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Brain anomaly networks uncover heterogeneous functional reorganization patterns after stroke
Stroke has a large physical, psychological, and financial burden on patients, their families, and society. Based on functional networks (FNs) constructed from resting state fMRI data, network connectivity after stroke is commonly conjectured to be more randomly reconfigured. We find that this hypothesis depends on the severity of stroke. Head movement-corrected, resting-state fMRI data were acquired from 32 patients after stroke, and 37 healthy volunteers. We constructed anomaly FNs, which combine time series information of a patient with the healthy control group. We propose data-driven techniques to automatically identify regions of interest that are stroke relevant. Graph analysis based on anomaly FNs suggests consistently that strong connections in healthy controls are broken down specifically and characteristically for brain areas that are related to sensorimotor functions and frontoparietal control systems, but new links in stroke patients are rebuilt randomly from all possible areas. Entropic measures of complexity are proposed for characterizing the functional connectivity reorganization patterns, which are correlated with hand and wrist function assessments of stroke patients and show high potential for clinical use.
Fully solvable lower dimensional dynamics of Cartesian product of Kuramoto models
Implementing a positive correlation between the natural frequencies of nodes and their connectivity on a single star graph leads to a pronounced explosive transition to synchronization, additionally presenting hysteresis behavior. From the viewpoint of network connectivity, a star has been considered as a building motif to generate a big graph by graph operations. On the other hand, we propose to construct complex synchronization dynamics by applying the Cartesian product of two Kuramoto models on two star networks. On the product model, the lower dimensional equations describing the ensemble dynamics in terms of collective order parameters are fully solved by the Watanabe-Strogatz method. Different graph parameter choices lead to three different interacting scenarios of the hysteresis areas of two individual factor graphs, which further change the basins of attraction of multiple fixed points. Furthermore, we obtain coupling regimes where cluster synchronization states are often present on the product graph and the number of clusters is fully controlled. More specifically, oscillators on one star graph are synchronized while those on the other star are not synchronized, which induces clustered state on the product model. The numerical results agree perfectly with the theoretic predictions. © 2019 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft.