Copula-Linked Parallel ICA: A Method for Coupling Structural and Functional MRI brain Networks

Different brain imaging modalities offer unique insights into brain function and structure. Combining them enhances our understanding of neural mechanisms. Prior multimodal studies fusing functional MRI (fMRI) and structural MRI (sMRI) have shown the benefits of this approach. Since sMRI lacks temporal data, existing fusion methods often compress fMRI temporal information into summary measures, sacrificing rich temporal dynamics. Motivated by the observation that covarying networks are identified in both sMRI and resting-state fMRI, we developed a novel fusion method, by combining deep learning frameworks, copulas and independent component analysis (ICA), named copula linked parallel ICA (CLiP-ICA). This method estimates independent sources for each modality and links the spatial sources of fMRI and sMRI using a copula-based model for more flexible integration of temporal and spatial data. We tested CLiP-ICA using data from the Alzheimer's Disease Neuroimaging Initiative (ADNI). Our results showed that CLiP-ICA effectively captures both strongly and weakly linked sMRI and fMRI networks, including the cerebellum, sensorimotor, visual, cognitive control, and default mode networks. It revealed more meaningful components and fewer artifacts, addressing the long-standing issue of optimal model order in ICA. CLiP-ICA also detected complex functional connectivity patterns across stages of cognitive decline, with cognitively normal subjects generally showing higher connectivity in sensorimotor and visual networks compared to patients with Alzheimer, along with patterns suggesting potential compensatory mechanisms.