Gradients of connectivity as graph Fourier bases of brain activity

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 on the other on 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. If results are promising in terms of interpretability and functional relevance, 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.

Distributed harmonic patterns of structure-function dependence orchestrate human consciousness

“…Recall that formally, the progression from low- to high-frequency connectome harmonics reflects increasing decoupling of functional brain activity from the underlying structural connectivity 53 , 76 , 77 (Fig. 1 ).…”

“…Similarly to the Fourier transform for the time domain, applications include filtering and spectral analysis 52 – 54 . The approach has found increasing application in neuroscience, albeit with a wide variety of names and mathematical operationalisations 53 . Graph Signal Processing is also mathematically and conceptually related to Graph Spectral Theory, which is primarily used for dimensionality reduction of graph-based data, including the well-known principal gradient of functional connectivity introduced by Margulies 55 , and subsequent applications to structural, microstructural, and other forms of connectivity 56 , 57 ; being nonlinear, this graph-based approach can provide a superior characterisation than what is obtained from linear approaches such as Independent Components Analysis and Principal Components Analysis 53 , 58 .…”

“…This latter approach has found increasing traction as a way to complement traditional analyses based on spatially localised regions-of-interest. In the words of Lioi and colleagues’ authoritative review on this topic: “Some processes may be best characterized in terms of nonoverlapping fixed regions, others in terms of delocalized, overlapping eigenmodes” 53 .…”

Mapping Pharmacologically-induced Functional Reorganisation onto the Brain’s Neurotransmitter Landscape

“…We then employed diffusion map embedding, a nonlinear manifold learning technique based on the graph Laplacian 140, 254 , to obtain a low dimensional representation of the joint drug- and disorder-susceptibility. A single parameter α controls the influence of the sampling density on the manifold (α = 0, maximal influence; α = 1, no influence).…”

Graph-LDA: Graph Structure Priors to Improve the Accuracy in Few-Shot Classification

“…However it is often possible to use other imaging techniques, as well as previous studies, to build a graph that models dependencies between brain areas [23]. Several prior studies have shown the potential of using transfer learning [24,25] or GSP to analyze fMRI data [26,27], resulting in better classification of signals using subsets of the obtained features [28,29,30].…”