  Functional connectivity (FC) has been widely used to study brain network
interactions underlying the emerging cognition and behavior of an individual.
FC is usually defined as the correlation or partial correlation between brain
regions. Although FC is proved to be a good starting point to understand the
brain organization, it fails to tell the causal relationship or the direction
of interactions. Many directed acyclic graph (DAG) based methods were applied
to study the directed interactions using functional magnetic resonance imaging
(fMRI) data but the performance was severely limited by the small sample size
and high dimensionality, hindering its applications. To overcome the obstacles,
we propose a score based joint directed acyclic graph model to estimate the
directed FC in fMRI data. Instead of using a combinatorial optimization
framework, the structure of DAG is characterized with an algebra equation and
further regularized with sparsity and group similarity terms. The simulation
results have demonstrated the improved accuracy of the proposed model in
detecting causality as compared to other existing methods. In our case-control
study of the MIND Clinical Imaging Consortium (MCIC) data, we have successfully
identified decreased functional integration, disrupted hub structures and
characteristic edges (CtEs) in schizophrenia (SZ) patients. Further comparison
between the results from directed FC and undirected FC illustrated the their
different emphasis on selected features. We speculate that combining the
features from undirected graphical model and directed graphical model might be
a promising way to do FC analysis.
