Assessment of anisotropic elasticity of small bone samples with resonant ultrasound spectroscopy: attenuation does not prevent the measurements

Resonant Ultrasound Spectroscopy (RUS) is the gold standard method for anisotropic elasticity assessment of millimeter-size samples. However, the usual implementation of RUS fails to measure bone because of its high mechanical damping, which prevents the resonance frequencies measurement. The aim of this study is to demonstrate that RUS method can be adapted to assess the elasticity of highly attenuating anisotropic materials such as cortical bone. A procedure for sample dimensions optimization is defined in order to reduce the number of frequencies to be measured for a precise elasticity assessment. We applied a dedicated signal processing method able to retrieve resonance frequencies even in the case of peaks overlapping. For a sample of transversely isotropic, attenuating, bone-mimetic material, we were able to measure 13 resonance frequencies among the 20 first predicted by theory in the frequency band [0-240 kHz]. Using a dedicated iterative optimization method we estimated the full set of independent elastic coefficients from the measured frequencies. The determined coefficients were validated by comparison with independent measurements. This work opens the way for precise elasticity assessment of small bone sample by RUS.