Fast Bayesian estimation of brain activation with cortical surface and subcortical fMRI data using EM
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Analysis of brain imaging scans is critical to understanding the way the human brain functions, which can be leveraged to treat injuries and conditions that affect the quality of life for a significant portion of the human population. In particular, functional magnetic resonance imaging (fMRI) scans give detailed data on a living subject at high spatial and temporal resolutions. Due to the high cost involved in the collection of these scans, robust methods of analysis are of critical importance in order to produce meaningful inference. Bayesian methods in particular allow for the inclusion of expected behavior from prior study into an analysis, increasing the power of the results while circumventing problems that arise in classical analyses, including the effects of smoothing results and sensitivity to multiple comparison testing corrections. Recent development of a surface-based spatial Bayesian general linear model for cortical surface fMRI (cs-fMRI) data provides the desired power increase in task fMRI data using stochastic partial differential equation (SPDE) priors. This model relies on the computational efficiencies of the integrated nested Laplace approximation (INLA) to perform powerful analyses that have been validated to outperform classical analyses. In this article, we develop an exact Bayesian analysis method for the GLM, employing an expectation-maximization (EM) algorithm to find maximum a posteriori (MAP) estimates of task-based regressors on cs-fMRI and subcortical fMRI data while using minimal computational resources. Our proposed method is compared to the INLA implementation of the Bayesian GLM, as well as a classical GLM on simulated data. A validation of the method on data from the Human Connectome Project is also provided.
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