Gradients of connectivity as graph Fourier bases of brain activity.

Giulia Lioi,Abdelbasset Brahim,François Rousseau,Nicolas Farrugia,Vincent Gripon

doi:10.1162/netn_a_00183

Abstract

The application of graph theory to model the complex structure and function of the brain has shed new light on its organization, prompting the emergence of network neuroscience. Despite the tremendous progress that has been achieved in this field, still relatively few methods exploit the topology of brain networks to analyze brain activity. Recent attempts in this direction have leveraged on the one hand graph spectral analysis (to decompose brain connectivity into eigenmodes or gradients) and the other graph signal processing (to decompose brain activity “coupled to” an underlying network in graph Fourier modes). These studies have used a variety of imaging techniques (e.g., fMRI, electroencephalography, diffusion-weighted and myelin-sensitive imaging) and connectivity estimators to model brain networks. Results are promising in terms of interpretability and functional relevance, but methodologies and terminology are variable. The goals of this paper are twofold. First, we summarize recent contributions related to connectivity gradients and graph signal processing, and attempt a clarification of the terminology and methods used in the field, while pointing out current methodological limitations. Second, we discuss the perspective that the functional relevance of connectivity gradients could be fruitfully exploited by considering them as graph Fourier bases of brain activity.

Highlights

Modern attempts at understanding brain function have leveraged the use of graph theory to grasp complex properties of neuronal networks, giving rise to the field of network neuroscience (Bassett & Sporns, 2017; Sporns, 2017)
In this paper we provided an overview of work that applied Laplacian spectral decomposition and graph signal processing (GSP) to analyze brain signals
We attempted to elucidate terminology and related approaches used in the “brain gradients” and GSP communities, systematically describing recent promising results

Summary

Introduction

Modern attempts at understanding brain function have leveraged the use of graph theory to grasp complex properties of neuronal networks, giving rise to the field of network neuroscience (Bassett & Sporns, 2017; Sporns, 2017). Despite the tremendous progress that has been achieved in network neuroscience, surprisingly relatively few methods such as graph signal processing (GSP; Shuman, Narang, Frossard, Ortega, & Vandergheynst, 2013) exploit brain connectivity (i.e., take into account the topology of brain networks) to characterize brain activity (Ju & Bassett, 2020). Increasing evidence of the functional relevance of these spectral components of brain networks Increasing evidence of the functional relevance of these spectral components of brain networks (i.e., connectivity gradients, eigenmodes, or harmonics; Atasoy, Donnelly, & Pearson, 2016; Belkin & Niyogi, 2003; W. Huang et al, 2016; see Table 1), has recently been shown with

Objectives

Methods

Conclusion