Structural co-modulation: An individualized measure of inter-component interactions in source-based morphometry

Source-based morphometry (SBM) is a powerful multivariate method for identifying covarying structural brain networks. However, standard SBM provides only a single loading value per component for each subject, which limits the characterization of relationships between these components. We propose a novel technical co-modulation approach to derive an individualized, network-like measure of structural brain organization. This method transforms the subject-specific SBM loading vector into a symmetric co-modulation matrix by computing the vector's outer product. Each element of this matrix quantifies the pairwise interaction between structural components, creating a subject-specific fingerprint. Analogous in structure to a functional connectivity matrix where each element represents the relationship between a pair of networks, this matrix maps their joint structural prominence, reflecting how strongly two networks co-occur within an individual. To demonstrate the utility of this method, we applied it to structural MRI data from 210 patients with schizophrenia (SZ) and 195 healthy controls (HC) from the fBIRN psychosis dataset using functional networks as priors for SBM. We observed widespread reductions in structural co-modulation in the SZ group, particularly within and between visual, default-mode, and cognitive control networks. Furthermore, co-modulation patterns were significantly correlated with cognitive performance and clinical symptom severity in patients. Structural co-modulation provides a robust framework for quantifying individualized relationships between structural brain features, overcoming key limitations of standard SBM and offering a new avenue for integrating structural and functional brain analyses.