Estimation of Viscoelastic Properties of Tissue with Arbitrary Power-Law Attenuation

Attenuation in soft solids are governed by power laws with non-integral exponents. Attenuation is a critical component for correctly modeling the wave propagation physics. For nonlinear waves, in particular nonlinear shear waves, it important to model the two competing effects accurately i.e. the generation of higher harmonics due to nonlinearity and its decay due to attenuation. Current numerical methods can model a linear attenuation power law using a single Kelvin or Maxwell body. In this work a collection of Maxwell bodies is used to model power laws with non-integral exponents, which is more general. Also, the nonlinear propagation of shear waves modeled using a system of hyperbolic PDEs together with the relaxation mechanisms is simulated using a custom high order finite volume method: piecewise parabolic method. The numerical method is validated using a set of power laws with different non-integral exponents, and also the dispersion incurred due to causality is validated. Further, attenuation law obtained from linear experiments of shear wave propagation in fresh porcine brain were used to validate the method. This method can be used to accurately determine the other unknown parameters like nonlinearity of soft tissues in brain, liver etc.