Detecting Dynamic Community Structure in Functional Brain Networks Across Individuals: A Multilayer Approach.

OBJECTIVE: We present a unified statistical framework for characterizing community structure of brain functional networks that captures variation across individuals and evolution over time. Existing methods for community detection focus only on single-subject analysis of dynamic networks; while recent extensions to multiple-subjects analysis are limited to static networks. METHOD: To overcome these limitations, we propose a multi-subject, Markov-switching stochastic block model (MSS-SBM) to identify state-related changes in brain community organization over a group of individuals. We first formulate a multilayer extension of SBM to describe the time-dependent, multi-subject brain networks. We develop a novel procedure for fitting the multilayer SBM that builds on multislice modularity maximization which can uncover a common community partition of all layers (subjects) simultaneously. By augmenting with a dynamic Markov switching process, our proposed method is able to capture a set of distinct, recurring temporal states with respect to inter-community interactions over subjects and the change points between them. RESULTS: Simulation shows accurate community recovery and tracking of dynamic community regimes over multilayer networks by the MSS-SBM. Application to task fMRI reveals meaningful non-assortative brain community motifs, e.g., core-periphery structure at the group level, that are associated with language comprehension and motor functions suggesting their putative role in complex information integration. Our approach detected dynamic reconfiguration of modular connectivity elicited by varying task demands and identified unique profiles of intra and inter-community connectivity across different task conditions. CONCLUSION: The proposed multilayer network representation provides a principled way of detecting synchronous, dynamic modularity in brain networks across subjects.

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.

A Markov-Switching Model Approach to Heart Sound Segmentation and Classification.

OBJECTIVE: We consider challenges in accurate segmentation of heart sound signals recorded under noisy clinical environments for subsequent classification of pathological events. Existing state-of-the-art solutions to heart sound segmentation use probabilistic models such as hidden Markov models (HMMs), which, however, are limited by its observation independence assumption and rely on pre-extraction of noise-robust features. METHODS: We propose a Markov-switching autoregressive (MSAR) process to model the raw heart sound signals directly, which allows efficient segmentation of the cyclical heart sound states according to the distinct dependence structure in each state. To enhance robustness, we extend the MSAR model to a switching linear dynamic system (SLDS) that jointly model both the switching AR dynamics of underlying heart sound signals and the noise effects. We introduce a novel algorithm via fusion of switching Kalman filter and the duration-dependent Viterbi algorithm, which incorporates the duration of heart sound states to improve state decoding. RESULTS: Evaluated on Physionet/CinC Challenge 2016 dataset, the proposed MSAR-SLDS approach significantly outperforms the hidden semi-Markov model (HSMM) in heart sound segmentation based on raw signals and comparable to a feature-based HSMM. The segmented labels were then used to train Gaussian-mixture HMM classifier for identification of abnormal beats, achieving high average precision of 86.1% on the same dataset including very noisy recordings. CONCLUSION: The proposed approach shows noticeable performance in heart sound segmentation and classification on a large noisy dataset. SIGNIFICANCE: It is potentially useful in developing automated heart monitoring systems for pre-screening of heart pathologies.

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 -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.

A Unified Estimation Framework for State-Related Changes in Effective Brain Connectivity.

OBJECTIVE: This paper addresses the critical problem of estimating time-evolving effective brain connectivity. Current approaches based on sliding window analysis or time-varying coefficient models do not simultaneously capture both slow and abrupt changes in causal interactions between different brain regions. METHODS: To overcome these limitations, we develop a unified framework based on a switching vector autoregressive (SVAR) model. Here, the dynamic connectivity regimes are uniquely characterized by distinct vector autoregressive (VAR) processes and allowed to switch between quasi-stationary brain states. The state evolution and the associated directed dependencies are defined by a Markov process and the SVAR parameters. We develop a three-stage estimation algorithm for the SVAR model: 1) feature extraction using time-varying VAR (TV-VAR) coefficients, 2) preliminary regime identification via clustering of the TV-VAR coefficients, 3) refined regime segmentation by Kalman smoothing and parameter estimation via expectation-maximization algorithm under a state-space formulation, using initial estimates from the previous two stages. RESULTS: The proposed framework is adaptive to state-related changes and gives reliable estimates of effective connectivity. Simulation results show that our method provides accurate regime change-point detection and connectivity estimates. In real applications to brain signals, the approach was able to capture directed connectivity state changes in functional magnetic resonance imaging data linked with changes in stimulus conditions, and in epileptic electroencephalograms, differentiating ictal from nonictal periods. CONCLUSION: The proposed framework accurately identifies state-dependent changes in brain network and provides estimates of connectivity strength and directionality. SIGNIFICANCE: The proposed approach is useful in neuroscience studies that investigate the dynamics of underlying brain states.

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.

An expectation-maximization algorithm based Kalman smoother approach for single-trial estimation of event-related potentials.

This paper applies an expectation-maximization (EM) based Kalman smoother (KS) approach for single-trial event-related potential (ERP) estimation. Existing studies assume a Markov diffusion process for the dynamics of ERP parameters which is recursively estimated by optimal filtering approaches such as Kalman filter (KF). However, these studies only consider estimation of ERP state parameters while the model parameters are pre-specified using manual tuning, which is time-consuming for practical usage besides giving suboptimal estimates. We extend the KF approach by adding EM based maximum likelihood estimation of the model parameters to obtain more accurate ERP estimates automatically. We also introduce different model variants by allowing flexibility in the covariance structure of model noises. Optimal model selection is performed based on Akaike Information Criterion (AIC). The method is applied to estimation of chirp-evoked auditory brainstem responses (ABRs) for detection of wave V critical for assessment of hearing loss. Results shows that use of more complex covariances are better estimating inter-trial variability.