Tetrahedral / Hexahedral Finite Element Meshing from Volumetric Imaging Data

The proposed research for the Computational Engineering and Science s (CES) option of the Computational and Applied Mathematics (CAM) Ph.D. program is in the area of tetrahed l/hexahedral finite element meshing from volumetric imaging data with defined boundaries. The proposed research work is to extract adaptive tetrahedral and h exahedral finite element meshes with guaranteed quality directly from volumetric imaging data, such as Computed Tomo graphy (CT), Magnetic Resonance Imaging (MRI) and Signed Distance Function (SDF) data. The extracted meshes should conform to a level set boundary defined as {(x,y,z)| f (x,y,z) = 0 or f ′(x,y,z) = 0}, where f ′ is a modified function of f by segmentation techniques. Both the interior and exterior volume of the bound ary eeds to be tetrahedralized or hexahedralized, and hanging nodes are prohibite d. A 3D mesh generation software called LBIE-Mesh (Level set Boundary and Interior-Exterior Meshe r) will be developed. The proposed approach to generate the required finite element meshes is a s follows: (i) Anisotropic diffusion with bilaterail prefiltering and the contour spectrum based interva l volume selection are set as a preprocessing. The preprocessing step removes noise in the scanne d imaging data, and helps to choose boundary isosurfaces if necessary. Segmentation techniques can dete ct level set boundaries, so they are proposed to be a part of preprocessing especially for scanned soft tis ue structures. (ii) A top-down octree subdivision coupled with the dual contouring method is used to rapidly extrac t adaptive 3D finite element meshes with correct topology from volumetric imaging data. The dual contour i g method is extended to crack-free 3D meshing with feature sensitive adaptation. (iii) The propos ed final step is to improve the quality of the extracted tetrahedral and hexahedral meshes. For tetrahe dral meshes, the edge-ratio and JoeLiu parameter are chosen to measure the quality. The coarsening and refin em nt method removes tetrahedra with bad edge-ratios, face/edge swapping and the smoothing method improves the mesh quality measured by the Joe-Liu parameters. The smoothing method can also be used to improve th e quality of hexahedral meshes measured by the Jacobian determinants. The discretization of the Lap lacian operator and physicallybased quality improvement will be studied. Anisotropic meshes can be obtained by the necessary refinement along the required direction and the extended Laplacian smoothing technique s. Preliminary work includes the development of adaptive tetrahedral mesh ex traction and uniform hexahedral mesh construction. The edge contraction method and a simple Laplac ian smoothing method are implemented to improve the quality of the extracted tetrahedral meshes. The prelimin ary version of LBIEMesh has been used to construct 3D meshes for some objects. For example , ada tive and quality tetrahedral meshes of the molecule mouse acetylcholinesterase (mAChE) are generated a nd have been successfully used in solving the diffusion problem using the finite element method (FEM). We also use the software to construct tetrahedral meshes of the human heart, which can be used for studying cardiac fluid dynamics. Sometimes people would like to choose hexahedral meshes instead of tetrahed ra nd guaranteed-quality tetra/hexa meshes are required in finite element calculations, therefore the p roposed future work includes adaptive hexahedral mesh generation, and the algorithm development in g enerating guaranteed-quality meshes. The current version of LBIE-Mesh supports interactive ope rations, so it is memory consuming. People may need finite element meshes from a very large volumetric data. For e xampl , the molecule microtubule has more than one million particles. In the future work, the data struc ture of LBIE-Mesh needs to be improved for arbitrary large datasets. Parallelization is also necessary in the performance improvement. The finite element meshing of the patient-specific human heart is very important for predictive medicine such as the heart valve replacement and cardiovascular disease. The r fore the proposed future work also includes editing a known heart model according to the segmentation results of scanned data to construct