Neurobridge: Bridging Functional and Anatomical Neural Connectivity through Dynamical Modeling

Overview

Neurobridge aims to investigate how to reconcile structural and functional brain connectivity using network clustering and structural refinement techniques, as a preparatory step for dynamical modeling.

The focus is on:

• identifying ordered or hierarchical clusters of functionally coherent brain regions;
• using those partitions to refine structural connectivity matrices into equitable versions;
• laying the foundation for later integration into neural dynamical models.

Objectives

• Load and preprocess functional and structural connectivity data.
• Apply functional clustering via Peixoto’s SBM framework (ordered and nested variants).
• Select a representative session using clustering consistency (Fowlkes–Mallows index).
• Derive an equitable structural matrix ( A_k ) compatible with the functional partition.
• Prepare the system for downstream dynamical simulation (not implemented here).

Approach

Tools

• Peixoto's stochastic block model via graph-tool (both ordered and nested SBM variants).
• Baruzzi et al.’s structural refinement method, enforcing equitable input across functionally clustered groups.

Pipeline Steps

1. Data Loading: Import fMRI-based functional matrices and diffusion MRI structural matrices across 10 sessions.
2. Functional Clustering:
   • Compute one clustering per session.
   • Select the most representative session via average Fowlkes–Mallows similarity.
   • Store clustering assignments and visualize inferred community structure.
3. Structural Matrix Averaging:
   • Compute the average of the 10 structural matrices → ( A_0 ).
4. Structural Refinement:
   • Solve a convex optimization problem to find matrix ( A_k ) as close as possible to ( A_0 ), while ensuring equitable connectivity w.r.t. the functional clusters.
5. Output:
   • Save ( A_0 ), ( A_k ), and the functional partition.
   • Save visualizations of the input and clustered graphs.

Dataset Format

• Functional matrices: session-level edgelists, 48x48 correlation matrices (after preprocessing).
• Structural matrices: session-level connectomes derived from diffusion tractography, also 48x48.

References

• Baruzzi, V., Lodi, M., Sorrentino, F., & Storace, M. (2023). Bridging functional and anatomical neural connectivity through cluster synchronization. Scientific Reports, 13, 22430.
  DOI: 10.1038/s41598-023-49746-2

• Peixoto, T.P. (2022). Ordered community detection in directed networks. Phys. Rev. E, 106(2), 024305.

Installation

This project uses Python and Conda for environment and package management.

Dependencies

• graph-tool
• numpy, scikit-learn, matplotlib, cvxpy, seaborn

Setup

conda env create -f environment.yml
conda activate neurobridge

Usage

1. Download the data from the open-neurodata portal:

   • Functional matrices
   • Structural matrices

2. Organize it under:

   ./data/subject-<ID>/
       ├── functional/
       └── structural/
   

3. Edit configuration in config/settings.json to reflect:

   • input paths
   • graph type
   • clustering model
   • thresholding strategy

4. Run the pipeline:

python scripts/run_pipeline.py

Output

All results are saved under:

results/subject-<ID>/

Including:

• graph_thresh-XX_directed.pdf: raw functional graph
• graph_nested_clustered.pdf: graph with inferred clusters
• A0_structural_mean.csv: mean structural matrix
• Ak_structural_equitable.csv: refined equitable matrix
• functional_partition.csv: selected clustering labels

Project Structure

src/
├── io/                  # loading and saving
├── graph/               # graph building
├── clustering/          # nested SBM
└── structural/          # A_k optimization

License

TBD