Heterogeneous and Anisotropic Model

The density, anisotropy, and microstructure are evaluated in this model for which micro CT can be used [16]. In addition to the density and macroscopic anisotropy, the microstructure, such as thickness and connectivity of the trabeculae, can be evaluated.

Because of ease of measurement, the bone density measurement has been widely used to predict material properties of the bone. Strong correlation between the material properties and bone density has been reported. However, the relationship between the bone density and the material properties has been reported to be nonlinear [6]. Clinical investigations show the limitation of the density measurement in predicting fracture risk. Changes in the trabecular orientation in osteoporotic patients is widely recognized by the clinician and sometimes evaluated in the grading system of osteoporosis in vertebral bodies and the proximal femur.

Even though the importance of the trabecular orientation is recognized to determine the material properties of the trabecular bone, this parameter has not been included in the analysis until recently because of the technical difficulties in quantifying the trabecular orientation. The trabecular bone has a lattice structure but it is not a perfect lattice structure and shows a variation of the orientation. Unlike histological images based on a thin section, the radiological images have a gray-level gradient. Fourier analysis is suitable to quantitate the preferred orientation based on such image data.

Material properties measured by compressive tests and ultrasound velocity (USV) showed high correlation with bone mineral density (BMD) measured from a soft X-ray of the test specimen. If the parameter of the trabecular orientation is incorporated, however, a higher correlation is obtained. The correlations between the compressive stiffness or USV and the BMD as well as the intensity of the trabecular orientation have been studied using human calcaneal trabecular bone. The trabecular orientation can be quantified with the 2D FFT of the soft X-ray image of the test specimens (Figs. 11a, b). Equivalent bone density oriented along the loading and ultrasound axis is calculated as the product of bone density and trabecular orientation intensity along the same axis (Fig. 12). The component of bone density oriented along the loading axis correlated significantly better than BMD with both compressive modulus and USV [31]. This investigation suggests the importance of the trabecular orientation in estimating the mechanical properties of the trabecular bone in addition to the bone mineral density.

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