Estimating the power law exponent of shear waves in soft tissue with a time-domain parametric model

In soft tissue, the attenuation of shear waves satisfies a power law. However, the values of power law exponents for shear waves in various soft tissues remain unknown due to windowing artifacts that limit the effectiveness of present methods that are based on two-dimensional fast Fourier transforms. To solve this problem, a time-domain signal processing approach is proposed. Robust shear wave parameter estimates are obtained by minimizing the least-squares error between measured time-domain shear wave data and stable probability density functions that describe the solution to a closely related fractional-order diffusion equation. Assessments are performed with measured shear wave data collected from ex vivo pig liver using a Verasonics system with an L7-4 linear array transducer. Power law exponents are obtained from measured shear wave data at the focal depth between 1.2 and 13.9 mm from the center of the push beam. The mean estimated power law exponent for these locations is 0.74, and the standard deviation is 0.05. The results suggest that fractional calculus models that support power law exponents less than one are needed for shear waves in pig liver.