Parameterized orthotropic cellular microstructures as mechanical models of cancellous bone

Abstract

Constitutive properties of cancellous bone depend on microstructural geometry. Evaluation of the interrelationship is a crucial issue in analysis of stresses and strains in bone tissues and simulation of their remodelling. Known limitations of experimental methods as well as of the micro-FE techniques make the analysis and homogenization of ‘equivalent’ trabecular microstructures an advantageous tool for this task. In this study, parameterized orthotropic constitutive models of cancellous bone are derived from finite element analysis of repeatable microstructure cells. The models are fully three-dimensional, have realistic curvilinear shapes and are parameterized with four shape parameters. Variation of the parameters allows to imitate most of the typical microstructure patterns observed in real bones, along with variety of intermediate geometries. The models are a geometrically enhanced version of those presented in the author’s previous work [1]. Static numerical tests are performed with the finite element method for an exhaustive number of parameter value sets (microstructure instances). Repeatability of the microstructure allows to test only a sigle cell with appropriate boundary conditions. Values of computed stresses and strains allow to determine all coefficients of elastic orthotropic stiffness matrix. Results have a form of tabularized functions of elastic constants versus the shape parameters. Comparison of the results with micro-FE data obtained for a large set of cancellous bone specimens [2] proves a good agreement.