Joint Bayesian Estimation of Voxel Activation and Inter-regional Connectivity in fMRI Experiments
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JOINT BAYESIAN ESTIMATION OF VOXEL ACTIVATION AND INTER-REGIONAL CONNECTIVITY IN FMRI EXPERIMENTS
Daniel Spencer , Rajarshi Guhaniyogi and Raquel Prado UNIVERSITY OF CALIFORNIA
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 multidimensional 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. Key words: Bayesian inference, brain activation, brain connectivity, functional magnetic resonance imaging, graphical modeling, multiway stick-breaking prior, PARAFAC decomposition, tensor response.
1. Introduction Recently, rapid advancements in different imaging modalities have generated massive neuroimaging data which are key in understanding how the human brain functions. For the present article, our motivation is mainly drawn from multi-subject functional MRI (fMRI) studies. Data from an fMRI scan are processed from the scanner as a four-dimensional tensor object, where the index of a datum within the tensor provides information about the location of the datum in space and time. In the context of an fMRI scan, the brain at a single point in time can be pictured as a three-dimensional tensor partitioned into small cubes, known as voxels (Lazar 2008). A relative measure of oxygen in the blood, referred to as the blood oxygen level-dependent (BOLD) response, is obtained from every voxel in each scan typically acquired a
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