Estimating Time-Varying Effective Connectivity in High-Dimensional fMRI Data Using Regime-Switching Factor Models

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.Comment: 21 page

Detecting state changes in community structure of functional brain networks using a markov-switching stochastic block model

Functional brain networks exhibit modular community structure with highly inter-connected nodes within a same module, but sparsely connected between different modules. Recent neuroimaging studies also suggest dynamic changes in brain connectivity over time. We propose a dynamic stochastic block model (SBM) to characterize changes in community structure of the brain networks inferred from neuroimaging data. We develop a Markov-switching SBM (MS-SBM) which is a non-stationary extension combining time-varying SBMs with a Markov process to allow for state-driven evolution of the network community structure. The time-varying connectivity parameters within and between communities are estimated from dynamic networks based on sliding-window approach, assuming a constant community membership of nodes recovered by using spectral clustering. We then partition the time-evolving community structure into recurring, piecewise constant regimes or states using a hidden Markov model. Simulation shows that the proposed MS-SBM gives accurate tracking of dynamic community regimes. Application to a task-evoked fMRI data reveals dynamic reconfiguration of the brain network modular structure in language processing between alternating blocks of story and math tasks

Statistical model for dynamically-changing correlation matrices with application to brain connectivity

Background: Recent studies have indicated that functional connectivity is dynamic even during rest. A common approach to modeling the dynamic functional connectivity in whole-brain resting-state fMRI is to compute the correlation between anatomical regions via sliding time windows. However, the direct use of the sample correlation matrices is not reliable due to the image acquisition and processing noises in resting-sate fMRI. New method: To overcome these limitations, we propose a new statistical model that smooths out the noise by exploiting the geometric structure of correlation matrices. The dynamic correlation matrix is modeled as a linear combination of symmetric positive-definite matrices combined with cosine series representation. The resulting smoothed dynamic correlation matrices are clustered into disjoint brain connectivity states using the k-means clustering algorithm. Results: The proposed model preserves the geometric structure of underlying physiological dynamic correlation, eliminates unwanted noise in connectivity and obtains more accurate state spaces. The difference in the estimated dynamic connectivity states between males and females is identified. Comparison with existing methods: We demonstrate that the proposed statistical model has less rapid state changes caused by noise and improves the accuracy in identifying and discriminating different states. Conclusions: We propose a new regression model on dynamically changing correlation matrices that provides better performance over existing windowed correlation and is more reliable for the modeling of dynamic connectivity

Linear dynamic models for classification of single-trial EEG

This paper investigates the use of linear dynamic models (LDMs) to improve classification of single-trial EEG signals. Existing dynamic classification of EEG uses discrete-state hidden Markov models (HMMs) based on piecewise-stationary assumption, which is inadequate for modeling the highly non-stationary dynamics underlying EEG. The continuous hidden states of LDMs could better describe this continuously changing characteristic of EEG, and thus improve the classification performance. We consider two examples of LDM: a simple local level model (LLM) and a time-varying autoregressive (TVAR) state-space model. AR parameters and band power are used as features. Parameter estimation of the LDMs is performed by using expectation-maximization (EM) algorithm. We also investigate different covariance modeling of Gaussian noises in LDMs for EEG classification. The experimental results on two-class motor-imagery classification show that both types of LDMs outperform the HMM baseline, with the best relative accuracy improvement of 14.8% by LLM with full covariance for Gaussian noises. It may due to that LDMs offer more flexibility in fitting the underlying dynamics of EEG. Keyword