LAUSR

The directed brain functional network construction gives us the new insights into the relationships between brain regions from the causality point of view. The Granger causality analysis is one of the powerful methods to model the directed network. The complex brain network is also hierarchically constructed, which is particularly suited to facilitate segregated functions and the global integration of the segregated functions. Therefore, it is of great interest to explore new approach to model the hierarchical architecture of the directed network. In the present study, we proposed a new approach, namely, stepwise multivariate Granger causality (SMGC), considering both the directed and hierarchical features of brain functional network to explore the stepwise causal relationship in the network. The simulation study demonstrated that the diverse and complex hierarchical organization could be embedded in the apparently simple directed network. The proposed SMGC method could capture the multiple hierarchy of the directed network. When applying to the real functional magnetic resonance imaging (fMRI) datasets, the core triple resting-state networks in human brain showed within-network directed connections in the first-level directed network and rich and diverse between-network pathways in the second-level hierarchical network. The default mode network (DMN) had a prominent role in the resting-state acting as both the causal source and the important relay station. Further exploratory research on the adaption of directed hierarchical network in athletes suggested the enhanced bidirectional communication between the DMN and the central executive network (CEN) and the enhanced directed connections from the salience network (SN) to the CEN in the athlete group. The SMGC approach is capable of capturing the hierarchical architecture of the brain directed functional network, which refreshes the new stepwise causal relationship in the directed network. This might shed light on the potential application for exploring the altered hierarchical organization of brain directed network in neuropsychiatric disorders.