Wave propagation in viscoelastic materials

Mechanical‐wave stimulation/excitation is usually the key aspect that determines the quality of elasticity imaging. This chapter discusses the exogenous harmonic‐wave stimulation and its applications in estimating mechanical properties of elastic and viscoelastic media. It briefly summarizes the equations that describe local displacements associated with shear waves as a function of the spatially varying complex shear modulus. Cylindrical waves and surface waves are widely used to mechanically excite tissues. Wave speed in an elastic material is constant with frequency. In contrast, viscoelastic materials are dispersive; that is the wave speed changes substantially with frequency. Dispersive behavior is determined by the components of the materials and their mechanical couplings. In standard rheological models, these components are represented by springs and dash‐pots. Shear‐wave and surface‐wave imaging offer quantitative estimates of intrinsic viscoelastic properties of dispersive tissues. Coupling dispersion behavior with rheological models parameterizes measurements as needed for imaging.