Local inversion of transient shear‐wave propagation for elasticity and viscosity mapping in soft tissues

Observation of transient shear‐wave propagation in soft tissue is of great interest for the study of tissue viscoelastic properties. In previous work, we introduced a technique, called Supersonic Shear Imaging (SSI), able to generate transient shear waves using the acoustic radiation force and image their propagation in real time in soft tissues. In this work, a local inverse problem of the shear wave propagation permitting the recovery of shear elasticity and viscosity is presented. Compressional and shear waves are decoupled by applying the curl operator to the experimental 2‐D displacement field. The role of viscosity on the accuracy of the elasticity estimation is studied. The influence of out of plane shear propagation on the inversion algorithm is discussed. Finally, in media presenting shear viscoelasticity heterogeneities, finite difference simulations are used to study the spatial resolution of the algorithm and its sensitivity to the signal‐to‐noise ratio. Experiments on calibrated tissue‐mimicking phantoms presenting different viscoelastic properties are presented validating the simulation results. First in vivo results on female breasts are presented.