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The Geometry of Cardiac Myofibers

Emmanuel Piuze-Phaneuf:
McGill University and University of Copenhagen

April 27, 2015 at  10:00 AM

ABSTRACT: Cardiac medical imaging technology has made significant advances over the last decades. By fusing information coming from complementary image modalities, such as magnetic resonance imaging (MRI) and computed tomography (CT), we can now build comprehensive atlases of the macro and microstructure of the heart. Yet, cardiovascular diseases are the leading cause of death in the world. For treatment plans to be effective, this extensive amount of information has to be processed in ways that can be useful for clinicians. In particular, the development of better computational tools for the analysis of cardiac images will provide additional support and guidance for cardiac clinicians through measures which are more precise, comprehensive, and deterministic than what is currently achievable. The analysis of cardiac muscle fibers is of particular interest since they play a key role in the mechanical function, electrophysiology and remodeling processes of the heart. Current models of heart wall fibers can be useful from an educational perspective but lack in precision and clinical practicality. In this thesis we develop novel computational tools for the analysis and processing of cardiac fiber data. Each modeled fiber is equipped with an orthonormal frame and its differential geometry is analyzed comprehensively via the method of moving frames. This allows us to go beyond current models of fiber organization, and also provides a rich geometrical interpretation. Methods are developed for estimating a variety of differential descriptors in local neighborhoods based on connection forms of the cardiac frame field, including a finite differencing scheme, an optimization scheme, and a novel closed-form solution. These methods are then applied to a statistical analysis of heart fiber geometry, conducted by studying connection forms of the frame field. Our results corroborate state of the art characterizations of muscle fiber orientation in the heart wall, and also provide a novel geometrical interpretation which has not yet been reported in the literature. In adition, we apply our methods to construct population atlases of cardiac fiber variation, and to completely reconstruct damaged or missing data in cardiac diffusion volumes. Our work could have many practical uses, including a deeper understanding of cardiac structure, the reconstruction of fiber patterns in ventricular restoration and tissue bioengineering, tools for differentiating between normal and pathological tissue, the integration of fiber geometry into patient-specific models, and the monitoring of changes in heart wall structure in studies of cardiac development and aging.