Functional brain connectivity is predictable from anatomic network's Laplacian eigen-structure

Abstract

How structural connectivity (SC) gives rise to functional connectivity (FC) is not fully understood. Here we mathematically derive a simple relationship between SC measured from diffusion tensor imaging, and FC from resting state fMRI. We establish that SC and FC are related via (structural) Laplacian spectra, whereby FC and SC share eigenvectors and their eigenvalues are exponentially related. This gives, for the first time, a simple and analytical relationship between the graph spectra of structural and functional networks. Laplacian eigenvectors are shown to be good predictors of functional eigenvectors and networks based on independent component analysis of functional time series. A small number of Laplacian eigenmodes are shown to be sufficient to reconstruct FC matrices, serving as basis functions. This approach is fast, and requires no time-consuming simulations. It was tested on two empirical SC/FC datasets, and was found to significantly outperform generative model simulations of coupled neural masses.

Spectral graph theory of brain oscillations

“…These eigen-relationships arise naturally from a biophysical abstraction of fine-scaled and complex brain activity into a simple linear model of how mutual dynamic influences or perturbations can spread within the underlying structural brain network, a notion that was advocated previously 30,42,43 . We had previously reported that the brain network Laplacian can be decomposed into its constituent "eigenmodes", which play an important role in both healthy brain function 30,31,[44][45][46] and pathophysiology of disease 44,[47][48][49] .…”

“…At this scale, graph theory involving network statistics can phenomenologically capture structure-function relationships [23][24][25] , but do not explicitly embody any details about neural physiology 14,15 . Strong correlations between functional and structural connections have also been observed at this scale 3,[26][27][28][29][30][31][32] , and important graph properties are shared by both SC and functional connectivity (FC) networks, such as small worldness, power-law degree distribution, hierarchy, modularity, and highly connected hubs 24,33 .…”

Longitudinal increases in structural connectome segregation and functional connectome integration are associated with better recovery after mild TBI

“…Some of the main goals in joint structure–function modeling are to increase the accuracy of noisy connectivity measurements, identify function‐specific subnetworks (Chu, Parhi, & Lenglet, ) or to predict one modality from the other (Honey et al, ). One recent publication with the goal of predicting function from structure used the network diffusion (ND) model (Abdelnour, Dayan, Devinsky, Thesen, & Raj, ; Abdelnour, Voss, & Raj, ), which assumes functional activation diffuses along white matter connections. This model is linear, has a simple, closed‐form solution and only one tuning parameter, making it computationally more tractable and less prone to overfitting than, for example, high‐dimensional, nonlinear neural mass models.…”

“…Some of the main goals in joint structurefunction modeling are to increase the accuracy of noisy connectivity measurements, identify function-specific subnetworks or to predict one modality from the other (Honey et al, 2009). One recent publication with the goal of predicting function from structure used the network diffusion (ND) model (Abdelnour, Dayan, Devinsky, Thesen, & Raj, 2018;Abdelnour, Voss, & Raj, 2014), which assumes functional activation diffuses along white matter connections.…”

Using structural connectivity to augment community structure in EEG functional connectivity

“…Understanding how flexible macroscopic functional architecture arises from the stable scaffold of anatomical white matter fiber tracts in the brain is a major field of inquiry in neuroscience. This has been investigated via the relationship between structural and functional connectivity (SC and FC, respectively) between brain regions in fMRI and MEG (Abdelnour, Dayan, Devinsky, Thesen, & Raj, 2018;Atasoy, Donnelly, & Pearson, 2016;Cabral et al, 2014;Damoiseaux & Greicius, 2009;Deco et al, 2013;Glomb, Ponce-Alvarez, Gilson, Ritter, & Deco, 2017;Goñi et al, 2014;Hagmann et al, 2008;Honey et al, 2009;Meier et al, 2016;Tewarie et al, 2019Tewarie et al, , 2014Vincent et al, 2007) . Concurring findings from these studies show that FC between regions of interest (ROIs)/sources located in the gray matter is in part shaped by anatomical connections of the SC, such that the strength of SC (fiber count, density) is predictive to some degree of the strength of FC (correlation, coherence, etc.)…”