Spectral graph theory of brain oscillations

Abstract

The relationship between the brain's structural wiring and the functional patterns of neural activity is of fundamental interest in computational neuroscience. We examine a hierarchical, linear graph spectral model of brain activity at mesoscopic and macroscopic scales. The model formulation yields an elegant closed-form solution for the structurefunction problem, specified by the graph spectrum of the structural connectome's Laplacian, with simple, universal rules of dynamics specified by a minimal set of global parameters. The resulting parsimonious and analytical solution stands in contrast to complex numerical simulations of high dimensional coupled non-linear neural field models. This spectral graph model accurately predicts spatial and spectral features of neural oscillatory activity across the brain and was successful in simultaneously reproducing empirically observed spatial and spectral patterns of alpha-band (8-12 Hz) and beta-band (15-30Hz) activity estimated from source localized scalp magnetoencephalography (MEG). This spectral graph model demonstrates that certain brain oscillations are emergent properties of the graph structure of the structural connectome and provides important insights towards understanding the fundamental relationship between network topology and macroscopic whole-brain dynamics. Significance StatementThe relationship between the brain's structural wiring and the functional patterns of neural activity is of fundamental interest in computational neuroscience. We examine a hierarchical, linear graph spectral model of brain activity at mesoscopic and macroscopic scales. The model formulation yields an elegant closed-form solution for the structurefunction problem, specified by the graph spectrum of the structural connectome's Laplacian, with simple, universal rules of dynamics specified by a minimal set of global parameters. This spectral graph model demonstrates that certain brain oscillations are emergent properties of the graph structure of the structural connectome and provides important insights towards understanding the fundamental relationship between network topology and macroscopic whole-brain dynamics.

Functional harmonics reveal multi-dimensional basis functions underlying cortical organization

“…The link between structural and functional connectivity is made by dynamical models, which suggest that space and time are linked via the oscillatory frequencies of certain brain networks (Atasoy et al, 2018). Further evidence for a link between spatial patterns and oscillations comes from applications of harmonic modes of the structural connectivity to faster timescales (i.e., M/EEG) (Glomb et al, 2020;Tokariev et al, 2019;Raj et al, 2020).…”

Spectral graph theory of brain oscillations – revisited and improved

“…For this dataset, MEG, anatomical MRI, and diffusion MRI was collected for 36 healthy adult subjects (23 males, 13 females; 26 left-handed, 10 right-handed; mean age 21.75 years, age range 7-51 years). Data collection procedure has already been described previously [28]. All study procedures were approved by the institutional review board at the University of California at San Francisco and are in accordance with the ethics standards of the Helsinki Declaration of 1975 as revised in 2008.…”

“…Indeed, it has been suggested that brain-wide neural activity can be independent of microscopic local activity of individual neurons [21,22,17,6,23,13], and instead may be regulated by long-range structural connectivity [24][25][26][27]. Based on this hypothesis, Raj and colleagues had earlier developed a hierarchical, linear, analytic spectral graph theory model (SGM) which could accurately capture empirical MEG spectra and spatial distribution of alpha and beta frequency bands [28].…”

Stability and dynamics of a spectral graph model of brain oscillations

“…A modeling approach lying between these two extremities was only recently demonstrated by a linear biophysical model called the spectral graph theory model (SGM) that can accurately capture the wide-band static frequency spectra obtained from MEG. This model incorporates biophysics while maintaining parsimony and requiring minimal computation speed [35].…”