Analytical model of Dynamic AcoustoElastic Testing measurements in trabecular bone tissue: a rheological approach

A dynamic acoustoelastic testing (DAET) method based on the interaction of two acoustical waves was developed to measure viscoelastic properties of trabecular bone tissue. While a sinusoidal low-frequency (LF) acoustic wave successively compresses and expands the medium, ultrasonic (US) pulses are generated to probe the uniformly stressed medium (quasi-static pressure, pLF). The US pulses velocity and amplitude (c, A) vary with respect to the medium stress level. These modulations (c(pLF)-c(0); A(pLF)-A(0)) are plotted as a function of the instantaneous LF pressure. From these rheograms, nonlinear elastic and viscous (dissipative) parameters, β' and β” respectively, are extracted. Since the US velocity is directly related to the medium viscoelastic modulus (M*), considering either the celerity variations or the modulus variations as a function of LF pressure is equivalent. In this perspective, we developed an analytical model of the variations of M*, derived from the Kelvin-Voigt approach (M* as a functio...