Micromechanics-based conversion of CT data into anisotropic elasticity tensors, applied to FE simulations of a mandible
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1132-Z01-03
Micromechanics-based conversion of CT data into anisotropic elasticity tensors, applied to FE simulations of a mandible Christian Hellmich1, Cornelia Kober2, Bodo Erdmann3 1 Vienna University of Technology (TU Wien), Institute for Mechanics of Materials and Structures, A-1040 Vienna, Austria 2 Hamburg University for Applied Sciences, Faculty of Life Sciences, 21033 Hamburg, Germany 3 Zuse Institute, 14195 Berlin-Dahlem, Germany ABSTRACT Computer Tomographic (CT) image data have become a standard basis for structural analyses of bony organs. In this context, regression functions between stiffness components and Hounsfields units (HU) from Computer Tomography, related to X-ray attenuation coefficients, are widely used for the definition of the (actually inhomogeneous and anisotropic) material behavior inside the organ. Herein, we suggest to derive the functional dependence of the fully orthotropic stiffness tensors on the Hounsfield units from the physical information contained in the X-ray attenuation coefficients: (i) Based on voxel average rules for the X-ray attenuation coefficients, we assign to each voxel the volume fraction occupied by water (marrow) and that occupied by solid bone matrix. (ii) By means of a continuum micromechanics representation for bone, which is based on voxel-invariant (species and whole bone-specific) stiffness properties of solid bone matrix and of water, we convert the aforementioned volume fractions into voxelspecific orthotropic stiffness tensor components. The micromechanics model, in combination with the average rule for X-ray attenuation coefficients, predicts a quasi-linear relationship between axial Young's modulus and HU, and highly nonlinear relationships for both circumferential and radial Young's moduli as well as for the shear moduli in all principal material directions. Corresponding whole-organ Finite Element analyses of a partially dentulous human mandible characterized by atrophy of the alveolar ridge show that volumetric strain concentrations/peaks within the organ are decreased when considering material anisotropy, and increased when considering material inhomogeneity. INTRODUCTION – STATE OF THE ART Image generation through 3D reconstruction and rendering from Computer Tomograhic (CT) data has become a standard biomedical tool for characterization of shape and internal inhomogeneities of skeletal tissues and organs. In addition, it often serves as basis for setting up computational structural simulations, e.g. based on the Finite Element method, for stress and strain analyses in bony organs with complicated geometrical shape. The value of such computations lies in their feasibility, while in vivo, stress and strain fields can hardly be determined through direct experiments. A major issue challenging the reliability of such computations for predicting untested or untestable situations seems to be the anisotropy and inhomogeneity of the material properties throughout such organs. Frequently, isotropy is assumed [1], and - if considered - the spatial distrib
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