A hierarchical model for probabilistic independent component analysis of multi-subject fMRI studies

An important goal in fMRI studies is to decompose the observed series of brain images to identify and characterize underlying brain functional networks. Independent component analysis (ICA) has been shown to be a powerful computational tool for this purpose. Classic ICA has been successfully applied to single-subject fMRI data. The extension of ICA to group inferences in neuroimaging studies, however, is challenging due to the unavailability of a pre-specified group design matrix. Existing group ICA methods generally concatenate observed fMRI data across subjects on the temporal domain and then decompose multi-subject data in a similar manner to single-subject ICA. The major limitation of existing methods is that they ignore between-subject variability in spatial distributions of brain functional networks in group ICA. In this article, we propose a new hierarchical probabilistic group ICA method to formally model subject-specific effects in both temporal and spatial domains when decomposing multi-subject fMRI data. The proposed method provides model-based estimation of brain functional networks at both the population and subject level. An important advantage of the hierarchical model is that it provides a formal statistical framework to investigate similarities and differences in brain functional networks across subjects, for example, subjects with mental disorders or neurodegenerative diseases such as Parkinson's as compared to normal subjects. We develop an EM algorithm for model estimation where both the E-step and M-step have explicit forms. We compare the performance of the proposed hierarchical model with that of two popular group ICA methods via simulation studies. We illustrate our method with application to an fMRI study of Zen meditation.