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. .

Background: Neuronal and circuit level abnormalities of excitation and inhibition are shown to be associated with tau and amyloid-beta (Aβ) in preclinical models of Alzheimer's disease (AD). These relationships remain poorly understood in patients with AD.Methods: Using empirical spectra from magnetoencephalography (MEG) and computational modeling (neural mass model; NMM) we examined excitatory and inhibitory parameters of neuronal subpopulations and investigated their specific associations to regional tau and Aβ, measured by positron emission tomography (PET), in patients with AD.Results: Patients with AD showed abnormal excitatory and inhibitory time-constants and neural gains compared to age-matched controls. Increased excitatory time-constants distinctly correlated with higher tau depositions while increased inhibitory time-constants distinctly correlated with higher Aβ depositions.Conclusions: Our results provide critical insights about potential mechanistic links between abnormal neural oscillations and cellular correlates of impaired excitatory and inhibitory synaptic functions associated with tau and Aβ in patients with AD.Funding: This study was supported by the National Institutes of Health grants: K08AG058749 (KGR), F32AG050434-01A1 (KGR), K23 AG038357 (KAV), P50 AG023501, P01 AG19724 (BLM), P50-AG023501 (BLM & GDR), R01 AG045611 (GDR); AG034570, AG062542 (WJ); NS100440 (SSN), DC176960 (SSN), DC017091 (SSN), AG062196 (SSN); a grant from John Douglas French Alzheimer's Foundation (KAV); grants from Larry L. Hillblom Foundation: 2015-A-034-FEL and (KGR); 2019-A-013-SUP (KGR); a grant from the Alzheimer's Association: (PCTRB-13-288476) (KAV), and made possible by Part the CloudTM, (ETAC-09-133596); a grant from Tau Consortium (GDR & WJJ), and a gift from the S. D. Bechtel Jr. Foundation.

The proposed approach is a statistical reconstruction approach based on a nonlinear forward model counting the full beam polychromaticity and applied directly to the projections without taking negative-log. Compared to the approaches based on linear forward models and the BHA correction approaches, it has advantages in noise robustness and reconstruction accuracy.