Graph neural fields: A framework for spatiotemporal dynamical models on the human connectome.

Area of Science:

• Computational Neuroscience
• Graph Signal Processing
• Neuroimaging Analysis

Background:

• Graph signal processing tools, like the graph Laplacian, are increasingly used to study brain structure-function relationships.
• Connectome harmonics (eigenvectors of the graph Laplacian) correlate with resting-state brain networks.
• Whole-brain modeling integrates structural connectivity and local dynamics to understand large-scale brain function.

Purpose of the Study:

• To define and implement novel neural activity models, termed graph neural fields, directly on the human connectome.
• To develop analytical methods for predicting spectral and connectivity properties of these graph neural field models.
• To demonstrate the utility of graph neural fields for modeling empirical brain activity data.

Main Methods:

• Employed the graph Laplacian to formulate stochastic integrodifferential equations on graphs, defining graph neural fields.
• Developed the Connectome-Harmonic Analysis Of Spatiotemporal Spectra (CHAOSS) technique for analytical predictions.
• Integrated graph neural fields with observation models for parameter estimation from EEG, MEG, and fMRI data.

Main Results:

• Analytically predicted harmonic and temporal power spectra, functional connectivity, and coherence matrices for graph neural fields.
• A stochastic Wilson-Cowan graph neural field model accurately reproduced empirical harmonic power spectra from resting-state fMRI.
• The model successfully predicted functional connectivity patterns from high-resolution diffusion tensor imaging and structural MRI data.

Conclusions:

• Graph neural fields provide a powerful framework for whole-brain modeling at mesoscopic scales, integrating anatomical and dynamical information.
• This approach facilitates fast computations and comparison with multimodal empirical data, advancing connectome-based structure-function research.
• Graph neural fields offer new avenues for investigating brain organization and dynamics using graph theory and signal processing.