Nonlinear structures in electroencephalogram signals

We apply a nonlinear prediction algorithm to investigate the presence of nonlinear structure in electroencephalogram (EEG) recordings. The EEG signal could be modeled as a realization of a nonlinear model plus a residual noise (uncorrelated Gaussian noise). Using linear and nonlinear models we analyze the statistical nature of these residual noises in the case of epileptic patients and normal subjects. We found that the residual noise presents Gaussian distribution for epileptic patients if a nonlinear model is used whereas in the case of normal subjects the residual noise will exhibit a Gaussian distribution only if a linear model (autoregressive) is used. These results provide another evidence of the nonlinear character of the epileptic seizure recordings, while the normal EEG seems to be better described as linearly correlated noise.     

Steady-state visual evoked potentials and phase synchronization in migraine patients

We investigate phase synchronization in EEG recordings from migraine patients. We use the analytic signal technique, based on the Hilbert transform, and find that migraine brains are characterized by enhanced alpha band phase synchronization in the presence of visual stimuli. Our findings show that migraine patients have an overactive regulatory mechanism that renders them more sensitive to external stimuli.     

Continuous EEG-fMRI in patients with partial epilepsy and focal interictal slow-wave discharges on EEG

Purpose

To verify whether in patients with partial epilepsy and routine electroenecephalogram (EEG) showing focal interictal slow-wave discharges without spikes combined EEG–functional magnetic resonance imaging (fMRI) would localize the corresponding epileptogenic focus, thus providing reliable information on the epileptic source.

Methods

Eight patients with partial epileptic seizures whose routine scalp EEG recordings on presentation showed focal interictal slow-wave activity underwent EEG–fMRI. EEG data were continuously recorded for 24 min (four concatenated sessions) from 18 scalp electrodes, while fMRI scans were simultaneously acquired with a 1.5-Tesla magnetic resonance imaging (MRI) scanner. After recording sessions and MRI artefact removal, EEG data were analyzed offline. We compared blood oxygen level-dependent (BOLD) signal changes on fMRI with EEG recordings obtained at rest and during activation (with and without focal interictal slow-wave discharges).

Results

In all patients, when the EEG tracing showed the onset of focal slow-wave discharges on a few lateralized electrodes, BOLD-fMRI activation in the corresponding brain area significantly increased. We detected significant concordance between focal EEG interictal slow-wave discharges and focal BOLD activation on fMRI. In patients with lesional epilepsy, the epileptogenic area corresponded to the sites of increased focal BOLD signal.

Conclusions

Even in patients with partial epilepsy whose standard EEGs show focal interictal slow-wave discharges without spikes, EEG–fMRI can visualize related focal BOLD activation thus providing useful information for pre-surgical planning.     

Integration of EEG source imaging and fMRI during continuous viewing of natural movies

Electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) are noninvasive neuroimaging tools which can be used to measure brain activity with excellent temporal and spatial resolution, respectively. By combining the neural and hemodynamic recordings from these modalities, we can gain better insight into how and where the brain processes complex stimuli, which may be especially useful in patients with different neural diseases. However, due to their vastly different spatial and temporal resolutions, the integration of EEG and fMRI recordings is not always straightforward. One fundamental obstacle has been that paradigms used for EEG experiments usually rely on event-related paradigms, while fMRI is not limited in this regard. Therefore, here we ask whether one can reliably localize stimulus-driven EEG activity using the continuously varying feature intensities occurring in natural movie stimuli presented over relatively long periods of time. Specifically, we asked whether stimulus-driven aspects in the EEG signal would be co-localized with the corresponding stimulus-driven BOLD signal during free viewing of a movie. Secondly, we wanted to integrate the EEG signal directly with the BOLD signal, by estimating the underlying impulse response function (IRF) that relates the BOLD signal to the underlying current density in the primary visual area (V1). We made sequential fMRI and 64-channel EEG recordings in seven subjects who passively watched 2-min-long segments of a James Bond movie. To analyze EEG data in this natural setting, we developed a method based on independent component analysis (ICA) to reject EEG artifacts due to blinks, subject movement, etc., in a way unbiased by human judgment. We then calculated the EEG source strength of this artifact-free data at each time point of the movie within the entire brain volume using low-resolution electromagnetic tomography (LORETA). This provided for every voxel in the brain (i.e., in 3D space) an estimate of the current density at every time point. We then carried out a correlation between the time series of visual contrast changes in the movie with that of EEG voxels. We found the most significant correlations in visual area V1, just as seen in previous fMRI studies (Bartels A, Zeki, S, Logothetis NK. Natural vision reveals regional specialization to local motion and to contrast-invariant, global flow in the human brain. Cereb Cortex 2008;18(3):705–717), but on the time scale of milliseconds rather than of seconds. To obtain an estimate of how the EEG signal relates to the BOLD signal, we calculated the IRF between the BOLD signal and the estimated current density in area V1. We found that this IRF was very similar to that observed using combined intracortical recordings and fMRI experiments in nonhuman primates. Taken together, these findings open a new approach to noninvasive mapping of the brain. It allows, firstly, the localization of feature-selective brain areas during natural viewing conditions with the temporal resolution of EEG. Secondly, it provides a tool to assess EEG/BOLD transfer functions during processing of more natural stimuli. This is especially useful in combined EEG/fMRI experiments, where one can now potentially study neural-hemodynamic relationships across the whole brain volume in a noninvasive manner.     

Multi-Scale Permutation Entropy: A Potential Measure for the Impact of Sleep Medication on Brain Dynamics of Patients with Insomnia

Insomnia is a common sleep disorder that is closely associated with the occurrence and deterioration of cardiovascular disease, depression and other diseases. The evaluation of pharmacological treatments for insomnia brings significant clinical implications. In this study, a total of 20 patients with mild insomnia and 75 healthy subjects as controls (HC) were included to explore alterations of electroencephalogram (EEG) complexity associated with insomnia and its pharmacological treatment by using multi-scale permutation entropy (MPE). All participants were recorded for two nights of polysomnography (PSG). The patients with mild insomnia received a placebo on the first night (Placebo) and temazepam on the second night (Temazepam), while the HCs had no sleep-related medication intake for either night. EEG recordings from each night were extracted and analyzed using MPE. The results showed that MPE decreased significantly from pre-lights-off to the period during sleep transition and then to the period after sleep onset, and also during the deepening of sleep stage in the HC group. Furthermore, results from the insomnia subjects showed that MPE values were significantly lower for the Temazepam night compared to MPE values for the Placebo night. Moreover, MPE values for the Temazepam night showed no correlation with age or gender. Our results indicated that EEG complexity, measured by MPE, may be utilized as an alternative approach to measure the impact of sleep medication on brain dynamics.     

Approximate Entropy of Brain Network in the Study of Hemispheric Differences

Human brain, a dynamic complex system, can be studied with different approaches, including linear and nonlinear ones. One of the nonlinear approaches widely used in electroencephalographic (EEG) analyses is the entropy, the measurement of disorder in a system. The present study investigates brain networks applying approximate entropy (ApEn) measure for assessing the hemispheric EEG differences; reproducibility and stability of ApEn data across separate recording sessions were evaluated. Twenty healthy adult volunteers were submitted to eyes-closed resting EEG recordings, for 80 recordings. Significant differences in the occipital region, with higher values of entropy in the left hemisphere than in the right one, show that the hemispheres become active with different intensities according to the performed function. Besides, the present methodology proved to be reproducible and stable, when carried out on relatively brief EEG epochs but also at a 1-week distance in a group of 36 subjects. Nonlinear approaches represent an interesting probe to study the dynamics of brain networks. ApEn technique might provide more insight into the pathophysiological processes underlying age-related brain disconnection as well as for monitoring the impact of pharmacological and rehabilitation treatments.     

Testing Jump-Diffusion in Epileptic Brain Dynamics: Impact of Daily Rhythms

Stochastic approaches to complex dynamical systems have recently provided broader insights into spatial-temporal aspects of epileptic brain dynamics. Stochastic qualifiers based on higher-order Kramers-Moyal coefficients derived directly from time series data indicate improved differentiability between physiological and pathophysiological brain dynamics. It remains unclear, however, to what extent stochastic qualifiers of brain dynamics are affected by other endogenous and/or exogenous influencing factors. Addressing this issue, we investigate multi-day, multi-channel electroencephalographic recordings from a subject with epilepsy. We apply a recently proposed criterion to differentiate between Langevin-type and jump-diffusion processes and observe the type of process most qualified to describe brain dynamics to change with time. Stochastic qualifiers of brain dynamics are strongly affected by endogenous and exogenous rhythms acting on various time scales—ranging from hours to days. Such influences would need to be taken into account when constructing evolution equations for the epileptic brain or other complex dynamical systems subject to external forcings.     

Approximate entropy (ApEn) as a complexity measure

Approximate entropy (ApEn) is a recently developed statistic quantifying regularity and complexity, which appears to have potential application to a wide variety of relatively short (greater than 100 points) and noisy time-series data. The development of ApEn was motivated by data length constraints commonly encountered, e.g., in heart rate, EEG, and endocrine hormone secretion data sets. We describe ApEn implementation and interpretation, indicating its utility to distinguish correlated stochastic processes, and composite deterministic/ stochastic models. We discuss the key technical idea that motivates ApEn, that one need not fully reconstruct an attractor to discriminate in a statistically valid manner-marginal probability distributions often suffice for this purpose. Finally, we discuss why algorithms to compute, e.g., correlation dimension and the Kolmogorov-Sinai (KS) entropy, often work well for true dynamical systems, yet sometimes operationally confound for general models, with the aid of visual representations of reconstructed dynamics for two contrasting processes. (c) 1995 American Institute of Physics.     

基于非线性预测效果的癫痫脑电信号的特征提取方法

在非线性时间序列预测研究的基础上,提出了基于非线性预测效果的癫痫脑电信号特征提取方法,从脑电信号中自动检测出癫痫脑电信号.采用基于可预测性的选取嵌入维数的方法确定脑电信号序列的嵌入维数,进行相空间重构.实验结果表明:基于非线性预测效果的特征提取方法提取的特征能明显地区分癫痫脑电信号与正常脑电信号,该非线性特征提取方法适合小数据量的情况且对噪声的稳定性好.     

Detrended fluctuation analysis of heart intrabeat dynamics

We investigate scaling properties of electrocardiogram (ECG) recordings of healthy subjects and heart failure patients based on detrended fluctuation analysis (DFA). While the vast majority of scaling analysis has focused on the characterization of the long-range correlations of interbeat (i.e., beat-to-beat) dynamics, in this work we consider instead the characterization of intrabeat dynamics. That is, here we use DFA to study correlations for time scales smaller than one heart beat period (about 0.75 s). Our results show that intrabeat dynamics of healthy subject are less correlated than for heart failure dynamics. As in the case of interbeat dynamics, the DFA scaling exponents can be used to discriminate healthy and pathological data. It is shown that 0.5 h recordings suffices to characterize the ECG correlation properties.     

Normal form transforms separate slow and fast modes in stochastic dynamical systems

Modelling stochastic systems has many important applications. Normal form coordinate transforms are a powerful way to untangle interesting long term macroscale dynamics from insignificant detailed microscale dynamics. We explore such coordinate transforms of stochastic differential systems when the dynamics have both slow modes and quickly decaying modes. The thrust is to derive normal forms useful for macroscopic modelling of complex stochastic microscopic systems. Thus we not only must reduce the dimensionality of the dynamics, but also endeavour to separate all slow processes from all fast time processes, both deterministic and stochastic. Quadratic stochastic effects in the fast modes contribute to the drift of the important slow modes. Some examples demonstrate that the coordinate transform may be only locally valid or may be globally valid depending upon the dynamical system. The results will help us accurately model, interpret and simulate multiscale stochastic systems.     

Pure phase-locking of beta/gamma oscillation contributes to the N30 frontal component of somatosensory evoked potentials

Background  

Evoked potentials have been proposed to result from phase-locking of electroencephalographic (EEG) activities within specific frequency bands. However, the respective contribution of phasic activity and phase resetting of ongoing EEG oscillation remains largely debated. We here applied the EEGlab procedure in order to quantify the contribution of electroencephalographic oscillation in the generation of the frontal N30 component of the somatosensory evoked potentials (SEP) triggered by median nerve electrical stimulation at the wrist. Power spectrum and intertrial coherence analysis were performed on EEG recordings in relation to median nerve stimulation.     

Zeno dynamics for open quantum systems

In this paper, we formulate limit Zeno dynamics of general open systems as the adiabatic elimination of fast components. We are able to exploit previous work on adiabatic elimination of quantum stochastic models to give explicitly the conditions under which open Zeno dynamics will exist. The open systems formulation is further developed as a framework for Zeno master equations, and Zeno filtering (that is, quantum trajectories based on a limit Zeno dynamical model). We discuss several models from the point of view of quantum control. For the case of linear quantum stochastic systems, we present a condition for stability of the asymptotic Zeno dynamics.     

Kinetic Theory of Jet Dynamics in the Stochastic Barotropic and 2D Navier-Stokes Equations

We discuss the dynamics of zonal (or unidirectional) jets for barotropic flows forced by Gaussian stochastic fields with white in time correlation functions. This problem contains the stochastic dynamics of 2D Navier-Stokes equation as a special case. We consider the limit of weak forces and dissipation, when there is a time scale separation between the inertial time scale (fast) and the spin-up or spin-down time (large) needed to reach an average energy balance. In this limit, we show that an adiabatic reduction (or stochastic averaging) of the dynamics can be performed. We then obtain a kinetic equation that describes the slow evolution of zonal jets over a very long time scale, where the effect of non-zonal turbulence has been integrated out. The main theoretical difficulty, achieved in this work, is to analyze the stationary distribution of a Lyapunov equation that describes quasi-Gaussian fluctuations around each zonal jet, in the inertial limit. This is necessary to prove that there is no ultraviolet divergence at leading order, in such a way that the asymptotic expansion is self-consistent. We obtain at leading order a Fokker–Planck equation, associated to a stochastic kinetic equation, that describes the slow jet dynamics. Its deterministic part is related to well known phenomenological theories (for instance Stochastic Structural Stability Theory) and to quasi-linear approximations, whereas the stochastic part allows to go beyond the computation of the most probable zonal jet. We argue that the effect of the stochastic part may be of huge importance when, as for instance in the proximity of phase transitions, more than one attractor of the dynamics is present.     

How the NPX data format handles EEG data acquired simultaneously with fMRI

There is a growing interest in combining EEG and (f)MRI data as they provide complementary information: EEG is characterized by a high temporal resolution but poor spatial one, while fMRI is characterized by a high spatial resolution but low temporal one. However, while a standard file format for storing EEG data is available since over a decade, it does not fulfill the needs of modern protocols and devices such as those involved in simultaneous EEG and fMRI recordings. The main reasons are the limited bit resolution, some difficulties encountered in handling and storing acquisition events or trace markers for off-line analyses and the impossibility to add some protocol-specific information that is not considered in the actual data formats. This, among others, hinders the release of free analysis software and makes it difficult to share data across different laboratories as every research unit develops its own tools according to its needs, stores data in proprietary formats and a lot of time is spent building software applications for converting data from one format to another. The NPX (NeuroPhysiological signals in eXtensible Markup Language) data format was defined to overcome these and other limitations, and here its main characteristics are reported as well as how some typical problems occurring in simultaneous EEG-fMRI recordings are also treated. Many tools based on the NPX technology can be freely downloaded, including a tool for removing artifacts occurring during simultaneous EEG-fMRI recordings.     

Noise-induced precursors of tonic-to-bursting transitions in hypothalamic neurons and in a conductance-based model

The dynamics of neurons is characterized by a variety of different spiking patterns in response to external stimuli. One of the most important transitions in neuronal response patterns is the transition from tonic firing to burst discharges, i.e., when the neuronal activity changes from single spikes to the grouping of spikes. An increased number of interspike-interval sequences of specific temporal correlations was detected in anticipation of temperature induced tonic-to-bursting transitions in both, experimental impulse recordings from hypothalamic brain slices and numerical simulations of a stochastic model. Analysis of the modelling data elucidates that the appearance of such patterns can be related to particular system dynamics in the vicinity of the period-doubling bifurcation. It leads to a nonlinear response on de- and hyperpolarizing perturbations introduced by noise. This explains why such particular patterns can be found as reliable precursors of the neurons' transition to burst discharges.     

Exploring the feasibility of simultaneous electroencephalography/functional magnetic resonance imaging at 7 T

The increased blood oxygenation level-dependent contrast available at high field makes the implementation of combined EEG/fMRI experiments at 7 T highly worthwhile from the point of view of fMRI data quality, but the higher field poses greater technical challenges for achieving good quality EEG data. A study of the feasibility of recording EEG signals from human subjects at 7 T using a commercially available, MR-compatible EEG system has therefore been carried out. This involved systematic measurement of the sources of noise in EEG recordings made in the 7 T scanner and measurement of RF heating effects on a gel phantom in the presence of a 32-electrode EEG cap. Having found no significant safety concerns and identified a set-up (involving switching off the magnet's cryo-cooler pumps and mounting the EEG amplifier on a cantilever) that limited scanner-induced noise, combined EEG/fMRI experiments employing visual stimulation were then successfully carried out on two human subjects. With the use of beamformer-based analysis of the EEG data, driven responses and alpha-band, event-related desynchronisation were identified in both subjects.     

基于递归量化分析与支持向量机的癫痫脑电自动检测方法

癫痫脑电信号的自动检测对癫痫的临床诊断与治疗具有重要意义.基于递归图(recurrence plot)的递归量化分析(recurrence quantification analysis,RQA)重现了非线性时间序列的动力学行为,分析了其递归特性,本文提出了基于RQA的癫痫脑电信号特征提取方法.实验结果表明:直接基于RQA特征的癫痫脑电的检测准确率较高,其中直接基于确定率DET的分类准确率可达到90.25%.本文还把提取的RQA特征值和变化系数、波动指数相结合组成特征向量,输入到SVM分类器,实现癫痫脑电信号的自动检测;实验结果表明:该方法的分类准确率可达到99%.     

Modified Langevin approach for a stochastic calcium puff model

In many cell types, intracellular calcium is released from internal stores through calcium release channels. Because these channels are distributed in clusters with a few tens of channels, the clusters show a strongly stochastic open and close dynamics, resulting in noisy localized Ca²⁺ signals called puffs. Using the Li-Rinzel model we compare the stochastic channel simulations for the Markov method and three different Langevin approaches. We suggest that a modified Langevin approach should be considered in order to more accurately simulate Markov channel noise for puff dynamics.