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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. .

Attention deficit hyperactivity disorder (ADHD) is a prevalent childhood neurodevelopmental disorder. Given the profound brain changes that occur during childhood and adolescence, it is important to examine longitudinal changes of both functional and structural brain connectivity across development in ADHD. This study aimed to examine the development of functional and structural connectivity in children with ADHD compared to controls using graph metrics. One hundred and seventy five individuals (91 children with ADHD and 84 non‐ADHD controls) participated in a longitudinal neuroimaging study with up to three waves. Graph metrics were derived from 370 resting state fMRI (197 Control, 173 ADHD) and 297 diffusion weighted imaging data (152 Control, 145 ADHD) acquired between the ages of 9 and 14. For functional connectivity, children with ADHD (compared to typically developing children) showed lower degree, local efficiency and betweenness centrality predominantly in parietal, temporal and visual cortices and higher degree, local efficiency and betweenness centrality in frontal, parietal, and temporal cortices. For structural connectivity, children with ADHD had lower local efficiency in parietal and temporal cortices and, higher degree and betweenness centrality in frontal, parietal and temporal cortices. Further, differential developmental trajectories of functional and structural connectivity for graph measures were observed in higher‐order cognitive and sensory regions. Our findings show that topology of functional and structural connectomes matures differently between typically developing controls and children with ADHD during childhood and adolescence. Specifically, functional and structural neural circuits associated with sensory and various higher order cognitive functions are altered in children with ADHD. [ABSTRACT FROM AUTHOR]

Traumatic brain injury (TBI) is a major public health problem. Caused by external mechanical forces, a major characteristic of TBI is the shearing of axons across the white matter, which causes structural connectivity disruptions between brain regions. This diffuse injury leads to cognitive deficits, frequently requiring rehabilitation. Heterogeneity is another characteristic of TBI as severity and cognitive sequelae of the disease have a wide variation across patients, posing a big challenge for treatment. Thus, measures assessing network‐wide structural connectivity disruptions in TBI are necessary to quantify injury burden of individuals, which would help in achieving personalized treatment, patient monitoring, and rehabilitation planning. Despite TBI being a disconnectivity syndrome, connectomic assessment of structural disconnectivity has been relatively limited. In this study, we propose a novel connectomic measure that we call network normality score (NNS) to capture the integrity of structural connectivity in TBI patients by leveraging two major characteristics of the disease: diffuseness of axonal injury and heterogeneity of the disease. Over a longitudinal cohort of moderate‐to‐severe TBI patients, we demonstrate that structural network topology of patients is more heterogeneous and significantly different than that of healthy controls at 3 months postinjury, where dissimilarity further increases up to 12 months. We also show that NNS captures injury burden as quantified by posttraumatic amnesia and that alterations in the structural brain network is not related to cognitive recovery. Finally, we compare NNS to major graph theory measures used in TBI literature and demonstrate the superiority of NNS in characterizing the disease. [ABSTRACT FROM AUTHOR]