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Stochastic Modeling and Prediction of Experimental Seizures in Sprague‐Dawley Rats
Abstract
Most seizure prediction methods are based on nonlinear dynamic techniques, which are highly computationally expensive, thus limiting their clinical usefulness. The authors propose a different approach for prediction that uses a stochastic Markov chain model. Seizure (Ts) and interictal (Ti) durations were measured from 11 rats treated with 3-mercaptopropionic acid. The duration of a seizure Ts was used to predict the time (Ti2) to the next one. Ts and Ti were distributed bimodally into short (S) and long (L), generating four probable transitions: S --> S, S --> L, L --> S, and L --> L. The joint probability density f (Ts, Ti2) was modeled, and was used to predict Ti2 given Ts. An identical model predicted Ts given the duration Ti1 of the preceding interictal interval. The median prediction error was 3.0 +/- 3.5 seconds for Ts (given Ti1) and 6.5 +/- 2.0 seconds for Ti2 (given Ts). In comparison, ranges for observed values were 2.3 seconds < Ts < 120 seconds and 6.6 seconds < Ti < 782 seconds. These results suggest that stochastic models are potentially useful tools for the prediction of seizures. Further investigation of the probable temporal interdependence between the ictal and interictal states may provide valuable insight into the dynamics of the epileptic brain.
... Since any endogenous and exogenous factors initiating the seizure are usually encountered randomly, to account for all factors related to seizure transition, a stochastic model seems to be appropriate. As we know, there are many stochastic models of seizure occurrence that do not take the physiological parameters into account (Hopkins et al. 1985; Milton et al. 1987; Albert 1991; Taubøll et al. 1991; Sunderam et al. 2001 Sunderam et al. , 2007 Franks et al. 2002; Suffczynski et al. 2006; Wong et al. 2007; Ullah and Wolkenhauer 2007). In fact, since the brain is too complex to consider all its underlying details deterministically , stochastic models have been designed to take some facts that cannot reasonably be modeled into account. ...
... It is not feasible to model the patterns that might lead to this phenomenon deterministically (Lytton 2008). The stochastic models such as exponential models (Milton et al. 1987), Poisson models (Milton et al. 1987; Suffczynski et al. 2006), Monte Carlo models (Franks et al. 2002), Markov models (Albert 1991; Sunderam et al. 2001; Wong et al. 2007) and other models (Hopkins et al. 1985; Taubøll et al. 1991; Sunderam et al. 2007) have been considered to simulate the random seizure genesis process. To our knowledge, the developed stochastic models until now either simulate EEG signals by modeling the stateduration or the sequences of the seizure count, or model brain activity at the cellular scale without attention to neuronal population activity. ...
... To our knowledge, the developed stochastic models until now either simulate EEG signals by modeling the stateduration or the sequences of the seizure count, or model brain activity at the cellular scale without attention to neuronal population activity. For example, in (Sunderam et al. 2001; Suffczynski et al. 2006 ) duration of inter-ictal/preictal/ictal intervals, the seizure counts, or the instances of seizure onset are drawn randomly from a distribution. In (Albert 1991; Sunderam et al. 2001) Markov models have been used to model seizure-occurrence times. ...
By assuming the brain as a multi-stable system, different scenarios have been introduced for transition from normal to epileptic state. But, the path through which this transition occurs is under debate. In this paper a stochastic model for seizure genesis is presented that is consistent with all scenarios: a two-level spontaneous seizure generation model is proposed in which, in its first level the behavior of physiological parameters is modeled with a stochastic process. The focus is on some physiological parameters that are essential in simulating different activities of ElectroEncephaloGram (EEG), i.e., excitatory and inhibitory synaptic gains of neuronal populations. There are many depth-EEG models in which excitatory and inhibitory synaptic gains are the adjustable parameters. Using one of these models at the second level, our proposed seizure generator is complete. The suggested stochastic model of first level is a hidden Markov process whose transition matrices are obtained through analyzing the real parameter sequences of a seizure onset area. These real parameter sequences are estimated from real depth-EEG signals via applying a parameter identification algorithm. In this paper both short-term and long-term validations of the proposed model are done. The long-term synthetic depth-EEG signals simulated by this model can be taken as a suitable tool for comparing different seizure prediction algorithms.
... Clinical investigations have found that seizure occurrence in epileptic patients follow complex patterns, ranging from periodic nature of seizure recurrence to situations when seizures are clustered around a particular time of the day to cases wherein there is no apparent identifiable timing pattern to seizure recurrence [39]. Stochastic models called Markov models and hidden Markov models have been proposed to explain and predict the existence of these complex seizure patterns [7,64,87]. The basic idea is that there are multiple attractor states within the brain. ...
... Based on this assumption, a probabilistic rule is identified that transitions the brain across various attractor states. This modeling approach has found applications for both seizure prediction [64] and also to assess the performance of statistical model based seizure prediction algorithms [87]. ...
Epilepsy is a neurological disease characterized by recurrent and spontaneous
seizures. It affects approximately 50 million people worldwide. In majority of
the cases accurate diagnosis of the disease can be made without using any
technologically advanced techniques and seizures are controlled using standard
treatment in the form of regular use of anti-epileptic drugs. However,
approximately 30% of the patients suffer from medically refractory epilepsy,
wherein seizures are not controlled by the use of anti-epileptic drugs.
Understanding the mechanisms underlying these forms of drug resistant epileptic
seizures and the development of alternative effective treatment strategies is a
fundamental challenge in modern epilepsy research. In this context, the need
for integrative approaches combining various modalities of treatment strategies
is high. Computational modeling has gained prominence in recent years as an
important tool for tackling the complexity of the epileptic phenomenon. In this
review article we present a survey of different computational models for
epilepsy and discuss how computer models can aid in our understanding of brain
mechanisms in epilepsy and the development of new epilepsy treatment protocols.
... The dynamics of the transition from the interictal to the ictal state have been investigated in other in vivo and in vitro animal models. Several investigators have used linear or stochastic methods such as power spectrum, wavelet entropy, and Markov chain modeling in their investigations (Khosravani et al., 2005; Paul et al., 2003; Sunderam et al., 2001). The results of these studies suggested detectable dynamical changes before and during seizures. ...
... In addition, noisy experimental data have limited the yield of analytical methods (Rapp et al., 1989; Lehnertz et al., 2001; Lai et al., 2003; Harrison et al., 2005; Iasemidis et al., 2005). Some studies have shown evidence of a deterministic process involved in the occurrence of epileptic seizures (Iasemidis et al., 1994), whereas other studies have used stochastic modeling to explain seizure occurrences (Sunderam et al., 2001). A qualitative model proposed to explain the results of dynamical investigations of human epilepsy was proposed by Lopes da Silva et al. (2003). ...
Analysis of intracranial electroencephalographic (iEEG) recordings in patients with temporal lobe epilepsy (TLE) has revealed characteristic dynamical features that distinguish the interictal, ictal, and postictal states and inter-state transitions. Experimental investigations into the mechanisms underlying these observations require the use of an animal model. A rat TLE model was used to test for differences in iEEG dynamics between well-defined states and to test specific hypotheses: 1) the short-term maximum Lyapunov exponent (STL(max)), a measure of signal order, is lowest and closest in value among cortical sites during the ictal state, and highest and most divergent during the postictal state; 2) STL(max) values estimated from the stimulated hippocampus are the lowest among all cortical sites; and 3) the transition from the interictal to ictal state is associated with a convergence in STL(max) values among cortical sites. iEEGs were recorded from bilateral frontal cortices and hippocampi. STL(max) and T-index (a measure of convergence/divergence of STL(max) between recorded brain areas) were compared among the four different periods. Statistical tests (ANOVA and multiple comparisons) revealed that ictal STL(max) was lower (p<0.05) than other periods, STL(max) values corresponding to the stimulated hippocampus were lower than those estimated from other cortical regions, and T-index values were highest during the postictal period and lowest during the ictal period. Also, the T-index values corresponding to the preictal period were lower than those during the interictal period (p<0.05). These results indicate that a rat TLE model demonstrates several important dynamical signal characteristics similar to those found in human TLE and support future use of the model to study epileptic state transitions.
... 2. Admission to the hospital is often associated with a decrease in seizure frequency (Riley et al., 1981), and the anesthesia patients receive for intracranial electrode implantation may alter transiently the seizure probability or duration (Boylan et al., 2000;Bruder and Bonnet, 2001). These effects complicate the assessment of the treatment effect if they do not operate uniformly during the CP and the EP. 3. The length of interictal intervals and seizures seems dependent on the duration and intensity of the preceding seizures (Sunderam et al., 2001), complicating the assessment of a treatment effect for any trial that compares stimulated and nonstimulated seizures or a sample of stimulated seizures. 4. The intensity, duration, and degree of spread of seizures varies considerably intraindividually, and clinical seizures often represent a small number of all recorded electrographic activity with ictal organization (subclinical seizures), whose duration and other characteristics are also variable (Osorio et al., unpublished observations). ...
... In this protocol, two sets of comparisons are performed: the first, between treated and untreated seizures during the EP and the second, between the EP and the CP. Not all seizures are treated during the EP because if there is a strong serial correlation in their duration (Sunderam et al., 2001), frequency, or intensity (related to length of hospitalization or discontinuation of antiseizure drugs), then this trend will confound the interpretation of the results. The treatment of every other seizure as opposed, for example, to every third or to every other cluster of three seizures reduces the effect of temporal trends (which may be dependent on the length of the observation periods) by limiting the interval between comparisons. ...
Automated seizure blockage is a top research priority of the American Epilepsy Society. This delivery modality (referred to herein as contingent or closed loop) requires for implementation a seizure detection algorithm for control of delivery of therapy via a suitable device. The authors address the many potential advantages of this modality over conventional alternatives (periodic or continuous), and the challenges it poses in the design and analysis of trials to assess efficacy and safety-in the particular context of direct delivery of electrical stimulation to brain tissue. The experimental designs of closed-loop therapies are currently limited by ethical, technical, medical, and practical considerations. One type of design that has been used successfully in an in-hospital "closed-loop" trial using subjects undergoing epilepsy surgery evaluation as their own controls is discussed in detail. This design performs a two-way comparison of seizure intensity, duration, and extent of spread between the control (surgery evaluation) versus the experimental phase, and, within the experimental phase, between treated versus untreated seizures. The proposed statistical analysis is based on a linear model that accounts for possible circadian effects, changes in treatment protocols, and other important factors such as change in seizure probability. The analysis is illustrated using seizure intensity as one of several possible end points from one of the subjects who participated in this trial. In-hospital ultra-short-term trials to assess safety and efficacy of closed-loop delivery of electrical stimulation for seizure blockage are both feasible and valuable.
... The complexity of these biological phenomena constitutes a major challenge to predict the outcome at the system level. Empirically, the system-level observations (i.e., seizures) can be well captured by a stochastic framework, 8,9 which does not exclude that the underlying dynamics could be perfectly deterministic (high-dimensional chaotic system). The study by Cousyn and colleagues uses clinical prodromal symptoms and conceives of the preictal state as a set of data for which machine learning promises to overcome shortcomings of classical statistics. ...
... At the spatial scale, epileptic models range from protein and membrane level to brain regions [68], whereas at the temporal scale the range is very broad: from millisecond to years. Designing a model that accounts for these spatiotemporal scales can be very hard [69], however, there is a rich repertoire of works showing how static [70,71] and dynamic models can be used to model the emergence of seizure [2,72,73]. Notably, the use of deterministic models of archicortical circuits successfully allowed to reproduce a wide variety of patterns that have been observed in patients [74,75]. ...
The investigation of synaptic functions remains one of the most fascinating challenges in the field of neuroscience and a large number of experimental methods have been tuned to dissect the mechanisms taking part in the neurotransmission process. Furthermore, the understanding of the insights of neurological disorders originating from alterations in neurotransmission often requires the development of (i) animal models of pathologies, (ii) invasive tools and (iii) targeted pharmacological approaches. In the last decades, additional tools to explore neurological diseases have been provided to the scientific community. A wide range of computational models in fact have been developed to explore the alterations of the mechanisms involved in neurotransmission following the emergence of neurological pathologies. Here, we review some of the advancements in the development of computational methods employed to investigate neuronal circuits with a particular focus on the application to the most diffuse neurological disorders.
... Additionally, the proportion of long-duration seizures was identified to be a more sensitive metric and increased with ISI, as compared to average seizure duration. Other studies 6,24,26,27 have utilized alternative approaches to studying the relationship between seizure duration and preceding ISI length. Supporting an association, stochastic models in rodents 27 illustrated that seizure duration can be modeled as a function of the ISI, which was further demonstrated to be a function of the duration of a prior seizure. ...
Objective
A major source of disability for people with epilepsy involves uncertainty surrounding seizure timing and severity. Although patients often report that long seizure‐free intervals are followed by more severe seizures, there is little experimental evidence supporting this observation. Optimal characterization of seizure severity is debated; however, seizure duration is associated with seizure type and can be quantified in electrographic recordings as a limited proxy of clinical seizure severity. Here, using chronic intracranial electroencephalography (cEEG), we investigate the relationship between interseizure interval (ISI) and duration of the subsequent seizure.
Methods
We performed a retrospective analysis of 14 subjects implanted with a responsive neurostimulation device (RNS System) that provides cEEG, including timestamps of electrographic seizures. We determined seizure durations for isolated seizures and for representative seizures from clusters determined through unsupervised methods. For each subject, the median ISI preceding long‐duration seizures, defined as the top quintile of seizure durations, was compared with the median ISI preceding seizures with durations in the residual quintiles. In a group analysis, the mean seizure duration and the proportion of long‐duration seizures were compared across ISI categories representing different lengths.
Results
For 5 out of 14 subjects (36%), the median ISI preceding long‐duration seizures was significantly greater than the median ISI preceding shorter‐duration seizures. In the group analysis, when ISI was categorized by length, the proportion of long‐duration seizures within the high ISI category was significantly higher than that of the low ISI category (P < 0.001).
Significance
By leveraging cEEG and accounting for seizure clusters, we found that the likelihood of long‐duration seizures positively correlates with ISI length, in a subset of individuals. These findings corroborate anecdotal clinical observations and support the existence of capacitor‐like long memory processes governing the dynamics of focal seizures.
... This is not always true. For many drug classes such as antiepileptics, anesthetics, and antiarrhythmics, the response is binary at the level of an individual-the desired effect is either present or not (Lö scher, 2011;Sunderam et al., 2001;Jürgens et al., 2003;Sonner, 2002). The population-based dose-response curve, in contrast, is a smooth graded function of drug concentration. ...
Traditionally, drug dosing is based on a concentration-response relationship estimated in a population. Yet, in specific individuals, decisions based on the population-level effects frequently result in over or under-dosing. Here, we interrogate the relationship between population-based and individual-based responses to anesthetics in mice and zebrafish. The anesthetic state was assessed by quantifying responses to simple stimuli. Individual responses dynamically fluctuated at a fixed drug concentration. These fluctuations exhibited resistance to state transitions. Drug sensitivity varied dramatically across individuals in both species. The amount of noise driving transitions between states, in contrast, was highly conserved in vertebrates separated by 400 million years of evolution. Individual differences in anesthetic sensitivity and stochastic fluctuations in responsiveness complicate the ability to appropriately dose anesthetics to each individual. Identifying the biological substrate of noise, however, may spur novel therapies, assure consistent drug responses, and encourage the shift from population-based to personalized medicine.
... In the 1990s, independent laboratories found indications for the existence of a preictal state from nonlinear EEG analyses several minutes prior to clinical symptoms in patients implanted with intracranial electrodes during evaluation for epilepsy surgery in the temporal lobes (Iasemidis et al., 1990(Iasemidis et al., , 1997Elger andLehnertz, 1994, 1998;Lehnertz and Elger, 1998;Martinerie et al., 1998;Lehnertz et al., 1999;Le Van Quyen et al., 1999b, 2000Moser et al., 1999). These findings were further supported by studies indicating detectability of preictal states in neocortical epilepsies Navarro et al., 2002) and in animal models of epilepsy (Geva and Kerem, 1998;Widman et al., 1999;Lian et al., 2001;Sunderam et al., 2001) as well as by studies demonstrating seizure anticipation from scalp-EEG recordings (Iasemidis et al., 1997;Le Van Quyen et al., 2001a;Protopopescu et al., 2001). More recent studies mostly employing bivariate measures indicate that the duration of a preictal state may extend to several tens of minutes and in some cases even several hours or days (Mormann et al., 2000(Mormann et al., , 2002Iasemidis et al., 2001;Le Van Quyen et al., 2001b;Litt et al., 2001). ...
... Modeling the occurrence times of seizures mainly involves Poisson and Markov models [7,32,143,182,211,343]. In many patients, seizure occurrence times appear to follow a Poisson process, while in others, seizures appear to be clustered and entrained to biologic rhythms, such as menstrual or sleep-wake cycles. ...
IntroductionComputational Models in Epilepsy ResearchMeasuring Interactions in Epileptic NetworksConclusion
References
... In the 1990s, independent laboratories found indications for the existence of a preictal state from nonlinear EEG analyses several minutes prior to clinical symptoms in patients implanted with intracranial electrodes during evaluation for epilepsy surgery in the temporal lobes (Iasemidis et al., 1990(Iasemidis et al., , 1997Elger andLehnertz, 1994, 1998;Lehnertz and Elger, 1998;Martinerie et al., 1998;Lehnertz et al., 1999;Le Van Quyen et al., 1999b, 2000Moser et al., 1999). These findings were further supported by studies indicating detectability of preictal states in neocortical epilepsies Navarro et al., 2002) and in animal models of epilepsy (Geva and Kerem, 1998;Widman et al., 1999;Lian et al., 2001;Sunderam et al., 2001) as well as by studies demonstrating seizure anticipation from scalp-EEG recordings (Iasemidis et al., 1997;Le Van Quyen et al., 2001a;Protopopescu et al., 2001). More recent studies mostly employing bivariate measures indicate that the duration of a preictal state may extend to several tens of minutes and in some cases even several hours or days (Mormann et al., 2000(Mormann et al., , 2002Iasemidis et al., 2001;Le Van Quyen et al., 2001b;Litt et al., 2001). ...
This chapter discusses the prediction of seizure occurrence by chaos analysis. Prediction of seizures is a challenge for both basic research and clinical epileptology. In majority of the patients, seizures strike like a bolt from the blue and this is one of the most disabling aspects of epilepsy. Although numerous studies have explored basic neuronal mechanisms that are likely to be associated with seizures, to date, no definite information is available as to how, when, or why a seizure occurs in humans. With the advent of the physical theory of nonlinear dynamical systems, colloquially often termed chaos theory, new analysis techniques have been developed that allow apparently irregular behavior, a distinctive feature of the electroencephalography (EEG), to be characterized. Lyapunov exponents, entropies, or recent approaches aiming to characterize interdependencies, synchronization, or similarities were shown to reliably characterize the different states of normal and pathological brain function, and promise to be important for clinical practice.
... Based on this assumption, a probabilistic rule is identified that transitions the brain across various attractor states. This modeling approach has found applications in both seizure prediction 74 and in the assessment of statistical model based seizure prediction algorithms. 75 ...
Purpose:
Approximately 30% of epilepsy patients suffer from medically refractory epilepsy, in which seizures can not controlled by the use of anti-epileptic drugs (AEDs). Understanding the mechanisms underlying these forms of drug-resistant epileptic seizures and the development of alternative effective treatment strategies are fundamental challenges for modern epilepsy research. In this context, computational modeling has gained prominence as an important tool for tackling the complexity of the epileptic phenomenon. In this review article, we present a survey of computational models of epilepsy from the point of view that epilepsy is a dynamical brain disease that is primarily characterized by unprovoked spontaneous epileptic seizures.
Method:
We introduce key concepts from the mathematical theory of dynamical systems, such as multi-stability and bifurcations, and explain how these concepts aid in our understanding of the brain mechanisms involved in the emergence of epileptic seizures.
Results:
We present a literature survey of the different computational modeling approaches that are used in the study of epilepsy. Special emphasis is placed on highlighting the fine balance between the degree of model simplification and the extent of biological realism that modelers seek in order to address relevant questions. In this context, we discuss three specific examples from published literature, which exemplify different approaches used for developing computational models of epilepsy. We further explore the potential of recently developed optogenetics tools to provide novel avenue for seizure control.
Conclusion:
We conclude with a discussion on the utility of computational models for the development of new epilepsy treatment protocols.
... In this model the stochastic influence induces transitions between these dynamical states. The authors showed that this type of dynamics leads to a Poisson distribution of interictal and ictal states (see also [111]), which deviated from their findings observed in certain biological systems. They argued that a randomly fluctuating parameter responsible for the state changes would lead to similar results. ...
... The HMM has an advantage over the supervised approaches because it does not require prior manual separation of data into different dynamics. The current approach of detecting seizure events using Markov models involves the estimation of either two (seizure and interictal) [27] or three (baseline, detected and seizure) [28] distinct states. Even though these proposed methods appear to detect seizure onsets, they failed to address the possibility of having multiple distinctive dynamics between non-ictal (interictal) and chronic seizure events, which may be an important aspect for the development of seizure therapy techniques. ...
Epilepsy is a common neurological disorder characterized by recurrent electrophysiological activities, known as seizures. Without the appropriate detection strategies, these seizure episodes can dramatically affect the quality of life for those afflicted. The rationale of this study is to develop an unsupervised algorithm for the detection of seizure states so that it may be implemented along with potential intervention strategies.
Hidden Markov model (HMM) was developed to interpret the state transitions of the in vitro rat hippocampal slice local field potentials (LFPs) during seizure episodes. It can be used to estimate the probability of state transitions and the corresponding characteristics of each state. Wavelet features were clustered and used to differentiate the electrophysiological characteristics at each corresponding HMM states. Using unsupervised training method, the HMM and the clustering parameters were obtained simultaneously. The HMM states were then assigned to the electrophysiological data using expert guided technique. Minimum redundancy maximum relevance (mRMR) analysis and Akaike Information Criterion (AICc) were applied to reduce the effect of over-fitting. The sensitivity, specificity and optimality index of chronic seizure detection were compared for various HMM topologies. The ability of distinguishing early and late tonic firing patterns prior to chronic seizures were also evaluated.
Significant improvement in state detection performance was achieved when additional wavelet coefficient rates of change information were used as features. The final HMM topology obtained using mRMR and AICc was able to detect non-ictal (interictal), early and late tonic firing, chronic seizures and postictal activities. A mean sensitivity of 95.7%, mean specificity of 98.9% and optimality index of 0.995 in the detection of chronic seizures was achieved. The detection of early and late tonic firing was validated with experimental intracellular electrical recordings of seizures.
The HMM implementation of a seizure dynamics detector is an improvement over existing approaches using visual detection and complexity measures. The subjectivity involved in partitioning the observed data prior to training can be eliminated. It can also decipher the probabilities of seizure state transitions using the magnitude and rate of change wavelet information of the LFPs.
... A large body of work over the last two decades has concentrated on prediction and control using nonlinear systems analysis and chaos theory (Babloyantz & Destexhe, 1986;Iasemidis, 2003). The problem of automated real-time prediction of epileptic seizures using electrophysiological recordings has been investigated extensively, yielding a variety of approaches, including neural networks ( Chiu et al., 2005), Markov chain methods ( Sunderam et al., 2001), and nonlinear time series analysis ( Martinerie et al., 1998;Lehnertz & Elger, 1998;Iasemidis et al., 2001). ...
We investigate the application of machine learning methods for the detection and control of seizure-like behavior in in vitro models of epilepsy. This research will form the basis for a new class of adaptive neurostimulation devices for the treatment of drug-resistant cases of epilepsy in humans. There are many technical obstacles to creating an adaptive control algorithm for these devices. At present, science has an incomplete understanding of the mechanisms and dynamics underlying both epilepsy and its treatments. This is reflected both in the long-standing problem of the detection or prediction of seizures and in the lack of clear criteria for optimizing an adaptive control algorithm. As in many medical problems, clinical data is sparse, expensive, and highly variable. We address the detection of epileptic states using boosted ensemble methods with a set of simple frequency spectrum features derived from electrophysiological recordings. While typical boosting methods are not designed for use with time series data, we present a recurrent boosting method that improves classification accuracy in our application domain. We also present an implementation of a biologically plausible model of epileptic neural tissue using a network of integrate and fire neurons with partially stochastic inputs and two time scales of refractory behavior. Finally, we train a reinforcement learning agent to control the dynamics of this network, reducing the occurrence of seizure-like events. This agent is intended to be a component of a closed-loop electrical stimulation device with a set of sensors and an adaptive stimulation strategy. Nous étudions l'application des méthodes d'apprentissage automatique pour la détection et le contrôle d'activité semblable à une crise convulsive dans les modèles d'épilepsie in vitro. Cette recherche formera la base d'une nouvelle classe de dispositifs de neurostimulation auto-adaptatifs pour le traitement des patients qui ne répondent pas aux drogues antiépileptiques. Il y a beaucoup d'obstacles techniques pour créer un algorithme adaptatif pour ces dispositifs. Actuellement, la science n'a pas encore expliqué entièrement les mécanismes définissant l'épilepsie et ses traitements. Ceci est important à deux niveaux: Pour le problème de la détection ou de la prévision des crises, et pour établir des critères clairs pour optimiser un algorithme de contrôle adaptatif. Comme beaucoup de problèmes médicaux, les données cliniques sont rares, chères, et fortement variables. Nous adressons la détection des états épileptiques en utilisant les méthodes “boosting” avec un groupe de traits simples de spectre de fréquences dérivés des enregistrements électrophysiologiques. Tandis que les méthodes boosting typiques n'ont pas été conçues pour utiliser l'information disponible avec des données de séries chronologiques, nous présentons une méthode boosting récurrente qui améliore le taux de classification dans notre domaine d'application. Nous présentons également une exécution d'un modèle biologiquement plausible d'un système neural épileptique employant un réseau de neurones intègre-et tire ayant les signals d'entrées partiellement stochastiques et ayant deux échelles de temps de comportement réfractaire. En conclusion, nous formons un agent d'apprentissage par renforcement pour réduire l'occurrence d'activité semblable à une crise. Cet agent est prévu pour être une composante d'un dispositif en boucle fermée de stimulation électrique ayant un ensemble de capteurs et un algorithme adaptatif.
... Osorio et al. [13] show that the correlation integral and the correlation dimension depend on the EEG frequency and amplitude, implying that changes in the former are due to trivial changes in the latter. Sunderam et al. [14] chemically induce seizures in rats and use a stochastic Markov chain model to predict the interictal duration, , from the seizure duration, , and vice-versa. Litt et al. [15] show that the energy in EEG increases as the seizure approaches. ...
Phase-space dissimilarity measures (PSDM) have been recently proposed to provide forewarning of impending epileptic events from scalp electroencephalographic (EEG) for eventual ambulatory settings. Despite high noise in scalp EEG, PSDM yield consistently superior performance over traditional nonlinear indicators, such as Kolmogorov entropy, Lyapunov exponents, and correlation dimension. However, blind application of PSDM may result in channel inconsistency, whereby multiple datasets from the same patient yield conflicting forewarning indications in the same channel. This paper presents a first attempt to solve this problem.
... Though they could not verify this idea, others later found varying degrees of predictability in temporal seizure patterns in human beings and animal models of epilepsy. [41][42][43] The late 1980s and 1990s saw the application of nonlinear dynamics as a technique for predicting seizures. Transient drops in the PLE were described by Iasemidis and colleagues as "a route to seizures" in temporal-lobe epilepsy. ...
For almost 40 years, neuroscientists thought that epileptic seizures began abruptly, just a few seconds before clinical attacks. There is now mounting evidence that seizures develop minutes to hours before clinical onset. This change in thinking is based on quantitative studies of long digital intracranial electroencephalographic (EEG) recordings from patients being evaluated for epilepsy surgery. Evidence that seizures can be predicted is spread over diverse sources in medical, engineering, and patent publications. Techniques used to forecast seizures include frequency-based methods, statistical analysis of EEG signals, non-linear dynamics (chaos), and intelligent engineered systems. Advances in seizure prediction promise to give rise to implantable devices able to warn of impending seizures and to trigger therapy to prevent clinical epileptic attacks. Treatments such as electrical stimulation or focal drug infusion could be given on demand and might eliminate side-effects in some patients taking antiepileptic drugs long term. Whether closed-loop seizure-prediction and treatment devices will have the profound clinical effect of their cardiological predecessors will depend on our ability to perfect these techniques. Their clinical efficacy must be validated in large-scale, prospective, controlled trials.
... that EEG data have noisy deterministic features that produce diverse behaviors, including chaos, although some investigators have challenged this idea (Ivanov et al., 1996;Jeong et al., 1999;Gribkov and Gribkova, 2000). The Journal of Clinical Neurophysiology published a recent focus issue (May 2001) on epilepsy prediction (Jerger et al., 2001;Lehnertz et al., 2001;Le Van Quyen et al., 2001;Osorio et al., 2001;Protopopescu et al., 2001;Savit et al., 2001;Sunderam et al., 2001). Litt (Chavez et al., 2003;D'Alessandro et al., 2003;Hively and Protopopescu, 2003;Iasemidis, 2003;Iasemidis et al., 2003;Lopes da Silva et al., 2003;McSharry et al., 2003;Notley and Elliott, 2003;Paul et al., 2003;Rieke et al., 2003;Slutzky et al., 2003;Witte et al., 2003). ...
The authors extend the recent application of phase-space dissimilarity measures for scalp EEG data in two directions. First, a forewarning window of up to 8 hours was used, thereby providing more forewarning time of the seizure event. This window was limited to a maximum of 1 hour in their previous work. Second, they combined information from two channels via a multichannel phase-space to improve the quality and confidence limits of the forewarning. Combining these two enhancements, they obtained two-channel results that were superior to the single-channel ones.
... The observations are also emitted probabilistically, conditional on the hidden state. Markovian dynamics have been successfully used to model the processes of seizure generation in the past, in experimental animals, and to detect antiepileptic drug compliance (Albert 1991; Hopkins et al. 1985; Le et al. 1992; Sunderam et al. 2001). The " hidden " feature of HMMs is attractive, in that we assume that observable EEG signals arise from underlying dynamical brain states. ...
Responsive, implantable stimulation devices to treat epilepsy are now in clinical trials. New evidence suggests that these devices may be more effective when they deliver therapy before seizure onset. Despite years of effort, prospective seizure prediction, which could improve device performance, remains elusive. In large part, this is explained by lack of agreement on a statistical framework for modeling seizure generation and a method for validating algorithm performance. We present a novel stochastic framework based on a three-state hidden Markov model (HMM) (representing interictal, preictal, and seizure states) with the feature that periods of increased seizure probability can transition back to the interictal state. This notion reflects clinical experience and may enhance interpretation of published seizure prediction studies. Our model accommodates clipped EEG segments and formalizes intuitive notions regarding statistical validation. We derive equations for type I and type II errors as a function of the number of seizures, duration of interictal data, and prediction horizon length and we demonstrate the model's utility with a novel seizure detection algorithm that appeared to predicted seizure onset. We propose this framework as a vital tool for designing and validating prediction algorithms and for facilitating collaborative research in this area.
... 1, 68, 78 A twostate Markov model was also able to fit an animal seizure model, where a long period in the seizure-prone state was associated with a long period in the following seizure-resistant state. 140 Markov modeling has also been used to determine the adequacy of seizure prediction algorithms. 162 A model for this purpose used 3 Markov brain states: Normal, Pre-seizure, and Seizure, with bidirectional transitions between any 2 states. ...
Epilepsy is a complex set of disorders that can involve many areas of the cortex, as well as underlying deep-brain systems. The myriad manifestations of seizures, which can be as varied as déjà vu and olfactory hallucination, can therefore give researchers insights into regional functions and relations. Epilepsy is also complex genetically and pathophysiologically: it involves microscopic (on the scale of ion channels and synaptic proteins), macroscopic (on the scale of brain trauma and rewiring) and intermediate changes in a complex interplay of causality. It has long been recognized that computer modelling will be required to disentangle causality, to better understand seizure spread and to understand and eventually predict treatment efficacy. Over the past few years, substantial progress has been made in modelling epilepsy at levels ranging from the molecular to the socioeconomic. We review these efforts and connect them to the medical goals of understanding and treating the disorder.
Detection of epileptic seizures is a major challenge of these days. There are lots of papers which pay their attention to this subject. Recently, some dynamical disease with attacks such as epilepsy are considered as a system in which critical slowing down can be seen before their attacks (seizure). Although there are not many researches on the prediction of seizures using this phenomenon. Recently [P. Milanowski, P. Suffczynski, Int. J. Neural Syst. 26, 1650053 (2016)] have investigated the application of critical slowing down indicators and surprisingly they found that only in 8% of nearby 300 epileptic patients have the evidence of critical slowing down before seizures. The main goal of this paper is finding the answer of the important question “can we trust that epileptic seizures are bifurcations in the neural system”. In order to find the answer, different studies on the prediction of seizure are investigated and we prove that features which are used in those papers are critical slowing down indicators although they are not aware of it. So we present some reasons for the occurrence of critical slowing down before the seizure. We hope that this study will be a motivation of future studies on the application of critical slowing down indicators for predicting epileptic seizures.
Advances in the field of signal processing, nonlinear dynamics, statistics, and optimization theory, combined with marked improvement in instrumenta tion and development of computers systems, have made it possible to apply the power of mathematics to the task of understanding the human brain. This verita ble revolution already has resulted in widespread availability of high resolution neuroimaging devices in clinical as well as research settings. Breakthroughs in functional imaging are not far behind. Mathematical tech niques developed for the study of complex nonlinear systems and chaos already are being used to explore the complex nonlinear dynamics of human brain phys iology. Global optimization is being applied to data mining expeditions in an effort to find knowledge in the vast amount of information being generated by neuroimaging and neurophysiological investigations. These breakthroughs in the ability to obtain, store and analyze large datasets offer, for the first time, exciting opportunities to explore the mechanisms underlying normal brain func tion as well as the affects of diseases such as epilepsy, sleep disorders, movement disorders, and cognitive disorders that affect millions of people every year. Ap plication of these powerful tools to the study of the human brain requires, by necessity, collaboration among scientists, engineers, neurobiologists and clini cians. Each discipline brings to the table unique knowledge, unique approaches to problem solving, and a unique language.
Recently, Mouse neuroblastoma cells are considered as an attractive model for the study of human neurological and
prion diseases, and intensively used as a model system in different areas. Among those areas, differentiation of neuro2a
(N2A) cells, receptor mediated ion current, and glutamate induced physiological response are actively investigated. The
reason for the interest to mouse neuroblastoma N2A cells is that they have a fast growing rate than other cells in neural
origin with a few another advantages. This study evaluated the calcium oscillations and neural spikes recording of mouse
neuroblastoma N2A cells in an epileptic condition. Based on our observation of neural spikes in mouse N2A cell with
our proposed imaging modality, we report that mouse neuroblastoma N2A cells can be an important model related to
epileptic activity studies. It is concluded that the mouse neuroblastoma N2A cells produce the epileptic spikes in vitro in
the same way as produced by the neurons or the astrocytes. This evidence advocates the increased and strong level of
neurotransmitters release by enhancement in free calcium using the 4-aminopyridine which causes the mouse
neuroblastoma N2A cells to produce the epileptic spikes and calcium oscillation.
Seizures are complex phenomena spanning multiple spatial and temporal scales, from ion dynamics to communication between brain regions, from milliseconds (spikes) to days (interseizure intervals). Because of the existence of such multiple scales, the experimental evaluation of the mechanisms underlying the initiation, propagation, and termination of epileptic seizures is a difficult problem. Theoretical models and numerical simulations provide new tools to investigate seizure mechanisms at multiple scales. In this chapter, we review different theoretical approaches and their contributions to our understanding of seizure mechanisms.
Epileptic seizures may be described as the population entrainment of low complexity activities. Multistage seizure detection implemented using hidden Markov model (HMM) was proposed for the analysis of intracranial EEG recordings of epilepsy patients. The number of hidden states and the number of Gaussian clusters of the HMM were obtained using an unsupervised method. Multiple dynamic stages had been found leading to ictal activity. High sensitivity and specificity can be achieved based on receiver operating characteristic curve analysis (with area > 0.85). Spatial generalisation features study suggested that HMM framework is independent of the subject and the testing recording location.
The performance of five seizure detection schemes, i.e., Nonlinear
embedding delay, Hurst scaling, Wavelet Scale, autocorrelation and
gradient of accumulated energy, in their ability to detect EEG seizures
close to the seizure onset time were evaluated to determine the
feasibility of their application in the development of a real time
closed loop seizure intervention program (RCLSIP). The criteria chosen
for the performance evaluation were, high statistical robustness as
determined through the predictability index, the sensitivity and the
specificity of a given measure to detect an EEG seizure, the lag in
seizure detection with respect to the EEG seizure onset time, as
determined through visual inspection and the computational efficiency
for each detection measure. An optimality function was designed to
evaluate the overall performance of each measure dependent on the
criteria chosen. While each of the above measures analyzed for seizure
detection performed very well in terms of the statistical parameters,
the nonlinear embedding delay measure was found to have the highest
optimality index due to its ability to detect seizure very close to the
EEG seizure onset time, thereby making it the most suitable dynamical
measure in the development of RCLSIP in rat model with chronic limbic
epilepsy.
We have previously reported preictal spatiotemporal transitions in human mesial temporal lobe epilepsy (MTLE) using short term Lyapunov exponent (STLmax
) and average angular frequency (\(
\Omega \)
). These results have prompted us to apply the quantitative nonlinear methods to a limbic epilepsy rat (CLE), as this model has several important features of human MTLE. The present study tests the hypothesis that preictal dynamical changes similar to those seen in human MTLE exist in the CLE model. Forty-two, 2-hr epoch data sets from 4 CLE rats (mean seizure duration 74±20 sec) are analyzed, each containing a focal onset seizure and intracranial data beginning 1 hr before the seizure onset. Three nonlinear measures, correlation integral, short-term largest Lyapunov exponent and average angular frequency are used in the current study. Data analyses show multiple transient drops in STLmax
values during the preictal period followed by a significant drop during the ictal period. Average angular frequency values demonstrate transient peaks during the preictal period followed by a significant peak during the ictal period. Convergence among electrode sites is also observed in both STLmax
and \(
\Omega \)
values before seizure onset. Results suggest that dynamical changes precede and accompany seizures in rat CLE. Thus, it may be possible to use the rat CLE model as a tool to refine and test real-time seizure prediction, and closed-loop intervention techniques.
Epilepsy is characterized by intermittent, paroxysmal, hypersynchronous electrical activity that may remain localized and/or spread and severely disrupt the brain's normal multitask and multiprocessing function. Epileptic seizures are the hallmarks of such activity. The ability to issue warnings in real time of impending seizures may lead to novel diagnostic tools and treatments for epilepsy. Applications may range from a warning to the patient to avert seizure-associated injuries, to automatic timely administration of an appropriate stimulus. Seizure prediction could become an integral part of the treatment of epilepsy through neuromodulation, especially in the new generation of closed-loop seizure control systems.
Epilepsy is a dynamical disorder with intermittent crises (seizures) that until recently were considered unpredictable. In this study, we investigated the predictability of epileptic seizures in chronically epileptic rats as a first step towards a subsequent timely intervention for seizure control. We look at the epileptic brain as a nonlinear complex system that undergoes spatio-temporal state transitions and the Lyapunov exponents as indices of its stability. We estimated the spatial synchronization or desynchronization of the maximum short-term Lyapunov exponents (STLmax, approximate measures of chaos) among multiple brain sites over days of electroencephalographic (EEG) recordings from 5 rats that had developed chronic epilepsy according to the lithium pilocarpine rodent model of epilepsy. We utilized this synchronization of EEG dynamics for the construction of a robust seizure prediction algorithm. The parameters of the algorithm were optimized using receiver operator curves (ROCs) on training EEG datasets from each rat for the algorithm to provide maximum sensitivity and specificity in the prediction of their seizures. The performance of the algorithm was then tested on long-term testing EEG datasets per rat. The thus optimized prediction algorithm on the testing datasets over all rats yielded a seizure prediction mean sensitivity of 85.9%, specificity of 0.180 false predictions per hour, and prediction time of 67.6 minutes prior to a seizure onset. This study provides evidence that prediction of seizures is feasible through analysis of the EEG within the framework of nonlinear dynamics, and thus paves the way for just-in-time pharmacological or physiological inter-ventions to abort seizures tens of minutes before their occurrence.
An informed answer to the question Will the new antiseizure devices fill the gap between drugs and surgery? requires that the therapeutic ratio and the devices' capacity to cost-effectively decrease disease burden globally be considered. Regarding therapeutic ratio, the answer is likely Yes, if and only if, and at a minimum, all relevant seizure variables are quantified, the spatiotemporal behavior of seizures at short and long time scales is better understood, and statistical analyses of efficacy conform to and address the multidimensional, complex nature of seizures. Regarding the capacity of devices to cost-effectively decrease disease burden globally, the answer is likely No, unless: (1) cost-effectiveness is demonstrable and maximal, which requires that devices become the sole therapy; (2) seizure comorbidities are prevented or their seriousness is reduced; (3) patients with pharmacoresistant seizures may rejoin society's mainstream; and (4) disruptive (revolutionary) conceptual and technological advances materialize.
We developed a screening methodology to test the ability of putative antiepileptic drugs delivered directly to a seizure focus to prevent epileptiform activity. The left hippocampi of 15 rats were implanted with an injection cannula and bipolar recording electrodes. Bone screws were used to record neocortical EEG activity. Diazepam (DZP) at one of four possible concentrations or control solution was injected into the hippocampus, followed 5 min later by bicuculline methiodide. DZP suppressed spikes and ictal events in a dose-dependent manner (P<0.0001). At 100 mM, DZP reduced spikes from 678+/-128 to 87+/-35 for a 15 min segment. Numbers of ictal events (seizure) and latency to the first event were reduced by prophylactic DZP. The study establishes a protocol for testing of intracranially-injected drugs to prevent focal seizures.
The possibility that seizures may be intercorrelated has not been sufficiently investigated. A handful of studies, the majority based on patient seizure diaries, provide disparate results: some claim that seizures are serially correlated and others that they are random events. This study investigates the effect that a seizure may have on the time of occurrence and severity of subsequent ones in subjects undergoing invasive surgical evaluation.
The Savit-Green statistic, a measure of time series lag dependency, was applied to seizure sequences derived from the ECoGs of 26 epilepsy surgery candidates. Seizure onset times, intensities and durations were obtained using a validated seizure detection algorithm, and from these, inter-seizure intervals (ISI) and severities were computed and their lag dependencies were compared to suitably randomized and amplitude-scaled linear surrogate sets.
The null hypothesis (seizures are uncorrelated) was rejected (p<0.05) for ISI in 12/26 subjects and for seizure severity in 13/26. The temporal correlations spanned up to three preceding seizures and were nonlinear in 7/12 subjects for ISI and in 8/13 for severity. An important finding is that dependencies may be related to the frequency of seizures in the sample.
This study demonstrates that under certain conditions, there are linear and nonlinear seizure dependencies of low order and at small time scales (minutes to hours), for ISI and seizure severity. This observation has important implications for studies of seizure predictability, which de facto treat seizures as independent occurrences. Given the study subjects' conditions, it is not clear if the dependencies reflect innate brain dynamics, drug withdrawal, local trauma or a combination of these.
The performance of five non-parametric, univariate seizure detection schemes (embedding delay, Hurst scale, wavelet scale, nonlinear autocorrelation and variance energy) were evaluated as a function of the sampling rate of EEG recordings, the electrode types used for EEG acquisition, and the spatial location of the EEG electrodes in order to determine the applicability of the measures in real-time closed-loop seizure intervention. The criteria chosen for evaluating the performance were high statistical robustness (as determined through the sensitivity and the specificity of a given measure in detecting a seizure) and the lag in seizure detection with respect to the seizure onset time (as determined by visual inspection of the EEG signal by a trained epileptologist). An optimality index was designed to evaluate the overall performance of each measure. For the EEG data recorded with microwire electrode array at a sampling rate of 12 kHz, the wavelet scale measure exhibited better overall performance in terms of its ability to detect a seizure with high optimality index value and high statistics in terms of sensitivity and specificity.
Epileptic seizures are manifestations of epilepsy, a serious brain dynamical disorder second only to strokes. Of the world's ∼50 million people with epilepsy, fully 1/3 have seizures that are not controlled by anti-convulsant medication. The field of seizure prediction, in which engineering technologies are used to decode brain signals and search for precursors of impending epileptic seizures, holds great promise to elucidate the dynamical mechanisms underlying the disorder, as well as to enable implantable devices to intervene in time to treat epilepsy. There is currently an explosion of interest in this field in academic centers and medical industry with clinical trials underway to test potential prediction and intervention methodology and devices for Food and Drug Administration (FDA) approval. This invited paper presents an overview of the application of signal processing methodologies based upon the theory of nonlinear dynamics to the problem of seizure prediction. Broader application of these developments to a variety of systems requiring monitoring, forecasting and control is a natural outgrowth of this field.
J. D. Hamilton's nonlinear Markovian filter is extended to allow state transitions to be duration dependent. Restrictions are imposed on the state transition matrix associated with a tau-order Markov system such that the corresponding first-order conditional transition probabilities are functions of both the inferred current state and also the number of periods the process has been in that state. High-order structure is parsimoniously summarized by the inferred duration variable. Applied to U.S. postwar real GNP growth rates, the authors obtain evidence in support of nonlinearity, asymmetry between recessions and expansions, and duration dependence for recessions but not for expansions.
The convulsant action of 3-mercaptopropionic acid (3-MPA), a known inhibitor of glutamate decarboxylase activity, was studied in 7-, 12-, 18- and 25-day-old rats and in adult animals. 3-MPA elicited predominantly clonic, minimal seizures as well as generalized tonicclonic (major) seizures at all developmental stages studied. The CD50 for major seizures did not change during development; CD50 for minimal seizures was significantly lower in 18-day-old rats than in older animals. Latency to the onset of seizures was shortest in 18-dayold rats and extremely long in 12- and, especially, in 7-day-old rats. This long latency might signify either changing molecular properties of glutamate decarboxylase during development or slow turnover of GABA at early postnatal stages. Electrocorticographic recordings demonstrated sharp EEG components in the frontal region as a first sign of 3-MPA action, and seizure patterns exhibited similar developmental changes as found with other seizure models (a decrease in duration of individual graphoelements and an increase in synchronization among various cortical regions). This indicates the primary importance of brain maturation in the expression of epileptic EEG phenomena. The correlation between EEG and motor phenomena was poor in the youngest animals and it ameliorated with age, but it never became perfectly coincidental.
A computationally efficient solution to the problem of minimum error thresholding is derived under the assumption of object and pixel grey level values being normally distributed. The method is applicable in multithreshold selection.
This paper discusses a model for a time series of epileptic seizure counts in which the mean of a Poisson distribution changes according to an underlying two-state Markov chain. The EM algorithm (Dempster, Laird, and Rubin, 1977, Journal of the Royal Statistical Society, Series B 39, 1-38) is used to compute maximum likelihood estimators for the parameters of this two-state mixture model and extensions are made allowing for nonstationarity. The model is illustrated using daily seizure counts for patients with intractable epilepsy and results are compared with a simple Poisson distribution and Poisson regressions. Some simulation results are also presented to demonstrate the feasibility of this model.
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.
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.
This tutorial provides an overview of the basic theory of hidden
Markov models (HMMs) as originated by L.E. Baum and T. Petrie (1966) and
gives practical details on methods of implementation of the theory along
with a description of selected applications of the theory to distinct
problems in speech recognition. Results from a number of original
sources are combined to provide a single source of acquiring the
background required to pursue further this area of research. The author
first reviews the theory of discrete Markov chains and shows how the
concept of hidden states, where the observation is a probabilistic
function of the state, can be used effectively. The theory is
illustrated with two simple examples, namely coin-tossing, and the
classic balls-in-urns system. Three fundamental problems of HMMs are
noted and several practical techniques for solving these problems are
given. The various types of HMMs that have been studied, including
ergodic as well as left-right models, are described