AitF: Collaborative Research: Topological Algorithms for 3D/4D Cardiac Images: Understanding Complex and Dynamic Structures

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The interiors of ventricles of a human heart are spanned by a fine net of muscle fibers that are difficult to resolve, even in high resolution CT images. An accurate account of these structures, however, could improve diagnosis of cardiac disease, evaluation of cardiac function, assessment of stroke risk, and simulation of cardiac blood flow. Topology is the branch of abstract mathematics that deals with connections; this project uses the theory of persistent homology to identify crucial topological handles that can be useful for accurate reconstruction and analysis of the complex cardiac dynamics from these CT images. The outcome of the project will not only advance our understanding of cardiac function, but also generate novel computational topology methods that are more efficient and effective for practical applications. This project not only bridges the gap between the theory of computational topology and the practical problem of cardiac image analysis, but also trains the next generation of researchers and educators to do so by a carefully integrated education plan. The PIs will engage undergraduate students, high school students, women and other underrepresented students in their proposed research.The goal of this project is to develop a topological approach to unveil the intrinsic structures from complex and dynamic 3D/4D cardiac data, and furthermore, to provide principled tools to quantitatively analyze these structures. The PIs will create new computational topology methodologies and algorithms to extract rich information from the intrinsic structure of cardiac data. They will develop novel methodologies to extract localized topological features and to track them based on their spatial and temporal coherence. They also plan to design new algorithms to untangle ambiguous and uncertain situations for tracking structures through time sequence data. The resulting techniques and software will be validated on cardiac CT data to produce quantitative assessments of accuracy and to characterize the advantages and limitations of these approaches. Domain experts will validate the quality of the approaches via scientific hypotheses and data exploration. The methods to be developed are general and will impact other scientific fields where intrinsic complex and dynamic structures exist.