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 using resonant ultrasound spectroscopy (RUS). The first mechanical resonance frequency f of a freestanding cuboid specimen is measured and used to back-calculate E. The steps of the back-calculation are (1) the apparent stiffness tensors C(E˜) is computed using micro-finite elements for a set of trial values of tissue Young's modulus E˜ based on the computed tomography image of the specimen; (2) the modeled free-vibration resonance frequencies f(E˜) of the specimen is calculated with the Rayleigh-Ritz method using C(E˜); (3) finally, E is obtained by interpolation using f and f(E˜). Four bovine bone specimens were tested (nominal size 5×6 ×6mm). Average (standard deviation) of E 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.