Abstract:
This dissertation develops and validates a suite of computational tools to enhance a continuum mechanics-based method for deformable image registration known as "Warping." The research addresses the fact that image registration is an inherently ill-posed inverse problem, requiring regularization to achieve a unique and physically meaningful solution. The author developed a series of preprocessing, integral, and postprocessing tools—including dynamic spatial filtering, histogram-matching, and finite element (FE) rezoning—to improve the robustness and accuracy of the Warping technique.
The enhanced Warping method was then applied to solve a variety of challenging biomechanical problems, such as calculating the stress and strain fields in a human spinal disc under compression, a human fingerpad under indentation, and a mouse tectorial membrane. In addition to these application tools, the dissertation introduces two novel quantitative techniques for assessing the quality of registration results. The first is a three-dimensional extension of Singular Value Decomposition (SVD), which provides a hierarchical method to compare the topology of the registered image with the target image. The second is an "image influence parameter," derived from the registration's potential energy function, which quantifies the relative influence of the image data versus the underlying mechanical model on the final solution. This comprehensive work provides a powerful and rigorously evaluated framework for extracting quantitative biomechanical information from medical images.
