG signals for non linearity by applying signal processing tools and use the non linear features for design of CAD system to classify epileptic seizures. To ensure the soundness of the proposed method and the suitability of the selected parameters, exhaustive statistical analysis of the descriptor components was performed. Highest classification accuracy of 98.4% was obtained with MLPNN classifier with high sensitivity and specificity followed by SVM and KNN classifiers. The promising performances observed are demonstrative of the efficiency and efficacy of systems developed for classification and prediction of normal and ictal conditions of epileptic patients.
One of the most important risk factors for seizure recurrence is the electroencephalogram (EEG) characteristics of children with a first unprovoked seizure. However, the nature of the relationship between the risk factors for subsequent epilepsy and EEG characteristics, especially the localization of EEG paroxysmal abnormalities (PAs), remains unclear. The importance of EEG characteristics, especially the localizations of PAs, as predictors for subsequent epilepsy in children with a first unprovoked seizure was investigated. The participants were recruited from University of Yamanashi Hospital between July 1, 1997 and June 30, 2010 and followed until December 31, 2014. Eligible candidates were children between 1 month and 15 years old who presented with their first unprovoked non-febrile seizure. Awake and sleep EEGs were performed on a 12- or 16-channel machine 7-20 days after a first unprovoked seizure. Agreement regarding the presence of a PA was required for inclusion of the patient in the study. EEG PAs were classified based on the presence of spikes, sharp waves, or spike-wave complexes, whether focal or generalized, that were considered abnormal for age and state. All subjects were followed for more than 4 years. Of 87 subjects, 48 (55.2%) experienced recurrence. On the other hand, of 87 subjects, 52 (59.8%) showed an EEG PA. Of 18 patients with paroxysms in the frontal region, 17 (94.4%) developed epilepsy. Patients with frontal EEG paroxysms had a significantly higher risk of developing epilepsy than those with focal paroxysms in other regions of EEG foci (p<0.05). Moreover, compared with generalized EEG foci, the odds ratios for patients with frontal, RD, occipital, and mid-temporal EEG foci were 85.0 (95% CI: 4.5-1617.1), 9.3 (0.9-96.0), 2.5 (0.1-62.6), and 7.5 (0.5-122.7), respectively. Children with a first unprovoked seizure presenting with frontal paroxysmal EEG abnormalities may be at risk for the development of epilepsy later in life.
IntroductionComputational Models in Epilepsy ResearchMeasuring Interactions in Epileptic NetworksConclusion
References
We propose a novel approach for detecting precursors to epileptic seizures in intracranial electroencephalograms (iEEGs), which is based on the analysis of system dynamics. In the proposed scheme, the largest Lyapunov exponent (LLE) of wavelet entropy of the segmented EEG signals are considered as the discriminating features. Such features are processed by a support vector machine classifier, whose outcomes (the label and its probability for each LLE) are post-processed and fed into a novel decision function to determine whether the corresponding segment of the EEG signal contains a precursor to an epileptic seizure. The proposed scheme is applied to the Freiburg data set, and the results show that seizure precursors are detected in a time frame that unlike other existing schemes is very much convenient to patients, with the sensitivity of 100% and negligible false positive detection rates.
The pattern of epileptic seizures is often considered unpredictable and the interval between events without correlation. A number of studies have examined the possibility that seizure activity respects a power-law relationship, both in terms of event magnitude and inter-event intervals. Such relationships are found in a variety of natural and man-made systems, such as earthquakes or Internet traffic, and describe the relationship between the magnitude of an event and the number of events. We postulated that human inter-seizure intervals would follow a power-law relationship, and furthermore that evidence for the existence of a long-memory process could be established in this relationship. We performed a post hoc analysis, studying eight patients who had long-term (up to 2 years) ambulatory intracranial EEG data recorded as part of the assessment of a novel seizure prediction device. We demonstrated that a power-law relationship could be established in these patients (β = − 1.5). In five out of the six subjects whose data were sufficiently stationary for analysis, we found evidence of long memory between epileptic events. This memory spans time scales from 30 min to 40 days. The estimated Hurst exponents range from 0.51 to 0.77 ± 0.01. This finding may provide evidence of phase-transitions underlying the dynamics of epilepsy.
Epilepsy is a dynamical disorder of the brain. The existence of an epileptogenic focus that progressively entrains normal brain areas results in transitions of the brain from chaotic to less chaotic spatiotemporal states, the epileptic seizures. Measures of chaos of the electrical activity (EEG) of the brain (e.g., Lyapunov exponents) can be used to quantify this entrainment. Using optimization theory, in particular quadratic integer programming, we were able to select the brain sites that are entrained to each other and subsequently follow their entrainment over long time periods in one patient with 24 seizures. This procedure, which is applied to epilepsy research for the first time, resulted in the identification of the epileptogenic focus and showed the possibility of prediction of epileptic seizures well in advance of their occurrence.
Epilepsy is a common neurological disorder characterized by recurrent seizures, most of which appear to occur spontaneously as a result of complex dynamical interactions among many regions of the brain. The most common type of epilepsy in adults is temporal lobe epilepsy. Employment of nonlinear dynamics techniques, based on the chaos theory, led us to the hypotheses that (1) seizures are a transition from spatiotemporal chaos to a more ordered ictal (symptomatic) state, (2) during the interictal (asymptomatic) state, the epileptogenic focus is dynamically isolated from other areas of the cerebral hemispheres, (3) the seizure discharge can occur only after a preictal transition state during which the focus starts to interact with other cortical areas (preictal state), and (4) the seizure serves to reset the brain, reversing the pathological interaction among critical cortical sites, thus dynamically isolating the seizure onset zone.
Through the analysis of long-term intracranial EEG recordings obtained in patients with medically intractable seizures, we observed: (1) drop in values of a dynamical measure (STL
max
) during the seizure, indicating increased temporal order of the EEG signal — hypothesis 1, (2) convergence of STL
max
values among almost all electrode pairs, indicating increased spatial order — hypothesis 1, (3) generally higher values of T index (divergent values of STL
max
) during the interictal state when the epileptogenic focus is compared to other sites — hypothesis 2, (4) the average differences in STL
max
values between the epileptogenic hippocampus and most other sites is typically reduced (low T-index values, “dynamical entrainment”) prior to each seizure — hypothesis 3, and (5) a divergence of STL
max
(increase in the T-index) between the epileptogenic hippocampus and other cortical sites after each seizure — hypothesis 4. These observations support our hypotheses regarding the preictal transitions in temporal lobe epilepsy. We anticipate that these observations will lead to a better understanding of the physiological processes involved in temporal lobe epilepsy.
About one percent of the people in the world suffer from epilepsy and 30% of epileptics are not helped by medication. Careful analyses of the EEG signals can provide valuable insight and improved understanding of the mechanisms causing epileptic disorders and helps in identifying epilepsy seizures. Manual analysis of the EEG signals for detection epilepsy is very time consuming, hence researchers are looking towards automatic detection of epilepsy seizures from EEG signals recordings. This paper proposed a Multi-Wavelet based epilepsy seizure detection using ANN as a classifier. The proposed technique is implemented, tested and compared with existing methods based on performance indices such as sensitivity, specificity, accuracy parameters, normal and epilepsy seizures signals were classified with an accuracy of 90%.
Epilepsy is one of the most serious neurological diseases, second only to stroke, with a prevalence of approximately 1% of the world's population. Electroencephalogram (EEG), a summation of electrical activities generated by cortical neurons, was first recorded in 1924 by Hans Berger. Over the past decades, many researchers found that epileptic EEG is very different from that of normal people. As a result, the unique information in epileptic EEG is of significance in diagnosis of epilepsy and epileptic seizure prediction. Therefore, the purpose of this review is to illustrate the most recent and significant patents related to epileptic EEG processing including artifacts removal, epileptic events detection and seizure prediction. Finally, the manuscript points out the potential for future development in the field.
Feature extraction and classification of electro physiological signals is an important issue in development of disease diagnostic expert system (DOES). Classification of electroencephalo gram (EEGs) signals (normal and abnormal) is still a challenge for engineers and scientists. Various signal processing techniques have already been proposed to solve this puzzle of classification of non linear signals like EEG. In this work, attempts have been taken to distinguish between normal, epileptic and non-epileptic EEG waves by use of Support Vector Machine (SVM). EEG signals from (healthy subject with eye open condition, healthy subject with eye close condition, signal from hippocampus region and signal from opposite to epileptogenic region and signal with seizure) were considered for the analysis. The signals were processed by using wavelet-chaos techniques. The nonlinear dynamics of the original EEGs are quantified in the form of the correlation dimension (CD, representing system complexity) and the largest Lyapunov exponent (LLE, representing system chaoticity), Capacitive Dimension (CAD) which show the randomness nature of the signal. SVM classifier applied on the extracted feature vectors for the classification purpose. From the results, it was clearly found that the classification accuracy was significantly higher i.e. more than ninety percentage. Hence the techniques can be implemented to design knowledge based expert disease diagnostic system.
Many brain disorders are diagnosed by analysing the EEG signals. EEG refers to the recording of the brain's spontaneous electrical activity over a short period of time. In this paper an efficient approach for detecting the presence of epileptic seizures in EEG signals is presented. Epilepsy is a disease due to temporary alternation in brain functions due to abnormal electrical activity of a group of brain cells and is termed as seizure. The analysis is performed in three stages. In the first step the Discrete wavelet transform is used for decompose the EEG signal into delta, theta, alpha, beta and gamma subbands. In the second step the statistical features are extracted from each subband and finally classification of the EEG signal that is epileptic seizure exists or not has been done using support vector machine. This method is applied for two different groups of EEG signals: 1) healthy (Normal) EEG dataset; 2) epileptic dataset during a seizure interval .The experimental results show that the proposed method efficiently detects the presence of epileptic seizure in EEG signals and also showed a reasonable accuracy in detection.
Signals generated by chaotic systems represent a potentially rich class of signals both for detecting and characterizing physical phenomena and in synthesizing new classes of signals for communications, remote sensing, and a variety of other signal processing applications. Since classical techniques for signal analysis do not exploit the particular structure of chaotic signals there is both a significant challenge and an opportunity in exploring new classes of algorithms matched to chaotic signals. The authors outline a variety of signal processing issues associated with the analysis and synthesis of chaotic signals. In addition two examples are described in detail, illustrating some possible ways in which the characteristics of chaotic signals and systems can be exploited. One example is a binary signaling scheme using chaotic signals. The second example is the use of synchronized chaotic systems for signal masking and recovery.
Electrocorticograms (ECoG's) from 16 of 68 chronically implanted subdural electrodes, placed over the right temporal cortex in a patient with a right medial temporal focus, were analyzed using methods from nonlinear dynamics. A time series provides information about a large number of pertinent variables, which may be used to explore and characterize the system's dynamics. These variables and their evolution in time produce the phase portrait of the system. The phase spaces for each of 16 electrodes were constructed and from these the largest average Lyapunov exponents (L's), measures of chaoticity of the system (the larger the L, the more chaotic the system is), were estimated over time for every electrode before, in and after the epileptic seizure for three seizures of the same patient. The start of the seizure corresponds to a simultaneous drop in L values obtained at the electrodes nearest the focus. L values for the rest of the electrodes follow. The mean values of L for all electrodes in the postictal state are larger than the ones in the preictal state, denoting a more chaotic state postictally. The lowest values of L occur during the seizure but they are still positive denoting the presence of a chaotic attractor. Based on the procedure for the estimation of L we were able to develop a methodology for detecting prominent spikes in the ECoG. These measures (L*) calculated over a period of time (10 minutes before to 10 minutes after the seizure outburst) revealed a remarkable coherence of the abrupt transient drops of L* for the electrodes that showed the initial ictal onset. The L* values for the electrodes away from the focus exhibited less abrupt transient drops. These results indicate that the largest average Lyapunov exponent L can be useful in seizure detection as well as a discriminatory factor for focus localization in multielectrode analysis.
A method of analysis for the extraction of inherent deterministic dependencies in a time series, recently developed by Savit and Green, is applied for the first time to EEG data. The defined indices d m () measure, within an uncertainty , the extent to which the i th element in a time series is a deterministic function of the j th element, with m = i-j. The estimation of these indices is based on conditional probabilities among the vectors in the phase space, a space that is reconstructed from the original time series with the method of delays. The required conditional probabilities are derived from the search for substrings of data of similar structure over the entire phase space. Therefore, the d m indices indicate global averages of the existing dependencies in a time series. The method has been proven very successful in detecting deterministic dependencies in the chaotic regime in a number of mathematical examples including the logistic, tent, and Henon maps, as well as the Lo...
In a long needed paper, R. T. Lacoss (1971) has presented many examples of spectra obtained by the maximum likelihood method and by the maximum entropy method and has shown that these newer techniques are in general superior to the more conventional spectral analysis methods. This short note shows that there exists a simple, exact relationship between maximum entropy spectra and maximum likelihood spectra when the correlation function is known at uniform intervals of lag. The data are of this form in almost all practical cases of time series analysis as well as in the special case of wavenumber spectral analysis of wave propagation as seen by a linear array of equally spaced sensors. The wavenumber case will be explicitly considered in this note since it requires the complex variable form of the theory.
• The analysis of the results of many well-designed, double-blind trials of anticonvulsant drugs has been unsophisticated. We draw attention to the nonrandom occurrence of seizures, which negates the simple comparison of average seizure frequency. We propose a method of taking into account clustering of seizures when deciding on the appropriate length of follow-up after introducing a new treatment. Deterministic and nondeterministic models were used to show why there may be reasons for sometimes using more than one drug in the treatment of epilepsy.
Burg (1972) established an analytical relationship between maximum entropy and maximum likelihood spectral density estimates. If SE(f,j), j = 0, 1,… M − 1 and M successive maximum entropy spectral density estimates at frequency f, then the M‐length maximum likelihood spectral density estimate SL(f,M) is given by 1SL(f,M)=1M∑j=0M-11SE(f,j). (1) The maximum entropy estimates are made via Burg's well‐known formula,SE(f,N)=PNΔt∑k=0NγkNe-i2πfkΔt2, (2) where γkN, k = 0, 1,…,N are the coefficients of the N‐length prediction‐error filter, PN is its error power, and Δt is the sample interval. These estimates can be recursively calculated as shown by Burg (Smylie et al, 1973).
Chaos poses a significant challenge for the time series analyst, since structure in strange attractors tends to be very intricate and nonuniform. Although frequently referred to as unpredictable deterministic behavior, chaotic systems can in fact be forecast over limited time scales. Techniques for constructing predictive models for chaotic dynamics are discussed, including a variety of functional interpolation schemes and several examples of connectionist approaches to the problem. Error estimates based on polynomial interpolation are provided. The underlying deterministic nature of chaotic signals motivates a nonlinear smoothing procedure for the reduction of noise.
There are two ways to perfectly shuffle a deck of 2n cards. Both methods cut the deck in half and interlace perfectly. The out shuffle O leaves the original top card on top. The in shuffle I leaves the original top card second from the top. Applications to the design of computer networks and card tricks are reviewed. The main result is the determination of the group 〈 I, O 〉 generated by the two shuffles, for all n. If 2n is not a power of 2, and if 2n ≠ 12,24, then 〈 I, O 〉 has index 1, 2, or 4 in the Weyl group Bn (the group of all 2nn! signed n × n permutation matrices). If 2n = 2k, then 〈 I, O 〉 is isomorphic to a semi-direct product of Z2k and Zk. When 2n = 24, 〈 I, O 〉 is isomorphic to a semi-direct product of Z211 and M12, the Mathieu group of degree 12. When 2n = 12, 〈 I, O 〉 is isomorphic to a semi-direct product of Z26 and the group PGL(2,5) of all linear fractional transformations over GF(5).
Experiments on nonlinear electrical oscillators, the Belousov-Zhabotinskii reaction, Rayleigh-Bénard convection, and Couette-Taylor flow have revealed several common routes to chaos that have also been found in numerical studies of models with a few degrees of freedom. Experimental results are presented illustrating the following transition sequences; period doubling and the U-sequence, intermittency, the periodic-quasiperiodic-chaotic sequence, frequency locking, and an alternating periodic-chaotic sequence.
A semipopular account of the universal scaling theory for the period doubling route to chaos is presented.
The invariant measures of maximal metric entropy are constructed explicitly for some maps of the interval, by iterating the maps backward. The construction illustrates in a particularly clear way the information flow in simple systems, as well as recently conjectured relationships between dimensions of invariant measures, Lyapunov exponents, and entropies. maps, it is conjectured that the natural measure is the invariant measure with strongest mixing.
We present a new method for analyzing time series which is designed to extract inherent deterministic dependencies in the series. The method is particularly suited to series with broad-band spectra such as chaotic series with or without noise. We derive quantities, δj(ε), based on conditional probabilities, whose magnitude, roughly speaking, is an indicator of the extent to which the kth element in the series is a deterministic function of the (k - j)th element to within a measurement uncertainty, ε. We apply our method to a number of deterministic time series generated by chaotic processes such as the tent, logistic and Hénon maps, as well as to sequences of quasi-random numbers. In all cases the δj correctly indicate the expected dependencies. We also show that the δj are robust to the addition of substantial noise in a deterministic process. In addition, we derive a predictability index which is a measure of the extent to which a time series is predictable given some tolerance, ε. Finally, we discuss the behavior of the δi as ε approaches zero.
In this paper we continue our development of new methods for the analysis of broad band time series by deriving quantities which are able to indicate deterministic dependence of an element in one time series on elements in other time series. These methods are very broadly applicable and are particularly well suited to the study of continuous time series, in which the value of the function may depend on derivatives of the function itself, or on other quantities. We apply our methods to a number of mathematical examples including the Lorentz equation, the Hénon-Heiles equations, the forced Brusselator and the Mackey-Glass equation. We show that our methods are very successful at indicating deterministic dependencies in these systems, even if the time series are highly chaotic. Statistical aspects of our procedure are discussed, as are a number of interesting and surprising epistomological implications.
We derive a normalized version of the indicators of Savit and Green, and prove that these normalized statistics have, asymptotically, a normal distribution with a mean of zero and standard deviation of one if the time series is random in the sense of being IID (independent and identically distributed). We verify this result numerically, and study the magnitude of the finite size effects. We also show that these statistics are very sensitive to the existence of deterministic effects in the series, even if the underlying deterministic structure is complex, such as those generated by a chaotic system. We show that with moderate amounts of data, the statistics can easily indicate the presence of an underlying attractor even in the presence of IID noise which is as large as, or greater than the signal. Finally, we discuss the generalization of our approach to include (1) other null hypotheses besides IID which express assumptions of specific dependencies and (2) the study of deterministic effects between more than one time series.
We study the correlation exponent v introduced recently as a characteristic measure of strange attractors which allows one to distinguish between deterministic chaos and random noise. The exponent v is closely related to the fractal dimension and the information dimension, but its computation is considerably easier. Its usefulness in characterizing experimental data which stem from very high dimensional systems is stressed. Algorithms for extracting v from the time series of a single variable are proposed. The relations between the various measures of strange attractors and between them and the Lyapunov exponents are discussed. It is shown that the conjecture of Kaplan and Yorke for the dimension gives an upper bound for v. Various examples of finite and infinite dimensional systems are treated, both numerically and analytically.
We describe a statistical approach for identifying nonlinearity in time series. The method first specifies some linear process as a null hypothesis, then generates surrogate data sets which are consistent with this null hypothesis, and finally computes a discriminating statistic for the original and for each of the surrogate data sets. If the value computed for the original data is significantly different than the ensemble of values computed for the surrogate data, then the null hypothesis is rejected and nonlinearity is detected. We discuss various null hypotheses and discriminating statistics. The method is demonstrated for numerical data generated by known chaotic systems, and applied to a number of experimental time series which arise in the measurement of superfluids, brain waves, and sunspots; we evaluate the statistical significance of the evidence for nonlinear structure in each case, and illustrate aspects of the data which this approach identifies.
This paper gives an exposition of linear prediction in the analysis of discrete signals. The signal is modeled as a linear combination of its past values and present and past values of a hypothetical input to a system whose output is the given signal. In the frequency domain, this is equivalent to modeling the signal spectrum by a pole-zero spectrum. The major part of the paper is devoted to all-pole models. The model parameters are obtained by a least squares analysis in the time domain. Two methods result, depending on whether the signal is assumed to be stationary or nonstationary. The same results are then derived in the frequency domain. The resulting spectral matching formulation allows for the modeling of selected portions of a spectrum, for arbitrary spectral shaping in the frequency domain, and for the modeling of continuous as well as discrete spectra. This also leads to a discussion of the advantages and disadvantages of the least squares error criterion. A spectral interpretation is given t
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We examined the seizure records of 13 patients (nine men and four women, ages 27-50 years) with intractable partial epilepsy, maintained with steady anti-epileptic drug dosages. Patients recorded daily seizure frequency on calendars. Periods of outpatient observation ranged from 99 to 1,710 days and the number of observed seizures ranged from 18 to over 400, with daily seizure rates of 0.1-4.3 per day. We used the quasi-likelihood regression model to examine the following four departures of the daily seizure counts from a Poisson (random) model: (1) linear increasing or decreasing time trends in expected seizure rates; (2) clustering, where the expected seizure rate on a given day depends on the number of seizures observed on the immediate prior days; (3) monthly cyclicity; and (4) increased variability (overdispersion). Linear time trends were seen in six patients (four increasing and two decreasing), clustering was seen in 10 patients, and a near-monthly cycle appeared in four patients (two of nine men and two of four women). A significant amount of extra variation (overdispersion) relative to a Poisson distribution was observed in all but one of the 13 patients. Departures from a Poisson (random) model appear more common in this population of patients with medically intractable epilepsy than is commonly recognized, and have clinical importance as well as implications for the design of clinical studies.
Seizure diaries were maintained prospectively in 24 epileptic patients (19 with partial complex, three with partial simple, and three with primary generalized seizures) who were selected consecutively, had stable seizure patterns, were reliable historians, and were known to be compliant with medications. Diaries were maintained for an average of 237 days (range, 61–365), and an average of 18 seizures were recorded per patient (range, 5–76). Seizure patterns were analyzed by using the methods appropriate for a time series of events (point process). Two patients had a decreasing trend in seizure frequency. For 12 patients, seizure occurrence was indistinguishable from that of a Poisson process. The remaining 10 patients had an exponential distribution of seizure intervals, but did not fit other criteria for a Poisson process; 3 of these showed evidence for seizure clustering; none showed evidence for a seizure cycle. It is concluded that the pattern of seizure occurrence in most epileptic people is random, but in approximately 50%, it is not occurring according to a Poisson process. These observations indicate that seizure cycling and/or clustering are not common in epileptic patients, but do not exclude the possibility that seizures have been precipitated by some randomly occurring event, such as sleep deprivation or increased stress.
RÉSUMÉ
Un relevé quotidien des crises a été effectué de façon prospective chez 24 patients épileptiques (19 présentant des crises par‐tielles complexes, 3 des crises partielles élémentaires et 3 des crises généralisées). Ces patients ont été sélectionnés consécu‐tivement, ont été jugés fiables dans le relevé des crises et dans l'observance thérapeutique. Les relevés ont été effectués pendant une moyenne de 237 jours (61 à 365) et une moyenne de 18 crises par patient a été enregistrde (de 5 à 76). La distribution des crises a étéétudiée par les moyens adaptés aux phénomènes répétés dans le temps. Chez 2 patients nous avons constaté une tendance à l'espacement des crises. Chez 12 patients, la fréquence des crises n'a pas été différente d'une répartition suivant la loi de Poisson. Les 10 patients restants présentaient une distribution exponentielle des intervalles entre les crises mais ne rgpondaient pas aux autres critères de la loi de Poisson. 3 d'entre eux présentaient des crises en séries; aucun ne présentait de cyclicité des crises. Nous concluons que la distribution des crises est, chez la plupart des patients, le fait du hasard, mais que, chez environ 50% des patients, cette répartition ne suit pas une loi de Poisson. Ces observations indiquent qu'une distribution cy‐clique ou en série des crises n'est pas fréquente chez les épilep‐tiques, mais n'excluent pas la possibilityé que les crises peuvent avoir été provoquées par quelque évènement survenant au hasard, comme un manque de sommeil ou un stress particulier.
RESUMEN
Se nan elaborado diarios con respecto al número de ataques, de modo prospectivo, en 24 enfermos epilépticos (19 con ataques complejos parciales, 3 con ataques simples parciales y 3 con ataques generalizados primarios) que se seleccionaron con‐secutivamente; Tenfan patrones de ataques estables, eran histor‐iadores Cables y eran conocidos por su nivel de confianza en la administration de medicamentos. Los diarios se mantuvieron durante un promedio de 237 días (rango de 61 a 365) registrán‐dose un promedio de 18 ataques por paciente (rango de 5 a 76). Los patrones de los ataques fueron analizados utilizando meto‐dología apropiada para la serie de acontecimientos en el tiempo (proceso puntual). Dos pacientes mostraron una reducción de la tendencia a la frecuentia de ataques. En 12 pacientes la aparición de los episodios fue indistinguible de la del proceso de Poisson. Los restantes 10 pacientes tenian una distribución exponential de los intervalos de ataques pero no encajó en otros criterios para un proceso Poisson; 3 de ellos mostraron evi‐dencia de “ataques acumulados”. Ninguno presentó un ciclo de ataques. Se concluye que el partón aparición de ataques en la mayor parte de las personas epilépticas es aleatorio pero que en, aproximadamente el 50%, no ocurre de acuerdo con un procese Poisson. Estas observaciones indican que los ciclos de los ataques y/o su “acumulo” no son comunes en enfermos epilép‐ticos pero no excluyen la posibilidad de que los ataques hayan sido precipitados por un acontecimiento que ocurra aleatoria‐ mente tales como la privacyón del sueno o el incremenlo de stress.
The analysis of the results of many well-designed, double-blind trials of anticonvulsant drugs has been unsophisticated. We draw attention to the nonrandom occurrence of seizures, which negates the simple comparison of average seizure frequency. We propose a method of taking into account clustering of seizures when deciding on the appropriate length of follow-up after introducing a new treatment. Deterministic and nondeterministic models were used to show why there may be reasons for sometimes using more than one drug in the treatment of epilepsy.
The time relations of epileptic events have been studied in 3 sets of data: (I) counts of individual epileptiform discharges in twelve 48 h EEG recordings, (IIa) seizure calendars of 30 therapy-resistant outpatients participating in a drug trial, (IIb) seizure calendars of 10 mentally subnormal epileptic patients resident in a long-stay unit. The EEG data I were characterized most often by a Poisson distribution of intervals between discharges and the occurrence of marked periodicities, particularly at night. The periods of rhythmic nocturnal events ranged from 13 to 142 min and did not appear to correspond to the REM/non-REM cycle. In the seizure data IIa and b a Poisson distribution of intervals between events was found in half the patients. Periodicities occurred only in group IIa and did not correspond to weekly or monthly cycles. A stochastic process is considered to be the model which best fits these data.
This tutorial presents an in-depth introduction to chaos in dynamical systems, and presents several practical techniques for recognizing and classifying chaotic behavior. These techniques include the poincaré map, Lyapunov exponents, capacity, information dimension, correlation dimension, Lyapunov dimension, and the reconstruction of attractors from a single time series.
A summary of many of the new techniques developed in the last two decades for spectrum analysis of discrete time series is presented in this tutorial. An examination of the underlying time series model assumed by each technique serves as the common basis for understanding the differences among the various spectrum analysis approaches. Techniques discussed include the classical periodogram, classical Blackman-Tukey, autoregressive (maximum entropy), moving average, autotegressive-moving average, maximum likelihood, Prony, and Pisarenko methods. A summary table in the text provides a concise overview for all methods, including key references and appropriate equations for computation of each spectral estimate.
The topic of this presentation is the investigation of the epileptic human brain as a nonlinear system that undergoes a phase transition (epileptic seizure). The estimated values of the largest Lyapunov exponent L over time indicated a more chaotic state postictally than ictally or preictally. The start of a seizure corresponds to a simultaneous drop in the values of L at the focal electrode sites. The observed slow cyclic variations in the temporal Lyapunov profiles imply attempts of the system to undergo a phase transition minutes before the seizure's onset. The analysis of the maximum rate of entropy production over space revealed an initial phase difference of minutes preictally at the sites overlying the seizure focus, which progressed to phase locking with a slow entrainment of the rest of the cortical sites shortly before the onset of a seizure. It is also conjectured that the abnormal spiking electrical activity of the brain plays a major role in the unfolding of the phenomeno...
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