The central nervous system coordinates many neural subpopulations connected via macroscale white matter architecture and surface cortical connections to produce complex behavior depending on environmental cues. The activity occurs over different scales, from information transfer between individual neurons at the synapse level, to macroscale coordination of neural populations used to maximize information transfer between specialized brain regions. The whole brain activity measured through functional Magnetic Resonance Imaging (fMRI), allows us to observe how these large neural populations interact over time. Researchers have developed a set of Brain Network Models (BNMs), that simulate brain activity using the macroscale structure and different mathematical models to represent populational neural activity. These simulations have been able to reproduce properties of fMRI especially those averaged over long periods of time. These models represent a step towards an individualized model of brain activity, which is of clinical interest, as they can be constructed from individual estimates of the structural network. To find a good BNM to fit the individual fMRI data, however, is a difficult problem as BNMs represent a large family of mathematical models. Moreover, a large set of BNMs have reproduced time averaged metrics that have been used so far to compare the models with the fMRI data. In this thesis, we extend previous work on BNM research by establishing new dynamic metrics that would allow us to better differentiate between BNMs simulations on how well they reproduce measured fMRI dynamics (Chapter 2). In Chapter 3, we directly compare transient short-term trajectories by synchronizing the outputs of a BNM in relation to observed fMRI timeseries using a novel Machine Learning Algorithm, Neural Ordinary Differential Equations (ODE). Finally, we show that the Neural ODE can be used as its own stand-alone generative model and is able to simulate more realistic fMRI signals as they are able to reproduce complex metrics that previous models have not been able to recapitulate (Chapter 4). In short, we demonstrate that we have made progress in developing and quantifying BNMs and advanced the research of more realistic whole brain simulations.Ph.D
