Brain connectivity is usually analyzed based on graph theory and pinning control theory. Previous studies suggested that the topological properties of structural and functional networks for brain networks may be altered in association with neurodegnerative diseases. To better understand and characterize these alterations, we introduce a new approach - robustness of network controllability to evaluate network robustness, and identify the critical nodes, whose removals maximally destroys the network’s functionality. These alterations are due to external or internal changes in the network. Understanding and describing these interactions at the level of large-scale brain circuitry may be a significant step towards unraveling dementia disease evolution. In this study, we analyze structural and functional brain networks for healthy controls, MCI and AD patients such that we reveal the connection between network robustness and architecture and the differences between patients’ groups. We determine the critical and driver nodes of these networks as the key components for robustness of network controllability. Our results suggest that healthy controls for both functional and structural connectivity have more critical nodes than AD and MCI networks, and that these critical nodes appear clustered in almost all networks. Our findings provide useful information for determining disease evolution in dementia under the aspects of controllability and robustness.
Brain networks can be naturally divided into clusters or communities where the cluster’s nodes dynamics have similar trajectories in phase space. This process is known as synchronization, and represents characteristics of intragroup features and not between groups. Fractional calculus represents a generalization of ordinary differentiation and integration to arbitrary non-integer order, and can be thought of as a smooth interpolation between different orders of differentiation/integration, providing the ability to probe the system from many different viewpoints of the dynamics. Fractional calculus has been explored as an excellent tool for the description of memory in many processes and may be more accurate for modeling brain processes than traditional integer-order ones. We apply the concept of cluster synchronization in fractional-order structural brain networks ranging from healthy controls to Alzheimer’s disease subjects and determine whether cluster synchronization can be achieved in these networks. We observe the existence of a hypersynchronization only in AD structural networks and consider that this could represent an excellent non-invasive biomarker for tracking the disease evolution and decide upon therapeutic interventions.
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