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

Abstract

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.