Article

Mathematical Structures for Epilepsy: High-Frequency Oscillation and Interictal Epileptic Slow (Red Slow)

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Abstract

In the present study, we attempted to characterize two characteristic features within the dynamic behavior of wideband electrocorticography data, which were recorded as the brain waves of epilepsy, comprising high-frequency oscillations (HFOs) and interictal epileptic slow (red slow). The results of power spectrum and nonlinear time series analysis indicate that, on one hand, HFOs at epileptic focus are characterized by one-dimensional dynamical systems in ictal onset time segments at an epileptic focus for two patients' datasets; on the other hand, an interictal epileptic slow is characterized by the residue of power spectrum. The results suggest that the degree of freedom of the brain dynamics during epileptic seizure with HFO degenerates to low-dimensional dynamics; hence, the interictal epileptic slow as the precursors of the seizure onset can be detected simply from interictal brain wave data for the dataset of one patient. Therefore, our results are essential to understand the brain dynamics in epilepsy.

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... In this review, we discuss the new concept of "ictal active DC shifts", and interictal co-occurrence of slow oscillations and HFOs, which we call "red slow", as the possible promising EEG biomarkers for the identification of the epileptic zone. Mathematical modeling of both ictal active DC shifts and interictal red slow has been published elsewhere (Namiki et al., 2019). ...
... Although ictal scalp EEG recordings with a 10 s long time constant may be subject to a lot of artifacts, it will be particularly interesting to characterize DC shifts with scalp-EEG recodings. In addition, mathematical analysis delineated the underlying principles by means of neuronal population, and the contribution of glia associated with extracellular potassium hometostasis is further warranted (Namiki et al., 2019). ...
... This rise would depolarize neurons, leading to HFO genesis. In addition, similar to ictal events, mathematical analysis delineated the underlying principles by means of neuronal population and glia, both being associated with extracellular potassium hometostasis is further warranted (Namiki et al., 2019). ...
Article
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An accurate identification of the epileptogenic zone is essential for patients with intractable epilepsy who are candidates to neurosurgery. EEG recordings can provide predictive biomarkers of the epileptogenic zone. Wide-band EEG makes it possible to record from infraslow (including DC shifts) to high frequency (HFO, over 300 Hz) oscillations for diagnostic purposes in patients with epilepsy. Although the presence of HFOs have been proposed to sign the epileptogenic zone, DC-like recordings demonstrate that DC shifts precede HFOs at seizure onset. This led to the proposal that "ictal active DC shifts" are causally related to seizure onset as opposed to "ictal passive DC shifts". Thus, active DC shifts may constitute predictive biomarkers of the epileptogenic zone in epilepsy. Since DC shift is commonly associated to a rise in extracellular potassium, potassium homeostasis regulated by Kir4.1 channels in astrocytes may play an key role at seizure onset. In addition, we hypothesize that, during the interictal period, the co-occurrence of slow events and interictal HFOs, so-called "Red slow", may also delineate an epileptogenic zone, even if a seizure would not be actually recorded.
... In this review, we discuss the new concept of "ictal active DC shifts", and interictal co-occurrence of slow oscillations and HFOs, which we call "red slow", as the possible promising EEG biomarkers for the identification of the epileptic zone. Mathematical modeling of both ictal active DC shifts and interictal red slow has been published elsewhere (Namiki et al., 2019). ...
... Although ictal scalp EEG recordings with a 10 s long time constant may be subject to a lot of artifacts, it will be particularly interesting to characterize DC shifts with scalp-EEG recodings. In addition, mathematical analysis delineated the underlying principles by means of neuronal population, and the contribution of glia associated with extracellular potassium hometostasis is further warranted (Namiki et al., 2019). ...
... This rise would depolarize neurons, leading to HFO genesis. In addition, similar to ictal events, mathematical analysis delineated the underlying principles by means of neuronal population and glia, both being associated with extracellular potassium hometostasis is further warranted (Namiki et al., 2019). ...
Article
Purpose: We reported the presence of interictal slow and high-frequency oscillations (HFOs) (IIS + HFO) and its temporal change so as to elucidate its clinical usefulness as a surrogate marker of epileptogenic zone in a patient with intractable focal epilepsy. Methods: We focused on one of the core electrodes of epileptogenicity, and investigated IIS + HFO in the pre- and post-segment of 30 minutes to all the 6 seizures. We adopted interictal slow in duration of 0.33 to 10 seconds, amplitude ≥50 μV and co-occurring with HFOs, and then divided into 5 groups depending on the amplitude of slow wave. Results: Before and after all the 6 seizures, the number of IIS + HFO was 2,890 at one electrode in the core epileptogenic zone. The number of IIS + HFO significantly decreased for 30 minutes after seizures. Furthermore, the number of IIS + HFO with the amplitude of 200 to 399 μV significantly decreased after seizures. Conclusions: IIS + HFO with the amplitude of 200 to 399 μV was influenced by and decreased after seizures. It may reflect the core part of epileptogenic area as similarly as ictal direct current shifts and ictal HFOs do. IIS + HFO could be called as the term "red slow," which may be useful to delineate at least a part of the epileptogenic zone.
... The cell cluster-based ('continuous') approach deals with the average characteristics of neural groups and focuses on a certain small number of states occurring in the neural dynamical system (da Silva et al., 2003). The averaged continuous model for the neural population contains a set of attractors gradually deforming the system evolution from pre-and interictal to ictal phases and back (Namiki et al., 2020). ...
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The mathematical modeling of epileptic seizures appearing in small neural populations can follow a few alternative ways: modeling of individual cells and their interaction vs. modeling groups and clusters on neurons. The purpose of this work is invention of a novel continuous (population-based) model for the appearance of the hyper-synchronized firing cells of the epileptiform type. In the same time, we use here the master equations based on the transition probabilities among different states of the cell excitation and hyper-synchronization. We developed an ODE model combining the dynamical equations for different sub-populations (unexcited, excited, and, as our novelty, hypersynchronized). Our model may serve as a simple but powerful tool to analyze the appearance and development of epileptiform dynamics in artificial neural networks. It can cover different cases of microepilepsy, and also may open the gate for studying drug-resistant epilepsy regime. Our dynamical set can be extended with the control inputs mimicking the external perturbations of the neural clusters with the electrical or optogenetic signals. In this case, the set of control algorithms can be applied to detect and suppress the epileptiform dynamics. Thus, the dynamic processes of epilepsy in small neural populations do not demand necessary the development of detailed models for individual neurons. Even the ‘averaged’ dynamical set for the unexcited, excited and hypersynchronized sub-populations can serve as an efficient tool for investigation and numerical simulations of microscopic seizures.
... Bongers et al. (2020) show that a specific component of the brain's power spectrum, the fractal or scale-free component as distinguished from the oscillatory features in EEG, increased specifically during the course of learning. Namiki et al. (2020) analyzed HFO in wideband ECoG of epilepsy patients, and found that interictal epileptic slow (red slow) phenomena was detected by residue of power spectrum. Suetani and Kitajo (2020) propose a manifold learning approach for visualizing individuality of human brain oscillations. ...
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Purpose: We reported the presence of interictal slow and high-frequency oscillations (HFOs) (IIS + HFO) and its temporal change so as to elucidate its clinical usefulness as a surrogate marker of epileptogenic zone in a patient with intractable focal epilepsy. Methods: We focused on one of the core electrodes of epileptogenicity, and investigated IIS + HFO in the pre- and post-segment of 30 minutes to all the 6 seizures. We adopted interictal slow in duration of 0.33 to 10 seconds, amplitude ≥50 μV and co-occurring with HFOs, and then divided into 5 groups depending on the amplitude of slow wave. Results: Before and after all the 6 seizures, the number of IIS + HFO was 2,890 at one electrode in the core epileptogenic zone. The number of IIS + HFO significantly decreased for 30 minutes after seizures. Furthermore, the number of IIS + HFO with the amplitude of 200 to 399 μV significantly decreased after seizures. Conclusions: IIS + HFO with the amplitude of 200 to 399 μV was influenced by and decreased after seizures. It may reflect the core part of epileptogenic area as similarly as ictal direct current shifts and ictal HFOs do. IIS + HFO could be called as the term "red slow," which may be useful to delineate at least a part of the epileptogenic zone.
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Objective: We assessed the temporal-spatial characteristics of ictal direct current (DC) shifts (or infraslow activity) and high frequency oscillations (HFOs) in 16 patients with intractable focal epilepsy. Methods: The underlying etiology consisted of cortical dysplasia, glioma, hippocampal sclerosis, and low-grade neuroepithelial tumor in nine, four, two, and one patients, respectively. The median number of analyzed seizure events was 8.0 per patient (range: 2-10). Chronic electrocorticographic recording was performed with (1) a band-pass filter of 0.016-600Hz (or 0.016-300Hz) and a sampling rate of 2000Hz (or 1000Hz). Results: Ictal DC shifts and a sustained form of ictal HFOs were observed in 75.0% and 50.0% of the patients, and 71.3% and 46.3% of the analyzed seizures. Visual assessment revealed that the onset of ictal DC shifts preceded that of ictal HFOs with statistical significance in 5/7 patients. The spatial extent of ictal DC shifts or HFOs was smaller than that of the conventionally defined seizure onset zone in 9/12 patients. Conclusion: Both ictal DC shifts and HFOs might represent the core of tissue generating seizures. Significance: The early occurrence of ictal DC shifts warrants further studies to determine the role of glia (possibly mediating ictal DC shifts) in seizure generation.
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In order to clarify further the characteristics of ictal direct current (DC) shifts in human epilepsy, we investigated them by subdural and scalp recording in six and three patients, respectively, both having mainly neocortical lobe epilepsy (five with frontal lobe epilepsy, two with parietal lobe epilepsy and two with temporal lobe epilepsy). By using subdural electrodes made of platinum, ictal DC shifts were observed in 85% of all the recorded seizures (89 seizures) among the six patients, and they were localized to just one or two electrodes at which the conventional initial ictal EEG change was also observed. They were closely accompanied by the electrodecremental pattern in all patients except for one in whom 1 Hz rhythmic activity was superimposed on clear negative slow shifts. Seizure control after resection of the cortex, including the area showing DC shifts, was favourable irrespective of histological diagnosis. Scalp-recorded ictal slow shifts were observed in 23% of all the recorded seizures (60 seizures) among the three patients. They were, like the subdurally recorded ones, mainly surface-negative in polarity, closely related to the electrodecremental pattern and consistent in their location. It seems that scalp-recorded DC shifts were detected particularly when seizures were clinically intense, while no slow shifts were observed in small seizures. It is concluded that at least subdurally recorded ictal slow shifts are clinically useful before epilepsy surgery to delineate more specifically an epileptogenic area as well as to further confirm the conventional initial ictal EEG change, and that scalp-recorded ictal slow shifts also have high specificity although their low sensitivity is to be taken into account.
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With advanced electroencephalography (EEG) technology, 'wideband EEG' ranging from slow shift to high frequency oscillation (HFO) is clinically available to study human epileptogenesis. The purpose of our study is to clarify the relationship between slow shift, HFO and conventional electrocorticographic (ECoG) change. A patient with right temporal lobe epilepsy who underwent presurgical evaluation with subdural electrodes was studied. Slow shift and HFO were evaluated in 16 habitual seizures with wideband EEG technique (bandpass filter of 0.016-600 Hz). Upon seizure occurrence in wideband ECoG, negative slow shifts coexisted with HFO (100-300 Hz) in the ictal onset zone in all investigated seizures. The former always preceded HFO and conventional initial EEG changes by mean value of 1.6 and 20.4s, respectively. The slow shifts and HFOs were observed only in the restricted ictal onset zone. In this particular patient, wideband EEG could delineate both ictal slow shift and HFO to define ictal onset zone, and the earliest occurrence of slow shifts may suggest an early role of glia in slow EEG shift generation than neurons. The time difference of the onset between ictal HFO and slow shift may help to understand epileptogenesis.
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Invasive ictal EEG recording is often necessary to delineate epileptogenic areas in patients with intractable partial epilepsy, but even intracranial ictal recordings often reveal ill-defined onset zones in neocortical epilepsy. We studied the physiologic significance of ictal direct current (DC) potentials recorded intracranially in human epilepsy. We made intracranial ictal EEG recordings in three patients with intractable partial seizures arising from frontal, lateral temporal, and parietal neocortical areas by using closely spaced subdural electrodes (platinum in two patients and stainless steel in one patient) with both standard (1.5 Hz) and open (0.016 Hz) low-frequency filter (LFF) settings. The initial ictal pattern was localized to two to nine subdural electrodes and characterized by very low voltage and high-frequency rhythmic activity ("electrodecremental pattern"). A slow-rising negative potential (DC potential) was seen in a slightly more restricted area (two to six electrodes) and occurred 1-10 s before the initial ictal EEG discharges in two patients. These results agree with those of previous studies of ictal DC shifts in animals and suggest that ictal DC shifts may be helpful in delineating the epileptogenic area more precisely in human epilepsy.
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The embedding dimensions of normal and epileptic electroencephalogram (EEG) time series are analyzed by two different methods, Cao's method and differential entropy method. The results of the two methods indicate consistently that the embedding dimensions of EEG signals during seizure will change and become different from that of normal EEG signals, and the embedding dimensions will vary intensively during seizure, whereas the embedding dimensions of normal EEG signals basically maintains stability. The embedding dimension results also reflect the variation of freedom degree of the human brain nonlinear dynamic system (NDS) during seizure. And based on the results of Cao's method, it is also found that normal EEG signals are of some degree of randomness, whereas epileptic EEG signals have determinism.
A comparison analysis of embedding dimensions between normal and epileptic EEG time series
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Babloyantz, A., Destexhe, A., 1986. A comparison analysis of embedding dimensions between normal and epileptic EEG time series. Proc. Natl. Sci. USA 83, 3513-3517.
Intracranially recorded ictal direct current shifts may precede high frequency oscillations in human epilepsy
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