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Phase space topography and the Lyapunov exponent of electrocorticograms in partial seizures
Abstract
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.
... Some studies [7] indicate the interictal state exists four hours before or after a seizure. EEG signals are different among patients based on seizure type and location, and many prediction methods are developed for patients specific [7], [11], [12]. These techniques typically employ supervised learning with two primary steps: feature extraction and detection between pre-ictal and interictal states. ...
... These techniques typically employ supervised learning with two primary steps: feature extraction and detection between pre-ictal and interictal states. Feature extraction approaches are categorized as univariate and bivariate or further classified as linear and nonlinear [12]. The extracted features utilized by ML applications can also be divided into three types: time, frequency domain as linear, and nonlinear features with classification models, i.e., support vector machine (SVM), Artificial neural network (ANN), Random forest (RF) classifier [12], [13]. ...
... Feature extraction approaches are categorized as univariate and bivariate or further classified as linear and nonlinear [12]. The extracted features utilized by ML applications can also be divided into three types: time, frequency domain as linear, and nonlinear features with classification models, i.e., support vector machine (SVM), Artificial neural network (ANN), Random forest (RF) classifier [12], [13]. The handicraft features are extracted based on existing knowledge to understand the changes in EEG activity. ...
Early epileptic seizure prediction (ESP) has informative challenges due to the complexity of electroencephalogram (EEG) signals, patient variability, privacy, security issues regarding consumer health data, and the on-time alarm triggers before an upcoming seizure to provide sufficient time for the patients and caregivers to take appropriate action. Therefore, the proposed study presents a novel patient-specific seizure prediction framework with the Consumer Internet of Things (CIoT) for the smart healthcare system to anticipate the onset of upcoming seizures and improve the quality of healthcare and early treatment. Initially, the multi-handicraft and deep features are extracted in feature engineering modules and then concatenated in the fusion module. The fused feature fed into the Bidirectional Long Short-term Memory (BiLSTM) network to present the temporal dependency of the EEG signals. The Attention Mechanism is applied to reduce the dimension of the feature. Moreover, the CIoT module is integrated for real-time seizure prediction and sending alerts to doctors and emergency units through the cloud platform. Testing via the Leave-One-Out cross-validation method revealed the model’s consistent performance across various seizure types, emphasizing real-time clinical applications. The model achieved 91.39± 3.34% accuracy, 91.30± 2.80% sensitivity, 90.06± 4.84% specificity, and a false positive rate (FPR) of 0.12± 0.04 h-1 in the case of seizure prediction Horizon (SPH) of 10 minutes. The CIoT remotely monitoring the patients ensures timely treatment, maintains data security and privacy, and improves the performance of real-time applications in smart consumer healthcare systems.
... LLEs are also helpful for finding the sources of epilepsy from recordings between seizures and for forecasting seizures. For instance, LLE has been found to drop at the start of the seizure and rise after the end of the seizure, providing evidence that LLEs can index pathological conditions [26]. ...
The acoustic startle reflex (ASR) relies on the sensorimotor system and is affected by aging, sex, and psychopathology. ASR can be modulated by the prepulse inhibition (PPI) paradigm, which achieves the inhibition of reactivity to a startling stimulus (pulse) following a weak prepulse stimulus. Additionally, neurophysiological studies have found that brain activity is characterized by irregular patterns with high complexity, which however reduces with age. Our study investigated the relationship between pre-startle nonlinear dynamics and prepulse inhibition in healthy children vs. adults. Fifty-six individuals took part in the experiment: 31 children and adolescents and 25 adults. Participants heard 51 pairs of tones (prepulse, startle) with a time difference of 30 to 500 ms. Subsequently, we assessed neural complexity by computing the largest Lyapunov exponent (LLE) during the pre-startle period and assessed PPI by analyzing the post-startle event-related potentials (ERPs). Results showed higher neural complexity for children compared to adults, in line with previous research showing reduced complexity in the physiological signals in ageing. As expected, PPI (as reflected in the P50 and P200 components) was enhanced in adults compared to children, potentially due to the maturation of the ASR for the former. Interestingly, pre-startle complexity was correlated with the P50 component in children only, but not in adults, potentially due to the different stage of sensorimotor maturation between age groups. Overall, our study offers novel contributions for investigating brain dynamics, linking nonlinear with linear measures. Our findings are consistent with the loss of neural complexity in ageing, and suggest differentiated links between nonlinear and linear metrics in children and adults.
... As early as 1990, Iasemidis et al. (1990) began to analyze iEEG signals of epileptic patients with the LLE, which quantifies the chaos and complexity of brain activity by the average exponential rate at which nearby trajectories diverge from each other in the phase space of the iEEG signal. They found that the LLE gradually decreased as the seizure approached, and the closer the seizure was, the less chaotic the system was, and the iEEG signal was gradually ordered. ...
At present, at least 30% of refractory epilepsy patients in the world cannot be effectively controlled and treated. The suddenness and unpredictability of seizures greatly affect the physical and mental health and even the life safety of patients, and the realization of early prediction of seizures and the adoption of interventions are of great significance to the improvement of patients’ quality of life. In this paper, we firstly introduce the design process of EEG-based seizure prediction methods, introduce several databases commonly used in the research, and summarize the commonly used methods in pre-processing, feature extraction, classification and identification, and post-processing. Then, based on scalp EEG and intracranial EEG respectively, we reviewed the current status of epileptic seizure prediction research from five commonly used feature analysis methods, and make a comprehensive evaluation of both. Finally, this paper describes the reasons why the current algorithms cannot be applied to the clinic, summarizes their limitations, and gives corresponding suggestions, aiming to provide improvement directions for subsequent research. In addition, deep learning algorithms have emerged in recent years, and this paper also compares the advantages and disadvantages of deep learning algorithms with traditional machine learning methods, in the hope of providing researchers with new technologies and new ideas and making significant breakthroughs in the field of epileptic seizure prediction.
... Most methods at that time were based on signal processing and pattern recognition, such as time series and spectral analysis [108], [109]. EEG complexity indices, such as Lyapunov exponents [110] and similarity indices [111], have also been used to predict seizures. However, the predicted outcomes of these methods are not particularly satisfactory because of the large individual differences between patients. ...
Epilepsy is a complex disease spanning across multiple scales, from ion channels in neurons to neuronal circuits across the entire brain. Over the past decades, computational models have been used to describe the pathophysiological activity of the epileptic brain from different aspects. Traditionally, each computational model can aid in optimizing therapeutic interventions, therefore, providing a particular view to design strategies for treating epilepsy. As a result, most studies are concerned with generating specific models of the epileptic brain that can help us understand the certain machinery of the pathological state. Those specific models vary in complexity and biological accuracy, with system-level models often lacking biological details. Here, we review various types of computational models of epilepsy and discuss their potential for different therapeutic approaches and scenarios, including drug discovery, surgical strategies, brain stimulation, and seizure prediction. We propose that we need to consider an integrated approach with a unified modelling framework across multiple scales to understand the epileptic brain. Our proposal is based on the recent increase in computational power, which has opened up the possibility of unifying those specific epileptic models into simulations with an unprecedented level of detail. A multi-scale epilepsy model can bridge the gap between biologically detailed models, used to address molecular and cellular questions, and brain-wide models based on abstract models which can account for complex neurological and behavioral observations. With these efforts, we move toward the next generation of epileptic brain models capable of connecting cellular features, such as ion channel properties, with standard clinical measures such as seizure severity.
... The rationale is that seizures may build up progressively before onset through progressive synchronization of assemblies of neurons, which in some patients corresponds to anticipatory symptoms such as auras (43) and thus could be detected from the EEG, even without patient notice. A major conceptual step was introduced in the 1980s, when the problem was approached with theoretical tools developed in the frame of the physics of non-linear dynamic systems (44)(45)(46)(47), which established both the principle of predictability horizons and provided qualitative analysis of complex signals such as the EEG. Early studies showed promising scores in terms of sensitivity and specificity, yet rigorous methodological design of evaluation suggested that more developments, in terms of algorithms and statistical approach, and/or by aggregating multimodal sensors such as body parts motion detectors or video monitoring, could help improve practical suitability (48)(49)(50)(51)(52)(53)(54)(55). ...
Knowing when seizures occur may help patients and can also provide insight into epileptogenesis mechanisms. We recorded seizures over periods of several days in the Genetic Absence Epileptic Rat from Strasbourg (GAERS) model of absence epilepsy, while we monitored behavioral activity with a combined head accelerometer (ACCEL), neck electromyogram (EMG), and electrooculogram (EOG). The three markers consistently discriminated between states of behavioral activity and rest. Both GAERS and control Wistar rats spent more time in rest (55–66%) than in activity (34–45%), yet GAERS showed prolonged continuous episodes of activity (23 vs. 18 min) and rest (34 vs. 30 min). On average, seizures lasted 13 s and were separated by 3.2 min. Isolated seizures were associated with a decrease in the power of the activity markers from steep for ACCEL to moderate for EMG and weak for EOG, with ACCEL and EMG power changes starting before seizure onset. Seizures tended to occur in bursts, with the probability of seizing significantly increasing around a seizure in a window of ±4 min. Furthermore, the seizure rate was strongly increased for several minutes when transitioning from activity to rest. These results point to mechanisms that control behavioral states as determining factors of seizure occurrence.
Analysis of Hindmarsh-Rose (HR) neural model and its network dynamics under different inputs or network topologies are the leading research of the structural dynamics of complex networks, but the typical three-variable HR neural model has limitations in describing the complex non-linear features and precise behavior patterns of neuron. Based on an extended HR neural model, the firing patterns and bifurcation behavior are analysed in this paper, and how the newly introduced variable affect discharge modes has also been explored. A two-dimensional lattice is constructed to study the mechanism of spiral wave formation and breakup in the neural network, and to explore its network dynamics and synchronous behavior. Obtained results show that the extended HR neural model has more rich and stable firing properties, and it can be observed that there are multimodal phenomena with both spiking and bursting states simultaneously. If the network topology is changed, the formation and breakup of spiral waves can be observed, and the synchronization factor exhibits a monotonically decreasing relationship with the coupling strength and the control parameters of the newly introduced variable. When HR neurons are in spiking state, the system is more prone to spiral waves, and the coupling strength range for spiral waves is wider. The above results provide valuable ideas to explore the modulation of network group behavior.
RÉSUMÉ
L'étude des changements dynamiques de l'activité neuronale précédant une crise épileptique permet une caractérisation d'un état pré‐ictal plusieurs minutes avant la crise. Ces résultats ouvrent de nouvelles perspectives pour l'étude des mécanismes de l'épileptogenèse mais aussi la possibilité de nouvelles interventions thérapeutiques avant l'occurrence de la crise. Dans cette revue, nous discutons les résultats obtenus par notre groupe dans ce domaine utilisant l'analyse non‐linéaire de l'activité électrique du cerveau et précisons les limites de ces résultats ainsi que les questions encore ouvertes.
The complexity of localising the epileptogenic zone (EZ) contributes to surgical resection failures in achieving seizure freedom. The distinct patterns of epileptiform activity during interictal and ictal phases, varying across patients, often lead to suboptimal localisation using electroencephalography (EEG) features. We posed two key questions: whether neural signals reflecting epileptogenicity generalise from interictal to ictal time windows within each patient, and whether epileptiform patterns generalise across patients. Utilising an intracranial EEG dataset from 55 patients, we extracted a large battery of simple to complex features from stereo-EEG (SEEG) and electrocorticographic (ECoG) neural signals during interictal and ictal windows. Our features (n = 34) quantified many aspects of the signals including statistical moments, complexities, frequency-domain and cross-channel network attributes. Decision tree classifiers were then trained and tested on distinct time windows and patients to evaluate the generalisability of epileptogenic patterns across time and patients, respectively. Evidence strongly supported generalisability from interictal to ictal time windows across patients, particularly in signal power and high-frequency network-based features. Consistent patterns of epileptogenicity were observed across time windows within most patients, and signal features of epileptogenic regions generalised across patients, with higher generalisability in the ictal window. Signal complexity features were particularly contributory in cross-patient generalisation across patients. These findings offer insights into generalisable features of epileptic neural activity across time and patients, with implications for future automated approaches to supplement other EZ localisation methods.
In this study, we investigate the problem of prediction of epileptiform activity from EEG data using a deep learning approach. We implement LSTM deep neural network and study how the quality of the prediction depends on the choice of measures of observational error, such as MAPE and RMSE. We show that comparison of results obtained using different metrics is important to obtain a comprehensive assessment of the problem.
Deterministic systems can display a form of highly irregular, quasirandom behavior called chaos. Even though the observed behavior is very complex, the systems which generate it can be very simple. Thus, in at least some instances, irregular biological systems may obey a simple, potentially discoverable, deterministic dynamical law. These systems can undergo reversible transitions to and from chaotic dynamics in response to small changes in parameter values. As a long term goal, this form of analysis may suggest more effective responses to disordered behavior in physiological control systems.
This contribution is concerned with chaos in neural systems and its possible role in epileptogenesis. Calculation of information dimension provides a procedure for distinguishing between chaotic and random behavior. This technique is applied to experimental data from two preparations: spontaneous activity of cortical neurons in the pre- and post-central gyri of the squirrel monkey and human electroen-cephalographic signals. In each case the results suggest that these systems can display low dimensional chaotic behavior.
In an important new contribution to the literature of chaos, two distinguished researchers in the field of physiology probe central theoretical questions about physiological rhythms. Topics discussed include: How are rhythms generated? How do they start and stop? What are the effects of perturbation of the rhythms? How are oscillations organized in space? Leon Glass and Michael Mackey address an audience of biological scientists, physicians, physical scientists, and mathematicians, but the work assumes no knowledge of advanced mathematics. Variation of rhythms outside normal limits, or appearance of new rhythms where none existed previously, are associated with disease. One of the most interesting features of the book is that it makes a start at explaining "dynamical diseases" that are not the result of infection by pathogens but that stem from abnormalities in the timing of essential functions. From Clocks to Chaos provides a firm foundation for understanding dynamic processes in physiology.
A class of piecewise continuous, piecewise C1 transformations on the interval J c R with finitely many discontinuities n are shown to have at most n invariant measures. 1. The way phenomena or processes evolve or change in time is often described by differential equations or difference equations. One of the sim- plest mathematical situations occurs when the phenomenon can be described by a single number and when this number can be estimated purely as a function of the previous number. That is, when the number xn+x can be written as xn+x = t(x") where t maps an interval J c R into itself. For x E J, let t°(x) denote x and t"+x(x) denote t(t"(x)) for n = 0,1.We will sayp E J is a periodic point with period n if p = t"(p) andp ¥= rk(p) for 1 1. In this paper we assume t is piecewise continuous and piecewise twice continuous differentiable. We also assume that a t ^ > 1 where Jx — j x E /, — t(x) exists \.