A Fast Algorithm for Generating Large Tetrahedral 3D Finite Element Meshes from Magnetic Resonance Tomograms

This paper addresses the problem of generating threedimensional (3D) finite element (FE) meshes from medical voxel datasets. With our background in cognitive neuroscience, we deal with brain MR tomograms of up to 256 voxels which contain a multitude of incompletely definable, complex-shaped objects. We describe an algorithm that allows the fast and stable creation of very large 3D meshes with well-defined geometric properties. The task of generating anisotropic meshes consisting of up to one million tetrahedra is fulfilled within minutes on a standard workstation. As the angles of the tetrahedra have a direct influence on the stability of the finite element analysis, special care has been taken to assess the element quality. Our algorithm is based on the idea of an image-based spatial decomposition of the problem domain yielding smaller subproblems that can efficiently be handled. Our primary purpose is to set up mechanical and electro-magnetical finite element models of the brain. However, our FE meshes could also be useful in other types of finite element analyses or as deformable volume models for shape descriptions and shape comparisons.