Effect of liquid elasticity on nonlinear pressure waves in a visco-elastic bubbly liquid

The importance of viscoelasticity of biological media that are used in medical ultrasounds has been discussed in the literature. Furthermore, the use of microbubbles in biological media drastically improves the efficiency of both diagnostic and therapeutic ultrasounds. Weakly nonlinear wave equations for ultrasound propagation in liquids containing microbubbles have long been studied,although the viscoelasticity of the liquid phase has been ignored for simplicity. In this study, we derived a nonlinear wave equation for ultrasound propagation in a viscoelastic liquid containing microbubbles by considering the effect of the elasticity of the liquid. Additionally, we evaluated how the elasticity of the liquid modifies the nonlinear, dissipation, and dispersion effects of the ultrasoundin a few tissue models (i.e., liver, muscle, breast cancer, fat, skin models and that without shear elasticity). The results revealed that liquid shear elasticity decreases the nonlinear and dissipation effects and increases the dispersion effect, and this tendency is more significantly observed in the breast cancer tissue compared with other tissues. Furthermore, we numerically solved the nonlinear wave equation and investigated the changes in ultrasonic wave evolution with and without shearelasticity.