The Importance of Being Negative: A serious treatment of non-trivial edges in brain functional connectome

Abstract

Understanding the modularity of fMRI-derived brain networks or connectomes can inform the study of brain function organization. However, fMRI connectomes additionally involve negative edges, which are not rigorously accounted for by existing approaches to modularity that either ignores or arbitrarily weight these connections. Furthermore, most Q maximization-based modularity algorithms yield variable results with suboptimal reproducibility. Here we present an alternative, reproducible approach that exploits how frequent the BOLD-signal correlation between two nodes is negative. We validated this novel probability-based modularity approach on two independent publicly-available resting-state connectome dataset (the Human Connectome Project and the 1000 Functional Connectomes) and demonstrated that negative correlations alone are sufficient in understanding resting-state modularity. In fact, this approach a) permits a dual formulation, leading to equivalent solutions regardless of whether one considers positive or negative edges; b) is theoretically linked to the Ising model defined on the connectome, thus yielding modularity result that maximizes data likelihood. We additionally were able to detect sex differences in modularity that the most widely utilized methods did not. Results confirmed the superiority of our approach in that: a) correlations with the highest probability of being negative are consistently placed between modules, b) due to the equivalent dual forms, no arbitrary weighting factor is required to balance the influence between negative and positive correlations, unlike existing Q maximization-based modularity approaches. As datasets like HCP become widely available for analysis by the neuroscience community at large, appropriate computational tools to understand the neurobiological information of negative edges in fMRI connectomes are increasingly important.