Higher-order information-theoretic measures provide a new way to quantify information transmission among brain regions. This study uses measures of higher-order information flow among brain regions by estimating their total correlation. To estimate total correlation, the unsupervised learning model CorEx was used, and CorEx approaches can be used as a metric to estimate indirect functional connectivity characteristics among brain regions more than other domain-specific traditional algorithms. Moreover, the majority of functional connectivity studies have focused on pairwise relationships only, and statistical dependency involving more than two brain regions, on the other hand, is rare. In this paper, we explain how to use total correlation to estimate multivariate connectivity in the brain. We validated our method with more extensive open fMRI datasets under different conditions, respectively. We found that total correlation can reveal substantial information sharing among brain regions, consistent with existing neuroscience studies. On the other hand, total correlation could estimate functional connectivity beyond pairwise brain regions and could be used as a new functional connectivity metric. Meanwhile, it can also be an effective tool to aid in the discovery of biomarkers for the diagnosis of brain diseases.