Element stiffness matrix integration in image-based Cartesian Grid Finite Element Method

Autores UPV
CONGRESO Element stiffness matrix integration in image-based Cartesian Grid Finite Element Method


Following traditional methods, before a FE model can be obtained, patient specific FE simulations usually require a time consuming, often manual, preliminary stage of segmentation and geometry creation in order to obtain a CAD model from the medical image, suitable to be meshed. The most common alternative is the direct creation of a uniform hexahedral mesh in which each pixel/voxel perfectly fits one element. The main drawback of this method is the great number of degrees of freedom in the FE mesh, which makes it challenging to solve the numerical problem due to the high computational cost. Image-based Cartesian grid Finite Element Method (image-based cgFEM) is a technique which allows to obtain h-adaptive Finite Element (FE) models with a reasonable number of degrees of freedom from images in an automatic way without the necessity of creating an intermediate geometrical model. Thus cgFEM represents an alternative to maintain accuracy with a low computational cost. In cgFEM the image is directly immersed into an initial uniform Cartesian mesh. The hierarchical structure of nested Cartesian grids on which cgFEM is based allows a fast and efficient h-adaptive process to be carried out in order to adapt the mesh to the bitmap representation of the body to simulate. The h-refinement process is performed by element splitting and guided by the evaluation of the pixel value distribution. In this paper a comparison between different integration strategies are presented for the calculation of the element stiffness matrices in imagebased cgFEM. These are a special integration technique based on the Riemann sum, one based on the standard Gauss quadrature applied on subdomains coinciding with the pixels, a Gauss quadrature of the whole element domain in which the material property field is interpolated using Least Squares (LS) fitting or by Superconvergent Patch Recovery (SPR).