Topological Data Analysis for Brain Network Dynamics

Recent developments in brain imaging techniques have expanded the size, scope and complexity of high temporal resolution neural data. These novel powerful techniques and methodologies measure the connections and interactions between the elements of neurobiological systems. The mathematical formalism of the graph theory and the network science play a vital role in understanding the interconnected architecture of the brain. One can model network dynamics of the brain by considering levels of activity in order to describe how a brain network evolves into another. The aim in this project is to apply the tools from topological data analysis (TDA) to discover meaningful patterns of neural network dynamics. TDA methods have ability to combine the best features of different methods such as principal component and cluster analyses to provide geometric representation of complex data sets. These methods have previously been used to stratify disease states, identify patient subgroups, conduct proteomics analyses and compare brain morphology. They stand promising for applications in dynamic networks. We intend to investigate the temporal dynamics of brain networks using the two main TDA methods: (i) Mapper algorithm and (ii) Persistent Homology. We will use these methods under different parameters and metrics to determine the patterns of temporal dynamics in a magnetoencephalography (MEG) data provided by The Human Connectome Project. Specifically, we are going to test if the emergence of cognitive control in fronto-parietal circuitry increases or decreases with the change of certain network parameters such as the receive centrality and the broadcast centrality.