Relations between the ultrasonic elastic moduli of compact bone and tissue microstructure

Abstract

Haversian compact bone behaves as a mildly transversely isotropic material that can be modeled as a fiber reinforced composite material. The method of ultrasound is appropriate for estimating moduli provided that the frequency is relatively low at 5 or lower such that the wavelength is greater than the characteristic dimensions that define the microstructure. The ultrasonic moduli are analogous to the mechanically measured moduli. Although the ultrasonic values may differ from the actual mechanically measured values, the ultrasonic moduli accurately predict the relative magnitudes of the anisotropic moduli in all principal directions. When used in combination with an additional mechanical tensile test, one can calculate absolute mechanical properties for Haversian compact bone as homogeneous solid. This study observed that mild changes in the microstructure can predict variations in the mechanical properties. All the tested material properties exhibit gradual increases for small positive changes in ash weight and gradual decreases for small changes in porosity. Longitudinal elastic moduli shows the greatest negative dependence on porosity. The transverse moduli and the shear moduli show greater dependence on ash weight percent. As one must use several parameters to capture variations in the microstructure, no single parameter completely predicts the differences in moduli. Although the results of this study are limited to equine specimens, compact bone from other species may show similar trends.