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GyralNet Subnetwork Partitioning via Differentiable Spectral Modularity Optimization

Yan Zhuang, Minheng Chen, Chao Cao, Tong Chen, Jing Zhang, Xiaowei Yu, Yanjun Lyu, Lu Zhang, Tianming Liu, Dajiang Zhu

TL;DR

This work tackles the challenge of decomposing cortical folding into meaningful subnetworks by focusing on three-hinge gyrus (3HG) landmarks within GyralNet. It introduces a fully differentiable framework that combines topological similarity and DTI-based connectivity as node attributes and optimizes a spectral modularity objective via a two-layer GCN with collapse regularization. The approach yields improved modularity and reduced conductance, while maintaining cross-subject consistency of 3HG subnetworks on the Human Connectome Project dataset, enabling robust, subject-aware brain network representations. The results suggest that integrating local topology with white-matter connectivity produces biologically plausible subnetworks that may aid in studying brain organization and identifying neurological disorders.

Abstract

Understanding the structural and functional organization of the human brain requires a detailed examination of cortical folding patterns, among which the three-hinge gyrus (3HG) has been identified as a key structural landmark. GyralNet, a network representation of cortical folding, models 3HGs as nodes and gyral crests as edges, highlighting their role as critical hubs in cortico-cortical connectivity. However, existing methods for analyzing 3HGs face significant challenges, including the sub-voxel scale of 3HGs at typical neuroimaging resolutions, the computational complexity of establishing cross-subject correspondences, and the oversimplification of treating 3HGs as independent nodes without considering their community-level relationships. To address these limitations, we propose a fully differentiable subnetwork partitioning framework that employs a spectral modularity maximization optimization strategy to modularize the organization of 3HGs within GyralNet. By incorporating topological structural similarity and DTI-derived connectivity patterns as attribute features, our approach provides a biologically meaningful representation of cortical organization. Extensive experiments on the Human Connectome Project (HCP) dataset demonstrate that our method effectively partitions GyralNet at the individual level while preserving the community-level consistency of 3HGs across subjects, offering a robust foundation for understanding brain connectivity.

GyralNet Subnetwork Partitioning via Differentiable Spectral Modularity Optimization

TL;DR

This work tackles the challenge of decomposing cortical folding into meaningful subnetworks by focusing on three-hinge gyrus (3HG) landmarks within GyralNet. It introduces a fully differentiable framework that combines topological similarity and DTI-based connectivity as node attributes and optimizes a spectral modularity objective via a two-layer GCN with collapse regularization. The approach yields improved modularity and reduced conductance, while maintaining cross-subject consistency of 3HG subnetworks on the Human Connectome Project dataset, enabling robust, subject-aware brain network representations. The results suggest that integrating local topology with white-matter connectivity produces biologically plausible subnetworks that may aid in studying brain organization and identifying neurological disorders.

Abstract

Understanding the structural and functional organization of the human brain requires a detailed examination of cortical folding patterns, among which the three-hinge gyrus (3HG) has been identified as a key structural landmark. GyralNet, a network representation of cortical folding, models 3HGs as nodes and gyral crests as edges, highlighting their role as critical hubs in cortico-cortical connectivity. However, existing methods for analyzing 3HGs face significant challenges, including the sub-voxel scale of 3HGs at typical neuroimaging resolutions, the computational complexity of establishing cross-subject correspondences, and the oversimplification of treating 3HGs as independent nodes without considering their community-level relationships. To address these limitations, we propose a fully differentiable subnetwork partitioning framework that employs a spectral modularity maximization optimization strategy to modularize the organization of 3HGs within GyralNet. By incorporating topological structural similarity and DTI-derived connectivity patterns as attribute features, our approach provides a biologically meaningful representation of cortical organization. Extensive experiments on the Human Connectome Project (HCP) dataset demonstrate that our method effectively partitions GyralNet at the individual level while preserving the community-level consistency of 3HGs across subjects, offering a robust foundation for understanding brain connectivity.

Paper Structure

This paper contains 13 sections, 9 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Methodology
  3. Preliminaries
  4. Structural Representation of 3-Hinge Gyrus
  5. Network Architecture
  6. Spectral Modularity Optimization
  7. Experiment
  8. Experimental Settings
  9. Dataset.
  10. Implementation details.
  11. Evaluation metrics.
  12. Results
  13. Conclusion

Figures (3)

  • Figure 1: Overall architecture of the proposed method. (a) The folding pattern of the cerebral cortex organized by 3HGs. (b) An illustration of the differentiable spectral modularity optimization, the structural representation of each 3HG integrates both structural similarity and structural connectivity patterns.
  • Figure 2: Partitioned GyralNets ($k=4$) from multiple subjects are shown in lateral (top: left hemisphere, middle: right hemisphere) and superior (bottom) views. Each block represents a subject, with distinct colors indicating subnetworks. Elliptical outlines highlight consistently observed subnetworks across subjects.
  • Figure 3: The figures on the left and right show the mean of the standard deviation of the localization descriptor ($k=8$) in the left and right hemispheres across all subjects from HCP dataset, respectively.