Element Stiffness Matrix Integration in Image-Based Cartesian Grid Finite Element Method

Patient specific Finite Element (FE) simulations are usually expensive. Time consuming geometry creation procedures are normally necessary to use standard FE meshing software, while direct pixel-based meshing techniques typically lead to a large number of degrees of freedom hence introducing a high computational cost. Image-based Cartesian grid Finite Element Method (image-based cgFEM) allows accurate models to be automatically obtained with a low computational cost without the necessity of defining geometries. In cgFEM the image is directly immersed into a Cartesian mesh which is h-adapted on the basis of the pixel value distribution. A hierarchical structure of nested Cartesian grids guarantees the efficiency of the process. In each element, the material elastic properties are heterogeneous, therefore a critical aspect of image-based cgFEM is the integration of the element stiffness matrices which homogenize the material elastic behavior at the element level. This paper compares accuracy and computational cost of different integration strategies: pixel direct integration schemes (Riemann sum and subdomain Gauss quadrature) and recovery based schemes (Least Squares fitting and Superconvergent Patch Recovery).