A BEM study on ultrasound guided wave propagation in bone-mimicking plates with microstructural effects

Ultrasound guided wave propagation in bones has been largely based on the classical theory of elasticity. However, the mechanical behavior of materials with microstructure such as bone can be successfully modeled macroscopically using enhanced theories of elasticity. By using the simplest theory of gradient elasticity we recently showed that microstructure results in significantly modified dispersion curves than those predicted by the Lamb theory. In this work, we numerically investigate guided wave propagation in 2D bone models with microstructure, by using a Boundary Element Method (BEM). The bone is modeled as an isotropic elastic material plate (4mm thick, density 1.5 g/cm³, longitudinal and shear velocity 4107 m/s and 1842 m/s, respectively). Two additional terms are introduced to account for bone´s microstructure i.e., the gradient coefficient g and the micro-inertia term h, whose values are at the order of the osteons´ size. Computational simulations are performed for three different combinations between g and h in which g¿h. The modes are analysed in the time-frequency (t-f) domain. In order to validate the computational results we superimposed the theoretical dispersion curves on the t-f representation of the waveforms. The results are compared to the theoretically obtained wave dispersion curves. Bone´s microstructure was found to significantly affect mode dispersion in the 2D bone plates by inducing geometrical and material dispersion. Thus, microstructure is an important factor and should be considered in theoretical and computational bone studies.