Bayesian Analysis of fMRI data with Spatial Priors

Functional Magnetic Resonance Imaging (fMRI) using Blood Oxygen Level Dependent (BOLD) contrast is an established method for making inferences about regionally specific activations in the human brain [7]. From measurements of changes in blood oxygenation one can use various statistical models, such as the General Linear Model (GLM) [8], to make inferences about task-specific changes in underlying neuronal activity. In previous work [21, 23, 22] we have developed a spatially regularised General Linear Model (GLM) for the analysis of fMRI data which allows for the characterisation of regionally specific effects using Posterior Probability Maps (PPMs). This spatial regularisation has been shown [23] to increase the sensitivity of inferences one can make. This paper reviews our body of work on spatially regularised GLMs and describes two new developments. These are (i) an approach for assessing multivariate contrasts and (ii) a method for choosing the thresholds that generate PPMs. The paper is structured as follows. Section 2 reviews the theoretical development of the algorithm. This includes a description of a Variational Bayesian algorithm in which inference is based on an approximation to the posterior distribution that has minimal KLdivergence from the true posterior. Sections 3 and 4 describe the new approaches for assessing multivariate contrasts and PPM thresholding. In section 5 we present results on null fMRI data, synthetic data and fMRI from functional activation studies of auditory and face processing. The paper finishes with a discussion in section 6.