High-Quality Model Generation for Finite Element Simulation of Tissue Deformation
In finite element simulation, size, shape, and placement of the elements in a model are significant factors that affect the interpolation and numerical errors of a solution. In medical simulations, such models are desired to have higher accuracy near features such as anatomical boundaries (surfaces) and they are often required to have element faces lying along these surfaces. Conventional modelling schemes consist of a segmentation step delineating the anatomy followed by a meshing step generating elements conforming to this segmentation. In this paper, a one-step energy-based model generation technique is proposed. An objective function is minimized when each element of a mesh covers similar image intensities while, at the same time, having desirable FEM characteristics. Such a mesh becomes essential for accurate models for deformation simulation, especially when the image intensities represent a mechanical feature of the tissue such as the elastic modulus. The use of the proposed mesh optimization is demonstrated on synthetic phantoms, 2D/3D brain MR images, and prostate ultrasound-elastography data.