An explicit functional-map framework for structure-function correspondence in brain connectivity

Characterizing the relationship between structural connectivity (SC) and functional connectivity (FC) is a central problem in multimodal neuroimaging. SC-to-FC prediction accuracy is often used to summarize this relationship, but a high score may largely reflect population-level regularities shared across subjects and does not reveal whether regional, network-level, or subject-specific correspondence is preserved. We therefore developed a framework that makes these different levels of SC-FC correspondence explicit and directly testable. Approach. For each subject, we constructed separate spectral representations of SC and FC and estimated an explicit linear map between them. Signal transfer was evaluated against matched controls that disrupted node identity, within-network organization, or subject pairing, allowing aggregate transfer to be distinguished from more specific forms of correspondence. A training-derived reference map was further used to define the functional component expected under a reference SC-FC relationship and the deviation from that expectation for downstream aging and disease-related analyses. Main results. Across four independent datasets, all primary matched-control gaps were positive after false-discovery-rate correction, although their magnitudes varied across cohorts. Strong aggregate transfer did not necessarily imply strong subject-level correspondence. Compared with external baselines, the proposed framework more consistently preserved regional identity, within-network organization, and correct subject pairing. In aging analyses, reduced alignment with a young-reference SC-FC relationship was robust in CamCAN but not significant in NKI, whereas empirical FC magnitude showed no comparable decline. In ADNI, reference-conditioned markers showed exploratory disease-related signals, but the associated uncertainty did not support definitive diagnostic or incremental-value claims. Significance. The proposed framework separates the ability to transfer SC-derived signals into FC space from the specificity of the correspondence being preserved. It provides an interpretable basis for testing population-level, network-level, and subject-sensitive SC-FC relationships and for constructing reference-conditioned individual deviation measures without treating prediction accuracy as direct evidence of biological constraint.