Research On Surface Reconstruction And Tetrahedral Technology For Biomedical Simulation

With the fast development of biomedical engineering and computer application technology, the research and development of biomedical simulation system has gradually penetrated into the various aspects of modern medicine. The study of virtual surgery system is a typical illus-tration. Virtual surgery is an application of virtual reality in modern medicine. It can present real reappearance of the operation for user by vision and force feed back. Compared with conventional surgery, virtual surgery system has many advantages such as pollution-free, reusable, low consumption and so on that is why it has become a hot topic in the academic and application fields.Biomedical simulation is a field in which multi-subject cooperate with each other, including medical image processing, computational geometry, biomechanics and so on. For different biological tissues and simulation tasks, we need to focus on different research contents. In this thesis, the general architecture and key technologies are proposed for biomedical simulation system. Then, we make an intensive study of geometric modeling techniques for deformation and cutting simulation of biological tissues. The specific contents are surface reconstruction techniques, interactive modeling techniques under CUDA and Delaunay tetrahedral techniques.Under the background of virtual endoscopic surgery, a full suite of development architecture is designed for Trainees, experts and research-ers. Key technologies are also discussed such as geometric modeling, deformation simulation, cutting simulation, collision detection, suture knot simulation and so on. In particular, for the balance between the re-alism and real-time, a general geometric modeling program is developed to meet the surface triangle modeling and tetrahedral modeling.In the terms of surface reconstruction techniques, two improved Marching cubes (MC) algorithm are presented to solve the problems about the ambiguity and generate mesh with high quality. Firstly, ambi-guity-detection index tables are constructed based on33'cases. Asymp- totic decider based on face state is then proposed to solve the two classes of the ambiguity and generate surface model with correct topologies. Secondly, according to the analysis of degenerate triangle generated in a single voxel, a novel improved strategy called data offset is proposed to improve the mesh quality. Combined with ambiguity-detection index ta-bles and face state based asymptotic decider, this improved method gen-erates surface with correct topologies and high quality which can be used for further numerical analysis as well as visualization.In the terms of real-time modeling, the CUDA architecture is in-troduced to meet the purpose of interactive surface modeling with high quality. Firstly, an improved data offset MC is proposed to adapt to the CUDA parallel programming model. In this method, the computations of active voxels, active edges and intersections are all designed in parallel modes. Then, another improved MC based on edge group is proposed to change the triangulation lookup table. Compared with the previous algo-rithm, this method transplants the MC to CUDA perfectly and meets the requirements for interactive surface modeling.In the terms of tetrahedral mesh generation, two kinds of improved Delaunay refinement algorithms are proposed based on theories and ex-periments. Firstly, an improved method based on non-weak correlation points is proposed to meet the realism. This method takes the surface generated by MC as boundary constraints and relaxes the limitation of the input angle. Importantly, we present a strict proof for the conver-gence of this algorithm. Secondly, taking into account the real-time and feasibility, a novel Delaunay refinement remeshing method is presented based on simplified organ surface to meet the Delaunay surface triangle modeling and Delaunay tetrahedral modeling. In this method, the initial surface is preprocessed to create polyhedron representation of the do-main including mesh simplification and internal redundant mesh dele-tion. Then a vertex protected sphere based Delaunay refinement algo-rithm is proposed to remesh the polyhedron and make it meet the De-launay criteria. The convergence and effectiveness can be guaranteed by theoretical proof and some experiments.