Combining Diffeomorphic Matching with Image Sequence Intensity Registration
Freeman, Jeffrey 1985-
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This thesis presents the research work completed over the past 4 years in the context of a collaborative project between The Methodist Hospital (TMH) and the University of Houston. We have developed and implemented novel algorithmic approaches to: develop patient-specific static mitral valve models from tagged 3D-Echocardiographic image data; incorporate this 3D-Echo data into a new methodology for diffeomorphic valve tracking; and investigate the strain distributions on valve leaflets derived from the deformations captured through valve tracking. First, we have applied spline techniques in order to generate static models of the mitral valves at discrete instants. Classical smoothing splines are applied to the modeling of valve boundary curves, while tensor product smoothing splines are used to fit surfaces to the mitral valve interior leaflets. Two approaches are presented for this surface modeling: one (lofting) works in all cases but requires more effort to execute, while the other (principal plane) is simpler in its approach but does not work for all mitral valves. These techniques are illustrated by the display of multiple mitral valve models. Next, we have considered optimal diffeomorphic matching of these mitral valve models by a variational approach based on Hilbert spaces of time dependent vector fields. Since models matched by diffeomorphisms are extracted from sequences of 3D-Echo images, we have proposed an equivalent formulation and solution of this problem, one that involves an iterative scheme that alternates between pure geometric diffeomorphic matching and image intensity registration. Several detailed, concrete examples are presented to validate the performance of our approach. Finally, we have developed the methods needed to compute, compare, and quantify the distribution of strain values on mitral valve leaflets. We adopted standard finite difference techniques for computing the strain tensor on a leaflet surface and applied the Kolmogorov-Smirnov tests to evaluate how 3 groups of mitral valves (normal, pre-surgery, post-surgery) compare in terms of strain values distributions. These results have been published in a joint paper between UH and TMH. A second joint paper will be submitted in May 2014.