Assessment of trabecular bone tissue elasticity with resonant ultrasound spectroscopy

The material properties of the trabeculae (tissue-level properties), together with the trabecular architecture and the bone volume fraction determine the apparent millimetre-scale bone mechanical properties. We present a novel method to measure trabecular tissue elastic modulus E_t using resonant ultrasound spectroscopy (RUS). The first mechanical resonance frequency f^e of a freestanding cuboid specimen is measured and used to back-calculate E_t. The steps of the back-calculation are (1) the apparent stiffness tensors C(E_t˜) is computed using micro-finite elements for a set of trial values of tissue Young's modulus E_t˜ based on the computed tomography image of the specimen; (2) the modeled free-vibration resonance frequencies f^m(E_t˜) of the specimen is calculated with the Rayleigh-Ritz method using C(E_t˜); (3) finally, E_t is obtained by interpolation using f^e and f^m(E_t˜). Four bovine bone specimens were tested (nominal size 5×6 ×6mm³). Average (standard deviation) of E_t was 13.12 (1.06)GPa. The measurement of a single resonance frequency enabled an estimation of tissue elasticity in line with available data. RUS is a non destructive technique relatively easy to implement compared to traditional mechanical testing. The novel method could contribute to a better documentation of bone tissue elasticity which is an important parameter of micro-finite element analyses for the clinical assessment of bone strength.