Quantifying elasticity and viscosity from measurement of shear wave speed dispersion

The propagation speed of shear waves is related to frequency and the complex stiffness (shear elasticity and viscosity) of the medium. A method is presented to solve for shear elasticity and viscosity of a homogeneous medium by measuring shear wave speed dispersion. Harmonic radiation force, introduced by modulating the energy density of incident ultrasound, is used to generate cylindrical shear waves of various frequencies in a homogeneous medium. The speed of shear waves is measured from phase shift detected over the distance propagated. Measurements of shear wave speed at multiple frequencies are fit with the theoretical model to solve for the complex stiffness of the medium. Experiments in gelatin phantoms show promising results validated by an independent method. Practical considerations and challenges in possible medical applications are discussed.