Estimating scale-free dynamic effective connectivity networks from fMRI using group-wise spatial–temporal regularizations

Abstract

Estimating dynamic effective connectivity (dEC) networks is crucial to understand the time-varying directional interconnections among brain regions. It is now widely understood that brain networks have the property of being scale-free. However, this property has seldom been considered and is often inadequately preserved using conventional dEC estimation methods. As a result, important hubs and network graphical characteristics cannot be accurately obtained. In this work, we develop a new method to use a group-wise penalty together with spatial sparsity and temporal smoothness regularizations (namely Group-wise Spatial–Temporal Regularizations, GSTR) for the inference of scale-free dEC networks from functional magnetic resonance imaging (fMRI). The method employs a time-varying vector autoregressive (VAR) model, where the model coefficients can be formed as adjacency matrices of the dEC networks. Meanwhile, the proposed group-wise regularization is able to preserve the connectivities of potential hubs in scale-free networks by grouping them as an entire set. To deal with the complexity of optimization with multiple regularizations, we propose an effective algorithm based on the augmented Lagrangian multiplier. The accuracy of the GSTR method is validated using a variety of synthetic datasets with the scale-free property. Furthermore, we apply the GSTR method to an open fMRI dataset recorded from a block design visual task-related experiment containing 255 healthy participants to estimate visual-induced dEC networks and find GSTR can achieve reasonable and interpretable dEC estimates. Results from both synthetic and real-world datasets suggest that the proposed GSTR method could serve as a powerful analytical tool to accurately infer scale-free dEC patterns.