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Time-frequency spectral estimation of multichannel EEG using the Auto-SLEX method

In this paper, we apply a new time-frequency spectral estimation method for multichannel data to epileptiform electroencephalography (EEG). The method is based on the smooth localized complex exponentials (SLEX) functions which are time-frequency localized versions of the Fourier functions and, hence, are ideal for analyzing nonstationary signals whose spectral properties evolve over time. The SLEX functions are simultaneously orthogonal and localized in time and frequency because they are obtained by applying a projection operator rather than a window or taper. In this paper, we present the Auto-SLEX method which is a statistical method that 1) computes the periodogram using the SLEX transform, 2) automatically segments the signal into approximately stationary segments using an objective criterion that is based on log energy, and 3) automatically selects the optimal bandwidth of the spectral smoothing window. The method is applied to the intracranial EEG from a patient with temporal lobe epilepsy. This analysis reveals a reduction in average duration of stationarity in preseizure epochs of data compared to baseline. These changes begin up to hours prior to electrical seizure onset in this patient.

Spectral synchronicity in brain signals: Spectral synchronicity in brain signals

This paper addresses the problem of identifying brain regions with similar oscillatory patterns detected from electroencephalograms. We introduce the hierarchical spectral merger (HSM) clustering method where the feature of interest is the spectral curve and the similarity metric used is the total variance distance. The HSM method is compared with clustering using features derived from independent-component analysis. Moreover, the HSM method is applied to 2 different electroencephalogram datasets. The first was recorded at resting state where the participant was not engaged in any cognitive task; the second was recorded during a spontaneous epileptic seizure. The results of the analyses using the HSM method demonstrate that clustering could evolve over the duration of the resting state and during epileptic seizure.

FreSpeD: Frequency-Specific Change-Point Detection in Epileptic Seizure Multi-Channel EEG Data

ABSTRACT The goal in this article is to develop a practical tool that identifies changes in the brain activity as recorded in electroencephalograms (EEG). Our method is devised to detect possibly subtle disruptions in normal brain functioning that precede the onset of an epileptic seizure. Moreover, it is able to capture the evolution of seizure spread from one region (or channel) to another. The proposed frequency-specific change-point detection method (FreSpeD) deploys a cumulative sum-type test statistic within a binary segmentation algorithm. We demonstrate the theoretical properties of FreSpeD and show its robustness to parameter choice and advantages against two competing methods. Furthermore, the FreSpeD method produces directly interpretable output. When applied to epileptic seizure EEG data, FreSpeD identifies the correct brain region as the focal point of seizure and the timing of the seizure onset. Moreover, FreSpeD detects changes in cross-coherence immediately before seizure onset which indicate an evolution leading up to the seizure. These changes are subtle and were not captured by the methods that previously analyzed the same EEG data. Supplementary materials for this article are available online.

Time-Dependent Dual-Frequency Coherence in Multivariate Non-Stationary Time Series

Coherence is one common metric for cross-dependence between components in multivariate time series. However, standard coherence does not sufficiently model many biological signals with complex dependence structures such as interactions between low frequency oscillations and high frequency oscillations. The notion of low-high frequency cross-dependence, defined in classical harmonizable processes, assumes time-invariance and thus is still inadequate for modeling cross-frequency interactions that evolve over time. We construct a novel framework for modeling and estimating these dependencies under the replicated time series setting. Under this framework we establish the novel concept of evolutionary dual-frequency coherence and develop time-localized estimators based on dual-frequency lo- cal periodograms. The proposed non-parametric estimation procedure does not suffer from model misspecification. It uses the localized fast Fourier transform (FFT) and hence is able to handle massive data. When applied to electroencephalograms, the proposed method uncovers interesting cross- oscillatory interactions that are neglected by the standard approaches.

Estimating Dynamic Connectivity States in fMRI Using Regime-Switching Factor Models

We consider the challenges in estimating the state-related changes in brain connectivity networks with a large number of nodes. Existing studies use the sliding-window analysis or time-varying coefficient models, which are unable to capture both smooth and abrupt changes simultaneously, and rely on ad-hoc approaches to the high-dimensional estimation. To overcome these limitations, we propose a Markov-switching dynamic factor model, which allows the dynamic connectivity states in functional magnetic resonance imaging (fMRI) data to be driven by lower-dimensional latent factors. We specify a regime-switching vector autoregressive (SVAR) factor process to quantity the time-varying directed connectivity. The model enables a reliable, data-adaptive estimation of change-points of connectivity regimes and the massive dependencies associated with each regime. We develop a three-step estimation procedure: 1) extracting the factors using principal component analysis, 2) identifying connectivity regimes in a low-dimensional subspace based on the factor-based SVAR model, and 3) constructing high-dimensional state connectivity metrics based on the subspace estimates. Simulation results show that our estimator outperforms

A scalable multi-resolution spatio-temporal model for brain activation and connectivity in fMRI data: A Multi-Resolution Model for fMRI Data

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A Bayesian Variable Selection Approach Yields Improved Detection of Brain Activation From Complex-Valued fMRI

-means clustering of time-windowed coefficients, providing more accurate estimate of time-evolving connectivity. It achieves percentage of reduction in mean squared error by 60% when the network dimension is comparable to the sample size. When applied to the resting-state fMRI data, our method successfully identifies modular organization in the resting-statenetworksin consistencywith other studies. It further reveals changes in brain states with variations across subjects and distinct large-scale directed connectivity patterns across states.Recent studies on analyzing dynamic brain connectivity rely on sliding-window analysis or time-varying coefficient models which are unable to capture both smooth and abrupt changes simultaneously. Emerging evidence suggests state-related changes in brain connectivity where dependence structure alternates between a finite number of latent states or regimes. Another challenge is inference of full-brain networks with large number of nodes. We employ a Markov-switching dynamic factor model in which the state-driven time-varying connectivity regimes of high-dimensional fMRI data are characterized by lower-dimensional common latent factors, following a regime-switching process. It enables a reliable, data-adaptive estimation of change-points of connectivity regimes and the massive dependencies associated with each regime. We consider the switching VAR to quantity the dynamic effective connectivity. We propose a three-step estimation procedure: (1) extracting the factors using principal component analysis (PCA) and (2) identifying dynamic connectivity states using the factor-based switching vector autoregressive (VAR) models in a state-space formulation using Kalman filter and expectation-maximization (EM) algorithm, and (3) constructing the high-dimensional connectivity metrics for each state based on subspace estimates. Simulation results show that our proposed estimator outperforms the K-means clustering of time-windowed coefficients, providing more accurate estimation of regime dynamics and connectivity metrics in high-dimensional settings. Applications to analyzing resting-state fMRI data identify dynamic changes in brain states during rest, and reveal distinct directed connectivity patterns and modular organization in resting-state networks across different states.

Statistical models for brain signals with properties that evolve across trials

Functional Magnetic Resonance Imaging (fMRI) is a primary modality for studying brain activity. Modeling spatial dependence of imaging data at different spatial scales is one of the main challenges of contemporary neuroimaging, and it could allow for accurate testing for significance in neural activity. The high dimensionality of this type of data (on the order of hundreds of thousands of voxels) poses serious modeling challenges and considerable computational constraints. For the sake of feasibility, standard models typically reduce dimensionality by modeling covariance among regions of interest (ROIs)-coarser or larger spatial units-rather than among voxels. However, ignoring spatial dependence at different scales could drastically reduce our ability to detect activation patterns in the brain and hence produce misleading results. We introduce a multi-resolution spatio-temporal model and a computationally efficient methodology to estimate cognitive control related activation and whole-brain connectivity. The proposed model allows for testing voxel-specific activation while accounting for non-stationary local spatial dependence within anatomically defined ROIs, as well as regional dependence (between-ROIs). The model is used in a motor-task fMRI study to investigate brain activation and connectivity patterns aimed at identifying associations between these patterns and regaining motor functionality following a stroke.

Statistical methods and challenges in connectome genetics

ABSTRACT Voxel functional magnetic resonance imaging (fMRI) time courses are complex-valued signals giving rise to magnitude and phase data. Nevertheless, most studies use only the magnitude signals and thus discard half of the data that could potentially contain important information. Methods that make use of complex-valued fMRI (CV-fMRI) data have been shown to lead to superior power in detecting active voxels when compared to magnitude-only methods, particularly for small signal-to-noise ratios (SNRs). We present a new Bayesian variable selection approach for detecting brain activation at the voxel level from CV-fMRI data. We develop models with complex-valued spike-and-slab priors on the activation parameters that are able to combine the magnitude and phase information. We present a complex-valued EM variable selection algorithm that leads to fast detection at the voxel level in CV-fMRI slices and also consider full posterior inference via Markov chain Monte Carlo (MCMC). Model performance is illustrated through extensive simulation studies, including the analysis of physically based simulated CV-fMRI slices. Finally, we use the complex-valued Bayesian approach to detect active voxels in human CV-fMRI from a healthy individual who performed unilateral finger tapping in a designed experiment. The proposed approach leads to improved detection of activation in the expected motor-related brain regions and produces fewer false positive results than other methods for CV-fMRI. Supplementary materials for this article are available online.

Multi-Scale Factor Analysis of High-Dimensional Brain Signals

ABSTRACT Most neuroscience cognitive experiments involve repeated presentations of various stimuli across several minutes or a few hours. It has been observed that brain responses, even to the same stimulus, evolve over the course of the experiment. These changes in brain activation and connectivity are believed to be associated with learning and/or habituation. In this paper, we present two general approaches to modeling dynamic brain connectivity using electroencephalograms (EEGs) recorded across replicated trials in an experiment. The first approach is the Markovian regime‐switching vector autoregressive model (MS‐VAR) which treats EEGs as realizations of an underlying brain process that switches between different states both within a trial and across trials in the entire experiment. The second is the slowly evolutionary locally stationary process (SEv‐LSP) which characterizes the observed EEGs as a mixture of oscillatory activities at various frequency bands. The SEv‐LSP model captures the dynamic nature of the amplitudes of the band‐oscillations and cross‐correlations between them. The MS‐VAR model is able to capture abrupt changes in the dynamics while the SEv‐LSP directly gives interpretable results. Moreover, it is nonparametric and hence does not suffer from model misspecification. For both of these models, time‐evolving connectivity metrics in the frequency domain are derived from the model parameters for both functional and effective connectivity. We illustrate these two models for estimating cross‐trial connectivity in selective attention using EEG data from an oddball paradigm auditory experiment where the goal is to characterize the evolution of brain responses to target stimuli and to standard tones presented randomly throughout the entire experiment. The results suggest dynamic changes in connectivity patterns over trials with inter‐subject variability. Highlights The goal of this paper is to develop statistical approaches to modeling dynamic brain connectivity in signals recorded across replicated trials in an experiment.Under the Markovian regime‐switching vector autoregressive model (MS‐VAR) models, signals switch between different states both within a trial and across trials.The second approach, slowly evolutionary locally stationary process, characterizes the observed EEGs as a mixture of oscillatory activities at various frequency bands.The SEv‐LSP model uses the Fourier waveforms as building blocks and captures the dynamic nature of the amplitudes and cross‐correlations of the band‐oscillations.The MS‐VAR model captures abrupt changes but the SEv‐LSP model directly gives interpretable results and does not suffer from model misspecification.