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Abstract There are a growing number of neuroimaging studies motivating joint structural and functional brain connectivity. Brain connectivity of different modalities provides insight into brain functional organization by leveraging complementary information, especially for brain disorders such as schizophrenia. In this paper, we propose a multi-modal independent component analysis (ICA) model that utilizes information from both structural and functional brain connectivity guided by spatial maps to estimate intrinsic connectivity networks (ICNs). Structural connectivity is estimated through whole-brain tractography on diffusion-weighted MRI (dMRI), while functional connectivity is derived from resting-state functional MRI (rs-fMRI). The proposed structural-functional connectivity and spatially constrained ICA (sfCICA) model estimates ICNs at the subject level using a multi-objective optimization framework. We evaluated our model using synthetic and real datasets (including dMRI and rs-fMRI from 149 schizophrenia patients and 162 controls). Multi-modal ICNs revealed enhanced functional coupling between ICNs with higher structural connectivity, improved modularity, and network distinction, particularly in schizophrenia. Statistical analysis of group differences showed more significant differences in the proposed model compared to the unimodal model. In summary, the sfCICA model showed benefits from being jointly informed by structural and functional connectivity. These findings suggest advantages in simultaneously learning effectively and enhancing connectivity estimates using structural connectivity. 

ABSTRACT Schizophrenia (SZ) patients exhibit abnormal static and dynamic functional connectivity across various brain domains. We present a novel approach based on static and dynamic inter‐network connectivity entropy (ICE), which represents the entropy of a given network's connectivity to all the other brain networks. This novel approach enables the investigation of how connectivity strength is heterogeneously distributed across available targets in both SZ patients and healthy controls. We analyzed fMRI data from 151 SZ patients and 160 demographically matched healthy controls (HC). Our assessment encompassed both static and dynamic ICE, revealing significant differences in the heterogeneity of connectivity levels across available functional brain networks between SZ patients and HC. These networks are associated with subcortical (SC), auditory (AUD), sensorimotor (SM), visual (VIS), cognitive control (CC), default mode network (DMN), and cerebellar (CB) functional brain domains. Elevated ICE observed in individuals with SZ suggests that patients exhibit significantly higher randomness in the distribution of time‐varying connectivity strength across functional regions from each source network, compared to HC. C‐means fuzzy clustering analysis of functional ICE correlation matrices revealed that SZ patients exhibit significantly higher occupancy weights in clusters with weak, low‐scale functional entropy correlation, while the control group shows greater occupancy weights in clusters with strong, large‐scale functional entropy correlation. K‐means clustering analysis on time‐indexed ICE vectors revealed that cluster with highest ICE have higher occupancy rates in SZ patients whereas clusters characterized by lowest ICE have larger occupancy rates for control group. Furthermore, our dynamic ICE approach revealed that in HC, the brain primarily communicates through complex, less structured connectivity patterns, with occasional transitions into more focused patterns. Individuals with SZ are significantly less likely to attain these more focused and structured transient connectivity patterns. The proposed ICE measure presents a novel framework for gaining deeper insight into mechanisms of healthy and diseased brain states and represents a useful step forward in developing advanced methods to help diagnose mental health conditions.