Nonlinear Dynamical Modeling in the Spontaneous Brain Activity

Abstract

Nonlinear dynamics have also received much attention in recent years for the purpose of investigating the underlying mechanism in the brain. They have been successful to explain and predict the dynamics of brain. The development of the analysis of nonlinear dynamical systems has provided a strong tool to neuroscience to understand the brain. In this thesis, we propose several of models constructed at different levels to investigate the emergent of function in the cortical networks in the context of nonlinear dynamics. We also demonstrate that building a large-scale brain network from the small blocks can be useful for understanding the brain activity. Recently, the dynamics of spontaneous brain activity have generated considerable recent research interest in the various neuroscience fields including the computational neuroscience. It is important to study the endogenous brain activity because experiment and modeling studies show that the activity reflects the underlying structure, which can help understanding the relationship between structural and functional network. So we apply the developed computational modeling with a large scale brain network to study the spontaneous brain activity. We develop the building blocks for the whole brain modeling. Using a compartment model of a non-uniform axon, the information processing in a signal neuron is studied. We find that the transmission efficiency in these axons has nonlinear mode-locking structure that depends on the relative ion channel density. The refractory period of the soma is found to be longer than that of its axon and this structure appears by it. Our study suggests that in addition to just conduct electrical signals, non-uniform axons can actively participate in information processing. Connecting the building elements, we study noise-induced dynamics of the cortical brain network of a macaque monkey in context with a large-scale network. We model each node of the network with a sub-network of interacting FitzHugh-Nagumo (FHN) neurons. Recently, the study of comparing between anatomical and functional networks using a large-scale brain model has received considerable attention. The main goal of these studies is that how functional networks are self-organized and emerged from the underlying structures. In this study, we mainly focus on the role of noise intensity in forming a functional network, which is interrelated with the structural network. We find that the anatomical cortical brain network functions optimally at a certain noise intensity. We also study that the noise can induce the reconfiguration of the functional networks, which may affect the information processing in terms of the segregation and integration of information.In the last, we study the dynamics patterns in spontaneous neural activity, using the whole brain modeling includes a large-scale brain network. Functional MRI studies show that the spontaneous BOLD signals during the resting have the characteristics of ultraslow rhythms ($<0.1$Hz) and topologically anticorrelated relationship between some cortical areas. Some modeling studies demonstrate that the brain activity during the resting state can be represented as a set of multiple attractors and their activity is organized by transitions between attractors. In this thesis, we propose a model to explain the particular pattern in the brain during the resting state. We adapt a simplified Wilson-Cowan model, which can describe the transition of each area from up (active) and down (quiescent) states using a combination of excitation and inhibition populations. Also we extend this model to a network model. Thus we extend our model to random networks and modular networks and find that the activity of network can be split into two anticorrelated clusters because of the motifs includes most inhibition-dominant links. Our model may provide the framework for the spontaneous brain activity and suggest that the spontaneous brain activity is represented as a transition between stable fixed points, constrained by the brain network. We find that our model can provide a framework to understand the spontaneous brain activity and hope that our study benefits for modeling the brain activity during the resting state.