The analysis of myocardial contractility is important to the understanding of intrinsic mechanics of cardiovascular diseases. In this thesis, a new technique based on Magnetic Resonance (MR) velocity mapping is presented, which uses attribute vector based image registration combined with harmonic mapping for revealing intra- and inter-subject contractile variability. With this technique, the myocardial velocity data obtained by MRI is first warped to a uniform domain followed by statistical analysis of the cardiac motion. The main contributions of this dissertation are as follows: Feature based registration and harmonic embedding - We combine harmonic mapping with an attribute vector based mesh matching method to obtain accurate matching of the anatomical volume to a uniform domain made of a hollow semi-spherical template. By harmonic mapping with manually identified landmarks, the epi- and endo-cardium surfaces of the left ventricle (LV) are first mapped to the template. This presents a good initial matching result and a smooth convex search region for subsequent mesh matching. The optimal position for each point in the template is found by solving a quadratic optimization problem based on these attribute vectors. The proposed method enables registration at sub-voxel accuracy and is more accurate than the usual feature based registration approach. In this thesis, the proposed method has also been generalized to cortical surface matching, for which further landmarks including central sulcus, precentral gyrus and postcentral gyrus are used to improve the matching results. This makes the cortical surface analysis more accurate, as required for cortical complexity analysis. Warping of myocardial velocity field for cardiac contraction analysis - By analyzing the relationship between vector bundle and manifold mapping, issues related to the use of Jacobian matrix for manifold mapping are identified. This is the mapping function of the manifold tangent vector bundle, which may work incorrectly, for example, for the normal vector bundle. In the thesis, a volumetric embedding framework is proposed for myocardial velocity mapping. This provides the basis for consistent volume matching and vector correspondence, in addition to the ease of calculating biomechanical indices such as radial, circumferential and longitudinal strain rates without the concern of boundary effects. Group-wise left ventricular volumetric matching and myocardial strain rate analysis – For this study, in vivo datasets from six subjects with different number of time frames (TF) were used. For group-wise myocardial contractility analysis, the LV volumes of all TF in the cardiac cycle are matched first. For temporal alignment, the LV volumes of different patients are interpolated into the same number of TF by linear interpolation.
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