Estimation of high-dimensional brain connectivity networks using functional magnetic resonance imaging data

Recent studies in neuroimaging show increasing interest in mapping the brain connectivity. It can be potentially useful as biomarkers in identifying neuropsychiatric diseases as well as tool for psychological studies. This study considers the problem of modeling high-dimensional brain connectivity using statistical approach and estimate the connectivity between functional magnetic resonance imaging (fMRI) time series data measured from brain regions. The high-dimension of fMRI data (N) corresponding to the number of brain regions, is typically much larger than sample size or the number of time points taken (T). In this setting, the conventional connectivity estimators such as sample covariance and least-square (LS) estimator are no longer consistent and reliable. In addition, the traditional analysis assumes the brain network to be timeinvariant but recent neuroimaging studies show brain connectivity is changing over the experimental time course. This study developed a novel shrinkage approach to characterize directed brain connectivity in high-dimension. The shrinkage method is involved in incorporating shrinkage-based estimators (Ledoit-Wolf (LW) and Rao- Blackwell LW (RBLW)) in the covariance matrix and LS-based linear regression fitting of vector autoregressive (VAR) model, to reduce the mean squared error of estimates in both high-dimensional functional and effective connectivity. This allows better conditioned and invertible estimated matrix which is important to generate a reliable estimator. Then, the shrinkage-based VAR estimator has been extended to estimate time-evolving effective brain connectivity. The shrinkage-based methods are evaluated via simulations and applied to fMRI resting-state data. Simulation results show reduced mean squared error of estimated connectivity matrix in LW and RBLWbased estimators as compared to conventional sample covariance and LS estimators in both static and dynamic connectivity analysis. These estimators show robustness towards the increasing dimension. Result on real resting-state fMRI data showed that the proposed methods are able to identify functionally-related resting-state brain connectivity networks and evolution of connectivity states across time. It provides additional insights into human whole-brain connectivity during at rest as compared to previous finding particularly in the directionality of connectivity in high-dimensional brain networks

Predictive assessment of models for dynamic functional connectivity

In neuroimaging, it has become evident that models of dynamic functional connectivity (dFC), which characterize how intrinsic brain organization changes over time, can provide a more detailed representation of brain function than traditional static analyses. Many dFC models in the literature represent functional brain networks as a meta-stable process with a discrete number of states; however, there is a lack of consensus on how to perform model selection and learn the number of states, as well as a lack of understanding of how different modeling assumptions influence the estimated state dynamics. To address these issues, we consider a predictive likelihood approach to model assessment, where models are evaluated based on their predictive performance on held-out test data. Examining several prominent models of dFC (in their probabilistic formulations) we demonstrate our framework on synthetic data, and apply it on two real-world examples: a face recognition EEG experiment and resting-state fMRI. Our results evidence that both EEG and fMRI are better characterized using dynamic modeling approaches than by their static counterparts, but we also demonstrate that one must be cautious when interpreting dFC because parameter settings and modeling assumptions, such as window lengths and emission models, can have a large impact on the estimated states and consequently on the interpretation of the brain dynamics