Multi-scale homogenization and FEM modeling of cortical bone -

Abstract

Unlike cancellous (spongy) bone, cortical bone is compact bone that forms the outer dense shell of most bones. Examining a cross section of a bone taken normal to the bone’s long axis (bone’s transverse direction) would reveal a microscopic architecture referred to as the osteon system. Mechanically speaking, one may describe this structure as comprised of lamella matrix punctuated by an array of porous inclusions of three types: Haversian canals, lacunae, and clusters of canaliculi. Developed in this research is a multi-scale methodology, the aim of which is to determine the cortical bone material elastic properties at the meso and macro scales as a function of the porous architecture based on analysis of transverse direction. In lieu of human bone, cortical bone from bovine will be used as an acceptable proxy of human bone. The methodology passes on data and information initially from the micro-to-meso scale and, then, from meso-to-macro scale. Four major steps are involved in applying this methodology. First, at the micro-scale, properly identify the micro-structural architecture by segmenting bone microstructure optical images via pulse coupled neural networks (PCNN) bone microstructure optical images. Taking advantage from said segmented images porosities' shape and volume fraction are related to radius from bone geometrical center. Second, an extended method of the homogenization theory is developed in this research. Specifically, in addition to classical measures of porosity based on geometric characteristics (shape and volume fraction), porosity distribution and orientation within the matrix are accounted for. This extension of the existing art in homogenization is described and validated through rapid prototyping (3D printing) and FE simulations of compression tests. A non linear prediction model relating Young's modulus to said geometric characteristics is developed as an alternative to the use of complex homogenization calculations. Third, perform micro-to-meso scale homogenization to