  Shear-wave elastography (SWE) measures shear-wave speed (SWS), which is
related to the underlying shear modulus of soft tissue. SWE methods generally
assume that soft tissue viscoelasticity is independent of mechanical loading,
however, soft tissues are known to have viscoelasticity changing nonlinearly
with pre-compression. Hence, characterization by SWS alone is insufficient,
where nonlinear properties can be seen as confounders but may also be utilized
as additional bio-markers. The viscoelastic nature of a medium is fully
characterized by its storage and loss moduli, which are related to SWS and
shear-wave attenuation (SWA). In this work, we study SWA characteristics as a
function of applied strain to measure nonlinear viscoelastic parameters in soft
tissues. For this purpose, we apply incremental quasi-static compression on the
samples while measuring SWS and SWA, from which we derive storage and loss
moduli to estimate nonlinear viscoelastic parameters as a function of applied
strain using acoustoelasticity (AE) theory. Results from tissue-mimicking
phantoms with varying oil percentages and ex-vivo porcine liver experiments
demonstrate the feasibility of the proposed approach. In both these
experiments, SWA was observed to decrease with applied strain. For 10 %
compression in ex-vivo livers, shear-wave attenuation decreased on average by
28 % (93 Np/m), while SWS increased on average by 20 % (0.26 m/s).
