Applications of an anisotropic parameter to cortical bone.
An equational description of the extent of the anisotropy in cortical bone is presented from both the perspective of plane stress (two-dimensional stress state) and plane strain (three-dimensional stress state). The orthotropic elastic properties that are incorporated in these states are used to provide a more thorough and refined description of planar and volumetric anisotropy in comparison to the commonly used ratio of elastic moduli. The resulting anisotropic parametric equations (eta(sigma) and eta(epsilon)) are applied to the elastic material properties measured from cortical bone within rats, dogs, cows and humans as reported in 12 previous studies. The resulting calculated parameters reduce the typically nine independent properties down to three parameters which in turn represent the degree of anisotropy within the three orthogonal planes of symmetry as are common in cortical bone. It was found that no statistical difference existed between the plane stress versus plane strain parameter in all but two studies (p > 0.10). Planar and volumetric anisotropies were compared to the isotropic condition (eta(sigma) = eta(epsilon) = 1.0) for all of the included studies. All of the studies reported cortical bone properties that were volumetrically anisotropic (p < 0.05), however, a common plane of isotropy was noted in the radial-circumferential (1-2) plane (p > 0.05). Future use of these parametric equations will allow further illucidation of the issue of mesomechanical and micromechanical levels of anisotropy within other tissues and materials of interest.
Kohles
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Departments of Biomedical and Mechanical Engineering, Worcester Polytechnic Institute, Worcester, MA 01609-2280, USA. kohles@wpi.edu