Viscoelasticity determined by measured wave absorption coefficient for modeling waves in soft tissues

Abstract This paper reports the construction of viscoelasticity models for simulation of wave propagation in soft tissues. Aided by the Carson transform, Fung’s model and Iatridis’s model are transformed into the frequency domain with the imaginary part of the transformed relaxation function shown to be related to wave absorption effect. Based on measured wave absorption coefficients, the viscoelasticity models in the time domain are determined. Results show that Fung’s model does not support the frequency-dependent damping effect, but Iatridis’ model does. To validate the approach, numerical simulation of propagating wavelets in a skeletal pig muscle is performed. The constructed relaxation function is discretized by parallelly connected Standard Linear Solid (SLS) models. The hereditary integration is then transformed into a set of partial differential equations by introducing the internal variables. Together, the governing equations include the equation of motion, the constitutive equation, and the equations of internal variables. Velocity, stress, and internal variables are the primary unknowns. The model equations are solved by using the space–time CESE method. The calculated wave absorption effect compares well with the measured data.