Automatic Grid-based Mesh Generation Techniques for Cardiac Electrophysiology Problems

Improved image acquisition techniques, e.g. high-frequency magnetic resonance tomography or micro computer tomography along with up-to-date supercomputing power have made a considerable step towards the development of micro-anatomically realistic cardiac computer models. The realistic representation of the anatomy and improved descriptions of the dynamic behavior of ionic membrane kinetics allow more reliable and precise answers to electrophysiological questions. The underlying work deals with the processing chain to obtain a cardiac finite element model based upon segmented image data. Although all the processing steps are important to arrive at a satisfying result, in-depth investigations were impossible and preprocessing of the image stacks (e.g. registration of the image stacks, image segmentation and conversion to a format suited for the mesh generation process) was considered to be more peripheral. The emphasis of the thesis was focused on the definition of the requirements for fully automatic octree-based grid-based mesh generation technique, which employs the modified dual mesh of an octree and produces conformal boundary-fitted, hexahedra-dominant meshes, the introduction of Ansatz functions in hybrid finite elements (e.g. hexahedra, prisms, pyramids and tetrahedra) for the computation of the electrical activity in the heart and the generation of rule-based fiber orientation data. Additional information from segmentation (e.g. manually segmented regions within the heart) or the preferred orientation of myocardial fibers, obtained from diffusion tensor MRI, can be seamlessly mapped onto the unstructured hybrid mesh. A rule-based method employing a-priori knowledge from published literature or from tissue preparations was developed to create fiber orientation data and map it onto the geometry. Several anatomically realistic models of a papillary muscle, a left ventricular wedge preparation and a human atria model were created at different resolutions. In the latter, it was shown, that with higher anisotropy ratios reentrant activity is sustained even after turning off the ectopic focus in the computer model after ring twice. A study of virtual electrode patterns on the cut surface of isolated wedge preparations concluded that the boundary conditions (permeable vs. impermeable) during the application of defibrillation shocks cannot be neglected, which is in stark contrast with findings of experimental work.