SPARK: Sparsity-based analysis of reliable k-hubness and overlapping network structure in brain functional connectivity.

Functional hubs are defined as the specific brain regions with dense connections to other regions in a functional brain network. Among them, connector hubs are of great interests, as they are assumed to promote global and hierarchical communications between functionally specialized networks. Damage to connector hubs may have a more crucial effect on the system than does damage to other hubs. Hubs in graph theory are often identified from a correlation matrix, and classified as connector hubs when the hubs are more connected to regions in other networks than within the networks to which they belong. However, the identification of hubs from functional data is more complex than that from structural data, notably because of the inherent problem of multicollinearity between temporal dynamics within a functional network. In this context, we developed and validated a method to reliably identify connectors and corresponding overlapping network structure from resting-state fMRI. This new method is actually handling the multicollinearity issue, since it does not rely on counting the number of connections from a thresholded correlation matrix. The novelty of the proposed method is that besides counting the number of networks involved in each voxel, it allows us to identify which networks are actually involved in each voxel, using a data-driven sparse general linear model in order to identify brain regions involved in more than one network. Moreover, we added a bootstrap resampling strategy to assess statistically the reproducibility of our results at the single subject level. The unified framework is called SPARK, i.e. SParsity-based Analysis of Reliable k-hubness, where k-hubness denotes the number of networks overlapping in each voxel. The accuracy and robustness of SPARK were evaluated using two dimensional box simulations and realistic simulations that examined detection of artificial hubs generated on real data. Then, test/retest reliability of the method was assessed using the 1000 Functional Connectome Project database, which includes data obtained from 25 healthy subjects at three different occasions with long and short intervals between sessions. We demonstrated that SPARK provides an accurate and reliable estimation of k-hubness, suggesting a promising tool for understanding hub organization in resting-state fMRI.