Developement and validation of resonant ultrasound spectroscopy for the measurement of cortical bone elasticity on small cylindrical samples

Abstract

Documentation of cortical bone elastic properties is important for orthopedic applications and fracture risk prediction. Cortical bone is heterogeneous and anisotropic. Ideally, measurements should be performed on cylindrical samples of characteristic size of a few millimeters, which are adapted to the native geometry and size of bones. Our objective was to measure bone with Resonant Ultrasound Spectroscopy (RUS), which is a powerful method to determine the elastic constants of a sample from a set of its resonant frequencies. Application of RUS to bone is difficult due to viscoelasticity, which causes resonance peaks to overlap. Some of the resonances in the investigated frequency band cannot be observed. The formulation of the inverse problem, which requires pairing measured and predicted frequencies, must be adapted in the case of bone. We developed a dedicated signal processing methods to retrieve resonant frequencies from overlapping peaks. A probabilistic approach was used, which allows an automated pairing based on a Bayesian criterion. The method was validated on PMMA for both isotropy an transverse isotropy assumptions. The adapted RUS method allows the automated assessment of bone elasticity with a precision of a few percents, which is a significant improvement over traditional methods based on velocity measurements. © 2013 Acoustical Society of America.