为了从医学体数据直接构造四面体网格,提出一种基于栅格的网格生成算法.该算法的主要思想是从背景栅格中提取并填充代表区域边界的等值面.首先,对医学体数据进行预处理与采样,构建一个背景栅格.其次,用对偶方法从栅格提取三角表面网格,用于分段线性逼近等值面.然后,对栅格中所有位于等值面之内或与等值面相交的立方体,用预定义的模板分解成四面体单元.最后,用Laplacian平滑技术优化四面体网格.在均匀网格的基础上,研究了自适应网格生成算法,在保持网格几何精度的同时精简单元数量,以提高有限元计算效率.给出了从CT数据生成人体股骨远端四面体网格的实例,该网格模型被用于虚拟膝关节镜手术.

A grid-based method is presented to extract tetrahedral meshes from the preprocessed volume data, during which the isosurface representing the domain boundary is extracted and the volume inside the domain is tetrahedralized. After the medical volume data is organized into an invisible background grid, a dual method is employed to construct a continuous triangular surface that piecewise linearly approximates the isosurface. To fill the isosurface with tetrahedra, cubes either intersecting with or lying within the isosurface are decomposed by using the precomputed stencils. Finally, Laplacian smoothing is conducted to improve the overall quality of the generated tetrahedral meshes. Regarding that the numerical analysis demands reduced number of elements and accurate geometry near the boundary, adaptive meshing method based on octree-structured grid is also explored. Example of meshing the human distal femur from CT scans is presented, which is applied in the virtual arthroscopic knee surgery.

Supported by the National Natural Science Foundation of China under Grant No.60773022 (国家自然科学基金); the National High-Tech Research and Development Plan of China under Grant No.2007AA01Z313 (国家高技术研究发展计划(863)); the Beijing Natural Science Foundation of China under Grant No.4062034 (北京市自然科学基金)