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

State-space modeling and estimation for multivariate brain signals

Brain signals are derived from underlying dynamic processes and interactions between populations of neurons in the brain. These signals are typically measured from distinct regions, in the forms of multivariate time series signals and exhibit non-stationarity. To analyze these multi-dimensional data with the latent dynamics, efficient statistical methods are needed. Conventional analyses of brain signals use stationary techniques and focus on analyzing a single dimensional signal, without taking into consideration the coherence between signals. Other conventional model is the discrete-state hidden Markov model (HMM) where the evolution of hidden states is characterized by a discrete Markov chain. These limitations can be overcome by modeling the signals using state-space model (SSM), that model the signals continuously and further estimate the interdependence between the brain signals. This thesis developed SSM based formulations for autoregressive models to estimate the underlying dynamics of brain activity based on measured signals from different regions. The hidden state and model estimations were performed by Kalman filter and maximum likelihood estimation based on the expectation maximization (EM) algorithm. Adaptive dynamic model time-varying autoregressive (TV-AR) was formulated into SSM, for the application of multi-channel electroencephalography (EEG) classification, where accuracy obtained was better than the conventional HMM. This research generalized the TV-AR to multivariate model to capture the dynamic integration of brain signals. Dynamic multivariate time-varying vector autoregressive (TV-VAR) model was used to investigate the dynamics of causal effects of one region has on another, which is known as effective connectivity. This model was applied to motor-imagery EEG and motortask functional magnetic resonance imaging (fMRI) data, where the results showed that the effective connectivity changes over time. These changing connectivity structures were found to reflect the behavior of underlying brain states. To detect the state-related change of brain activities based on effective connectivity, this thesis further developed a novel unified framework based on the switching vector autoregressive (SVAR) model. The framework was applied to simulation signals, epileptic EEG and motor-task fMRI. The results showed that the novel framework is able to simultaneously capture both slow and abrupt changes of effective connectivity according to the brain states. In conclusion, the developed SSM based approaches were effective for modeling the nonstationarity and connectivity in brain signals

Fractals in the Nervous System: conceptual Implications for Theoretical Neuroscience

This essay is presented with two principal objectives in mind: first, to document the prevalence of fractals at all levels of the nervous system, giving credence to the notion of their functional relevance; and second, to draw attention to the as yet still unresolved issues of the detailed relationships among power law scaling, self-similarity, and self-organized criticality. As regards criticality, I will document that it has become a pivotal reference point in Neurodynamics. Furthermore, I will emphasize the not yet fully appreciated significance of allometric control processes. For dynamic fractals, I will assemble reasons for attributing to them the capacity to adapt task execution to contextual changes across a range of scales. The final Section consists of general reflections on the implications of the reviewed data, and identifies what appear to be issues of fundamental importance for future research in the rapidly evolving topic of this review