Finite element analysis of broadband acoustic pulses through inhomogenous media with power law attenuation.

Acoustic waves in tissues and weakly attenuative fluids often have an attenuation parameter, alpha(omega), satisfying alpha(omega)= alpha0omegay in which alpha0 is a constant, omega is the frequency, and y is between 1 and 2. This power law attenuation is not predicted by the classical thermoviscous wave equation and researchers have proposed different modified viscous wave equations in which the loss term is a convolution operator or a fractional spatial or temporal derivative. In this paper, acoustic waves undergoing power law attenuation are modeled by a modification to the thermoviscous wave equation in which the time derivative of the viscous term is replaced by a fractional time derivative. An explicit time domain, finite element formulation leads to a stable algorithm capable of simulating axisymmetric, broadband acoustic pulses propagating through attenuative and dispersive media. The algorithm does not depend on the Born approximation, long wavelength limit, or plane wave assumptions. The algorithm is validated for planar and focused transducers and results include radiation patterns from a viscous scatterer in a lossless background and signals reflected from a viscous layer. The program can be used to determine scattering parameters for large, strong, possibly viscous scatterers, in either a lossless or viscous background, for which analytic results are scarce.