A review on dependence measures in exploring brain networks from fMRI data

Abstract

Functional magnetic resonance imaging (fMRI) technique allows us to capture activities occurring in a human brain via signals related to cerebral blood flow, oxygen metabolism and blood volume, known as BOLD (blood oxygen level-dependent) signals. Exploring relationships between brain regions inside human brains from fMRI data is an active and challenging research topic. Relationships or associations between brain regions are commonly referred to as brain connectivity or brain network. This connectivity can be divided into three groups; (i) structural connectivity representing physically anatomical connections between regions, (ii) the functional connectivity which describes the statistical information among brain regions and (iii) the effective connectivity which specifies how one region interacts with others by a causal model. This survey paper provides a review on learning brain connectivities via fMRI data where detailed mathematical definitions of dependence measures widely-used for functional and effective connectivities are described. These measures include correlation, partial correlation, coherence, partial coherence, directed coherence, partial directed coherence, Granger causality, and other concepts such as dynamical causal modeling or structural equation modeling. Interpretation and relations of these measures as well as relevant estimation techniques that are widely used in the problems of fMRI modeling are summarized in this paper.