Abstract
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).
