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

Abstract

Tools from the field of graph signal processing, in particular the graph Laplacian operator, have recently been successfully applied to the investigation of structure-function relationships in the human brain. The eigenvectors of the human connectome graph Laplacian, dubbed “connectome harmonics”, have been shown to relate to the functionally relevant resting-state networks. Whole-brain modelling of brain activity combines structural connectivity with local dynamical models to provide insight into the large-scale functional organization of the human brain. In this study, we employ the graph Laplacian and its properties to define and implement a large class of neural activity models directly on the human connectome. These models, consisting of systems of stochastic integrodifferential equations on graphs, are dubbed graph neural fields, in analogy with the well-established continuous neural fields. We obtain analytic predictions for harmonic and temporal power spectra, as well as functional connectivity and coherence matrices, of graph neural fields, with a technique dubbed CHAOSS (shorthand for Connectome-Harmonic Analysis Of Spatiotemporal Spectra). Combining graph neural fields with appropriate observation models allows for estimating model parameters from experimental data as obtained from electroencephalography (EEG), magnetoencephalography (MEG), or functional magnetic resonance imaging (fMRI). As an example application, we study a stochastic Wilson-Cowan graph neural field model on a high-resolution connectome graph constructed from diffusion tensor imaging (DTI) and structural MRI data. We show that the model equilibrium fluctuations can reproduce the empirically observed harmonic power spectrum of resting-state fMRI data, and predict its functional connectivity, with a high level of detail. Graph neural fields natively allow the inclusion of important features of cortical anatomy and fast computations of observable quantities for comparison with multimodal empirical data. They thus appear particularly suitable for modelling whole-brain activity at mesoscopic scales, and opening new potential avenues for connectome-graph-based investigations of structure-function relationships.

Gradients of connectivity as graph Fourier bases of brain activity

“…The authors also show that excitatory or inhibitory states can be reconstructed through a finite number of eigenfunctions and that these largely overlap with Laplacian eigenvectors of a connectivity matrix estimated from DWI imaging. Interestingly enough, and in line with our attempt at giving an unified view of the gradients and GSP methodologies, this approach linking neural field equations and Laplacian decomposition has been revisited in a GSP perspective in a recent publication 29 that introduce the Graph neural fields framework (see Table 1).…”

DotMotif: an open-source tool for connectome subgraph isomorphism search and graph queries

“…Our hope is that this tool and others like it will reduce the barrier-to-entry for researchers unacquainted with graph theory or graph databases, and will enable researchers to interrogate increasingly common connectome datasets with ease. Though the undirected graphs from the graph atlas study may not directly provide answers to open questions in neuroscience, this broad search can narrow down where it may be most impactful to dig deeper, perhaps leading to more interesting directed graph searches or neural simulations over smaller directed versions 55 . Such exhaustive motif searches may also enable better characterization of local network properties and dynamics 39 .…”

Resting brain activity emerges from wave propagating along spatiotemporal varying hyper-structural connectome

“…However, it should be noted that, although the proposed wave equation is capable of modeling the negative correlations between brain regions, in the present study, we obtain the sign matrix from the measured FC directly due to the inability of dMRI to measure directed interactions between brain regions. Alternative approaches such as using graph neural fields [41] and deep learning modeling [42] or developing optimal noninvasive in vivo imaging techniques with high spatial and temporal resolution [43].…”