How to Achieve Fast Entrainment? The Timescale to Synchronization

Entrainment, where oscillators synchronize to an external signal, is ubiquitous in nature. The transient time leading to entrainment plays a major role in many biological processes. Our goal is to unveil the specific dynamics that leads to fast entrainment. By studying a generic model, we characterize the transient time to entrainment and show how it is governed by two basic properties of an oscillator: the radial relaxation time and the phase velocity distribution around the limit cycle. Those two basic properties are inherent in every oscillator. This concept can be applied to many biological systems to predict the average transient time to entrainment or to infer properties of the underlying oscillator from the observed transients. We found that both a sinusoidal oscillator with fast radial relaxation and a spike-like oscillator with slow radial relaxation give rise to fast entrainment. As an example, we discuss the jet-lag experiments in the mammalian circadian pacemaker.     

Gap Junctions and Epileptic Seizures – Two Sides of the Same Coin?

Electrical synapses (gap junctions) play a pivotal role in the synchronization of neuronal ensembles which also makes them likely agonists of pathological brain activity. Although large body of experimental data and theoretical considerations indicate that coupling neurons by electrical synapses promotes synchronous activity (and thus is potentially epileptogenic), some recent evidence questions the hypothesis of gap junctions being among purely epileptogenic factors. In particular, an expression of inter-neuronal gap junctions is often found to be higher after the experimentally induced seizures than before. Here we used a computational modeling approach to address the role of neuronal gap junctions in shaping the stability of a network to perturbations that are often associated with the onset of epileptic seizures. We show that under some circumstances, the addition of gap junctions can increase the dynamical stability of a network and thus suppress the collective electrical activity associated with seizures. This implies that the experimentally observed post-seizure additions of gap junctions could serve to prevent further escalations, suggesting furthermore that they are a consequence of an adaptive response of the neuronal network to the pathological activity. However, if the seizures are strong and persistent, our model predicts the existence of a critical tipping point after which additional gap junctions no longer suppress but strongly facilitate the escalation of epileptic seizures. Our results thus reveal a complex role of electrical coupling in relation to epileptiform events. Which dynamic scenario (seizure suppression or seizure escalation) is ultimately adopted by the network depends critically on the strength and duration of seizures, in turn emphasizing the importance of temporal and causal aspects when linking gap junctions with epilepsy.     

小波能量评价EEG的不同成分对癫痫发作预报的价值

癫痫是一种严重危害人类健康的常见疾病,对癫痫发作进行预报具有重要的重要意义。通过对3例部分性继发全身性发作的癫痫病人在发作最长约30min的8导EEG进行小波分解,将EEG中的棘波、尖波成分与慢波成分分别突出到不同的尺度上,并计算相应尺度上这些成分的能量,考察这些不同成分在发作前的变化趋势。发现在发作前的若干分钟,8导EEG的慢波能量都有显著增大,而与棘波／尖波有关的快波能量基本上没有什么变化趋势,说明EEG慢波成分的增大对部分性继发全身性发作的预报具有重要价值,EEG的“慢波过大”可能是癫痫从发作间状态转变为发作的重要因素。     

Phase computations and phase models for discrete molecular oscillators

Background

Biochemical oscillators perform crucial functions in cells, e.g., they set up circadian clocks. The dynamical behavior of oscillators is best described and analyzed in terms of the scalar quantity, phase. A rigorous and useful definition for phase is based on the so-called isochrons of oscillators. Phase computation techniques for continuous oscillators that are based on isochrons have been used for characterizing the behavior of various types of oscillators under the influence of perturbations such as noise.

Results

In this article, we extend the applicability of these phase computation methods to biochemical oscillators as discrete molecular systems, upon the information obtained from a continuous-state approximation of such oscillators. In particular, we describe techniques for computing the instantaneous phase of discrete, molecular oscillators for stochastic simulation algorithm generated sample paths. We comment on the accuracies and derive certain measures for assessing the feasibilities of the proposed phase computation methods. Phase computation experiments on the sample paths of well-known biological oscillators validate our analyses.

Conclusions

The impact of noise that arises from the discrete and random nature of the mechanisms that make up molecular oscillators can be characterized based on the phase computation techniques proposed in this article. The concept of isochrons is the natural choice upon which the phase notion of oscillators can be founded. The isochron-theoretic phase computation methods that we propose can be applied to discrete molecular oscillators of any dimension, provided that the oscillatory behavior observed in discrete-state does not vanish in a continuous-state approximation. Analysis of the full versatility of phase noise phenomena in molecular oscillators will be possible if a proper phase model theory is developed, without resorting to such approximations.     

Transient and steady state phase response curves of limit cycle oscillators

The experiment of phase shifts resulting from discrete perturbations of stable biological rhythms has been carried out to study entrainment behavior of oscillators. There are two kinds of phase response curves, which are measured in experiments, according to as one measures the phase shifts immediately or long after the perturbation. The former is the first transient phase response curve and the latter is the steady state phase response curve. We redefine both curves within the framework of dynamical system theory and homotopy theory. Several topological properties of both curves are clarified. Consequently, it is shown that we must compare the shapes of both two phase response curves to investigate the inner structures of biological oscillators. Moreover, we prove that a single limit cycle oscillator involving only two variables cannot simulate transient resetting behavior reported by Pittendrigh and Minis (1964). In other words, the circadian oscillator of Drosophila pseudoobscura does not consist of a single oscillator of two variables. Finally we show that a model which consists of two limit cycle oscillators is able to simulate qualitatively the phase response curves of Drosophila.     

Characterization of synchronization in interacting groups of oscillators: application to seizures

We investigate the emergence of synchronization in two groups of oscillators; one group acts as a synchronization source, and the other as the target. Based on phase model simulations, we construct a synchrony index (SI): a combination of intra- and intergroup synchronies. The SI characterizes the extent of induced synchrony in the population. We demonstrate the usefulness of the measure in a test case of mesial temporal lobe epilepsy: the SI can be readily calculated from standard electroencephalographic measurements. We show that the synchrony index has a statistically significant increased value for the ictal periods and that the epileptic focus can be located by identifying the most synchronous pairs of electrodes during the initial part of ictal period of the seizure. We also show that it is possible in this pilot case to differentiate clinical and subclinical seizures based on the dynamical features of the synchronization. The synchronization index was found to be a useful quantity for the characterization of “pathological hypersynchronization” within a well-characterized patient with mesial temporal lobe epilepsy and thus has potential medical value in seizure detection, localizing ability, and association with later surgical outcome.     

The control of seizure-like activity in the rat hippocampal slice

The sudden and transient hypersynchrony of neuronal firing that characterizes epileptic seizures can be considered as the transitory stabilization of metastable states present within the dynamical repertoire of a neuronal network. Using an in vitro model of recurrent spontaneous seizures in the rat horizontal hippocampal slice preparation, we present an approach to characterize the dynamics of the transition to seizure, and to use this information to control the activity and avoid the occurrence of seizure-like events. The transition from the interictal activity (between seizures) to the seizure-like event is aborted by brief (20-50 s) low-frequency (0.5 Hz) periodic forcing perturbations, applied via an extracellular stimulating electrode to the mossy fibers, the axons of the dentate neurons that synapse onto the CA3 pyramidal cells. This perturbation results in the stabilization of an interictal-like low-frequency firing pattern in the hippocampal slice. The results derived from this work shed light on the dynamics of the transition to seizure and will further the development of algorithms that can be used in automated devices to stop seizure occurrence.     

Evidence for spreading seizure as a cause of theta-alpha activity electrographic pattern in stereo-EEG seizure recordings

Intracranial electroencephalography is a standard tool in clinical evaluation of patients with focal epilepsy. Various early electrographic seizure patterns differing in frequency, amplitude, and waveform of the oscillations are observed. The pattern most common in the areas of seizure propagation is the so-called theta-alpha activity (TAA), whose defining features are oscillations in the θ − α range and gradually increasing amplitude. A deeper understanding of the mechanism underlying the generation of the TAA pattern is however lacking. In this work we evaluate the hypothesis that the TAA patterns are caused by seizures spreading across the cortex. To do so, we perform simulations of seizure dynamics on detailed patient-derived cortical surfaces using the spreading seizure model as well as reference models with one or two homogeneous sources. We then detect the occurrences of the TAA patterns both in the simulated stereo-electroencephalographic signals and in the signals of recorded epileptic seizures from a cohort of fifty patients, and we compare the features of the groups of detected TAA patterns to assess the plausibility of the different models. Our results show that spreading seizure hypothesis is qualitatively consistent with the evidence available in the seizure recordings, and it can explain the features of the detected TAA groups best among the examined models.     

A Computational Study of Stimulus Driven Epileptic Seizure Abatement

Active brain stimulation to abate epileptic seizures has shown mixed success. In spike-wave (SW) seizures, where the seizure and background state were proposed to coexist, single-pulse stimulations have been suggested to be able to terminate the seizure prematurely. However, several factors can impact success in such a bistable setting. The factors contributing to this have not been fully investigated on a theoretical and mechanistic basis. Our aim is to elucidate mechanisms that influence the success of single-pulse stimulation in noise-induced SW seizures. In this work, we study a neural population model of SW seizures that allows the reconstruction of the basin of attraction of the background activity as a four dimensional geometric object. For the deterministic (noise-free) case, we show how the success of response to stimuli depends on the amplitude and phase of the SW cycle, in addition to the direction of the stimulus in state space. In the case of spontaneous noise-induced seizures, the basin becomes probabilistic introducing some degree of uncertainty to the stimulation outcome while maintaining qualitative features of the noise-free case. Additionally, due to the different time scales involved in SW generation, there is substantial variation between SW cycles, implying that there may not be a fixed set of optimal stimulation parameters for SW seizures. In contrast, the model suggests an adaptive approach to find optimal stimulation parameters patient-specifically, based on real-time estimation of the position in state space. We discuss how the modelling work can be exploited to rationally design a successful stimulation protocol for the abatement of SW seizures using real-time SW detection.     

Anticonvulsant properties of the cerebrospinal fluid during activation of the antiepileptic system of the brain

Cerebrospinal fluid (CSF) was obtained after 30-40 sessions of daily electrical stimulation of the cat cerebellum vermis. The intraventricular injection of CSF (10 microliters) to Wistar rats increased the latent period of initial seizure manifestations, significantly reduced the number of animals with seizures and reduced the severity of seizures induced by korazol injection (40 mg/kg). Analogous seizure changes were observed in rats after intraventricular injection of CSF (10 microliters) from cats subject to 3-10 electroshock seizure fits. Intraventricular injection of CSF (250 microliters) obtained from cats after electroshock to cats with strychnine-induced epileptic foci in the brain cortex led to the suppression of the epileptic activity. The conclusion was made that different ways of antiepileptic system activation cause the accumulation of endogenous antiepileptic substances in CSF.     

Analysis of Epileptic Discharges from Implanted Subdural Electrodes in Patients with Sturge-Weber Syndrome

ObjectiveAlmost two-thirds of patients with Sturge-Weber syndrome (SWS) have epilepsy, and half of them require surgery for it. However, it is well known that scalp electroencephalography (EEG) does not demonstrate unequivocal epileptic discharges in patients with SWS. Therefore, we analyzed interictal and ictal discharges from intracranial subdural EEG recordings in patients treated surgically for SWS to elucidate epileptogenicity in this disorder.MethodsFive intractable epileptic patients with SWS who were implanted with subdural electrodes for presurgical evaluation were enrolled in this study. We examined the following seizure parameters: seizure onset zone (SOZ), propagation speed of seizure discharges, and seizure duration by visual inspection. Additionally, power spectrogram analysis on some frequency bands at SOZ was performed from 60 s before the visually detected seizure onset using the EEG Complex Demodulation Method (CDM).ResultsWe obtained 21 seizures from five patients for evaluation, and all seizures initiated from the cortex under the leptomeningeal angioma. Most of the patients presented with motionless staring and respiratory distress as seizure symptoms. The average seizure propagation speed and duration were 3.1 ± 3.6 cm/min and 19.4 ± 33.6 min, respectively. Significant power spectrogram changes at the SOZ were detected at 10–30 Hz from 15 s before seizure onset, and at 30–80 Hz from 5 s before seizure onset.SignificanceIn patients with SWS, seizures initiate from the cortex under the leptomeningeal angioma, and seizure propagation is slow and persists for a longer period. CDM indicated beta to low gamma-ranged seizure discharges starting from shortly before the visually detected seizure onset. Our ECoG findings indicate that ischemia is a principal mechanism underlying ictogenesis and epileptogenesis in SWS.     

Dynamic Imaging of Coherent Sources Reveals Different Network Connectivity Underlying the Generation and Perpetuation of Epileptic Seizures

The concept of focal epilepsies includes a seizure origin in brain regions with hyper synchronous activity (epileptogenic zone and seizure onset zone) and a complex epileptic network of different brain areas involved in the generation, propagation, and modulation of seizures. The purpose of this work was to study functional and effective connectivity between regions involved in networks of epileptic seizures. The beginning and middle part of focal seizures from ictal surface EEG data were analyzed using dynamic imaging of coherent sources (DICS), an inverse solution in the frequency domain which describes neuronal networks and coherences of oscillatory brain activities. The information flow (effective connectivity) between coherent sources was investigated using the renormalized partial directed coherence (RPDC) method. In 8/11 patients, the first and second source of epileptic activity as found by DICS were concordant with the operative resection site; these patients became seizure free after epilepsy surgery. In the remaining 3 patients, the results of DICS / RPDC calculations and the resection site were discordant; these patients had a poorer post-operative outcome. The first sources as found by DICS were located predominantly in cortical structures; subsequent sources included some subcortical structures: thalamus, Nucl. Subthalamicus and cerebellum. DICS seems to be a powerful tool to define the seizure onset zone and the epileptic networks involved. Seizure generation seems to be related to the propagation of epileptic activity from the primary source in the seizure onset zone, and maintenance of seizures is attributed to the perpetuation of epileptic activity between nodes in the epileptic network. Despite of these promising results, this proof of principle study needs further confirmation prior to the use of the described methods in the clinical praxis.     

基于脑电信号的癫痫发作预测特征及识别

解码癫痫发作前脑电信号的神经元集群异常痫样放电活动,对癫痫发作进行有效预测并实施病前干预,可显著减少疾病病损,是癫痫防治的研究热点之一。基于脑电信号的癫痫发作预测研究关键在于发作间期和前期的异常状态识别,研究上述两状态间的神经动力学特征差异对明确癫痫发病机制、选取高分辨特征,进而有效识别该渐进性疾病所处的发作阶段具有重要价值。目前,研究者已对当前主流特征提取及模式识别方法进行了充分的调研梳理,但忽视了神经动态特征变化对于癫痫发作预测的重要意义。基于此,本文归纳总结了5类典型的发作预测特征分析方法及其优缺点,重点剖析了发作间期至前期神经生理特征的动态变化及其动力学特性,类比分析了当前该领域主流的机器学习和深度学习特征识别方法,以期为进一步建立精准、高效的癫痫发作预测技术提供新思路。     

Application of a dissimilarity index of EEG and its sub-bands on prediction of induced epileptic seizures from rat's EEG signals

ObjectiveEpileptic seizures are defined as manifest of excessive and hyper-synchronous activity of neurons in the cerebral cortex that cause frequent malfunction of the human central nervous system. Therefore, finding precursors and predictors of epileptic seizure is of utmost clinical relevance to reduce the epileptic seizure induced nervous system malfunction consequences. Researchers for this purpose may even guide us to a deep understanding of the seizure generating mechanisms. The goal of this paper is to predict epileptic seizures in epileptic rats.MethodsSeizures were induced in rats using pentylenetetrazole (PTZ) model. EEG signals in interictal, preictal, ictal and postictal periods were then recorded and analyzed to predict epileptic seizures. Epileptic seizures were predicted by calculating an index in consecutive windows of EEG signal and comparing the index with a threshold. In this work, a newly proposed dissimilarity index called Bhattacharyya Based Dissimilarity Index (BBDI), dynamical similarity index and fuzzy similarity index were investigated.ResultsBBDI, dynamical similarity index and fuzzy similarity index were examined on case and control groups and compared to each other. The results show that BBDI outperforms dynamical and fuzzy similarity indices. In order to improve the results, EEG sub-bands were also analyzed. The best result achieved when the proposed dissimilarity index was applied on Delta sub-band that predicts epileptic seizures in all rats with a mean of 299.5 s.ConclusionThe dissimilarity of neural network activity between reference window and present window of EEG signal has a significant increase prior to an epileptic seizure and the proposed dissimilarity index (BBDI) can reveal this variation to predict epileptic seizures. In addition, analyzing EEG sub-bands results in more accurate information about constituent neuronal activities underlying the EEG since certain changes in EEG signal may be amplified when each sub-band is analyzed separately.SignificanceThis paper presents application of a dissimilarity index (BBDI) on EEG signals and its sub-bands to predict PTZ-induced epileptic seizures in rats. Based on the results of this work, BBDI will predict epileptic seizures more accurately and more reliably compared to current indices that increases epileptic patient comfort and improves patient outcomes.     

Effects of activation and lesions of the superior colliculi of the lamina quadrigemina on epileptic activity in rats]

In acute experiments on rats it was shown that activation of SC by bilateral microinjection of penicillin (5-15 IU) or bicuculline (25-50 ng) resulted in the increased latency and decreased severity of i.p. picrotoxin-induced seizures (2 mg/kg). The suppression of behavioral convulsions and the decreased epileptic activity in the hippocampus and cerebral cortex were followed by occurrence of spike discharges in SC with an amplitude of 200-500 mcV and frequency of 5-12/sec which testifies to the formation of penicillin- or bicuculline-induced generator excitation in SC. The lesions of SC by kainic acid administration resulted in the decreased seizure threshold and, also, facilitated the development of seizure under conditions of picrotoxin kindling. The conclusion is made that SC activation plays an important role in the realization of functional integrative activity of the antiepileptic system.     

Are circadian oscillators structurally unstable?

The common belief is that all biological oscillations are of limit cycle type. It is shown in this article that the phase response curves simulated on a two-species Lotka-Volterra linear (i.e. non-limit cycle type) oscillator, do look similar to those obtained by experimental methods by different workers. The form of the phase response curves, the existence of singularities and the mirror-image symmetry of opposite perturbations are modelled on the Lotka-Volterra system. The study, which is strongly indicative of the possibility that the underlying oscillator (or oscillators) is (are) not structurally stable, also indicates the necessity of designing critical experiments, capable of distinguishing between limit cycle and non-limit cycle oscillators, since the single-pulse phase resetting does nothing to distinguish between them.     

Data-driven method to infer the seizure propagation patterns in an epileptic brain from intracranial electroencephalography

Surgical interventions in epileptic patients aimed at the removal of the epileptogenic zone have success rates at only 60-70%. This failure can be partly attributed to the insufficient spatial sampling by the implanted intracranial electrodes during the clinical evaluation, leading to an incomplete picture of spatio-temporal seizure organization in the regions that are not directly observed. Utilizing the partial observations of the seizure spreading through the brain network, complemented by the assumption that the epileptic seizures spread along the structural connections, we infer if and when are the unobserved regions recruited in the seizure. To this end we introduce a data-driven model of seizure recruitment and propagation across a weighted network, which we invert using the Bayesian inference framework. Using a leave-one-out cross-validation scheme on a cohort of 45 patients we demonstrate that the method can improve the predictions of the states of the unobserved regions compared to an empirical estimate that does not use the structural information, yet it is on the same level as the estimate that takes the structure into account. Furthermore, a comparison with the performed surgical resection and the surgery outcome indicates a link between the inferred excitable regions and the actual epileptogenic zone. The results emphasize the importance of the structural connectome in the large-scale spatio-temporal organization of epileptic seizures and introduce a novel way to integrate the patient-specific connectome and intracranial seizure recordings in a whole-brain computational model of seizure spread.     

The Search for New Screening Models of Pharmacoresistant Epilepsy: Is Induction of Acute Seizures in Epileptic Rodents a Suitable Approach?

Epilepsy, a prevalent neurological disease characterized by spontaneous recurrent seizures (SRS), is often refractory to treatment with anti-seizure drugs (ASDs), so that more effective ASDs are urgently needed. For this purpose, it would be important to develop, validate, and implement new animal models of pharmacoresistant epilepsy into drug discovery. Several chronic animal models with difficult-to-treat SRS do exist; however, most of these models are not suited for drug screening, because drug testing on SRS necessitates laborious video-EEG seizure monitoring. More recently, it was proposed that, instead of monitoring SRS, chemical or electrical induction of acute seizures in epileptic rodents may be used as a surrogate for testing the efficacy of novel ASDs against refractory SRS. Indeed, several ASDs were shown to lose their efficacy on acute seizures, when such seizures were induced by pentylenetetrazole (PTZ) in epileptic rather than nonepileptic rats, whereas this was not observed when using the maximal electroshock seizure test. Subsequent studies confirmed the loss of anti-seizure efficacy of valproate against PTZ-induced seizures in epileptic mice, but several other ASDs were more potent against PTZ in epileptic than nonepileptic mice. This was also observed when using the 6-Hz model of partial seizures in epileptic mice, in which the potency of levetiracetam, in particular, was markedly increased compared to nonepileptic animals. Overall, these observations suggest that performing acute seizure tests in epileptic rodents provides valuable information on the pharmacological profile of ASDs, in particular those with mechanisms inherent to disease-induced brain alterations. However, it appears that further work is needed to define optimal approaches for acute seizure induction and generation of epileptic/drug refractory animals that would permit reliable screening of new ASDs with improved potential to provide seizure control in patients with pharmacoresistant epilepsy.     

Epilepsy and electromagnetic fields: effects of simulated atmospherics and 100-Hz magnetic fields on audiogenic seizure in rats

In order to study the possible association between epileptic seizures and natural electromagnetic fields, 32 female audiogenic seizure (AGS)-susceptible rats were exposed to simulated 10 kHz and 28 kHz atmospherics and to a sinusoidally oscillating magnetic field with a frequency of 100 Hz and field strength of 1 A/m. After the electromagnetic exposure, seizures were induced in the rats with a sound stimulus. The severity of the seizure was determined on an ordinal scale, the audiogenic response score (ARS). The time from the beginning of the sound stimulus to the onset of the seizure (seizure latency) and the duration of the convulsion was measured. No differences from the control experiments were found in the experiments with simulated atmospherics, but the 100 Hz magnetic field increased the seizure latency by about 13% (P<0.02). The results do not support the hypothesis that natural atmospheric electromagnetic signals could affect the onset of epileptic seizures, but they suggest that AGS-susceptible rats may be a useful model for studying the biological effects of electromagnetic fields.     

Synchronization regulation in a model of coupled neural masses

A model of coupled neural masses can generate seizure-like events and dynamics similar to those observed during interictal to ictal transitions and thus can be used for theoretical study of the control of epileptic seizures. In an effort to understand the mechanisms underlying epileptic seizures and how to avoid them, we added a control input to this model. Epileptic seizures are always accompanied by hypersynchronous firing of neurons, so research on synchronization among cortical areas is significant for seizure control. In this study, principal component analysis (PCA) was used to identify synchronization clusters composed of several neural masses. A method for calculating the synchronization cluster strength and participation rate is presented. The synchronization cluster strength can be used to identify synchronization clusters and the participation rate can be employed to identify neural masses that participate in the clusters. Each synchronization cluster is controlled as a whole using a proportional-integral-derivative (PID) controller. We illustrate these points using coupled neural mass models of synchronization to show their responses to increased (between node) coupling with and without control. Experiment results indicated that PID control can effectively regulate synchronization between neural masses and has the potential for seizure prevention.