A Linear Generative Framework for Structure-Function Coupling in the Human Brain (2507.06136v1)

Abstract: Brain function emerges from coordinated activity across anatomically connected regions, where structural connectivity (SC) -- the network of white matter pathways - provides the physical substrate for functional connectivity (FC) -- the correlated neural activity between brain areas. While these structural and functional networks exhibit substantial overlap, their relationship involves complex, indirect mechanisms, including the dynamic interplay of direct and indirect pathways, recurrent network interactions, and neuromodulatory influences. To systematically untangle how structural architecture shapes functional patterns, this work aims to establish a set of rules that decode how direct and indirect structural connections and motifs give rise to FC between brain regions. Specifically, using a generative linear model, we derive explicit rules that predict an individual's resting-state fMRI FC from diffusion-weighted imaging (DWI)-derived SC, validated against topological null models. Examining the rules reveals distinct classes of brain regions, with integrator hubs acting as structural linchpins promoting synchronization and mediator hubs serving as structural fulcrums orchestrating competing dynamics. Through virtual lesion experiments, we demonstrate how different cortical and subcortical systems distinctively contribute to global functional organization. Together, this framework disentangles the mechanisms by which structural architecture drives functional dynamics, enabling the prediction of how pathological or surgical disruptions to brain connectivity cascade through functional networks, potentially leading to cognitive and behavioral impairments.

• The paper introduces a linear generative model that quantifies the coupling between structural and functional connectivity using a rule matrix derived from DWI and fMRI data.
• The methodology employs LASSO regression and group-level Kronecker product analysis to estimate connectivity patterns and manage individual variations.
• The model effectively predicts network dynamics and spots critical regional hubs, offering potential clinical applications in disorders like schizophrenia.

A Linear Generative Framework for Structure-Function Coupling in the Human Brain

Introduction

Complexity characterizes the relationship between structural connectivity (SC) and functional connectivity (FC) in the human brain, stemming from both direct and indirect pathways and their dynamic interplay. The presented framework elucidates this relationship through a generative linear model, driving predictive insights from diffusion-weighted imaging (DWI) into the resting-state fMRI-derived FC. This approach achieves the twin objectives of unraveling how specific structural motifs underlie functional dynamics and enabling sound predictions on the functional ramifications of structural alterations.

Figure 1: Network motifs and connectivity patterns captured by structural generative rules.

Methodological Framework

Generative Linear Model

The FC matrix, denoted as $B$, is formulated from SC data $X$ using a symmetric rule matrix $O$: $B = XOX^T$. This linear model establishes direct and indirect SC's influence on FC, capturing the delicate interdependence between these patterns.

Rule Matrix Estimation

By employing LASSO regression, the paper estimates the rule matrix on an individual basis. High robustness in prediction is verified by scatterplot analyses which demonstrate a tight linear correlation between predicted and actual FC values (Figure 2).

Figure 2: Predicted FC from SC.

Group-Level Analysis

A group-level rule matrix is constructed using the Kronecker product, unveiling SC-FC coupling principles universally applied across subjects. Despite observable reductions in fit statistics compared to individual-level analysis, the outcomes solidify foundational structural principles, though individual variations imply unique subject-specific nuances.

Model Evaluation

Accuracy and Sparsity

The model sustains accuracy, with optimal predictive capabilities until approximately 30% sparsity in the rule matrix—a finding substantiated by linear regression analysis (Figure 3). Individualized structural parameters perform poorly with datasets from different subjects, confirming the subject-specific nature of the SC-FC interplay.

Figure 3: Impact of thresholding the rule matrix on prediction accuracy.

Structural and Functional Dynamics

Identifying Structural Linchpins and Fulcrums

Weighted stochastic block modeling (WSBM) categorizes brain regions into clusters, offering clarity on regional roles. Identified are integrator hubs, which synchronize functions, and mediator hubs that balance dynamics (Figures 4 and 5).

Figure 4: Structural linchpins and fulcrums of functional dynamics.

Figure 5: Rule matrix clusters overlap with resting-state networks.

Default Mode and Other Networks

Detailed exploration of networks such as the default mode network (DMN) shed light on their impactful contributions to global FC, enhancing the framework's applicability in understanding the complex inter-network dynamics (Figure 6).

Figure 6: Default mode network's influence on global FC patterns.

Pathological Implications

Application of this model to pathological data highlights its capability to pinpoint SC-FC coupling disruptions in conditions like schizophrenia (Figure 7). Alterations suggest not just structural but also potentially compensatory adaptations underlying clinical symptoms.

Figure 7: Pathological changes in the SC-FC coupling rules.

Conclusion

The generative linear framework effectively advances our understanding of the brain's intrinsic structure-function relationships. By capturing these dynamics in rule matrices, it facilitates the prediction of FC alterations due to structural changes. Its predictive utility in both clinical and personalized medicine contexts opens pathways for transformative applications in neuroscientific research and therapeutic strategy development, bridging the gap between individual anatomical variations and holistic functional interpretations.