Organizations: School of Medicine, University of Dundee, UK · College of Medicine and Biological Information Engineering, Northeastern University, China · School of Airspace Science and Engineering, Shandong University, China · College of Medical Informatics, Chongqing Medical University, China · School of Science and Engineering, University of Dundee, UK · Department of Applied Mathematics and Theoretical Physics, University of Cambridge, UK · Chinese Institute for Brain Research, China · Department of Clinical Neurosciences, University of Cambridge, UK
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.
Figures & tables
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 obtain 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 are fused for the downstream prediction task.
Fig. 2: PMPool includes prototypical ROI selection and community assignment for 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.
Fig. 3: Architecture of AHCM. Within-hierarchy coupling is computed via bidirectional attention, while cross-hierarchy coupling is captured by two cross-attention branches. These hierarchical coupling signals are aggregated to obtain enriched hierarchical multiscale representations.
Fig. 4: The coupling-guided clustering loss LCC . 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 divergence between SC and FC assignment matrices, promoting cross-modal consistency driven by SFC.
Method
HCPYA
NKI-Rockland
UKB
MAE ↓
RMSE ↓
MAE ↓
RMSE ↓
MAE ↓
RMSE ↓
GCN [ 29 ]
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 [ 60 ]
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 [ 20 ]
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 [ 15 ]
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 [ 32 ]
6.02 (1.38)
7.14 (1.32)
14.41 (0.34)
19.44 (0.52)
6.64 (0.65)
7.93 (0.72)
Table 1: Comparison results on HCPYA, NKI-Rockland and UKB for brain age prediction based on FC and SC.
Method
HCPYA (MMSE)
UKB (Fluid Intelligence Score)
MAE ↓
RMSE ↓
MAE ↓
RMSE ↓
GCN [ 29 ]
3.73 (0.57)
5.18 (1.43)
3.17 (0.26)
3.69 (0.23)
GIN [ 60 ]
3.52 (0.43)
4.09 (0.30)
3.60 (0.30)
4.01 (0.43)
GraphSage [ 20 ]
3.65 (0.68)
5.18 (1.43)
3.14 (0.43)
3.66 (0.40)
M-GCN [ 15 ]
1.48 (0.11)
1.95 (0.21)
3.23 (1.43)
5.30 (3.98)
MME-GCN [ 32 ]
6.12 (0.33)
6.61 (0.32)
2.72 (0.06)
3.17 (0.09)
Table 2: Comparison results on HCPYA and UKB for MMSE and fluid intelligence score prediction based on FC and SC.
Method
ACC ↑
AUC ↑
Sen ↑
Spec ↑
GCN [ 29 ]
0.68 (0.06)
0.60 (0.14)
0.50 (0.15)
0.74 (0.16)
GIN [ 60 ]
0.64 (0.04)
0.71 (0.03)
0.61 (0.16)
0.68 (0.15)
GraphSAGE [ 20 ]
0.68 (0.07)
0.62 (0.14)
0.67 (0.15)
0.69 (0.15)
M-GCN [ 15 ]
0.73 (0.07)
0.70 (0.06)
0.61 (0.23)
0.74 (0.22)
MME-GCN [ 32 ]
0.74 (0.07)
0.72 (0.10)
0.66 (0.14)
0.79 (0.08)
Joint-GCN [ 31 ]
0.75 (0.08)
0.70 (0.08)
0.61 (0.20)
0.79 (0.21)
Table 3: Comparison results on ADNI for disease classification based on FC and SC.
Fig. 5: Cognitive score prediction performance of the proposed method with different pooling ratios, number of hierarchies, and regularization weight of LCC on (a) HCPYA and (b) ADNI.
HCPYA: 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
Table 4: Ablation study on PMPool, AHCM, and CgC-Loss on HCPYA (MMSE prediction) and ADNI (disease classification).
HCPYA: MMSE prediction
Method
MAE ↓
RMSE ↓
PCC ↑
GIN
1.11 (0.04)
1.33 (0.17)
0.18 (0.06)
GraphSAGE
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
ACC ↑
Sen ↑
Spec ↑
Table 5: Results of MMSE score prediction on HCPYA and disease classification on ADNI using different GNN encoders.
Fig. 6: Multiscale coupling strength learned by the proposed model. Regional-level maps show global coupling strength, whereas modular-level maps show local coupling strength, for (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 (DAN), Ventral Attention (VAN), Limbic (LN), Frontoparietal (FPN), and Default Mode (DMN) networks).
HCPYA: 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
ACC ↑
Sen ↑
Spec ↑
softmax
0.76 (0.17)
0.66 (0.12)
0.77 (0.14)
Table 6: Results of MMSE score prediction on HCPYA and disease classification on ADNI using entmax and softmax.
Fig. 7: Visualization of age-group (40–50 vs. 60–70 years) differences in learned coupling strength in UKB at the regional (Schaefer 500 ROIs) and modular levels (a), the overlap percentage between regional and modular coupling-difference patterns across top-k% ROIs (b), and their projection onto the canonical seven modules (Visual (VN), Somatomotor (SMN), Dorsal Attention (DAN), Ventral Attention (VAN), Limbic (LN), Frontoparietal (FPN), and Default Mode (DMN) networks) (c).
Fig. 8: Visualization of subgroup differences (HC vs. dementia) in learned coupling strength in ADNI at the regional (Schaefer 500 ROIs) and modular levels (a), the overlap percentage between regional and modular coupling-difference patterns across top-k% ROIs (b), and their projection onto the canonical seven modules (Visual (VN), Somatomotor (SMN), Dorsal Attention (DAN), Ventral Attention (VAN), Limbic (LN), Frontoparietal (FPN), and Default Mode (DMN) networks) (c).
School of Information Technology, Monash University Malaysia · School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore · Department of Radiology, University of North Carolina at Chapel Hill, Chapel Hill, NC, USA
Department of Computer Science, Georgia State University · Tri-Institutional Center for Translational Research in Neuroimaging and Data Science (TReNDS), Georgia State University, Georgia Institute of Technology, and Emory University · Neuroscience Institute, Georgia State University
Department of Biomedical Engineering, Michigan State University, USA. · Department of Electrical and Computer Engineering, Michigan State University, USA.