AF: Small: Algorithms in Computational Geometry and Medical Applications

University Of Notre Dame, Notre Dame IN

Investigators

Abstract

Modern medical research and imaging technologies together present physicians and clinicians with mind-boggling amounts of detailed molecular or cellular structures. For example, one 2-dimensional image slide can contain millions of cells. In fact, pathologists use microscopes to examine only tens or hundreds of cells at a time, missing most cells, and also missing possible patterns in the intermediate range. This project addresses the need to study patterns in cell images through powerful computational and analytic techniques in computational geometry, and to validate these algorithmic techniques, and software built from them, in medical research and applications. The project formulates challenging geometric and algorithmic problems that emerge in the diagnosis, prognosis, and analysis of diseases (e.g., breast cancer, inflammatory bowel disease, and rheumatoid arthritis), identification and classification of different types of immune cells (e.g., neutrophils, eosinophils, plasma cells, and lymphocytes), and tracking and analysis of collectively moving and swarming bacteria (e.g., Myxococcus xanthus and Pseudomonas aeruginosa) in terms of a class of Voronoi diagrams (developed by the lead investigator) in which collections of cells influence nearby neighbors. Specific geometric techniques include clustering-induced Voronoi diagrams, coupled optimal shape approximation, and matching based on earth mover's distance. Exploring these geometric structures in important medical problems will not only lead to new methods in combinatorial optimization and machine learning, and new publically-available software for medical applications, but also train students in the broad range of interdisciplinary research and education from geometric algorithms, software development, to medical applications. By providing appropriate analysis tools for the physicians, this project and its students will help save lives.