Changes in Elastic Modulus During Cyclic Loading Measured Using Ultrasound – Implications for Fragility Fracture Detection

Introduction: Nondestructive ultrasound testing has been applied to bone in order to improve predictions of fragility . When ultrasound propagates through thin shells such as bone cortices, multiple guided wave modes (termed lamb waves), are generated that propagate through the cortical bone. Because of the complexity in isolating these multiple guided wave modes, typical application of ultrasonic methods utilize the measurement of the first arrival speed of sound (FASS) through the specimen as a predictor of overall health, including bone mineral density and risk of fracture . Yet, the FASS is dependent on a variety of factors including the diameter of the bone, angle of incidence, mineral density, and the ultrasound carrier frequency. The susceptibility of the FASS to so many variables makes it difficult to get a clear indication of the bone health. In this study, we present a novel ultrasound based means of detecting the extent of damage in bone. Note: in this study, damage is defined as change in modulus (instantaneous elastic or secant modulus). The proposed technique relies on measuring speed of sound during cyclic loading. The hypothesis to be tested is that changes in instantaneous modulus (damaged bone has a non-linear stress-strain behavior with constantly varying modulus during the loading cycle) are correlated to changes in ultrasound velocities. Theory: Current ultrasonic methods treat the elastic/young modulus as a static variable through which speed of sound properties are determined. Yet, a change in modulus, as happens with cumulative damage, will cause a proportional change in the FASS. The speed of sound (V) through the bone will be proportional to elastic modulus (E) and bone density (ρ) according to: V = √(E/ρ) (1) Note that regardless of the type of guided wave used for damage detection, the speed of sound will be an integral part of the FASS.