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, and show that the model equilibrium fluctuations can reproduce the empirically observed harmonic power spectrum of BOLD fMRI data. 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.Author summaryThe human brain can be seen as an interconnected network of many thousands neuronal “populations”; in turn, each population contains thousands of neurons, and each is connected both to its neighbors on the cortex, and crucially also to distant populations thanks to long-range white matter fibers. This extremely complex network, unique to each of us, is known as the “human connectome graph”. In this work, we develop a novel approach to investigate how the neural activity that is necessary for our life and experience of the world arises from an individual human connectome graph. For the first time, we implement a mathematical model of neuronal activity directly on a high-resolution connectome graph, and show that it can reproduce the spatial patterns of activity observed in the real brain with magnetic resonance imaging. This new kind of model, made of equations implemented directly on connectome graphs, could help us better understand how brain function is shaped by computational principles and anatomy, but also how it is affected by pathology and lesions.

Diffusion-Informed Spatial Smoothing of fMRI Data in White Matter Using Spectral Graph Filters

“…When structural connectomes are interpreted as graphs, a number of their Laplacian eigenvectors manifest spatial patterns that are reminiscent of well-established functional networks, as shown by Atasoy et al (2016). Under this framework, methods have been proposed for spatio-temporal deconvolution of fMRI data (Bolton et al, 2019), quantification of the coupling strength of resting-state fMRI data with underlying structure (Medaglia et al, 2018;Preti and Van De Ville, 2019), implementation of neural field models (Aqil et al, 2020), prediction of brain disorders (Itani and Thanou, 2020) or behaviorally relevant scores (Bolton and van De Ville, 2020), and for characterization of functional connectivity dynamics in health (Huang et al, 2018b), and its changes, for instance, due to concussion (Sihag et al, 2020), and under hallucinogenic drugs (Atasoy et al, 2017).…”

Diffusion-informed spatial smoothing of fMRI data in white matter using spectral graph filters

“…When structural connectomes are interpreted as graphs, a number of their Laplacian eigenvectors manifest spatial patterns that are reminiscent of well-established functional networks, as shown by Atasoy et al (2016) . Under this framework, methods have been proposed for spatio-temporal deconvolution of fMRI data ( Bolton et al, 2019 ), quantification of the coupling strength of resting-state fMRI data with underlying structure ( Medaglia et al, 2018 ; Preti and Van De Ville, 2019 ), implementation of neural field models ( Aqil et al, 2021 ), prediction of brain disorders ( Itani and Thanou, 2020 ) or behaviorally relevant scores (Bolton and van De Ville, 2020), and for characterization of functional connectivity dynamics in health ( Huang et al, 2018b ), and its changes, for instance, due to concussion ( Sihag et al, 2020 ), and under hallucinogenic drugs ( Atasoy et al, 2017 ).…”

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 the Laplacian eigenvectors of a connectivity matrix estimated from DWI. Interestingly enough, and in line with our attempt at giving a 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 (Aqil, Atasoy, Kringelbach, & Hindriks, 2020) introducing the graph neural fields framework (see Table 1).…”