Dynamical Graph Theory Networks Methods for the Analysis of Sparse Functional Connectivity Networks and for Determining Pinning Observability in Brain Networks - Meyer-Bäse, Anke; Roberts, Rodney G.; Illan, Ignacio A.; Meyer-Bäse, Uwe; Lobbes, Marc; Stadlbauer, Andreas; Pinker-Domenig, Katja (Frontiers in Computational Neuroscience, 2017)
Neuroimaging in combination with graph theory has been success- ful in analyzing the functional connectome. However almost all anal- ysis are performed based on static graph theory. The derived quan- titative graph measures can only describe a snap shot of the disease over time. Neurodegenerative disease evolution is poorly understood and treatment strategies are consequently only of limited efficiency. Fusing modern dynamic graph network theory techniques and mod- eling strategies at different time scales with pinning observability of complex brain networks will lay the foundation for a transformational paradigm in neurodegnerative diseases research regarding disease evo- lution at the patient level, treatment response evaluation and revealing some central mechanism in a network that drives alterations in these diseases. We model and analyze brain networks as two-time scale sparse dynamic graph networks with hubs (clusters) representing the fast sub-system and the interconnections between hubs the slow sub- system. Alterations in brain function as seen in dementia can be dy- namically modeled by determining the clusters in which disturbance inputs have entered and the impact they have on the large-scale de- mentia dynamic system. Observing a small fraction of specific nodes in dementia networks such that the others can be recovered is accom- plished by the novel concept of pinning observability. In addition, how to control this complex network seems to be crucial in understanding the progressive abnormal neural circuits in many neurodegenerative diseases. Detecting the controlling regions in the networks, which serve as key nodes to control the aberrant dynamics of the networks to a desired state and thus influence the progressive abnormal behavior, will have a huge impact in understanding and developing therapeutic solutions and also will provide useful information about the trajectory of the disease. In this paper, we present the theoretical framework and derive the necessary conditions for (1) area aggregation and time-scale mod- eling in brain networks and for (2) pinning observability of nodes in dynamic graph networks. Simulation examples are given to illustrate the theoretical concepts.