Joint Bayesian Estimation of Voxel Activation and Inter-regional Connectivity in fMRI Experiments

Brain activation and connectivity analyses in task-based functional magnetic resonance imaging (fMRI) experiments with multiple subjects are currently at the forefront of data-driven neuroscience. In such experiments, interest often lies in understanding activation of brain voxels due to external stimuli and strong association or connectivity between the measurements on a set of pre-specified groups of brain voxels, also known as regions of interest (ROI). This article proposes a joint Bayesian additive mixed modeling framework that simultaneously assesses brain activation and connectivity patterns from multiple subjects. In particular, fMRI measurements from each individual obtained in the form of a multi-dimensional array/tensor at each time are regressed on functions of the stimuli. We impose a low-rank parallel factorization decomposition on the tensor regression coefficients corresponding to the stimuli to achieve parsimony. Multiway stick-breaking shrinkage priors are employed to infer activation patterns and associated uncertainties in each voxel. Further, the model introduces region-specific random effects which are jointly modeled with a Bayesian Gaussian graphical prior to account for the connectivity among pairs of ROIs. Empirical investigations under various simulation studies demonstrate the effectiveness of the method as a tool to simultaneously assess brain activation and connectivity. The method is then applied to a multi-subject fMRI dataset from a balloon-analog risk-taking experiment, showing the effectiveness of the model in providing interpretable joint inference on voxel-level activations and inter-regional connectivity associated with how the brain processes risk. The proposed method is also validated through simulation studies and comparisons to other methods used within the neuroscience community.