Differentially Variable Component Analysis: Identifying Multiple Evoked Components Using Trial-to-Trial Variability

Brain Evoked Response Qualification Using Multi-Set Consensus Clustering: Toward Single-Trial EEG Analysis

In event-related potential (ERP) analysis, it is commonly assumed that individual trials from a subject share similar properties and originate from comparable neural sources, allowing reliable interpretation of group-averages. Nevertheless, traditional group-level ERP analysis methods, including cluster analysis, often overlook critical information about individual subjects' neural processes due to using fixed measurement intervals derived from averaging. We developed a multi-set consensus clustering pipeline to examine cognitive processes at the individual subject level. Initially, consensus clustering from diverse methods was applied to single-trial EEG epochs of individual subjects. Subsequently, a second level of consensus clustering was performed across the trials of each subject. A newly modified time window determination method was then employed to identify individual subjects' ERP(s) of interest. We validated our method with simulated data for ERP components N2 and P3, and real data from a visual oddball task to confirm the P3 component. Our findings revealed that estimated time windows for individual subjects provide precise ERP identification compared to fixed time windows across all subjects. Additionally, Monte Carlo simulations with synthetic single-trial data demonstrated stable scores for the N2 and P3 components, confirming the reliability of our method. The proposed method enhances the examination of brain-evoked responses at the individual subject level by considering single-trial EEG data, thereby extracting mutual information relevant to the neural process. This approach offers a significant improvement over conventional ERP analysis, which relies on the averaging mechanism and fixed measurement interval.

Second Order Blind Identification of Event Related Potentials Sources

Event-related potentials (ERPs) recorded on the surface of the head are a mixture of signals from many sources in the brain due to volume conductions. As a result, the spatial resolution of the ERPs is quite low. Blind source separation can help to recover source signals from multichannel ERP records. In this study, we present a novel implementation of a method for decomposing multi-channel ERP into components, which is based on the modeling of second-order statistics of ERPs. We also report a new implementation of Bayesian Information Criteria (BIC), which is used to select the optimal number of hidden signals (components) in the original ERPs. We tested these methods using both synthetic datasets and real ERPs data arrays. Testing has shown that the ERP decomposition method can reconstruct the source signals from their mixture with acceptable accuracy even when these signals overlap significantly in time and the presence of noise. The use of BIC allows us to determine the correct number of source signals at the signal-to-noise ratio commonly observed in ERP studies. The proposed approach was compared with conventionally used methods for the analysis of ERPs. It turned out that the use of this new method makes it possible to observe such phenomena that are hidden by other signals in the original ERPs. The proposed method for decomposing a multichannel ERP into components can be useful for studying cognitive processes in laboratory settings, as well as in clinical studies.

Mapping information flow between the inferotemporal and prefrontal cortices via neural oscillations in memory retrieval and maintenance

Interaction between the inferotemporal (ITC) and prefrontal (PFC) cortices is critical for retrieving information from memory and maintaining it in working memory. Neural oscillations provide a mechanism for communication between brain regions. However, it remains unknown how information flow via neural oscillations is functionally organized in these cortices during these processes. In this study, we apply Granger causality analysis to electrocorticographic signals from both cortices of monkeys performing visual association tasks to map information flow. Our results reveal regions within the ITC where information flow to and from the PFC increases via specific frequency oscillations to form clusters during memory retrieval and maintenance. Theta-band information flow in both directions increases in similar regions in both cortices, suggesting reciprocal information exchange in those regions. These findings suggest that specific subregions function as nodes in the memory information-processing network between the ITC and the PFC.

Parametric separation of phase-locked and non-phase-locked activity

Brain dynamics recorded via electroencephalography (EEG) is conceptualized as a sum of two components: "phase-locked" and "non-phase-locked" to the stimulus. Phase-locked activity is often implicitly studied as event-related potentials (ERPs), and the trial-averaged estimates-evoked potentials (EP) considered both time-locked and phase-locked to the stimulus. The non-phase-locked activity, on the other hand, refers to an increase in power in a narrow band or broadband frequencies in the signal emerging at variable phases from stimulus initiation. Both components are understood to stem from different neuronal mechanisms; hence, accurately characterizing them is of immense importance to neuroscientific studies. Here, we discuss the drawbacks of currently used methods to separate the phase-locked and non-phase-locked activity and propose a novel concurrent phaser method (CPM) that simultaneously decomposes the two components. First, we establish that the single-trial separation of phase-locked and non-phase-locked power is an ill-posed problem. Second, using simulations where ground truth validation is possible, we elucidate how the estimation of non-phase-locked power gets biased by phase-locked power in the state-of-the-art averaging method and ways to resolve the issue using CPM. Next, we use two experimental EEG datasets-audio oddball and auditory steady-state responses (ASSR) to show that empirical signal-to-noise estimates warrant the usage of CPM to separate phase-locked and non-phase-locked activity. Thus, using ground truth validation from simulations and demonstration in real experimental scenarios, the efficacy of the proposed CPM is established.NEW & NOTEWORTHY Parametric models for estimation of phase-locked and non-phase-locked brain signals reveals how estimation of non-phase-locked component is biased by the variability of phase-locked component and at the level of single trial becomes an ill-posed problem. Furthermore, the modeling framework delimits the boundaries where traditional averaging approach can be trusted to estimate the phase-locked and non-phase-locked components.

Oscillatory Bursting as a Mechanism for Temporal Coupling and Information Coding

Even the simplest cognitive processes involve interactions between cortical regions. To study these processes, we usually rely on averaging across several repetitions of a task or across long segments of data to reach a statistically valid conclusion. Neuronal oscillations reflect synchronized excitability fluctuations in ensembles of neurons and can be observed in electrophysiological recordings in the presence or absence of an external stimulus. Oscillatory brain activity has been viewed as sustained increase in power at specific frequency bands. However, this perspective has been challenged in recent years by the notion that oscillations may occur as transient burst-like events that occur in individual trials and may only appear as sustained activity when multiple trials are averaged together. In this review, we examine the idea that oscillatory activity can manifest as a transient burst as well as a sustained increase in power. We discuss the technical challenges involved in the detection and characterization of transient events at the single trial level, the mechanisms that might generate them and the features that can be extracted from these events to study single-trial dynamics of neuronal ensemble activity.

ReSync: Correcting the trial-to-trial asynchrony of event-related brain potentials to improve neural response representation

BACKGROUND

For various reasons, the brain response activities in electroencephalography (EEG) signals are not perfectly synchronized between trials with respect to event markers-a problem commonly referred to as latency jitter. Experimental technologies have been greatly advanced to reduce technical timing errors and thereby reduce jitter. However, there remain intrinsic sources of jitter that are difficult to remove. The problem becomes more complicated when multiple sub-components possess different degrees and features of jitter. The jitter issue renders trial-averaged ERP inaccurate and even misleading. Effective methods for correcting ERP distortion due to latency jitter are needed.

NEW METHOD

This study developed a simple and easy-to-use method and toolbox for correcting ERP jitter based on simple signal processing theories, named ReSync. ReSync can be used to correct multiple overlapping ERP sub-components with different degrees of jitter (including static sub-components) without their affecting each other.

RESULTS

The theories, principles, technical details, and limitations of ReSync are presented in this paper, along with a series of simulation and real data examples used to evaluate and validate the method.

COMPARISON WITH EXISTING METHODS

ReSync was conceptually compared with previous methods in the literature that are related to tackling of the jitter issue from theoretical, methodological, and technical perspectives.

CONCLUSIONS

Providing a novel approach to latency jitter estimation with automatic dominant frequency identification and integrated decomposition and reconstruction, the ReSync method was validated using both simulation and empirical data, and demonstrated to be an effective jitter-correction approach with implementational simplicity.

Histogram of Gradient Orientations of Signal Plots Applied to P300 Detection

The analysis of Electroencephalographic (EEG) signals is of ulterior importance to aid in the diagnosis of mental disease and to increase our understanding of the brain. Traditionally, clinical EEG has been analyzed in terms of temporal waveforms, looking at rhythms in spontaneous activity, subjectively identifying troughs and peaks in Event-Related Potentials (ERP), or by studying graphoelements in pathological sleep stages. Additionally, the discipline of Brain Computer Interfaces (BCI) requires new methods to decode patterns from non-invasive EEG signals. This field is developing alternative communication pathways to transmit volitional information from the Central Nervous System. The technology could potentially enhance the quality of life of patients affected by neurodegenerative disorders and other mental illness. This work mimics what electroencephalographers have been doing clinically, visually inspecting, and categorizing phenomena within the EEG by the extraction of features from images of signal plots. These features are constructed based on the calculation of histograms of oriented gradients from pixels around the signal plot. It aims to provide a new objective framework to analyze, characterize and classify EEG signal waveforms. The feasibility of the method is outlined by detecting the P300, an ERP elicited by the oddball paradigm of rare events, and implementing an offline P300-based BCI Speller. The validity of the proposal is shown by offline processing a public dataset of Amyotrophic Lateral Sclerosis (ALS) patients and an own dataset of healthy subjects.

An Improved Multi-Source Data Fusion Method Based on the Belief Entropy and Divergence Measure

Dempster–Shafer (DS) evidence theory is widely applied in multi-source data fusion technology. However, classical DS combination rule fails to deal with the situation when evidence is highly in conflict. To address this problem, a novel multi-source data fusion method is proposed in this paper. The main steps of the proposed method are presented as follows. Firstly, the credibility weight of each piece of evidence is obtained after transforming the belief Jenson–Shannon divergence into belief similarities. Next, the belief entropy of each piece of evidence is calculated and the information volume weights of evidence are generated. Then, both credibility weights and information volume weights of evidence are unified to generate the final weight of each piece of evidence before the weighted average evidence is calculated. Then, the classical DS combination rule is used multiple times on the modified evidence to generate the fusing results. A numerical example compares the fusing result of the proposed method with that of other existing combination rules. Further, a practical application of fault diagnosis is presented to illustrate the plausibility and efficiency of the proposed method. The experimental result shows that the targeted type of fault is recognized most accurately by the proposed method in comparing with other combination rules.

Investigating large-scale brain dynamics using field potential recordings: analysis and interpretation

New technologies to record electrical activity from the brain on a massive scale offer tremendous opportunities for discovery. Electrical measurements of large-scale brain dynamics, termed field potentials, are especially important to understanding and treating the human brain. Here, our goal is to provide best practices on how field potential recordings (electroencephalograms, magnetoencephalograms, electrocorticograms and local field potentials) can be analyzed to identify large-scale brain dynamics, and to highlight critical issues and limitations of interpretation in current work. We focus our discussion of analyses around the broad themes of activation, correlation, communication and coding. We provide recommendations for interpreting the data using forward and inverse models. The forward model describes how field potentials are generated by the activity of populations of neurons. The inverse model describes how to infer the activity of populations of neurons from field potential recordings. A recurring theme is the challenge of understanding how field potentials reflect neuronal population activity given the complexity of the underlying brain systems.

P300 Detection Based on EEG Shape Features

We present a novel approach to describe a P300 by a shape-feature vector, which offers several advantages over the feature vector used by the BCI2000 system. Additionally, we present a calibration algorithm that reduces the dimensionality of the shape-feature vector, the number of trials, and the electrodes needed by a Brain Computer Interface to accurately detect P300s; we also define a method to find a template that best represents, for a given electrode, the subject's P300 based on his/her own acquired signals. Our experiments with 21 subjects showed that the SWLDA's performance using our shape-feature vector was 93%, that is, 10% higher than the one obtained with BCI2000-feature's vector. The shape-feature vector is 34-dimensional for every electrode; however, it is possible to significantly reduce its dimensionality while keeping a high sensitivity. The validation of the calibration algorithm showed an averaged area under the ROC (AUROC) curve of 0.88. Also, most of the subjects needed less than 15 trials to have an AUROC superior to 0.8. Finally, we found that the electrode C4 also leads to better classification.

Tracking markers of response inhibition in electroencephalographic data: why should we and how can we go beyond the N2 component?

Response inhibition is a pivotal component of executive control, which is especially difficult to assess. Indeed, it is a substantial challenge to gauge brain-behavior relationships because this function is precisely intended to suppress overt measurable behaviors. A further complication is that no single neuroimaging method has been found that can disentangle the accurate time-course of concurrent excitatory and inhibitory mechanisms. Here, we argue that this objective can be achieved with electroencephalography (EEG) on some conditions. Based on a systematic review, we emphasize that the standard event-related potential N2 (N200) is not an appropriate marker of prepotent response inhibition. We provide guidelines for assessing the cortical brain dynamics of response inhibition with EEG. This includes the combined use of inseparable data processing steps (source separation, source localization, and single-trial and time-frequency analyses) as well as the amendment of the classical experimental designs to enable the recording of different kinds of electrophysiological activity predicted by different models of response inhibition. We conclude with an illustration based on recent findings of how fruitful this approach can be.

Detecting single-trial EEG evoked potential using a wavelet domain linear mixed model: application to error potentials classification

OBJECTIVE

The main goal of this work is to develop a model for multisensor signals, such as magnetoencephalography or electroencephalography (EEG) signals that account for inter-trial variability, suitable for corresponding binary classification problems. An important constraint is that the model be simple enough to handle small size and unbalanced datasets, as often encountered in BCI-type experiments.

APPROACH

The method involves the linear mixed effects statistical model, wavelet transform, and spatial filtering, and aims at the characterization of localized discriminant features in multisensor signals. After discrete wavelet transform and spatial filtering, a projection onto the relevant wavelet and spatial channels subspaces is used for dimension reduction. The projected signals are then decomposed as the sum of a signal of interest (i.e., discriminant) and background noise, using a very simple Gaussian linear mixed model.

MAIN RESULTS

Thanks to the simplicity of the model, the corresponding parameter estimation problem is simplified. Robust estimates of class-covariance matrices are obtained from small sample sizes and an effective Bayes plug-in classifier is derived. The approach is applied to the detection of error potentials in multichannel EEG data in a very unbalanced situation (detection of rare events). Classification results prove the relevance of the proposed approach in such a context.

SIGNIFICANCE

The combination of the linear mixed model, wavelet transform and spatial filtering for EEG classification is, to the best of our knowledge, an original approach, which is proven to be effective. This paper improves upon earlier results on similar problems, and the three main ingredients all play an important role.

Individual trial-to-trial variability of different components of neuromagnetic signals associated with self-paced finger movements

We measured magnetic cortical responses to self-paced finger movements. Wide frequency band measurements revealed sharp elements of the response wave-shape, and allowed analysis of individual trials. The signal time course was decomposed into three components in the time window from 600ms before to 600ms after the movement. Each component had its own wave-shape and highly individual behavior. Two components displayed large trial-to-trial amplitude variations, whereas the amplitude of the third, high-frequency component remained stable. The frequency spectrum of the high-frequency component decayed exponentially, which indicates deterministic dynamics for the processes generating this magnetic signal. In spite of the large variations in the movement-related cortical signals, the movement itself, as measured by accelerometer attached to the finger tip, remained stable from trial to trial. The magnetic measurements are well-suited to reveal fine details of the process of movement initiation.

Shifted factor analysis for the separation of evoked dependent MEG signals

Decomposition of evoked magnetoencephalography (MEG) data into their underlying neuronal signals is an important step in the interpretation of these measurements. Often, independent component analysis (ICA) is employed for this purpose. However, ICA can fail as for evoked MEG data the neuronal signals may not be statistically independent. We therefore consider an alternative approach based on the recently proposed shifted factor analysis model, which does not assume statistical independence of the neuronal signals. We suggest the application of this model in the time domain and present an estimation procedure based on a Taylor series expansion. We show in terms of synthetic evoked MEG data that the proposed procedure can successfully separate evoked dependent neuronal signals while standard ICA fails. Latency estimation of neuronal signals is an inherent part of the proposed procedure and we demonstrate that resulting latency estimates are superior to those obtained by a maximum likelihood method.

Graph-based variability estimation in single-trial event-related neural responses

Extracting information from multitrial magnetoencephalography or electroencephalography (EEG) recordings is challenging because of the very low SNR, and because of the inherent variability of brain responses. The problem of low SNR is commonly tackled by averaging multiple repetitions of the recordings, also called trials, but the variability of response across trials leads to biased results and limits interpretability. This paper proposes to decode the variability of neural responses by making use of graph representations. Our approach has several advantages compared to other existing methods that process single-trial data: first, it avoids the a priori definition of a model for the waveform of the neural response; second, it does not make use of the average data for parameter estimation; third, it does not suffer from initialization problems by providing solutions that are global optimum of cost functions; and last, it is fast. We proceed in two steps. First, a manifold learning algorithm, based on a graph Laplacian, offers an efficient way of ordering trials with respect to the response variability, under the condition that this variability itself depends on a single parameter. Second, the estimation of the variability is formulated as a combinatorial optimization that can be solved very efficiently using graph cuts. Details and validation of this second step are provided for latency estimation. Performance and robustness experiments are conducted on synthetic data, and results are presented on EEG data from a P300 oddball experiment.

Temporal envelope of time-compressed speech represented in the human auditory cortex

Speech comprehension relies on temporal cues contained in the speech envelope, and the auditory cortex has been implicated as playing a critical role in encoding this temporal information. We investigated auditory cortical responses to speech stimuli in subjects undergoing invasive electrophysiological monitoring for pharmacologically refractory epilepsy. Recordings were made from multicontact electrodes implanted in Heschl's gyrus (HG). Speech sentences, time compressed from 0.75 to 0.20 of natural speaking rate, elicited average evoked potentials (AEPs) and increases in event-related band power (ERBP) of cortical high-frequency (70-250 Hz) activity. Cortex of posteromedial HG, the presumed core of human auditory cortex, represented the envelope of speech stimuli in the AEP and ERBP. Envelope following in ERBP, but not in AEP, was evident in both language-dominant and -nondominant hemispheres for relatively high degrees of compression where speech was not comprehensible. Compared to posteromedial HG, responses from anterolateral HG-an auditory belt field-exhibited longer latencies, lower amplitudes, and little or no time locking to the speech envelope. The ability of the core auditory cortex to follow the temporal speech envelope over a wide range of speaking rates leads us to conclude that such capacity in itself is not a limiting factor for speech comprehension.

Independent component analysis: comparison of algorithms for the investigation of surface electrical brain activity

We compared the performance of 22 algorithms for independent component analysis with the aim to find suitable algorithms for applications in the field of surface electrical brain activity analysis. The quality of the separation is assessed with four performance measures: a correlation coefficient based index, a signal-to-interference ratio, a signal-to-distortion-ratio and the computational demand. Artificial data are used consisting of typical electroencephalogram and evoked potentials signal patterns, e.g. spikes, polyspikes, sharp waves and spindles. We evaluate different noise scenarios and the influence of pre-whitening. The comparisons reveal considerable differences between the algorithms, especially concerning the computational load. Algorithms based on the time structure of the data set seem to have advantages in separation quality especially for sine-shaped signals. Derivates of FastICA and Infomax also attain good results. Our results can serve as a reference for selecting a task-specific algorithm to analyze a large number of signal patterns occurring in the surface electrical brain activity.

Estimating Granger causality after stimulus onset: a cautionary note

How the brain processes sensory input to produce goal-oriented behavior is not well-understood. Advanced data acquisition technology in conjunction with novel statistical methods holds the key to future progress in this area. Recent studies have applied Granger causality to multivariate population recordings such as local field potential (LFP) or electroencephalography (EEG) in event-related paradigms. The aim is to reveal the detailed time course of stimulus-elicited information transaction among various sensory and motor cortices. Presently, interdependency measures like coherence and Granger causality are calculated on ongoing brain activity obtained by removing the average event-related potential (AERP) from each trial. In this paper we point out the pitfalls of this approach in light of the inevitable occurrence of trial-to-trial variability of event-related potentials in both amplitudes and latencies. Numerical simulations and experimental examples are used to illustrate the ideas. Special emphasis is placed on the important role played by single trial analysis of event-related potentials in experimentally establishing the main conclusion.

A subspace method for dynamical estimation of evoked potentials

It is a challenge in evoked potential (EP) analysis to incorporate prior physiological knowledge for estimation. In this paper, we address the problem of single-channel trial-to-trial EP characteristics estimation. Prior information about phase-locked properties of the EPs is assesed by means of estimated signal subspace and eigenvalue decomposition. Then for those situations that dynamic fluctuations from stimulus-to-stimulus could be expected, prior information can be exploited by means of state-space modeling and recursive Bayesian mean square estimation methods (Kalman filtering and smoothing). We demonstrate that a few dominant eigenvectors of the data correlation matrix are able to model trend-like changes of some component of the EPs, and that Kalman smoother algorithm is to be preferred in terms of better tracking capabilities and mean square error reduction. We also demonstrate the effect of strong artifacts, particularly eye blinks, on the quality of the signal subspace and EP estimates by means of independent component analysis applied as a prepossessing step on the multichannel measurements.

Trial-by-trial estimation of amplitude and latency variability in neuronal spike trains

The rate function underlying single-trial spike trains can vary from trial to trial. We propose to estimate the amplitude and latency variability in single-trial neuronal spike trains on a trial-by-trial basis. The firing rate over a trial is modeled by a family of rate profiles with trial-invariant waveform and trial-dependent amplitude scaling factors and latency shifts. Using a Bayesian inference framework we derive an iterative fixed-point algorithm from which the single-trial amplitude scaling factors and latency shifts are estimated. We test the performance of the algorithm on simulated data and then apply it to actual neuronal recordings from the sensorimotor cortex of the monkey.

Stochastic modeling of neurobiological time series: power, coherence, Granger causality, and separation of evoked responses from ongoing activity

In this article we consider the stochastic modeling of neurobiological time series from cognitive experiments. Our starting point is the variable-signal-plus-ongoing-activity model. From this model a differentially variable component analysis strategy is developed from a Bayesian perspective to estimate event-related signals on a single trial basis. After subtracting out the event-related signal from recorded single trial time series, the residual ongoing activity is treated as a piecewise stationary stochastic process and analyzed by an adaptive multivariate autoregressive modeling strategy which yields power, coherence, and Granger causality spectra. Results from applying these methods to local field potential recordings from monkeys performing cognitive tasks are presented.