Topological characterizations of neuronal fibers​

Topological characterizations of neuronal fibers​

The human brain consists of billions of neurons that form functional neural networks across different brain regions. Brain functions involve complex interactions between these regions that are poorly understood and lack quantitative characterizations. So, a natural question to ask is: Can we spatially model the information flow in the complex brain networks? Existing methods model the neural connections with connectivity matrices that overlook the topology of connections and oversimplify the network complexity to 2D matrices. Modeling the topology of brain connections can be transformative in understanding neurological disorders and can also explain information flow in neural networks. Towards that end, I will present a new computational geometry perspective to discover the complex network topology in the brain. For this, I will describe the development of a sub-trajectory clustering problem that constructs Reeb graphs as evolution of level sets in 3D.