2D and 3D finite element pre- and post-processing in orthopaedy.

Abstract

The present widespread tomographic techniques based on computed tomography (CT), magnetic resonance imaging (MRI) and automatic 2D and 3D reconstructions also involve numerous new points of view for planning surgical techniques in orthopaedy. These require efficient pre- and post-processing methods. By pre-processing and post-processing is meant both the generation of a finite element mesh that numerically models human joints and the visualization of the results obtained as required by the surgeon. Since the numerical reconstructions of human joints are based on the finite element approximation of contact problems assuming linear elasticity, the main goal of pre-processing is to generate triangular (2D) and tetrahedral (3D) meshes of objects with a 'reasonable' boundary-human joints. In our paper we restrict ourselves, for the sake of simplicity, to polygonal (resp. polyhedral) objects. The idea of preprocessing is based on the modified method of Delaunay Mangulalia and on the so-called relaxation technique. After the generation of the finite element mesh and after numerical simulation of surgical problems of orthopaedy, the results obtained as stress-strain fields, temperature, etc. may be visualized in a graphical form on the computer screen as well as on other media.