A Bayesian Hierarchical Framework for Spatial Modeling of fMRI Data

Functional neuroimaging techniques enable investigations into the neural basis of human cognition, emotions, and behaviors. In practice, applications of functional magnetic resonance imaging (fMRI) have provided insights into the pathophysiology of major psychiatric, neurologic, and substance abuse disorders, as well as into the neural responses to treatments. Modern activation studies often compare localized stimulus-induced brain activity between experimental groups. One may also extend voxel-level analyses by simultaneously considering the ensemble of voxels constituting an anatomically defined region of interest (ROI) or by considering means or quantiles of the ROI. In this work we present a Bayesian extension of voxel-level analyses that offers several notable benefits. First, it combines whole-brain voxel-by-voxel modeling and ROI analyses within a unified framework. Secondly, an unstructured variance/covariance for regional mean parameters allows for the study of inter-regional functional connectivity, provided enough subjects are available to allow for accurate estimation. Finally, an exchangeable correlation structure within regions allows for the consideration of intra-regional functional connectivity. We perform estimation for our model using Markov Chain Monte Carlo (MCMC) techniques implemented via Gibbs sampling which, despite the high throughput nature of the data, can be executed quickly (less than one half an hour). We apply our Bayesian hierarchical model to a novel data set considering verbal memory in subjects at high risk for Alzheimer's disease. The unifying hierarchical model presented in this manuscript is shown to shed considerable light on these data.