Elastography applications of surface waves: Examples in biomechanics and in the beef industry

The use of surface waves for estimating shear elasticity in soft tissues is an emerging method. There are numerous examples of in vivo and ex vivo applications in literature. Most of these examples base their inversion methods on Rayleigh surface waves, Rayleigh–Lamb dispersion curves, or even the Timoshenko beam model. In this work, we show that there is a critical distance from the source where near-field effects prevent the use of these models. This distance is given by the interference of the Rayleigh surface wave with the so-called leaky surface wave, which arises as a complex solution of the Rayleigh secular equation for materials with large Poisson's ratio [Benech et al., JASA 142(5), 2017]. This leaky wave has been observed experimentally in geophysical applications, and here we show its existence in tissue-mimicking phantoms [Benech et al., J. Phys. Condens. Matter, 34 (2022)]. We then show that a similar behavior is observed in transversely isotropic solids such as skeletal muscle. Finally, we demonstrate two different applications. First, in estimating the elasticity of the concentric contraction of the biceps brachii in vivo. Second, in monitoring the enzymatic maturation process by aging in beef samples. We highlight the advantages of surface waves over traditional ultrasound elastography in these two applications.