Computer simulation of tagged magnetic resonance (MR) images is presented using signals derived from connected solid triangular or tetrahedral elements. Simulation provides precisely-known deformations for validating tag quantification algorithms. MR imaging signal is derived by Fourier-transforming over a standard element, then mapping to actual elements via transformations. Linear intensity v...

We present a new shape measure for tetrahedral elements that is optimal in the sense that it gives the distance of a tetrahedron from the set of inverted elements. This measure is constructed from the condition number of the linear transformation between a unit equilateral tetrahedron and any tetrahedron with positive volume. We use this shape measure to formulate two optimization objective fun...

The finite-element (FE) method is commonly used in biomedical engineering to simulate the behaviour of biological structures because of its ability to model complex shapes in a subject-specific manner. However, generating FE meshes from medical images remains a bottleneck. We present a template-based technique for semi-automatically generating FE meshes which is applicable to prospective studie...

We present an algorithm for constructing families of conforming (i.e. face-to-face) nonobtuse tetrahedral finite element meshes for convex 3D cylindrical-type domains. In fact, the algorithm produces only path-tetrahedra.

It is a common issue in solid deformation simulation that material models will collapse and even permanently invert. In this paper, we present an algorithm for finite element simulation of isotropic tetrahedral mesh that is capable of robustly restoring from inverted configuration to uninverted state in the deformation process. We perform singular value decomposition of deformation gradient to ...

Finite element simulations in computer graphics are typically based on tetrahedral or hexahedral elements, which enables simple and efficient implementations, but in turn requires complicated remeshing in case of topological changes or adaptive refinement. We propose a flexible finite element method for arbitrary polyhedral elements, thereby effectively avoiding the need for remeshing. Our poly...