CAREER: Topology-Driven Learning for Biomedical Imaging Informatics

Suny At Stony Brook, Stony Brook NY

Investigators

Abstract

This award is funded in whole or in part under the American Rescue Plan Act of 2021 (Public Law 117-2). Thanks to decades of technology development, scientists are now able to visualize in high quality complex biomedical structures such as neurons, vessels, trabeculae and breast tissues. These complex and dynamic structures encode important information about underlying biological mechanisms. Innovative approaches are needed to fully exploit these structures and to predict biological and clinical outcomes. By identifying crucial structural patterns, scientists can better explain disease progression and discover novel structure-informed diagnosis and prognosis biomarkers. The challenge is that the structures are often highly complex in geometry and topology, and highly variable. Topology is the branch of abstract mathematics that deals with structures such as connections and loops; this project combines advanced mathematical theory from topology (in particular, persistent homology) and modern deep learning to develop novel methodology for accurate reconstruction and analysis of these complex, dynamic and heterogeneous biomedical structures. The outcome of the project will not only generate novel learning methods that are better suited for these topology-rich structures, but also advance the understanding of the functionality of different biomedical structural systems. This project also trains the next generation of researchers and educators through a carefully integrated educational and outreach plan. By implementing a Play-With-Data (PWD) principle, the investigator will engage students and the public through direct interactions with real-world data. The goal of this project is to create a foundational topology-driven learning paradigm for biomedical structures, including segmentation, generation, and analysis. Using the theory of persistent homology, which provides robust and differentiable representations involving topology, the investigator will (1) explicitly capture and reason in a topological feature space, and (2) seamlessly incorporate topological reasoning into modern learning in an end-to-end fashion, so that critical topological patterns can be learned in a data-driven and task-driven manner. Technical contributions are proposed to address key theoretical and algorithmic challenges in formulating topological information as a topological loss. The loss is used to train image-segmentation models with high topological accuracy, which is crucial for structural analysis. The investigator will also develop topology-aware deep generative models that can learn topology from the real data. Novel topological representation and learning algorithms will be developed to fully exploit the topology-rich structures and identify crucial patterns differentiating populations. The investigator will also investigate new time-varying topology representations and address the challenging problem of learning the dynamics. The resulting techniques and software will be validated on public datasets and real-world biomedical problems. The methods to be developed are general and will impact data from other scientific domains, such as ecology and geographic information science, where intrinsic complex and dynamic structures exist. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.