Synchronization and traveling wave classification in hippocampal network

Abstract

In this dissertation, we investigate the influence of the radius of connection and the coupling strength on the synchronization and the emergence of traveling waves in a hippocampal layer of excitatory neurons. The electrical activity of each neuron is given by the adaptive exponential integrate-and-fire model. We noticed that for some values of connection radius, the coupling strength greatly influences the dynamics exhibited in the network. For some values spike synchronization is achieved, however, by increasing the coupling strength for higher values the network starts to display bursting activity. For specific values of coupling strength burst synchronization is observed, a state associated with epileptic seizures. Therefore, the radius of connection and coupling strength controls the firing pattern and the synchronization of action potentials. An interesting spatial pattern that emerges in our neuronal network is the traveling waves. Such waves are present in different regions of the brain and are related to diverse cognitive tasks for instance spatial information and memory. Thus, understanding the factors that give rise to such phenomena is crucial for better insight into brain signaling. We observe that the hippocampal excitatory layer generates diverse wave patterns from ring-shaped waves to spiral waves. Spiral wave pattern is not fully understood, however, it is theorized that such wave modulates the activation and deactivation of some brain regions during cognitive tasks. We show that spiral waves emerge in our network for a vast range of connection radius and coupling strength. Motivated by the lack of simple and reliable methods for quantitatively detecting spiral waves we develop a novel and trustworthy method based on synchronization tools for measuring spiral waves. We show that spiral wave patterns are strongly dependent on the radius of connection and also on the initial conditions considered. We show that for some values of radius of connection and coupling strength, wave pattern and synchronous bistable regimes are observable.