Characterizing Brain Network Dynamics using Persistent Homology in Patients with Refractory Epilepsy

Epilepsy is a common serious neurological disorder that affects more than 65 million persons worldwide and it is characterized by repeated seizures that lead to higher mortality and disabilities with corresponding negative impact on the quality of life of patients. Network science methods that represent brain regions as nodes and the interactions between brain regions as edges have been extensively used in characterizing network changes in neurological disorders. However, the limited ability of graph network models to represent high dimensional brain interactions are being increasingly realized in the computational neuroscience community. In particular, recent advances in algebraic topology research have led to the development of a large number of applications in brain network studies using topological structures. In this paper, we build on a fundamental construct of cliques, which are all-to-all connected nodes with a k-clique in a graph G (V, E), where V is set of nodes and E is set of edges, consisting of k-nodes to characterize the brain network dynamics in epilepsy patients using topological structures. Cliques represent brain regions that are coupled for similar functions or engage in information exchange; therefore, cliques are suitable structures to characterize the dynamics of brain dynamics in neurological disorders. We propose to detect and use clique structures during well-defined clinical events, such as epileptic seizures, to combine non-linear correlation measures in a matrix with identification of geometric structures underlying brain connectivity networks to identify discriminating features that can be used for clinical decision making in epilepsy neurological disorder.