| Cardiac diseases claim more lives than any other disease in the world. Early diagnosis and treatment can save many lives and reduce the associated socio-economic costs. Cardiac diseases are characterized by both changes in the myocardial structure as well as changes in cardiac function. Diffuse cardiomyopathies in particular are difficult to diagnose by structural changes. Advances in imaging methods have enabled us to acquire high-resolution 4D images of the heart that capture the structural and functional characteristics of individual hearts. However large inter and intra-observer variability in the interpretation of these images for the diagnosis of diffuse cardiomyopathies has been reported. This has created the need for sophisticated and highly automated image analysis methods, which can identify and precisely quantify subtle and spatially complex patterns of functional changes in the heart. The development of such methods is the primary goal of this project. We propose a method for the analysis of MR cardiac images with the goal of reconstructing the motion of the myocardial tissue. The main feature of our method is that the inversion parameter field is the active contraction of the myocardial fibers. This is accomplished with a biophysically-constrained, four-dimensional (space plus time) formulation that aims to complement information that can be gathered from the images by a priori knowledge of cardiac mechanics and electrophysiology. Incorporating biomechanical priors introduces major computational challenges, which constitute the main issue tackled by this thesis. Our main hypothesis is that by incorporating biophysical information, we can generate more informative priors and thus, more accurate predictions of the ventricular wall motion. In this thesis, we outline the formulation, discuss the computational methodology for solving the inverse motion estimation, and present results using synthetic and tagged MR data. The major contribution in this regard is the development of a parallel octree-based adaptive meshing for finite element computations. This allows us to model complex geometries in an adaptive manner and solve them in parallel. For the purpose of cardiac motion estimation, we present methods for generating and solving using the spatially non-uniform octree meshing scheme with an adjoint-based inversion solver. The method uses myocardial fiber information, adapted to the subject, to reconstruct the motion. |
