Shape reconstruction from medical images and quality mesh generation via implicit surfaces

The ability of automatically reconstructing physiological shapes, of generating computational meshes, and of calculating flow solutions from medical images is enabling the introduction of computational fluid dynamics (CFD) techniques as an additional tool to aid clinical practice. This article presents a set of procedures for the shape reconstruction and triangulation of geometries derived from a set of medical images representing planar cross sections of the object. The reconstruction of the shape of the boundary is based on the interpolation of an implicit function through a set of points obtained from the segmentation of the images. This approach is favoured for its ability of smoothly interpolating between sections of different topology. The boundary of the object is an iso-surface of the implicit function that is approximated by a triangulation extracted by the method of marching cubes. The quality of this triangulation is often neither suitable for mesh generation nor for flow solution. We discuss the use of mesh enhancement techniques to maximize the quality of the triangulation together with curvature adaption to optimize mesh resolution. The proposed methodology is applied to the reconstruction and discretization of two physiological geometries: a femoral by-pass graft and a nasal cavity.