May 3 (Fri) @ 3:00pm: ”Reeb Graphs for Topological Connectomics,” S. Shailja, ECE PhD Defense

Abstract

The human brain, comprising billions of neurons, forms complex neural networks that are spatially distributed across various regions and change structurally over time. However, our understanding of the brain connectivity remains limited, lacking scalable quantifiers. Traditional methods, like the 2D adjacency matrices, oversimplify these connections and omit topological information, despite well documented topological deteriorations and irregularities associated with neurological and developmental disorders. This dissertation poses a central research question: Can we model the structural connections in brain networks in a scalable way to represent spatial information flow? Utilizing diffusion MRI data, this work introduces a novel Reeb graph-based method that efficiently encodes the topology and geometry of the brain’s white matter pathways. By defining the evolution of level sets, we re-bundle 3D trajectories of neuronal fiber pathways, capturing critical geometric events – akin to a brain fingerprint. This method proves valuable in detecting disease-related and age-dependent topology alterations in studies on Alzheimer’s and brain tumors. Beyond neuroscience, the approach has broader applications, demonstrated through the development of a general algorithm for discovering structure in spatio-temporal trajectories of human behavior, as recorded by GPS. This algorithm identifies deviations in human movement, signaling anomalies against normal activities. In summary, this thesis presents an extensive exploration of spatial Reeb graphs, detailing their implementation for spatiotemporal data and discussing their potential as general purpose tools for scalable trajectory modeling.

Bio

Shailja is a Ph.D. candidate in the Electrical and Computer Engineering Department at the University of California, Santa Barbara, advised by Prof. B. S. Manjunath. In 2016, she graduated with a Bachelor's degree from the Electrical Engineering Department at the Indian Institute of Technology, Kharagpur. Shailja joined UCSB in 2018 and received an M.Sc. in ECE from UCSB in 2020. In 2023, Shailja was awarded the Fiona and Michael Goodchild best graduate student mentor award. She has also been named an NSF iRedefine ECE Fellow. Shailja’s research vision is to model multi-modal healthcare data for precise diagnostics using AI and integration of domain knowledge to “close-the-loop” between surgeons, research scientists, and engineers.

Hosted by: Professor B. S. Manjunath

Submitted by: Shailja <shailja@ucsb.edu>