Hierarchical Multiscale Structure-Function Coupling for Brain Connectome Integration

Medical Image Analysis (2026) Contents lists av ailable at ScienceDirect Medical Image Analysis journal homepage: www .elsevier .com/locate/media Hierarchical Multiscale Structure-Function Coupling for Brain Connectome Integration Jianwei Chen a , Zhengyang Miao c , W enjie Cai e , Jiaxue T ang d , Boxing Liu b , Y unfan Zhang a , Y uhang Y ang d , Hao T ang a , Carola-Bibiane Sch ¨ onlieb g , Zaixu Cui f , Du Lei d , Shouliang Qi c, ∗ , Chao Li a,b,g,h, ∗ a School of Medicine, Univer sity of Dundee, UK b School of Science and Engineering, Univer sity of Dundee, UK c Colle ge of Medicine and Biological Information Engineering, Northeastern Univer sity , China d Colle ge of Medical Informatics, Chongqing Medical University , China e School of Airspace Science and Engineering , Shandong University , China f Chinese Institute for Brain Resear ch, China g Department of Applied Mathematics and Theor etical Physics, University of Cambridge, UK h Department of Clinical Neur osciences, University of Cambridge, UK A R T I C L E I N F O Article history : Receiv ed - Receiv ed in final form - Accepted - A vailable online - Communicated by - K eywor ds: Structure-function coupling, Structural connectome, Functional con- nectome, Multi-modal graph learning A B S T R A C T Integrating structural and functional connectomes remains challenging because their re- lationship is non-linear and organized ov er nested modular hierarchies. W e propose a hierarchical multiscale structure–function coupling framework for connectome integra- tion that jointly learns individualized modular organization and hierarchical coupling across structural connecti vity (SC) and functional connectivity (FC). The frame work in- cludes: (i) Prototype-based Modular Pooling (PMPool), which learns modality-specific multiscale communities by selecting prototypical R OIs and optimizing a di ff erentiable modularity-inspired objectiv e; (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. W e ev aluate the model’ s performance across four cohorts for pre- dicting brain age, cognitive score, and disease classification. Our model consistently outperforms baselines and other state-of-the-art approaches across three tasks. Abla- tion and sensitivity analyses verify the contrib utions of key components. Finally , the visualizations of learned coupling re veal interpretable di ff erences, suggesting that the framew ork captures biologically meaningful structure–function relationships. The code is av ailable at github . © 2026 Elsevier B. V . All rights reserved. 1. Introduction The brain connectome is a graphical representation of neural wiring in the brain, providing a unified frame work for studying its complex, dynamic, hierarchical organization. Specifically , ∗ co-corresponding author . e-mail: cl647@cam.ac.uk (Chao Li) the brain is parcellated into re gions using anatomical atlases, with structural connectivity (SC) among these regions inferred from white matter pathways via di ff usion MRI (dMRI) ( ˇ Skoch et al. , 2022 ), and functional connectivity (FC) is estimated from co-activ ations of the BOLD signals from functional MRI (fMRI) ( Hu et al. , 2024 ). These multimodal connectomes of- fer complementary insights into brain organization and its dy- namics throughout development, aging ( Ball et al. , 2014 ; Chan 2 Jianwei Chen et al. / Medical Image Analysis (2026) et al. , 2014 ), and v arious disorders ( Fornito et al. , 2015 ; W ei et al. , 2021 , 2023 ; Sinha et al. , 2020 ). Integrating multimodal connectomes can pro vide a comprehensi ve characterization of the brain. Howe ver , simple fusion strategies, such as concatena- tion ( Sebenius et al. , 2021 ) or element-wise summation ( Zhang et al. , 2021 ), are limited in their ability to model non-linear in- teractions across multimodal connectomes and f ail to reflect the complex brain or ganization. The structure-function coupling (SFC), as elucidated by neu- roscience research, highlights how brain structure supports or constrains functional dynamics in physiological and pathologi- cal conditions ( Su ´ arez et al. , 2020 ; Zhang et al. , 2022 ). As such, modeling SFC o ff ers a promising approach to more compre- hensiv ely integrate multimodal connectomes with neuroscience interpretability . Recent studies hav e incorporated structure- function interactions e xplicitly as coupling signals to guide multimodal integration. F or example, studies hav e proposed coupling SC and FC into a joint graph via learnable interaction edges, to predict brain age or disorders ( Li et al. , 2022 ; Xia et al. , 2025 ). Other studies learn SFC by modeling interactions between SC and FC representations through cross-modal align- ment objectives such as mutual learning and contrastive learn- ing ( Y ang et al. , 2023 ; Y e et al. , 2023b ). Despite their success, these models typically operate at the regional lev el and tend to ov erlook the intrinsic organization of the brain. Recent advances suggest that SFC follows a hierarchical, modular architecture ( Fotiadis et al. , 2024 ; T ang et al. , 2025 ), where brain regions are organized into communities nested within coarser-grained modules across multiple levels of brain hierarchy , forming a multiscale partition of the brain connec- tome and reflecting intrinsic brain organization ( Meunier et al. , 2009 ). This observation has inspired connectome integration approaches that e xplore hierarchical SFC, such as network communication models ( Zamani Esf ahlani et al. , 2022 ), and the mapping of functional signals onto the structural graph har - monics ( Sun et al. , 2024 ). Despite advancements, these ap- proaches often rely on handcrafted features and shallow aggre- gation strategies, which restrict their ability to capture comple x, nonlinear interactions between modalities. More recent graph learning approaches e xplore SFC through regional subgraphs using graph trav ersal algorithms ( Y e et al. , 2023a ; Huang et al. , 2025 ), or community partitions based on prior functional modules ( Xia et al. , 2024 ; Y eo et al. , 2011 ). Despite e ff orts, these approaches face limitations. First , most methods rely on fix ed modular templates or atlas-based par- cellations, e.g., a canonical functional modular template ( Y eo et al. , 2011 ), before learning the SFC ( Xia et al. , 2024 ). An- other study ( Mess ´ e , 2020 ) derives SFC across resolutions us- ing a family of cortical atlases that define increasing numbers of nodes, progressing from coarser to finer scales. Ho we ver , rare studies account for individualized, modality-specific brain organization ( Fotiadis et al. , 2024 ), due to their reliance on pre-defined partitions from priors or atlases. Second , neuro- science research suggests that the brain is organized as a hi- erarchical system: within-hierarchy communities support spe- cialized and segregated processing, while interactions across hi- erarchy are crucial for propagating information throughout the system ( Jiang et al. , 2023 ; Pines et al. , 2023 ). Ho wev er , ex- isting models predominantly focus on within-hierarchy inter- actions, employing graph transformers ( Feng et al. , 2025 ) or GNNs ( Xia et al. , 2025 ), and largely ne glect cross-hierarchy interactions, leading to incomplete hierarchical coupling repre- sentations. Third , before modeling SFC, many studies deri ve structural and functional community structure using two sepa- rate community-detection methods ( Su ´ arez et al. , 2020 ; Betzel et al. , 2013 ; Lurie et al. , 2024 ). This approach may overlook cross-modal constraints in modeling the brain or ganization that jointly shape the community structure in SC and FC ( Se guin et al. , 2022 ). T o address the above challenges, we propose a GNN- based framew ork that models hierarchical multiscale structure- function coupling ( HiM-SFC ) for integrating multimodal brain connectomes. First , we propose a Prototype-based Mod- ular Pooling (PMPool) strategy with two modality-specific branches. W ithin each modality , PMPool identifies prototyp- ical R OIs as community anchors and clusters them by proto- type distances, yielding modality-specific community structure. T o learn indi vidualized community structures, a di ff erentiable modularity-inspired pooling objectiv e is introduced to encour - age community assignments to approximate each connectome’ s modularity , rather than fixed partition. Second , we introduce an Attention-based Hierarchical Coupling Module (AHCM) to jointly model within- and cross-hierarchy structure–function in- teractions across scales. Specifically , within-hierarchy inter - actions are modeled via a bidirectional attention mechanism, while cross-hierarchy interactions are captured via a cross- attention mechanism and embedded as a coupling bias to enrich hierarchical coupling representations. Lastly , to incorporate cross-modal interactions into community structure learning, we introduce a Coupling-guided Clustering loss (CgC-Loss) that regularizes the SC and FC assignment matrices with coupling signals, enabling learned communities to be jointly constrained by both structure and function at each hierarchical le vel. Our main contributions are summarized as fourfold. • A GNN-based framework for integrating structural and functional connectomes through modelling hierarchical SFC, and jointly learns individualized, modality-specific hierarchical modular organization of the brain. • A Prototype-based Modular Pooling (PMPool) strategy with two modality-specific branches that identify proto- typical R OIs to assign communities, and a di ff erentiable, modularity-inspired pooling objectiv e encourages commu- nity structures to approximate individualized modularity . • An Attention-based Hierarchical Coupling Module (AHCM) that captures both within- and cross-hierarchy structure–function interactions, employing bidirectional and cross attention mechanisms to aggre gate multiscale interactions into rich hierarchical SFC representations. • A Coupling-guided Clustering loss (CgC-Loss) that lever - ages coupling signals to regularize SC and FC assignment matrices at each hierarchical lev el, yielding community structure jointly constrained by structure and function. Jianwei Chen et al. / Medical Image Analysis (2026) 3 2. Related work 2.1. Hierar chical modular or ganization of the connectome Hierarchical modular organization refers to a nested com- munity structure in which smaller communities are embedded within larger modules, forming a multiscale organization. In structural networks, this typically reflects locally dense clusters supported by short-range white matter connections, combined with long-range pathways for global integration ( Bullmore and Sporns , 2009 ). In functional netw orks, modular structure re- flects coordinated activity patterns. A canonical example is the functional parcellations by Y eo ( Y eo et al. , 2011 ), who deriv ed 7- and 17-network templates by clustering resting-state fMRI connectivity patterns from a lar ge population. SFC explicitly characterizes how anatomical wiring con- strains functional interactions. Hierarchical modular organiza- tion and SFC are tightly linked, where coupling v aries within and across hierarchical scales. Several studies have in vestigated this relationship using linear statistics and descriptiv e network analysis. Zamani Esfahlani et al. ( 2022 ) systematically bench- mark a broad family of communication- and geometry-based predictors for SFC, sho wing that coupling is more informativ e and heterogeneous at the regional scale than at the whole-brain lev el. Sun et al. ( 2024 ) quantify hierarchical structure-function discrepancies using a structural decoupling index derived from structural graph harmonics and demonstrate that Alzheimer’ s disease exhibits a characteristic spatial pattern of abnormal de- coupling that relates to cognition and supports diagnostics. 2.2. Multimodal brain connectome inte gration Structural and functional connectomes provide complemen- tary views of brain connectivity . Consequently , man y studies hav e proposed methods to integrate both modalities. A common strategy is to concatenate modality-specific features and use a multilayer perceptron (MLP) ( Salas-Gonzalez et al. , 2010 ). Con volutional approaches, such as BrainNetCNN ( Kawahara et al. , 2017 ), instead treat connectivity matrices as structured inputs and lev erage operations over edge- and node-like rep- resentations to capture topological patterns. More recently , GNNs ha ve become a prominent frame work for multimodal in- tegration because they can model non-Euclidean relationships in graph-structured data. For example, multi-modal GCNs (M- GCNs) ( Dsouza et al. , 2021 ) use subject-specific SC to guide learning on FC, whereas multi-view GCNs (MV -GCNs) ( Zhang et al. , 2018 ) learn separate encoders for each modality and fuse the resulting representations for classification. Despite their progress, many of these approaches still behav e largely as feature-lev el fusion schemes and ha ve limited capacity to rep- resent non-linear , region-specific cross-modal interactions. 2.3. Modeling SFC for connectome inte gration Modeling SFC, therefore, o ff ers a principled route for mul- timodal integration, with the benefit of impro ved interpretabil- ity relati ve to naive feature combination. For instance, Joint- GCN ( Li et al. , 2022 ) models R OI-wise SFC by introducing learnable coupling edges between corresponding R OIs in SC and FC. Cross-GNN ( Y ang et al. , 2023 ) further captures inter- modal dependencies via dynamic graph learning and mutual learning, and has been applied to disease classification. While these methods move beyond nai ve fusion, they typically model connectomes as flat graphs at a single scale (primarily at the R OI level), thereby ignoring the hierarchical modular structure of the brain. This risks o verlooking key biological constraints on cross-modal interactions. 2.4. Modeling Hierar chical modular SFC T o capture non-linear SFC within a hierarchical modular structure, recent graph learning models have begun incorpo- rating modular priors and multi-scale representations. IMG- GCN ( Xia et al. , 2024 ) uses canonical functional modules as guidance to compute module-specific structure-function inter- action. Feng et al. ( 2025 ) constrain FC self-attention using an SC-deriv ed enhanced mask at each layer and apply cross-modal top- k pooling to progressi vely coarsen the graph, enabling cou- pling and multiscale representations to be learned jointly for brain disease diagnosis. Howe ver , these methods primarily fo- cus on within-lev el interactions (e.g., R OI-to-R OI or module- to-module), whereas cross-lev el coupling (e.g., ROI-to-module) is less explicitly represented. Our aim is to address these gaps by learning hierarchical mul- tiscale SFC in a data-dri ven and subject-specific manner, while jointly constraining the hierarchical organization of SC and FC, rather than learning them independently . In our frame work, cross-modal interactions activ ely guide module formation and alignment across modalities, and the learned hierarchy , in turn, structures how coupling is modeled across multiple scales. This joint, multile vel design is intended to capture richer, more bio- logically plausible structure-function relationships, improve in- terpretability , and support stronger downstream predictions. 3. Methodology Fig. 1 demonstrates the overall framework. W e treat paired SC and FC as two graphs per subject, and input their adja- cency matrices and node features. First, prototype-based mod- ular pooling (PMPool) encodes each modality with a GNN, selects prototype R OIs, and learns an assignment matrix to pool R OIs into community-lev el super nodes, producing multi- scale representations regularized by a modularity loss (Fig. 1 a). The attention-based hierarchical coupling block (AHCM) en- courages SC and FC features to align via contrasti ve learning, then uses attention to model both within-hierarchy and cross- hierarchy structure function interactions, yielding hierarchical multiscale representations (Fig. 1 b). A coupling-guided clus- tering loss ( CgC-Loss ) uses the learned coupling strength to regularize SC and FC assignments, so cross-modal interactions can guide the assignment of the community (Fig. 1 c). Finally , the hierarchical features are fused for downstream prediction. 3.1. Preliminary Giv en a multimodal brain connectome dataset D = {P 1 , . . . , P P } with P subjects, each subject P p is processed with a paired structural connectome G p S deriv ed from dMRI, and a functional connectome G p F deriv ed from rsfMRI. Each subject 4 Jianwei Chen et al. / Medical Image Analysis (2026) GN N     C o m m un itie s To p - k p r o to ty p e s      A ssi g n m e n t M a t r i x         Ce n tralit y T o p - k p ro to ty p e S e lec ti o n    C o m m u n it y A s s ig n m e n t Po o led G r a p h    P r o to ty p e - b ased P o o lin g GN N               Ce n tra lit y T o p - k p ro to ty p e S e lec ti o n To p - k p r o to ty p e s C o m m u n it y A s s ig n m e n t    Co m m u n iti e s Po o led G r a p h P r o to ty p e - b ased P o o lin g A ssi g n m e n t M a t r i x    (a ) P r o to type - b a s ed M o dul a r P o o l i ng (b) A ttenti o n - b a s ed H i era r chi ca l C o upl i ng M o dul e (c) C o upl i ng - g u i ded C l us ter i ng L oss C T ask Pr ed ictio n    C ontr ast i ve A l i gnme nt           Pa t i e n t i Pa t i e n t j           B idi re ct io na l At t ent io n P u ll P u s h P u s h                   W i t h i n - h i e r ar ch y c o u p l i n g       Bid irec ti o n a l A tt e n ti o n Cro s s - hiera rc hy I nte ra ct io n Cro s s - hiera rc hy I nte ra ct io n      Wi t hi n - hi erarc hy Int eract i on    C r o s s A tten tio n C r o ss - h i e r a r c h y c o u p l i n g               C r o s s A tten tio n C r o ss - h i e r a r c h y c o u p l i n g       Featu r e Up d ate Featu r e Up d ate              FC A dj ac enc y N ode feat ur es      N ode f ea t ur es      SC A dj ac enc y          C C onc a tena ti on Ce n tralit y De g re e c e ntra li t y & ML P Fig. 1. Framework of HiM-SFC. Paired SC and FC are encoded with a GNN and coarsened by (a) prototype-based modular pooling (PMPool) to ob- tain hierarchical community representations. (b) The attention-based hierarchical coupling module (AHCM) then models within- and cross-hierarchy structure–function interactions to produce coupling-enhanced features, while (c) a coupling-guided clustering loss (CgC-Loss) encourages cross-modal consistency of community assignments. The resulting hierarchical features ar e fused for the do wnstream prediction task.      I nput N et w or k N ode f ea t ur es X A dj ac enc y m at r i x A GN N De gr e e Ce n t r ali t y M L P C e n t r a l i t y e mb e d d i n g s    C e n t r a l i t y e mb e d d i n g s   C C o n v M LP T o p - k s e lec t io n P r o t o t y p e sco r e s P r o t o t y p e e mb e d d i n g s M L P N o d e rep rese n t a t i o n Cos in e S im il ar it y e n t m a x ( )    -                              Modul ar N et w or k R andom N et w or k A ssi g n me n t M a t r i x  P r o t o t yp e - b a s ed Mo d ul a r P o o l i ng T op - k Prot ot y pes C om m uni t i es Pro t o t y p e S el ec t i o n C o m m u n i t y A ssi g n m e n t    Fig. 2. PMPool includes prototypical ROI selection and community assign- ment f or pooling the connectome into a coarsened network. A modularity- inspired pooling objective encourages PMPool to capture the intrinsic modular structure of each subject’ s connectome. has a corresponding label y p for the prediction task. Each graph G = ( V , A , X ) consists of a node set V , an adjacency matrix A ∈ R N × N and a node feature matrix X ∈ R N × d , where N = | V | denotes the number of brain re gions and d is the feature di- mension. In this study , the structural and functional node fea- tures ( X S , X F ) are initialized by the corresponding rows of the structural and functional adjacency matrices, respectively . The goal of multimodal connectome fusion is to learn a mapping f : ( G S , G F ) → y that predicts the label from paired structural and functional graphs. 3.2. Pr ototype-based Modular P ooling Prototype-based Pooling. Adv anced studies hav e rev ealed that hierarchical structure-function interactions occur within the hi- erarchical modular organization. Therefore, our frame work first aims to obtain the community structure for each modality . In this study , we dev elop a GNN pooling framework to simu- late the hierarchical structure of the brain connectome. Each GNN pooling layer learns a community structure and guides the structure-function interactions. T o learn ho w R OIs clus- ter within each hierarchy , we first identify the anchor of each cluster , namely the prototypical ROIs, and then learn ho w the remaining R OIs cluster around these prototypes. Consider a graph G = ( V , A , X ) for a gi ven modality , where A is the adjacency matrix and X denotes the node features. For each node i , we characterize its importance as a prototype based on both structural and semantic perspecti v es. T o ev aluate the structural importance, we compute the degree centrality for each node using A , which reflects the extent to which a node is structurally connected to other nodes in the network, and em- beds it as a centrality representation as follows: Z cen = M L P d egree max ( d egree ) ! . (1) In parallel, we use a one-layer GCN to embed node features X as semantic representations: Z sem = GC N ( A , X ) = σ  ¯ AX W  , (2) where ¯ A = D − 1 2 AD − 1 2 denotes the normalized adjacency ma- trix of A , and D is the corresponding degree matrix with entries D ii = P j A i j , W is the learnable con volution weight matrix and σ is a non-linear activ ation function, for which we use the rec- tified linear unit (ReLU). Then the concatenated embeddings of these two representations ˜ Z = [ Z cen , Z sem ] ∈ R N × 2 d ′ are inte- grated as node representations. Subsequently , we con vert the inte grated representation ˜ Z into prototype scores that quantify the likelihood of each node acting as a community anchor . A conv olution operation is employed Jianwei Chen et al. / Medical Image Analysis (2026) 5 with a filter h ∈ R N × 2 d ′ on the embeddings ˜ Z , follo wed by a multilayer perceptron (MLP) to map the high-dimension repre- sentation for each node into a prototype score: U = M L P  h ∗  ˜ Z  , (3) where U ∈ R N × 1 , and a lar ger v alue of U i indicates that node i is more representativ e of its prototype. Next, we select top- k prototypes using I top- k = T opK ( U , k ) , and use the correspond- ing ro ws of ˜ Z to form the prototype embeddings P ∈ R k × 2 d ′ . T o determine community assignments, we compute the dot prod- uct similarity between all nodes and prototypes and apply the entmax function row-wise to obtain a sparse soft assignment matrix: S = entma x  ˜ Z P  ∈ R N × k . (4) The i t h row of the assignment matrix S indicates the sparse probability of node i being assigned to k communities. Finally , a coarser graph G ′ = ( V ′ , A ′ , X ′ ) containing k super-nodes and aggregated features are obtained as follo ws: X ′ = S ⊤ X , A ′ = S ⊤ AS . (5) Modularity-inspired P ooling Objective. Brain connectomes are kno wn to exhibit modular or ganization, where regions form densely connected communities with comparativ ely sparse links between them. Modularity compares the observed con- nectivity within these communities by comparing it to what would be expected under a degree-preserving random graph, making it a standard measure for analyzing community struc- ture. Building on this concept, we treat the soft assignment ma- trix S obtained above as a di ff erentiable indicator for commu- nity membership follo wing a previous method ( Tsitsulin et al. , 2023 ), and regularize it using an objecti ve based on modularity: Q ( A , S ) = 1 2 m T r  S ⊤ BS  , (6) where 2 m = P i d i denotes the total edge weight, and B = A − dd ⊤ 2 m . The Q is high when nodes that share strong assignments in S are more densely connected than e xpected from their de- grees. W e then follow the deep modularity formulation in graph clustering and deriv e the final optimized objecti ve: L modular ity = − Q ( A , S ) + √ k N ∥ X i S ⊤ i ∥ F − 1 , (7) where √ k N ∥ P i S ⊤ i ∥ F − 1 is a collapse regularizer that penalizes degenerate solutions where all nodes fall into a single commu- nity . By optimizing the loss function L modular ity , the assignment matrix S is encouraged to group densely connected ROIs into the same community , guiding the PMPool to capture each sub- ject’ s intrinsic community structure rather than forming arbi- trary clusters. By stacking sev eral PMPooI layers, we obtain an individualized hierarchical multiscale representation as the basis for the subsequent hierarchical SFC module.                   W i t h i n - h i e r a r c h y c o u p l i n g       Cro s s - hiera rc hy I nte ra ct io n Cro s s - hier a rc hy I nte ra ct io n      Wi t hi n - hi erarc hy I nt er act i on               C r o ss - h i e r a r c h y c o u p l i n g           Lin e a r Lin e a r Lin e a r Lin e a r Lin e a r Lin e a r Lin e a r Lin e a r S c a le e n tm a x A ssi g n m e n t M a t r i x    A ssi g n m e n t M a t r i x    e n tm a x C r o ss - h i e r a r c h y c o u p l i n g    e n tm a x e n tm a x     At t en t i on - b a s ed Hi er a r chi ca l Co up l i ng Mo d ul e P ro d u c t A d d it io n Fig. 3. Ar chitecture of AHCM. W ithin-hierarchy coupling is computed via bidirectional attention, while cross-hierarch y coupling is captured by two cross-attention branches. These hierar chical coupling signals are aggre- gated to obtain enriched hierarchical multiscale r epresentations. 3.3. Attention-based Hierar chical Coupling Module After obtaining the pooled embeddings from PMPool, it re- mains challenging to obtain fine-grained coupling from the de- riv ed attention weights, as structural and functional representa- tions live in separate feature spaces. T o address this, we first implement a lightweight contrasti ve alignment between the two modalities at each hierarchical level. Specifically , given the structural and functional community embeddings X l S and X l F , we generate graph-level summaries using mean pooling and then process them through small projection heads. W e apply an InfoNCE-style loss to bring together representations from the same subject across modalities while pushing apart repre- sentations from di ff erent subjects. This process aligns X l S and X l F into a latent space, allo wing subsequent attention to reflect the coupling between structure and function rather than merely trivial di ff erences in scale or orientation. Within-hierar chy Interaction. Rather than employing two independent cross-modal attention blocks, we model the SFC at layer l using a specifically designed bidirectional attention mechanism. W e first apply linear projections to the embeddings of both modalities and then compute a similarity matrix ¯ A l S , F , which is shared between the structural and functional represen- tations, as follows: ¯ A l S , F = R S R ⊤ F √ d ∈ R N l × N l , (8) where R S = X l S W R , R F = X l F W R . This shared-similarity matrix captures bidirectional coupling symmetrically . Cross-Hierar chy Interaction. Interactions within a single hi- erarchy are insu ffi cient for capturing couplings across di ff erent hierarchical le vels, which are essential for inte grating and prop- agating information throughout the system. T o address this, we introduce the concept of cross-hierarchy interaction and utilize 6 Jianwei Chen et al. / Medical Image Analysis (2026) Ass ig nm ent M a t rix      Ass ig nm ent M a t rix      H adam ar d pr oduct R OI C o u p lin g s tr en g th   Co up l i ng - g u i d ed Clus t er i n g L o s s Hier ar ch ical co u p lin g       A s s ig n m e n t Ma trix    A s s ig n m e n t Ma tr ix    M e a n & No rm R OI co u p lin g w eig h ts Ro w su m Co lu m n s u m KL Div e rg e n c e     E lem en t - w is e p r o d u ct Fig. 4. The coupling-guided clustering loss L CC . ROI-wise coupling weights are computed from the hierarchical coupling matrix via row and column aggregation and normalization, and used to weight a symmetric KL diver - gence between SC and FC assignment matrices, promoting cross-modal consistency driven by SFC. it to create a bias term that adjusts the shared similarity ma- trix. For example, in the case of the functional connectome, let X l − 1 S ∈ R N l − 1 × d represent the finer structural regional embed- dings at level l − 1, and let S l S ∈ R N l − 1 × N l denote the structural assignment matrix that connects regions to communities. W e begin by computing attention from functional communities at lev el l to structural regions at lev el l − 1 through cross-hierarchy attention: H l F → S = entma x Q F K ⊤ S √ d ! ∈ R N l × N l − 1 , (9) where Q F = W Q X l F , K S = W K X l − 1 S . H l F → S represent functional communities and their relationships with structural regions. Hierarchical Interactions Aggregation. W e then aggre gate the relationships using the structural assignments with B l F =  H l F → S S l S  ⊤ ∈ R N l × N l . B l F can be viewed as a coupling bias, which incorporates information about how cross-hierarchy sup- port for coupling between functional communities and struc- tural regions. Finally , this bias matrix is aggre gated to the shared similarity matrix ¯ A l S , F . T o obtain the hierarchy cou- pling from the functional to structural viewpoint, we apply the column-wise entmax function, which updates the functional representations as follows: ˜ X l F = entma x col  ¯ A l S , F + B l F  V F ∈ R N l × d , (10) where V F = W V X l F . The hierarchy coupling from the structure to function vie w , and the updated structural representations can be computed in a symmetric manner . In this way , we obtain enriched hierarchical multiscale representations ˜ X l F and ˜ X l S for downstream prediction tasks. 3.4. Coupling-guided Clustering Loss Function Prior knowledge indicates that the hierarchical modular structure within the brain connectome is not arbitrary but or- ganized according to the pattern of structure-function cou- pling( Seguin et al. , 2022 ; Betzel et al. , 2013 ). In our frame- work, PMPool is first used to learn hierarchical modular organi- zations from structural and functional connectomes, which are denoted by the structural and functional assignment matrices at each le vel. Next, we con vert the coupling at each hierarchy Algorithm 1 T wo-stage training procedure of HiM-SFC Input: Paired structural and functional connectomes with labels ( G S , G F , y ) Output: Prediction ˆ y 1: Initialize parameters of PMPool, AHCM, and the prediction MLP 2: Stage 1: Self-supervised optimization of PMPool 3: for epoch = 1 to E 1 do 4: Extract node representations ˜ Z S and ˜ Z F from G S and G F 5: Select top- k prototype nodes based on ˜ Z S and ˜ Z F 6: Compute assignment matrices S S and S F 7: Pool connectomes hierarchically: X ′ = S ⊤ X , A ′ = S ⊤ AS 8: Compute modularity-inspired pooling loss L modularity 9: Update PMPool parameters by minimizing L modularity 10: end for 11: Stage 2: Supervised optimization of the full framework 12: for epoch = 1 to E 2 do 13: Obtain multiscale SC and FC representations using pretrained PMPool 14: Model hierarchical structure–function coupling with AHCM and obtain enriched representations ˜ X S and ˜ X F 15: Concatenate hierarchical representations to predict ˆ y 16: Compute task loss L task and CgC-Loss L CC 17: Compute total loss L total = L task + λ L CC 18: Update model parameters by minimizing L total 19: end for 20: return ˆ y into meaningful signals to guide the community assignments for both modalities. With the shared similarity matrix ¯ A l S , F at lev el l , we first compute a region-wise coupling weight from bidirectional coupling views through the follo wing process: w l i = normalize         1 2         X j | ¯ A l S , F ( i , j ) | + X j | ¯ A l S , F ( j , i ) |                 . (11) Intuitiv ely , ROIs with stronger coupling weights exhibit more similarity in their structural and functional assignment matri- ces. Therefore, we can view i th rows of the assignment matrices s l S , i and s l F , i as probability vectors and calculate the distribution distance between them. Then we use the coupling weights to modulate how similar the y are: L CC = 1 N l N l X i = 1 w l i 2  K L  s l S , i || s l F , i  + K L  s l F , i || s l S , i  , (12) where K L ( · ) denotes the K ullback-Leibler di ver gence that is used to measure the distance between distributions. T ogether with the PMPool, this yields an indi vidualized modular struc- ture that is not only internally coherent within each modality but also maintains cross-modality consistency in regions of the brain where structure and function are closely connected. 3.5. T raining Objective and Optimization T o e ff ectiv ely capture hierarchical multiscale SFC, we adopt a two-stage training strategy . Because hierarchical coupling relies on community structure, we optimize the modularity- inspired pooling objecti ve L modular ity of the PMPool module in a Jianwei Chen et al. / Medical Image Analysis (2026) 7 self-supervised manner in stage one, so as to obtain stable and individualized community assignments for structural and func- tional connectomes. After establishing this modality-specific modular organization, we introduce the AHCM and jointly op- timize the full frame work in a supervised manner in stage two. The enriched hierarchical multiscale representations ˜ X F and ˜ X S produced by AHCM are concatenated and passed to an MLP for task-specific prediction. Meanwhile, the Coupling-guided Clustering loss L CC is incorporated as a regularization term dur - ing supervised training, where it le verages learned hierarchical coupling signals to constrain and refine the structural and func- tional community assignment matrices. The detailed training procedure of HiM-SFC can be found in Algorithm 1 . 4. Implementation details 4.1. Datasets W e ev aluate our model on brain age and cognition prediction, as well as on disease classification. F or brain-age prediction, we utilized three healthy cohorts. The first includes 196 subjects aged 4-85 years from the Nathan Kline Institute Rockland Sam- ple (NKI-Rockland) ( Nooner et al. , 2012 ), with corresponding T1w , rsfMRI, and DTI images, preprocessed using MRtrix3 toolbox ( https: // www .mrtrix.or g / ) ( T ournier et al. , 2019 ). SC and FC were constructed with 188 R OIs, based on the Craddock 200 spectral clustering atlas ( Craddock et al. , 2012 ) in the prior study ( Brown et al. , 2012 ). The second includes 241 subjects aged 22-35 years from the Human Connectome Project Y oung Adult (HCPY A) dataset (release S900) ( V an Essen et al. , 2013 ). SC and FC were constructed from minimally preprocessed T1w , rsfMRI, and di ff usion MRI using the MRtrix3 ( Chen et al. , 2024 ) and eXtensible Connectivity Pipelines (XCP-D; https: // xcp-d.readthedocs.io / en / latest / ) ( Mehta et al. , 2024 ), re- spectiv ely , following the Schaefer atlas ( Schaefer et al. , 2018 ) containing 400 ROIs. Due to limited computational resources, the third includes 3,000 subjects aged 40-69 years from the UKBiobank (UKB) ( Alfaro-Almagro et al. , 2018 ), selected via stratified sampling from the ∼ 40,000 publicly released imag- ing participants as a subset. The MRI images were prepro- cessed using the UKB standard pipeline. SC and FC were constructed from the prior study ( Di Biase et al. , 2023 ) using the Schaefer atlas, which contains 500 ROIs ( Di Biase et al. , 2023 ). For cognitiv e score prediction, we use the same cohort from HCPY A and UKB, with Mini-Mental State Examination (MMSE) scores for HCPY A (range 23-30) and Fluid Intelli- gence Score for the UKB (range 0-13), respectiv ely . For disease classification, we curated a subset of the Alzheimer’ s Disease Neuroimaging Initiati ve (ADNI) ( Petersen et al. , 2010 ) cohort by selecting baseline ADNI3 participants with high-resolution multi-shell di ff usion MRI and multiband resting-state fMRI, ensuring su ffi cient data quality for reliable structural and func- tional connectome construction. This resulted in 72 healthy controls and 67 patients with dementia, aged 51-90 years. W e reproduce the UKB standard pipeline on preprocessed multi- modal MRI and construct the SC and FC, following the Schae- fer atlas ( Schaefer et al. , 2018 ) with 500 R OIs. For each dataset, the structural edges represent the stream- line counts between R OIs, while functional edges represent the Pearson correlation coe ffi cients between ROIs. This study fo- cuses on positi ve functional connecti vity and retains the top 20% of strongest connections in each FC matrix to create a sparse functional network ( V an Den Heuvel and Pol , 2010 ). 4.2. Implementation details The experiments of this study were conducted using PyT orch and Pytorch Geometric on an NVIDIA R TX A5000 GPU with 24GB of memory . W e employed 5-fold cross-validation and reported the results in mean ( std ). All hyperparameters were fine-tuned to achie ve optimal performance on each dataset. The number of pooling ratio r for SC and FC in PMPool was set to 0.12. The regularization weight of L CC was established at 0.11. As will be studied later , increasing GNN and pooling lay- ers can make the model learn smoother representations, which impairs its e xpressi ve po wer on prediction tasks. Therefore, we set the number of pooling layers and GNN encoders as 1 and 2, respectiv ely . The proposed framew ork was trained for 300 epochs, with a batch size of 32 and a learning rate of 0.001 using the Adam optimizer ( Adam et al. , 2014 ). 4.3. Comparison models W e e valuate the e ff ectiv eness of our proposed method by comparing it with v arious competing approaches across multi- ple datasets. The competing methods are grouped into three cat- egories: (i) multimodal GNN baselines with simple fusion (e.g., feature concatenation), (ii) state-of-the-art SFC-based methods that model SFC on a flat graph, and (iii) recent SFC-based ap- proaches that further incorporate hierarchical or modular orga- nization of the connectome. (i) Multimodal GNN baselines. W e include three baselines, GIN ( Xu et al. , 2018 ), GCN ( Kipf , 2016 ) and GraphSA GE ( Hamilton et al. , 2017 ), as well as ear- lier GNN-based connectome fusion methods that use simple feature fusion, i.e., M-GCN ( Dsouza et al. , 2021 ) and MME- GCN ( Liu et al. , 2022 ), which do not explicitly model non- linear structure–function interactions. (ii) Flat-graph SFC SO- T As. W e include four coupling-based methods that explicitly model the non-linear structure-function interaction. Among these, Joint-GCN ( Li et al. , 2022 ) is one of the first approaches to model SFC using GNNs, le veraging cross-modal interactions for prediction. Similarly , Cross-GNN ( Y ang et al. , 2023 ) and the more recent MS-Inter-GCN ( Xia et al. , 2025 ) propose learn- ing multimodal interactions between SC and FC, which typi- cally capture coupling from a flat graph perspectiv e, ignoring the intricate brain connectome or ganization. (iii) Hierar chi- cal / modular SFC SO T As. CBGT ( Feng et al. , 2025 ) and IMG- GCN ( Xia et al. , 2024 ) model SFC in a hierarchical or modular manner . RH-BrainFS ( Y e et al. , 2023a ) proposes to learn in- direct SFC through sampled local subgraph structure. Y et, they do not fully characterize indi vidualized hierarchical modular or- ganization, or how such an organization both constrains and is shaped by SFC. T able 1 , 2 and 3 demonstrate the comparison results on HCPY A, NKI-Rockland, UKB and ADNI datasets. 8 Jianwei Chen et al. / Medical Image Analysis (2026) T able 1. Comparison results on HCPY A, NKI-Rockland and UKB for brain age prediction based on FC and SC. Method HCPY A NKI-Rockland UKB MAE ↓ RMSE ↓ MAE ↓ RMSE ↓ MAE ↓ RMSE ↓ GCN ( Kipf , 2016 ) 4.46 (0.62) 6.02 (1.26) 16.20 (1.49) 21.67 (2.78) 5.97 (0.23) 7.15 (0.29) GIN ( Xu et al. , 2018 ) 4.17 (0.60) 5.16 (0.55) 17.70 (2.44) 23.40 (3.43) 6.17 (0.67) 7.39 (0.78) GraphSage ( Hamilton et al. , 2017 ) 4.15 (0.43) 5.50 (0.83) 15.96 (2.08) 18.48 (1.31) 6.06 (0.51) 8.58 (2.87) M-GCN ( Dsouza et al. , 2021 ) 3.45 (0.34) 4.36 (0.52) 17.36 (0.49) 20.16 (0.56) 7.59 (0.57) 12.55 (0.47) MME-GCN ( Liu et al. , 2022 ) 6.02 (1.38) 7.14 (1.32) 14.41 (0.34) 19.44 (0.52) 6.64 (0.65) 7.93 (0.72) Joint-GCN ( Li et al. , 2022 ) 3.34 (0.41) 4.15 (0.43) 13.70 (0.57) 17.91 (0.76) 5.47 (0.12) 6.71 (0.07) Cross-GNN ( Y ang et al. , 2023 ) 5.21 (0.33) 6.32 (0.35) 13.25 (1.76) 16.62 (1.85) 6.82 (0.10) 7.56 (0.11) MS-Inter-GCN ( Xia et al. , 2025 ) 3.33 (0.36) 3.95 (0.50) 15.76 (1.07) 19.04 (1.50) 5.74 (0.17) 6.85 (0.10) RH-BrainFS ( Y e et al. , 2023a ) 3.28 (0.27) 3.93 (0.31) 13.42 (2.46) 17.84 (2.21) 5.95 (0.53) 7.29 (0.49) IMG-GCN ( Xia et al. , 2024 ) 3.97 (0.36) 4.59 (0.38) 14.04 (1.49) 17.63 (1.31) 5.57 (0.46) 6.74 (0.50) CBGT ( Feng et al. , 2025 ) 3.46 (0.15) 4.18 (0.11) 14.63 (0.76) 19.24 (0.32) 5.89 (0.15) 7.68 (0.16) HiM-SFC(ours) 2.77 (0.17) 3.42 (0.19) 12.86 (0.69) 16.92 (0.59) 5.35 (0.08) 6.50 (0.08) T able 2. Comparison results on HCPY A and UKB for MMSE and fluid intelligence score pr ediction based on FC and SC. Method HCPY A (MMSE) UKB (Fluid Intelligence Score) MAE ↓ RMSE ↓ MAE ↓ RMSE ↓ GCN ( Kipf , 2016 ) 3.73 (0.57) 5.18 (1.43) 3.17 (0.26) 3.69 (0.23) GIN ( Xu et al. , 2018 ) 3.52 (0.43) 4.09 (0.30) 3.60 (0.30) 4.01 (0.43) GraphSage ( Hamilton et al. , 2017 ) 3.65 (0.68) 5.18 (1.43) 3.14 (0.43) 3.66 (0.40) M-GCN ( Dsouza et al. , 2021 ) 1.48 (0.11) 1.95 (0.21) 3.23 (1.43) 5.30 (3.98) MME-GCN ( Liu et al. , 2022 ) 6.12 (0.33) 6.61 (0.32) 2.72 (0.06) 3.17 (0.09) Joint-GCN ( Li et al. , 2022 ) 3.95 (0.95) 4.61 (0.96) 2.18 (0.31) 2.69 (0.33) Cross-GNN ( Y ang et al. , 2023 ) 5.59 (0.44) 5.68 (0.44) 2.88 (0.18) 3.39 (0.18) MS-Inter-GCN ( Xia et al. , 2025 ) 1.60 (0.04) 2.02 (0.18) 1.91 (0.04) 2.20 (0.05) RH-BrainFS ( Y e et al. , 2023a )11 1.64 (0.11) 2.17 (0.23) 1.93 (0.04) 2.22 (0.06) IMG-GCN ( Xia et al. , 2024 ) 1.72 (0.05) 2.13 (0.03) 2.04 (0.05) 2.18 (0.06) CBGT ( Feng et al. , 2025 ) 1.78 (0.19) 2.06 (0.22) 2.10 (0.15) 2.59 (0.17) HiM-SFC(ours) 1.01 (0.24) 1.25 (0.25) 1.66 (0.04) 2.07 (0.05) T able 3. Comparison results on ADNI f or disease classification based on FC and SC. Method A CC ↑ A UC ↑ Sen ↑ Spec ↑ GCN ( Kipf , 2016 ) 0.68 (0.06) 0.60 (0.14) 0.50 (0.15) 0.74 (0.16) GIN ( Xu et al. , 2018 ) 0.64 (0.04) 0.71 (0.03) 0.61 (0.16) 0.68 (0.15) GraphSA GE ( Hamilton et al. , 2017 ) 0.68 (0.07) 0.62 (0.14) 0.67 (0.15) 0.69 (0.15) M-GCN ( Dsouza et al. , 2021 ) 0.73 (0.07) 0.70 (0.06) 0.61 (0.23) 0.74 (0.22) MME-GCN ( Liu et al. , 2022 ) 0.74 (0.07) 0.72 (0.10) 0.66 (0.14) 0.79 (0.08) Joint-GCN ( Li et al. , 2022 ) 0.75 (0.08) 0.70 (0.08) 0.61 (0.20) 0.79 (0.21) Cross-GNN ( Y ang et al. , 2023 ) 0.70 (0.10) 0.71 (0.12) 0.51 (0.25) 0.73 (0.24) MS-Inter-GCN ( Xia et al. , 2025 ) 0.72 (0.05) 0.75 (0.12) 0.65 (0.21) 0.71 (0.18) RH-BrainFS ( Y e et al. , 2023a ) 0.73 (0.14) 0.75 (0.05) 0.62 (0.26) 0.75 (0.33) IMG-GCN ( Xia et al. , 2024 ) 0.75 (0.08) 0.77 (0.08) 0.67 (0.15) 0.76 (0.13) CBGT ( Feng et al. , 2025 ) 0.76 (0.05) 0.76 (0.03) 0.68 (0.13) 0.79 (0.13) HiM-SFC(ours) 0.78 (0.07) 0.79 (0.10) 0.69 (0.10) 0.81 (0.13) 4.4. Comparison metrics W e report performance using mean absolute error (MAE), root mean squared error (RMSE) for both brain-age and cognitiv e-score prediction; accuracy (A CC), sensiti vity (Sen), specificity (Spec) and the area under the recei ver operating characteristic curve (A UC) for disease classification. 5. Results & Discussion 5.1. Comparison studies 5.1.1. Brain age pr ediction T o assess the e ff ectiveness and generalization of the pro- posed model, we conduct brain age prediction on three datasets that span a wide age range (HCPY A focuses on young adults (21-35 yrs), UKB targets mid-to-late adults (40-70 yrs), NKI- Rockland includes healthy participants across a broad range (4-85 yrs). Results for all eight competing methods on brain age prediction are demonstrated in T able. 1 . The three mul- timodal GNN baselines achiev e the worst performance across the three datasets, primarily due to their inability to capture the SFC associated with aging. By contrast, the models with ex- plicit structure-function coupling, e.g., Joint-GCN and Cross- GNN, achie ve superior performance compared to simple multi- modal GNN fusion methods. In particular , the Joint-GCN im- prov es performance to 3.34 MAE on HCPY A and 5.47 MAE on UKB, probably attributed to its R OI-to-R OI coupling design. Other state-of-the-art methods, i.e., IMG-GCN and CBGT , also Jianwei Chen et al. / Medical Image Analysis (2026) 9 R egular iz a tion W eigh t of 𝑳 𝑪𝑪 Numb er of PMP oo l hier ar ch ies Numb er of P ooling r a tios r (a ) Perfo rmance chan ge on HCPY A (b) Per fo rm ance chang e on AD NI R egula riz a tion W eigh t of 𝑳 𝑪𝑪 Number of PM Poo l hier a r chies Number of P ooling r a tios r Fig. 5. Cognitive score prediction performance of the proposed method with di ff erent pooling ratios, number of hierarchies, and regularization weight of L CC on (a) HCPY A and (b) ADNI. T able 4. Ablation study on PMPool, AHCM, and CgC-Loss on HCPY A (MMSE prediction) and ADNI (disease classification). HCPY A: MMSE prediction Method MAE ↓ RMSE ↓ PCC ↑ w / o PMPool 2.02 (0.33) 2.32 (0.41) 0.12 (0.04) w / o AHCM 2.63 (0.31) 3.35 (0.41) 0.09 (0.03) w / o CgC-Loss 1.17 (0.18) 1.57 (0.44) 0.16 (0.04) HiM-SFC(ours) 1.01 (0.24) 1.25 (0.25) 0.25 (0.09) ADNI: disease classification Method A CC ↑ Sen ↑ Spec ↑ w / o PMPool 0.72 (0.08) 0.63 (0.11) 0.73 (0.14) w / o AHCM 0.70 (0.09) 0.56 (0.12) 0.71 (0.15) w / o CgC-Loss 0.76 (0.07) 0.67 (0.09) 0.77 (0.10) HiM-SFC(ours) 0.78 (0.07) 0.69 (0.10) 0.81 (0.13) outperform the GNN baselines on HCPY A and NKI-Rockland datasets, which verifies that the SFC is shaped and guided by the complex topological or ganization of the brain network. The proposed HiM-SFC framework achie ves the best ov er- all performance across the three datasets, with 2.77 MAE on HCPY A and 12.86 MAE on NKI-Rockland, impro ving by 0.51 and 0.39 points o ver the second-best methods, respecti v ely . The superior performance of the proposed framework across three datasets verifies that the hierarchical modular organization bet- ter captures age-related coupling, thereby improving the e ff ec- tiv eness and generalization of the multimodal frame work. 5.1.2. Cognitive scor e pr ediction As seen from T able. 2 , HiM-SFC achiev es consistently su- perior performance on the two datasets ov er the competing methods. In contrast to brain age prediction, methods that capture the coupling from a flat graph perspectiv e, i.e., Joint- GCN and Cross-GNN, perform worse than GNN baselines on HCPY A, probably because they ignore the complex topology T able 5. Results of MMSE score prediction on HCPY A and disease classi- fication on ADNI using di ff erent GNN encoders. HCPY A: MMSE prediction Method MAE ↓ RMSE ↓ PCC ↑ GIN 1.11 (0.04) 1.33 (0.17) 0.18 (0.06) GraphSA GE 1.05 (0.02) 1.27 (0.15) 0.20 (0.12) GCN 1.01 (0.24) 1.25 (0.25) 0.25 (0.09) ADNI: disease classification Method A CC ↑ Sen ↑ Spec ↑ GIN 0.75 (0.03) 0.64 (0.13) 0.78 (0.11) GraphSA GE 0.77 (0.06) 0.67 (0.13) 0.79 (0.15) GCN 0.78 (0.07) 0.69 (0.10) 0.81 (0.13) of the brain network and fail to learn coupling aligned with functional modules. In contrast, adv anced coupling methods, e.g., IMG-GCN and CBGT , achieve better performance on cog- nitiv e score prediction. Specifically , IMG-GCN achie ves 1.72 MAE on HCPY A and 1.84 MAE on UKB, respecti vely , prob- ably because it incorporates functional modular organization to guide the learning of coupling patterns linked to cognition. The proposed HiM-SFC attains a mean absolute error of 1.01 on HCPY A and 1.66 on UKB, respecti vely , outperforming the second-best model by 0.47 and 0.25 in prediction error , demon- strating the benefit of modeling hierarchical modular coupling. 5.1.3. Disease classification The proposed method is e valuated on the ADNI dataset for disease classification. The results are presented in T able. 3 . Our results indicate that coupling-based fusion methods, such as Joint-GCN, IMG-GCN, and CBGT , outperform the multimodal GNN baselines. Meanwhile, in addition to sensitivity , the pro- posed method consistently outperforms all competing methods. Specifically , the proposed method achie ves an accurac y of 0.78 and a specificity of 0.81, indicating that the proposed hierar- 10 Jianwei Chen et al. / Medical Image Analysis (2026) (a) Lea rned couplin g str eng th for bra in - a g e pr ediction Co upl i ng s tr en gt h 1 0 (b) Lea rned couplin g str eng th for disea se cla ss ificatio n C o upl i ng str eng t h 1 0 Reg io na l level M o dula r level M o dula r level Reg io na l level (c) O v erla p o f top - 5 0 % co upling pa tt erns a cr o ss ( a ) a nd ( b) V4 VN S M N DAN V AN LN FPN DM N M o dula r level Reg io na l level (c) Cr o ss - tas k o v erla p of top - 5 0 % co upling pa tt erns a t r eg io na l a nd m o dula r lev els (cano nica l 7 m o dules) Fig. 6. Multiscale coupling str ength learned by the proposed model. Regional-level maps show global coupling strength, whereas modular-le vel maps show local coupling strength, f or (a) brain-age prediction in UKB and (b) disease classification in ADNI; (c) Overlapping of the top-50% coupling pattern between brain age and disease prediction tasks at regional and modular levels, mapped to canonical seven modules (Visual (VN), Somatomotor (SMN), Dorsal Attention (D AN), V entral Attention (V AN), Limbic (LN), Frontoparietal (FPN), and Default Mode (DMN) networks). chical modular coupling framework is promising for capturing disease-related patterns. 5.2. Ablation studies 5.2.1. Ke y hyperpar ameters T o assess the influence of ke y hyperparameters on prediction performance, we conduct hyperparameter analyses on HCPY A and ADNI for MMSE score prediction and disease classifica- tion, respecti vely . The key hyperparameters include the pooling ratio of the PMPool, the number of PMPool hierarchies within the framework, and the regularization weight of the CgC-Loss. Fig. 5 a presents the results on HCPY A using MAE and RMSE, while Fig. 5 b presents the results on ADNI using accuracy (A CC), specificity (Spec), and sensiti vity (Sen). The number of pooling ratios. As introduced in Section 3.2 , the size of the assignment matrix S ∈ R N × k is controlled by the number of prototypes k , which guides the model to learn hierarchical modular organization at di ff erent resolutions. In this study , we use a pooling ratio r to determine k through k l = N l − 1 × r l , where N l − 1 is the number of nodes in layer l − 1. W ith this setting, a larger r l leads to a larger k l , allo w- ing PMPool to retain more modular communities. As shown in Fig. 5 , v arying the pooling ratio can a ff ect performance on both datasets. On HCPY A, the model starts from the flat baseline without PMPool ( r = 0) and achiev es consistently better per- formance once hierarchical pooling is introduced, with the best MAE and RMSE obtained at r = 0 . 12. A similar trend is ob- served on ADNI, where A CC, Spec, and Sen all improv e from the baseline and reach their best at r = 0 . 12. The number of PMPool hierarchies. W e in vestigate how the PMPool hierarchies influence prediction performance. As il- lustrated in Fig. 5 , introducing hierarchical PMPool improves performance on both HCPY A and ADNI compared with the T able 6. Results of MMSE score prediction on HCPY A and disease classi- fication on ADNI using entmax and softmax. HCPY A: MMSE prediction Method MAE ↓ RMSE ↓ PCC ↑ softmax 1.17 (0.03) 1.33 (0.16) 0.18 (0.04) entmax 1.01 (0.24) 1.25 (0.25) 0.25 (0.09) ADNI: disease classification Method A CC ↑ Sen ↑ Spec ↑ softmax 0.76 (0.17) 0.66 (0.12) 0.77 (0.14) entmax 0.78 (0.07) 0.69 (0.10) 0.81 (0.13) baseline setting without PMPool. On HCPY A, the best MMSE prediction is achieved with a single PMPool hierarchy , while deeper hierarchies gradually degrade performance. In ADNI, the best classification performance is also achie ved at one hier- archy , with higher A CC, Spec, and Sen than in the baseline and deeper hierarchies. When the number of hierarchies increases to 2 and 3, performance declines on both datasets, which is probably due to ov er-smoothing caused by excessi vely stacked GNN layers ( Li et al. , 2018 ). The r egularization weight of CgC-Loss. In addition, we ev al- uate ho w the coupling-guided clustering loss L CC a ff ects per- formance under di ff erent regularization weights in the range of [0 . 05 : 0 . 03 : 0 . 17]. Here, the baseline framework includes only the PMPool and AHCM. As shown in Fig. 5 , incorporating the CgC-Loss improves performance on both datasets, and the best results are achieved when the regularization weight is set to 0.11. Specifically , on HCPY A, the lowest MAE and RMSE are obtained at 0.11, while on ADNI, A CC, Spec, and Sen also reach their best ov erall values at the same weight. Jianwei Chen et al. / Medical Image Analysis (2026) 11 T op - k% Ove rl a p P e r c e nt a ge (% ) M o dul a r l ev el 1 0 R eg i o na l l ev el V 5 c) C o upl i ng di ffer ence pr o jected o nto pri o r ca no ni ca l m o dul es a ) C o upl i ng di ffer en ce pa tterns i n r eg i o na l a nd m o dul a r l ev el b) o v erl a p to p - k % pa tterns a cr o s s r eg i o na l a nd m o dul a r l ev el s S u p e r ior S u p e r ior L e f t m e d ial Le f t m e di al Re gion al L e ve l M od u lar L e ve l M od u le nam e M od u le nam e VN LN FPN FPN DM N DM N DAN DAN V AN S M N S M N VN 1 0 V AN LN Fig. 7. Visualization of age-group (40–50 vs. 60–70 years) di ff er ences in learned coupling strength in UKB at the regional (Schaefer 500 ROIs) and modular levels (a), the overlap percentage between regional and modular coupling-di ff erence patterns across top-k% ROIs (b), and their projection onto the canonical seven modules (Visual (VN), Somatomotor (SMN), Dorsal Attention (DAN), V entral Attention (V AN), Limbic (LN), Frontoparietal (FPN), and Default Mode (DMN) networks) (c). 5.2.2. Ke y components T o verify the e ffi cacy of (1) PMPool, (2) AHCM, and (3) CgC-Loss, we conduct ablation studies on the HCPY A and ADNI datasets, additionally reporting PCC as a complementary ev aluation metric. Results from T able. 4 suggest that all three components contribute meaningfully . In HCPY A MMSE score prediction, removing AHCM results in the largest degradation, with 2.63 MAE and 3.35 RMSE, indicating that modeling hier - archical coupling is essential for inte grating structural and func- tional brain connectomes. Ablating PMPool also degrades the performance, implying that the proposed prototype-based pool- ing can help learn the subject-le vel hierarchical modular organi- zation. Removing CgC-Loss yields a smaller but still functional model, because it mainly serves as a regularization term to help learn the hierarchical modular structure driv en by coupling. A similar trend is observed in ADNI disease classification. The largest decline occurs during AHCM ablation, highlighting the importance of coupling-aware interactions for connectome integration. The CgC-Loss brings a modest yet consistent de- cline across ACC, Sensitivity , and Specificity . Ov erall, the full HiM-SFC achiev es the best and most balanced performance. 5.2.3. GNN encoders W e also e valuate alternati ve GNN encoders within the pro- posed framew ork. As seen from the T able. 5 , di ff erent GNN encoders may a ff ect the performance, but do not diminish the ov erall advantage of HiM-SFC. In HCPY A MMSE score pre- diction, GCN achiev es the best performance with an MAE of 1.01, an RMSE of 1.25, and a PCC of 0.25, outperforming GraphSA GE and GIN. A similar trend is observed on ADNI disease classification, where GCN achie ves the best ACC with 0.78. Notably , the improv ement over GraphSA GE is modest but consistent across both datasets, implying that the most con- tribution arises from the proposed coupling frame work, while the GNN encoder primarily modulates how structural and func- tional signals are propagated. Ov erall, we use GCN as the de- fault backbone for our frame work, as it provides robust gener- alization across both regression and classification settings. 5.2.4. Modular sparsity T o ev aluate the e ff ectiv eness of the sparse normalization op- erator , entmax, used in both PMPool and AHCM, we conduct the experiments on HCPY A and ADNI datasets. As shown in T able. 6 , entmax yields a consistent impro vement on both tasks. On the HCPY A MMSE prediction, entmax reduces MAE from 1.17 to 1.01 and RMSE from 1.33 to 1.25, whilst increasing PCC from 0.18 to 0.25. A similar pattern can be observed on the ADNI disease classification with a higher A CC. This ad- vantage is likely attributed to the sparsity-inducing behavior of entmax, which can produce sparser assignments and attention maps ( Zhang et al. , 2024 ). This aligns well with prior knowl- edge, as brain community structure is typically modular, with dense intra-community and sparse inter-community connecti v- ity , while SFC is regionally heterogeneous rather than uni- formly strong across the corte x ( Zhang et al. , 2024 ; Zamani Es- fahlani et al. , 2022 ). In practice, sparse normalization, such as entmax, is likely to reduce spurious community assignments in PMPool and suppress noisy couplings in AHCM, thereby im- proving multimodal representations. Therefore, we adopt ent- max as the default normalization throughout the frame work. 5.3. Interpretability 5.3.1. Learned hierar chical multiscale SFC T o examine the task-specific hierarchical multiscale coupling learned by AHCM, we estimate group-wise coupling strength at both regional and modular levels. Results are computed 12 Jianwei Chen et al. / Medical Image Analysis (2026) M o dul a r l ev el R eg i o na l l ev el 1 0 a ) C o upl i ng di ffer en ce pa tterns i n r eg i o na l a nd m o dul a r l ev el c) C o upl i ng di ffer ence pr o jected o nto pri o r ca no ni ca l m o dul es V 5 b) o v erl a p to p - k % pa tterns a cr o s s r eg i o na l a nd m o dul a r l ev el s S u p e r ior S u p e r ior L e f t m e d ial L e f t m e d ial Re gion al L e ve l M od u lar Le ve l M od u le nam e M od u le nam e 1 0 VN VN LN LN FPN FPN DM N DM N DAN DAN V AN V AN S M N S M N T op - k% O ve r l a p Pe r c e nt a ge ( % ) Fig. 8. Visualization of subgroup di ff erences (HC vs. dementia) in learned coupling strength in ADNI at the regional (Schaefer 500 ROIs) and modular le vels (a), the overlap percentage between regional and modular coupling-di ff erence patterns across top-k% ROIs (b), and their projection onto the canonical seven modules (Visual (VN), Somatomotor (SMN), Dorsal Attention (DAN), V entral Attention (V AN), Limbic (LN), Frontoparietal (FPN), and Default Mode (DMN) networks) (c). within each fold and av eraged across the 5-fold training and testing splits for UKB and ADNI. At the regional le vel, we av- erage the attention matrices produced by AHCM across sub- jects. For modular -lev el coupling, we deri ve group-wise com- munities from the structural and functional assignment matrices and av erage them across subjects, and apply spectral clustering to identify representativ e communities. These communities are then used to aggregate R OI-wise coupling strength into module- wise strength for visualization using BrainNet V ie wer ( Di Bi- ase et al. , 2023 ). The resulting multiscale coupling patterns are shown in Fig. 6 . At the regional level, coupling strength is strongest in dis- tributed association cortices, indicating that the learned inter- actions reflect widespread coordination. In brain-age predic- tion, stronger coupling is concentrated in medial and lateral prefrontal–parietal regions and posterior midline areas, consis- tent with circuits implicated in age-related reconfiguration of higher-order cognition ( Sala-Llonch et al. , 2015 ). In contrast, the ADNI disease prediction shows stronger in v olvement of posterior and temporoparietal regions, indicating that AHCM emphasizes coupling signals that align with disease-sensiti ve systems ( Baum et al. , 2020 ). At the modular le vel, these re- gional signals organize into clearer mesoscale patterns. After aggregating coupling through the learned community hierarch y and projecting onto prior functional modules, the maps become smoother and more spatially contiguous. This suggests that the model preserves regional variability while organizing coupling di ff erences into clearer module-lev el patterns. W e further e xamine the cross-task consistency of the learned coupling patterns, shown in Fig. 6 c. W e identified the top 50% R OIs with the strongest coupling strength for each task at both regional and modular levels. Overlapping R OIs were extracted and mapped onto the canonical sev en modules ( Y eo et al. , 2011 ) for neurobiological interpretation. Consistent overlaps were ob- served across both scales, primarily in volving the visual cortex and default-mode network (DMN), which are associated with aging- and dementia-related brain changes. Alterations in vi- sual netw ork or ganization and reduced SFC in occipital regions hav e been reported in both normal aging and neurodegenera- tiv e conditions ( Andrews-Hanna et al. , 2007 ). The DMN, in- cluding the medial prefrontal and posterior cingulate areas, is known to be particularly vulnerable in Alzheimer’ s disease and age-related cogniti ve decline ( Damoiseaux et al. , 2006 ; Buck- ner et al. , 2008 ). These overlapping patterns suggest that the model captures biologically meaningful structure–function in- teractions shared across tasks. 5.3.2. Di ff erence of hier ar chical multiscale coupling T o examine di ff erences in hierarchical multiscale coupling and modular or ganization, we conducted subgroup analyses. In UKB, participants were divided into two age subgroups (40–50 yrs: n = 900; 60–70 yrs: n = 1,058). In ADNI, the analysis was performed for healthy controls (n = 72) and dementia patients (n = 67). Follo wing the procedure in Subsection 5.3.1 , we com- puted subgroup-averaged coupling strength at both regional and modular lev els, then calculated the di ff erences between sub- groups. The resulting di ff erence maps were rescaled using min–max normalization for visualization. T o assess whether the model captures consistent multiscale patterns, we quanti- fied the spatial ov erlap across scales by selecting the top-k% R OIs with the lar gest coupling di ff erences and calculating their ov erlap across the range of [100% : 10% : 10%]. F or neu- robiological interpretation, the coupling di ff erence maps were projected onto the canonical sev en modules ( Y eo et al. , 2011 ). The results are shown in Figs. 7 and 8 . As sho wn in Fig. 7 a, similar coupling di ff erence patterns are observ ed between the two age groups at both regional and Jianwei Chen et al. / Medical Image Analysis (2026) 13 modular lev els, particularly in the medial frontal cortex, lateral temporal areas, and posterior cortical regions. The consistency across scales suggests that the model captures coherent multi- scale alterations in SFC. In Fig. 7 b, we quantify this similar- ity , showing that the ov erlap remains abov e 50% e ven when considering only the top 20% ROIs (100 re gions), indicating that similar patterns are preserved at both scales. For inter - pretation, we project the coupling di ff erences onto the canon- ical seven modules. As sho wn in Fig. 7 c, both representations exhibit similar coupling di ff erences across the se ven modules, with notable di ff erences in the limbic, def ault-mode, and dorsal attention networks. These findings align with previous studies showing that aging preferentially a ff ects higher -order associ- ation networks, particularly the default-mode and limbic sys- tems, which are related to substantial structural and functional reorganization throughout the adult lifespan. Additionally , cou- pling modulation in control networks highlights the intercon- nectedness of functional systems in age-related changes ( Jock- witz and Caspers , 2021 ; Huang et al. , 2022 ; W ang et al. , 2024 ; Khalilian et al. , 2024 ). As shown in Fig. 8 a, similar coupling di ff erence patterns are observed between healthy controls (HC) and dementia patients at both lev els. Notably , coupling di ff erences are seen in several cortical regions, particularly the medial frontal corte x, poste- rior medial areas, and lateral temporal re gions, suggesting that the model captures coherent multiscale alterations in SFC in dementia. In Fig. 8 b, the ov erlap between regional and mod- ular coupling-di ff erence maps remains high across thresholds, with overlap exceeding 50% ev en for the top 30% R OIs (150 regions), indicating that similar patterns are preserved at both scales. For interpretation, we project the coupling di ff erences onto the canonical sev en modules. As shown in Fig. 8 c, both regional and modular representations exhibit consistent patterns across the sev en modules, with notable e ff ects in the visual, frontoparietal, and default-mode networks. These observations are consistent with prior studies indicating that neurodegener - ativ e disorders, particularly Alzheimer’ s disease, preferentially a ff ect large-scale brain systems such as the default-mode, fron- toparietal, and visual networks, which sho w substantial struc- tural and functional reorg anization along the disease contin- uum. Additionally , the modulation of coupling in control net- works further reflects the interconnected nature of functional systems in neurodegeneration. ( Seeley et al. , 2009 ; Franzmeier et al. , 2019 ; Jones et al. , 2011 ). 6. Conclusion In this work, we introduce a hierarchical multiscale struc- ture–function coupling frame work for multimodal brain con- nectome integration, motiv ated by the prior that SC–FC rela- tionships are nonlinear and organized over nested modular hi- erarchies rather than a single flat graph. Building on this view , our method jointly learns (i) individualized, modality-specific multiscale community structures via Prototype-based Modu- lar Pooling (PMPool), (ii) within- and cross-hierarchy struc- ture–function interactions via an Attention-based Hierarchical Coupling Module (AHCM), and (iii) coupling-guided coordina- tion of structural and functional hierarchies through a Coupling- guided Clustering loss (CgC-Loss), allowing cross-modal in- teractions to shape community structure. Across multiple co- horts and tasks, including age prediction, cognitiv e score pre- diction, and dementia classification, the proposed model consis- tently outperforms multimodal GNN baselines as well as recent coupling-based and hierarchy-a ware methods. Ablation and sensitivity analyses further confirm the contributions of each component and identify stable operating regimes. Beyond per- formance, our interpretability analyses indicate that the learned coupling patterns and community assignments capture biolog- ically plausible, group-specific signatures: both aging and de- mentia are associated with systematic shifts in high-coupling regions and reconfiguration of large-scale modules. T aken to- gether , these results suggest that explicitly modeling hierarchi- cal multiscale coupling is an e ff ectiv e approach for multimodal connectome fusion, improving generalization and interpretabil- ity while supporting studies of de velopment, aging, and brain disorders. Future work will extend this framework to dynam- ically model hierarchical multiscale coupling and explore its potential to uncov er mechanisms underlying a wider range of brain disorders. 7. Acknowledgments The ADNI dataset used in this study were obtained from the Alzheimer’ s Disease Neuroimaging Initiativ e (ADNI) database (adni.loni.usc.edu). The in v estigators within ADNI contributed to the design and implementation of ADNI and / or pro vided data, but did not participate in analysis or writing of this re- port. A complete list of ADNI inv estigators can be found at: . Data collection and sharing for ADNI is funded by the Na- tional Institute on Aging (National Institutes of Health Grant U19A G024904). This research has been conducted using the UK Biobank Resource under Application Number 52802. The authors are grateful to UK Biobank and all study participants for making the data av ailable. Chao Li ackno wledge Guarantors of Brain. Data were pro- vided [in part] by the Human Connectome Project, WU-Minn Consortium (Principal In vestigators: David V an Essen and Kamil Ugurbil; 1U54MH091657) funded by the 16 NIH In- stitutes and Centers that support the NIH Blueprint for Neuro- science Research; and by the McDonnell Center for Systems Neuroscience at W ashington Univ ersity . References Adam, K.D.B.J., et al., 2014. A method for stochastic optimization. arXiv preprint arXiv:1412.6980 1412. Alfaro-Almagro, F ., Jenkinson, M., Bangerter , N.K., Andersson, J.L., Gri ff anti, L., Douaud, G., Sotiropoulos, S.N., Jbabdi, S., Hernandez-Fernandez, M., V allee, E., et al., 2018. Image processing and quality control for the first 10,000 brain imaging datasets from uk biobank. Neuroimage 166, 400–424. Andrews-Hanna, J.R., Snyder , A.Z., V incent, J.L., Lustig, C., Head, D., Raichle, M.E., Buckner , R.L., 2007. Disruption of lar ge-scale brain systems in advanced aging. Neuron 56, 924–935. Ball, G., Aljabar, P ., Zebari, S., Tusor , N., Arichi, T ., Merchant, N., Robin- son, E.C., Ogundipe, E., Rueckert, D., Edwards, A.D., et al., 2014. Rich- club organization of the ne wborn human brain. Proceedings of the National Academy of Sciences 111, 7456–7461. 14 Jianwei Chen et al. / Medical Image Analysis (2026) Baum, G.L., Cui, Z., Roalf, D.R., Ciric, R., Betzel, R.F ., Larsen, B., Cies- lak, M., Cook, P .A., Xia, C.H., Moore, T .M., et al., 2020. Development of structure–function coupling in human brain networks during youth. Pro- ceedings of the National Academy of Sciences 117, 771–778. Betzel, R.F ., Gri ff a, A., A vena-Koenigsber ger , A., Go ˜ ni, J., Thiran, J.P ., Hag- mann, P ., Sporns, O., 2013. Multi-scale community organization of the hu- man structural connectome and its relationship with resting-state functional connectivity . Network Science 1, 353–373. Brown, J.A., Rudie, J.D., Bandrowski, A., V an Horn, J.D., Bookheimer , S.Y ., 2012. The ucla multimodal connecti vity database: a web-based platform for brain connectivity matrix sharing and analysis. Frontiers in neuroinformatics 6, 28. Buckner , R.L., Andre ws-Hanna, J.R., Schacter , D.L., 2008. The brain’ s default network: anatomy , function, and relev ance to disease. Annals of the new Y ork Academy of Sciences 1124, 1–38. Bullmore, E., Sporns, O., 2009. Complex brain networks: graph theoretical analysis of structural and functional systems. Nature reviews neuroscience 10, 186–198. Chan, M.Y ., Park, D.C., Sav alia, N.K., Petersen, S.E., W ig, G.S., 2014. De- creased segregation of brain systems across the healthy adult lifespan. Pro- ceedings of the National Academy of Sciences 111, E4997–E5006. Chen, P ., Y ang, H., Zheng, X., Jia, H., Hao, J., Xu, X., Li, C., He, X., Chen, R., Okubo, T .S., et al., 2024. Group-common and indi vidual-specific e ff ects of structure–function coupling in human brain networks with graph neural networks. Imaging Neuroscience 2, 1–21. Craddock, R.C., James, G.A., Holtzheimer III, P .E., Hu, X.P ., Mayberg, H.S., 2012. A whole brain fmri atlas generated via spatially constrained spectral clustering. Human brain mapping 33, 1914–1928. Damoiseaux, J.S., Rombouts, S.A., Barkhof, F ., Scheltens, P ., Stam, C.J., Smith, S.M., Beckmann, C.F ., 2006. Consistent resting-state networks across healthy subjects. Proceedings of the national academy of sciences 103, 13848–13853. Di Biase, M.A., Smith, R.E., Zalesk y , A., Se guin, C., et al., 2023. Connec- tomes for 40,000 uk biobank participants: A multi-modal, multi-scale brain network resource. NeuroImage 283, 120407. Dsouza, N.S., Nebel, M.B., Crocetti, D., Robinson, J., Mostofsky , S., V enkataraman, A., 2021. M-gcn: A multimodal graph convolutional net- work to integrate functional and structural connectomics data to predict mul- tidimensional phenotypic characterizations, in: Medical Imaging with Deep Learning, PMLR. pp. 119–130. Feng, J., Xu, H., Cai, J., Chang, Y ., Zhang, D., Du, S., W ang, J., 2025. Cross- modal brain graph transformer via function-structure connectivity network for brain disease diagnosis, in: International Conference on Medical Image Computing and Computer-Assisted Interv ention, Springer . pp. 247–256. Fornito, A., Zalesky , A., Breakspear , M., 2015. The connectomics of brain disorders. Nature revie ws neuroscience 16, 159–172. Fotiadis, P ., Parkes, L., Davis, K.A., Satterthwaite, T .D., Shinohara, R.T ., Bas- sett, D.S., 2024. Structure–function coupling in macroscale human brain networks. Nature Revie ws Neuroscience 25, 688–704. Franzmeier , N., Rubinski, A., Neitzel, J., Kim, Y ., Damm, A., Na, D.L., Kim, H.J., L yoo, C.H., Cho, H., Finsterwalder , S., et al., 2019. Functional con- nectivity associated with tau lev els in ageing, alzheimer’ s, and small vessel disease. Brain 142, 1093–1107. Hamilton, W ., Y ing, Z., Leskovec, J., 2017. Inducti ve representation learning on large graphs. Advances in neural information processing systems 30. Hu, H., Zhang, H., Li, C., 2024. D-corp: Di ff erentiable connecti vity refinement for functional brain networks, in: International Conference on Medical Im- age Computing and Computer -Assisted Intervention, Springer . pp. 119–129. Huang, J., W ei, S., Gao, Z., Jiang, S., W ang, M., Sun, L., Ding, W ., Zhang, D., 2025. Local structural–functional coupling with counterfactual e xplanations for epilepsy prediction. NeuroImage 306, 120978. Huang, Q., Ren, S., Zhang, T ., Li, J., Jiang, D., Xiao, J., Hua, F ., Xie, F ., Guan, Y ., 2022. Aging-related modular architectural reorganization of the metabolic brain network. Brain Connectivity 12, 432–442. Jiang, L., Li, F ., Chen, Z., Zhu, B., Y i, C., Li, Y ., Zhang, T ., Peng, Y ., Si, Y ., Cao, Z., et al., 2023. Information transmission velocity-based dynamic hierarchical brain networks. NeuroImage 270, 119997. Jockwitz, C., Caspers, S., 2021. Resting-state networks in the course of ag- ing—di ff erential insights from studies across the lifespan vs. amongst the old. Pfl ¨ ugers Archiv-European Journal of Physiology 473, 793–803. Jones, D., Machulda, M., V emuri, P ., McDade, E., Zeng, G., Senjem, M., Gunter , J., Przybelski, S., A vula, R., Knopman, D., et al., 2011. Age-related changes in the default mode network are more advanced in alzheimer dis- ease. Neurology 77, 1524–1531. Kawahara, J., Brown, C.J., Miller, S.P ., Booth, B.G., Chau, V ., Grunau, R.E., Zwicker , J.G., Hamarneh, G., 2017. Brainnetcnn: Con volutional neural net- works for brain networks; towards predicting neurode velopment. NeuroIm- age 146, 1038–1049. Khalilian, M., T oba, M.N., Roussel, M., T asseel-Ponche, S., Godefroy , O., Aarabi, A., 2024. Age-related di ff erences in structural and resting-state functional brain network org anization across the adult lifespan: A cross- sectional study . Aging Brain 5, 100105. Kipf, T ., 2016. Semi-supervised classification with graph convolutional net- works. arXiv preprint arXi v:1609.02907 . Li, Q., Han, Z., W u, X.M., 2018. Deeper insights into graph con volutional networks for semi-supervised learning, in: Proceedings of the AAAI confer- ence on artificial intelligence. Li, Y ., W ei, Q., Adeli, E., Pohl, K.M., Zhao, Q., 2022. Joint graph con volution for analyzing brain structural and functional connectome, in: International Conference on Medical Image Computing and Computer-Assisted Interven- tion, Springer . pp. 231–240. Liu, L., W ang, Y .P ., W ang, Y ., Zhang, P ., Xiong, S., 2022. An enhanced multi- modal brain graph network for classifying neuropsychiatric disorders. Med- ical image analysis 81, 102550. Lurie, D.J., Pappas, I., D’Esposito, M., 2024. Cortical timescales and the mod- ular organization of structural and functional brain networks. Human Brain Mapping 45, e26587. Mehta, K., Salo, T ., Madison, T .J., Adebimpe, A., Bassett, D.S., Bertolero, M., Cieslak, M., Covitz, S., Houghton, A., Keller , A.S., et al., 2024. Xcp-d: A robust pipeline for the post-processing of fmri data. Imaging Neuroscience 2, 1–26. Mess ´ e, A., 2020. Parcellation influence on the connectivity-based structure– function relationship in the human brain. Human brain mapping 41, 1167– 1180. Meunier , D., Lambiotte, R., Fornito, A., Ersche, K., Bullmore, E.T ., 2009. Hi- erarchical modularity in human brain functional networks. Frontiers in neu- roinformatics 3, 571. Nooner , K.B., Colcombe, S.J., T obe, R.H., Mennes, M., Benedict, M.M., Moreno, A.L., Panek, L.J., Brown, S., Zavitz, S.T ., Li, Q., et al., 2012. The nki-rockland sample: a model for accelerating the pace of discovery science in psychiatry . Frontiers in neuroscience 6, 152. Petersen, R.C., Aisen, P .S., Beckett, L.A., Donohue, M.C., Gamst, A.C., Har- vey , D.J., Jack Jr, C.R., Jagust, W .J., Shaw , L.M., T oga, A.W ., et al., 2010. Alzheimer’ s disease neuroimaging initiati ve (adni) clinical characterization. Neurology 74, 201–209. Pines, A., K eller , A.S., Larsen, B., Bertolero, M., Ashourv an, A., Bassett, D.S., Cieslak, M., Covitz, S., Fan, Y ., Feczko, E., et al., 2023. De velopment of top-down cortical propagations in youth. Neuron 111, 1316–1330. Sala-Llonch, R., Bartr ´ es-Faz, D., Junqu ´ e, C., 2015. Reorganization of brain networks in aging: a revie w of functional connectivity studies. Frontiers in psychology 6, 663. Salas-Gonzalez, D., G ´ orriz, J., Ram ´ ırez, J., Ill ´ an, I., L ´ opez, M., Sego via, F ., Chav es, R., Padilla, P ., Puntonet, C., Initiati ve, A.D.N., 2010. Feature selec- tion using factor analysis for alzheimer’ s diagnosis using pet images. Medi- cal physics 37, 6084–6095. Schaefer , A., K ong, R., Gordon, E.M., Laumann, T .O., Zuo, X.N., Holmes, A.J., Eickho ff , S.B., Y eo, B.T ., 2018. Local-global parcellation of the human cerebral cortex from intrinsic functional connectivity mri. Cerebral cortex 28, 3095–3114. Sebenius, I., Campbell, A., Morgan, S.E., Bullmore, E.T ., Li ` o, P ., 2021. Multi- modal graph coarsening for interpretable, mri-based brain graph neural net- work, in: 2021 ieee 31st international workshop on machine learning for signal processing (mlsp), IEEE. pp. 1–6. Seeley , W .W ., Crawford, R.K., Zhou, J., Miller , B.L., Greicius, M.D., 2009. Neurodegenerati ve diseases target large-scale human brain networks. Neu- ron 62, 42–52. Seguin, C., Sporns, O., Zalesky , A., Calamante, F ., et al., 2022. Network communication models narrow the gap between the modular or ganization of structural and functional brain networks. Neuroimage 257, 119323. Sinha, R., Dijkshoorn, A.B., Li, C., Manly , T ., Price, S.J., 2020. Glioblas- toma surgery related emotion recognition deficits are associated with right cerebral hemisphere tract changes. Brain communications 2, fcaa169. ˇ Skoch, A., Reh ´ ak Bu ˇ ckov ´ a, B., Mare ˇ s, J., T int ˇ era, J., Sanda, P ., Jajcay , L., Hor ´ a ˇ cek, J., ˇ Spaniel, F ., Hlinka, J., 2022. Human brain structural connecti v- Jianwei Chen et al. / Medical Image Analysis (2026) 15 ity matrices–ready for modelling. Scientific Data 9, 486. Su ´ arez, L.E., Markello, R.D., Betzel, R.F ., Misic, B., 2020. Linking structure and function in macroscale brain networks. T rends in cogniti ve sciences 24, 302–315. Sun, Y ., W ang, P ., Zhao, K., Chen, P ., Qu, Y ., Li, Z., Zhong, S., Zhou, B., Lu, J., Zhang, X., et al., 2024. Structure–function coupling rev eals the brain hi- erarchical structure dysfunction in alzheimer’ s disease: A multicenter study . Alzheimer’ s & Dementia 20, 6305–6315. T ang, H., Chen, J., T ang, X., W u, Y ., Miao, Z., Li, C., 2025. Hierarchical brain structure modeling for predicting genotype of glioma, in: International W orkshop on Computational Mathematics Modeling in Cancer Analysis, Springer . pp. 160–169. T ournier, J.D., Smith, R., Ra ff elt, D., T abbara, R., Dhollander , T ., Pietsch, M., Christiaens, D., Jeurissen, B., Y eh, C.H., Connelly , A., 2019. Mrtrix3: A fast, flexible and open software framework for medical image processing and visualisation. Neuroimage 202, 116137. Tsitsulin, A., Palo witch, J., Perozzi, B., M ¨ uller , E., 2023. Graph clustering with graph neural networks. Journal of Machine Learning Research 24, 1–21. V an Den Heuvel, M.P ., Pol, H.E.H., 2010. Exploring the brain network: a revie w on resting-state fmri functional connectivity . European neuropsy- chopharmacology 20, 519–534. V an Essen, D.C., Smith, S.M., Barch, D.M., Behrens, T .E., Y acoub, E., Ugurbil, K., Consortium, W .M.H., et al., 2013. The wu-minn human connectome project: an overview . Neuroimage 80, 62–79. W ang, X., Huang, C.C., Tsai, S.J., Lin, C.P ., Cai, Q., 2024. The aging trajec- tories of brain functional hierarchy and its impact on cognition across the adult lifespan. Frontiers in Aging Neuroscience 16, 1331574. W ei, Y ., Chen, X., Sch ¨ onlieb, C.B., Price, S.J., Li, C., 2023. Predicting con- version of mild cognitive impairment to alzheimer’ s disease by modelling healthy ageing trajectories, in: 2023 IEEE 20th International Symposium on Biomedical Imaging (ISBI), IEEE. pp. 1–5. W ei, Y ., Li, C., Price, S.J., 2021. Quantifying structural connectivity in brain tumor patients, in: International Conference on Medical Image Computing and Computer-Assisted Interv ention, Springer . pp. 519–529. Xia, J., Chan, Y .H., Girish, D., Rajapakse, J.C., 2024. Img-gcn: Interpretable modularity-guided structure-function interactions learning for brain cogni- tion and disorder analysis, in: International Conference on Medical Image Computing and Computer-Assisted Interv ention, Springer . pp. 470–480. Xia, J., Chan, Y .H., Girish, D., Rajapakse, J.C., 2025. Interpretable modality- specific and interactiv e graph conv olutional netw ork on brain functional and structural connectomes. Medical Image Analysis 102, 103509. Xu, K., Hu, W ., Leskovec, J., Je gelka, S., 2018. How powerful are graph neural networks? arXiv preprint arXi v:1810.00826 . Y ang, Y ., Y e, C., Guo, X., W u, T ., Xiang, Y ., Ma, T ., 2023. Mapping multi- modal brain connectome for brain disorder diagnosis via cross-modal mutual learning. IEEE Transactions on Medical Imaging 43, 108–121. Y e, H., Zheng, Y ., Li, Y ., Zhang, K., K ong, Y ., Y uan, Y ., 2023a. Rh-brainfs: re- gional heterogeneous multimodal brain networks fusion strategy . Advances in Neural Information Processing Systems 36, 59286–59303. Y e, K., T ang, H., Dai, S., Guo, L., Liu, J.Y ., W ang, Y ., Leow , A., Thompson, P .M., Huang, H., Zhan, L., 2023b . Bidirectional mapping with contrastive learning on multimodal neuroimaging data, in: International conference on medical image computing and computer-assisted intervention, Springer . pp. 138–148. Y eo, B.T ., Krienen, F .M., Sepulcre, J., Sabuncu, M.R., Lashkari, D., Hollinshead, M., Ro ff man, J.L., Smoller, J.W ., Z ¨ ollei, L., Polimeni, J.R., et al., 2011. The organization of the human cerebral cortex estimated by intrinsic functional connectivity . Journal of neurophysiology . Zamani Esfahlani, F ., Fasko witz, J., Slack, J., Mi ˇ si ´ c, B., Betzel, R.F ., 2022. Local structure-function relationships in human brain networks across the lifespan. Nature communications 13, 2053. Zhang, J., Guo, Y ., Zhou, L., W ang, L., W u, W ., Shen, D., 2024. Construct- ing hierarchical attentiv e functional brain networks for early ad diagnosis. Medical Image Analysis 94, 103137. Zhang, L., W ang, L., Gao, J., Risacher, S.L., Y an, J., Li, G., Liu, T ., Zhu, D., Initiativ e, A.D.N., et al., 2021. Deep fusion of brain structure-function in mild cognitiv e impairment. Medical image analysis 72, 102082. Zhang, L., W ang, L., Zhu, D., Initiative, A.D.N., et al., 2022. Predicting brain structural network using functional connectivity . Medical image analysis 79, 102463. Zhang, X., He, L., Chen, K., Luo, Y ., Zhou, J., W ang, F ., 2018. Multi-view graph con volutional network and its applications on neuroimage analysis for parkinson’ s disease, in: AMIA annual symposium proceedings, p. 1147.