The missing third dimension-Functional correlations of BOLD signals incorporating white matter

Correlations between magnetic resonance imaging (MRI) blood oxygenation level-dependent (BOLD) signals from pairs of gray matter areas are used to infer their functional connectivity, but they are unable to describe how white matter is engaged in brain networks. Recently, evidence that BOLD signals in white matter are robustly detectable and are modulated by neural activities has accumulated. We introduce a three-way correlation between BOLD signals from pairs of gray matter volumes (nodes) and white matter bundles (edges) to define the communication connectivity through each white matter bundle. Using MRI images from publicly available databases, we show, for example, that the three-way connectivity is influenced by age. By integrating functional MRI signals from white matter as a third component in network analyses, more comprehensive descriptions of brain function may be obtained.