Modeling the mechanical anisotropy in the trabecular bone with the measurement and consideration of the structural anisotropy

The most accurate understanding of the material properties of the trabecular bone tissue of the jawbone is essential for certain oral surgery procedures and for the design of bone replacement materials and implants. The material properties obtained from micro-structural analyses can be used to study the behavior of dental implants and other prostheses implanted in the jawbone. The structural anisotropy of trabecular bone samples from the jawbone was measured using the method of inserted ellipsoids. Using the developed method, it has been shown that bone samples from the close environment of the living tooth-root show anisotropy that can be effectively measured using micro-CT. In this article, we present a method that uses the eigenvalues of the fabric tensor describing structural anisotropy to generate a micro-structural frame model of the trabecular bone. A homogenization method is applied to describe macro-mechanical behavior of the orthotropic bone tissue, which uses the normal-, bending- and torsional stiffness of the beams in the elementary cell in an elastic spring model. With the homogenization of the frame model, the orthotropic material properties of the trabecular bone could be estimated. The method developed is demonstrated using the micro-CT of a bone sample with 0.2636 relative density. The eigenvalues of the fabric tensor of the sample were measured to be 0.5386, 0.3330 and 0.1306, which, after the homogenization of the elementary cell with an identical fabric tensor, resulted in a mechanically orthotropic macro-structure. The apparent moduli obtained were calculated to be 0.6920 GPa, 1.3668 GPa and 0.0503 GPa.