Hierarchical Multiscale Structure-Function Coupling for Brain Connectome Integration

Integrating structural and functional connectomes remains challenging because their relationship is non-linear and organized over nested modular hierarchies. We propose a hierarchical multiscale structure-function coupling framework for connectome integration that jointly learns individualized modular organization and hierarchical coupling across structural connectivity (SC) and functional connectivity (FC). The framework includes: (i) Prototype-based Modular Pooling (PMPool), which learns modality-specific multiscale communities by selecting prototypical ROIs and optimizing a differentiable modularity-inspired objective; (ii) an Attention-based Hierarchical Coupling Module (AHCM) that models both within-hierarchy and cross-hierarchy SC-FC interactions to produce enriched hierarchical coupling representations; and (iii) a Coupling-guided Clustering loss (CgC-Loss) that regularizes SC and FC community assignments with coupling signals, allowing cross-modal interactions to shape community alignment across hierarchies. We evaluate the model's performance across four cohorts for predicting brain age, cognitive score, and disease classification. Our model consistently outperforms baselines and other state-of-the-art approaches across three tasks. Ablation and sensitivity analyses verify the contributions of key components. Finally, the visualizations of learned coupling reveal interpretable differences, suggesting that the framework captures biologically meaningful structure-function relationships.

Hybrid eTFCE-GRF: Exact Cluster-Size Retrieval with Analytical p-Values for Voxel-Based Morphometry

Threshold-free cluster enhancement (TFCE) integrates cluster extent across thresholds to improve voxel-wise neuroimaging inference, but permutation testing makes it prohibitively slow for large datasets. Probabilistic TFCE (pTFCE) uses analytical Gaussian random field (GRF) p-values but discretises the threshold grid. Exact TFCE (eTFCE) eliminates discretisation via a union-find data structure but still requires permutations. We combine eTFCE's union-find for exact cluster-size retrieval with pTFCE's analytical GRF inference. The union-find builds the cluster hierarchy in one pass over sorted voxels and enables exact size queries at any threshold; GRF theory then converts these sizes to analytical p-values without permutations. Validation on synthetic phantoms (64^3, 80 subjects): FWER controlled at nominal level (0/200 null rejections, 95% CI [0.0%, 1.9%]); power matches baseline pTFCE (Dice >= 0.999); smoothness error below 1%; concordance r > 0.99. On UK Biobank (N=500) and IXI (N=563), significance maps form strict subsets of reference R pTFCE, which supports conservative error control. Implemented in pytfce (pip install pytfce): baseline completes whole-brain VBM in ~5s (75x faster than R pTFCE), hybrid in ~85s (4.6x faster) with exact cluster sizes; both >1000x faster than permutation TFCE.