Peiró Joaquim, Sherwin Spencer J, Giordana Sergio
Department of Aeronautics, Imperial College London, South Kensington Campus, London, SW72AZ, UK.
Med Biol Eng Comput. 2008 Nov;46(11):1069-83. doi: 10.1007/s11517-008-0390-3. Epub 2008 Sep 16.
We describe a set of procedures for the shape reconstruction and mesh generation of unstructured high-order spatial discretization of patient-specific geometries from a series of medical images and for the simulation of flows in these meshes using a high-order hp-spectral solver. 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 initially represented as an iso-surface of an implicit function defined in terms of radial basis functions. This surface is approximated by a triangulation extracted by the method of marching cubes. The triangulation is then suitably smoothed and refined to improve its quality and permit its approximation by a quilt of bi-variate spline surface patches. Such representation is often the standard input format required for state-of-the-art mesh generators. The generation of the surface patches is based on a partition of the triangulation into Voronoi regions and dual Delaunay triangulations with an even number of triangles. The quality of the triangulation is optimized by imposing that the distortion associated with the energy of deformation by harmonic maps is minimized. Patches are obtained by merging adjacent triangles and this representation is then used to generate a mesh of linear elements using standard generation techniques. Finally, a mesh of high-order elements is generated in a bottom-up fashion by creating the additional points required for the high-order interpolation and projecting them on the edges and surfaces of the quilt of patches. The methodology is illustrated by generating meshes for a by-pass graft geometry and calculating high-order CFD solutions in these meshes.
我们描述了一套程序，用于从一系列医学图像中对特定患者几何形状进行非结构化高阶空间离散化的形状重建和网格生成，并使用高阶 hp 谱求解器在这些网格中模拟流动。边界形状的重建基于通过从图像分割获得的一组点对隐函数进行插值。这种方法因其能够在不同拓扑的截面之间进行平滑插值而受到青睐。物体的边界最初表示为根据径向基函数定义的隐函数的等值面。该表面通过移动立方体方法提取的三角剖分进行近似。然后对三角剖分进行适当的平滑和细化，以提高其质量，并允许用双变量样条曲面片的拼接来近似它。这种表示通常是最先进的网格生成器所需的标准输入格式。曲面片的生成基于将三角剖分划分为 Voronoi 区域和具有偶数个三角形的对偶 Delaunay 三角剖分。通过使与调和映射的变形能量相关的畸变最小化来优化三角剖分的质量。通过合并相邻三角形获得面片，然后使用标准生成技术将这种表示用于生成线性单元网格。最后，通过创建高阶插值所需的额外点并将它们投影到面片拼接的边缘和表面上，以自底向上的方式生成高阶单元网格。通过为旁路移植几何形状生成网格并在这些网格中计算高阶 CFD 解来说明该方法。
