CHECKERBOARD CONTROL IN 3D ANALYSIS OF BONE REMODELING

Bárbara Belisa Soffiatti¹; Jucélio Tomas Pereira¹; José Eduardo Gubaua¹; Gabriela Wessling Oening Dicati¹

¹ Federal University of Paraná

doi:10.20906/CPS/CILAMCE2017-1076

Resumo

Bone is a living tissue that supports the human body and together with muscles provides the power of movement. In general, many factors stimulate bone deposition and resorption. In response of stress and strain fields, bone cells are actively rebuilding and remodeling the bone. Engineering knowledge can contribute to the analysis of this type of medical problems. Mathematical formulations for bone remodeling in union with numerical simulation, as Finite Element Method (FEM), present results of bone behaviour similar to those observed in real life. The simulation produces two phenomena. The first one happens in areas that are far from the loading application, where can notice regions of low and high densities, which represent trabecular and cortical bone respectively. By contrast, areas close to loadings show a highly oscillatory aspect, where densities intercalate between the highest and the lowest. The last one is a numerical problem called checkerboard, which represent a tendency of the algorithm for bone remodeling models. The purpose of this paper is to evaluate different types of numerical smoothing treatment in a tridimensional model of a human femur, which is suffering bone remodeling and have checkerboard pattern in densities field. The FEM simulation of femur is made by using the software Abaqus along with the subroutine for the Isotropic model of Stanford in Fortran language. In this paper three approaches are discussed according to the proposed objectives: density smoothing, stress smoothing, and stress and density smoothing. For this, the software MATLAB is the computational tool to make the connexion with Abaqus. Preliminary results show that, although the smoothing of the density fields reduces the numerical problem, there is a tendency to present a great amount of cortical bone than what is seen in a real femoral tomography. On the other hand, the expected result for stress smoothing is to minimize this discrepancy of densities, by inputting the smoothing before density update. That being so, at th

Palavras-chave: Smoothing Treatment; Checkerboard; Finite Element Methods; Bone remodeling; Abaqus