Atividade síncrona em redes complexas: uma abordagem matemática para estudos sobre epilepsia

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Universidade Federal de Goiás


Synchronization in complex networks is a phenomenon present in several complex systems, ranging from neurological to electrical and mechanical to social. The most successful archetype in describing the emergence of this collective behavior in complex systems is provided by Kuramoto model. Neurological disorders such as epilepsy can be abstracted mathematically as synchronous activities in complex networks. Epilepsy is a neural disorder related to the intense synchronous neural activities due to the increase of blood flow in the cerebral cortex, causing seizures followed by fainting. Seizures can be prevented by antiepileptic drugs that fend off the emergence of synchrony in neural networks. However, about a third of medicated patients experience seizures again. Thus, the importance of studies on the recognition of synchronous patterns associated with the disorder is justified. This work does not claim to be an ultimate in the modeling of such a complex neural disorder. Therefore, the objective is to investigate which are the most influential areas of the cerebral cortex and how they influence the dynamics of synchronization associated with epilepsy. To this end, a feline's cerebral cortex was modeled as a complex network and, in order to study synchronization, Kuramoto model was used to govern of the dynamics between the areas of the cortex. The Hypertext Induced Topic Search (HITS) algorithm was used to classify pages web, in order to identify the most influential nodes in the feline cerebral cortex network. Metrics concerning the characteristics of the feline neural network and its most influential nodes, were obtained. Regarding the dynamics and measures of global, mesoscopic and microscopic synchrony, results were obtained for a scenario using the original network and two other scenarios, in which it was considered a disturbance, in order to simulate the action of an antiepileptic drug, the disturbance reduced the intensity of connections of a group containing random nodes and the group with nodes chosen by the HITS algorithm by 50%. Finally, it was found that the applied disturbance lagged the global, microscopic and mesoscopic levels of the network.



Algoritmo HITS, Modelo de Kuramoto, Neurociência computacional, Redes complexas, Sincronização, Complex networks, Computational neuroscience, HITS algorithm, Kuramoto model, Synchronization


OLIVEIRA, J. F. Atividade síncrona em redes complexas: uma abordagem matemática para estudos sobre epilepsia. 2021. 87 f. Dissertação (Mestrado em Modelagem e Otimização) - Universidade Federal de Goiás, Catalão, 2021.