Random Effects Models for Understanding Variability and Association between Brain Functional and Structural Connectivity

The human brain is organized as a complex network, where connections between regions are characterized by both functional connectivity (FC) and structural connectivity (SC). While previous studies have primarily focused on network-level FC-SC correlations (i.e., the correlation between FC and SC across all edges within a predefined network), edge-level correlations (i.e., the correlation between FC and SC across subjects at each edge) has received comparatively little attention. In this study, we systematically analyze both network-level and edge-level FC-SC correlations, demonstrating that they lead to divergent conclusions about the strength of brain function-structure association. To explain these discrepancies, we introduce new random effects models that decompose FC and SC variability into different sources: subject effects, edge effects, and their interactions. Our results reveal that network-level and edge-level FC-SC correlations are influenced by different effects, each contributing differently to the total variability in FC and SC. This modeling framework provides the first statistical approach for disentangling and quantitatively assessing different sources of FC and SC variability and yields new insights into the relationship between functional and structural brain networks.