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 structure–function 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 nonlinear 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 (15–30 Hz) activity estimated from source localized 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. .
Highlights
It is considered paradigmatic in neuroscience that the brain's structure at various spatial scales is critical for determining its function
Network or graph, whose nodes represent gray matter regions, and whose edges have weights given by the structural connectivity (SC) of white matter fibers between them? We address this critical open problem here, as the structural and functional networks estimated at various scales are not trivially predictable from each other (Honey et al, 2009)
Since the spectral graph model (SGM) relies on connectome topology, we demonstrate in Figure 2 that different connectivity matrices produce different frequency responses: (a) the individual's structural connectivity matrix, (b) Human Connectome Project (HCP) average template connectivity matrix, (c) uniform connectivity matrix of ones, (d) a randomly generated matrix, (e) and (f) are randomly generated matrices with 75% and 95% sparsity respectively
Summary
It is considered paradigmatic in neuroscience that the brain's structure at various spatial scales is critical for determining its function. The traditional computational neuroscience paradigm at the microscopic scale does not extend to whole-brain macroscopic phenomena, as large neuronal ensembles exhibit emergent properties that can be unrelated to individual neuronal behavior (Abdelnour, Voss, & Raj, 2014; Destexhe & Sejnowski, 2009; Mišic et al, 2015; Mišic, Sporns, & McIntosh, 2014; Robinson, Rennie, Rowe, O'Connor, & Gordon, 2005; Shimizu & Haken, 1983), and are instead largely governed by long-range connectivity (Abdelnour, Raj, Dayan, & Devinsky, 2015a; Deco, Senden, & Jirsa, 2012; Jirsa, Jantzen, Fuchs, & Kelso, 2002; Nakagawa et al, 2014) At this scale, graph theory involving network statistics can phenomenologically capture structure–function relationships (Achard, Salvador, Whitcher, Suckling, & Bullmore, 2006; Bullmore, Bullmore, Sporns, & Sporns, 2009; Strogatz, 2001), but do not explicitly embody any details about neural physiology (Mišic et al, 2014; Mišic et al, 2015). In contrast to existing less parsimonious models in the literature that invoke spatially-varying parameters or local rhythm generators, to our knowledge, this is the first account of how the spectral graph structure of the structural connectome can parsimoniously explain the spatial power distribution of alpha and beta frequencies over the entire brain measurable on MEG
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