  Shear wave elastography (SWE) has emerged as a new imaging modality that
brings tissue mechanical properties as biomarkers potentially useful for early
and precise diagnosis. While different SWE methods have been proposed, how to
relate the frequency SWE measurements to quasi-static stiffnesses of tissues
sensed by cells when prestresses are involved remains challenging. Here we
suggest an incremental dynamics theory for prestressed viscoelastic solids and
investigate its application in SWE across a broad frequency range. To model the
power-law dispersion relation with minimal parameters, we introduce the
Kelvin-Voigt fractional derivation model (KVFD) in the constitutive modeling of
material viscoelasticity. To validate the usefulness of the theory, we
performed experiments on prestressed soft materials and biological tissues. The
results show that the theoretical solution fits the experimental dispersion
curve well over a broad frequency range and accurately captures the effect of
prestress. The theory also reveals the correlation of phase velocities and
attenuations of shear waves with principal stresses and leads to a method for
probing the prestress in a viscoelastic solid without prior knowledge of the
constitutive parameters as validated by our numerical experiments. Taken
together, our results show that the theory presented here enables the
development of spatially resolved SWE when high-frequency shear waves get
involved, and provides insights into wave motions in soft materials subject to
prestresses.
