Kramers–Kronig relationships applied to shear wave propagation in soft tissues.

Abstract

Multiple methods have been proposed to characterize the viscoelastic material properties of soft tissues to differentiate normal from pathological tissue. Shearwave dispersion ultrasound vibrometry is a method that uses the dispersion of the shear wave velocity to characterize tissue shear elasticity and viscosity. It has recently been shown [M. W. Urban and J. F. Greenleaf, Phys. Med. Biol. 54, 5919–5933 (2009)] that the Kramers–Kronig relationships can be applied to shear wave measurements in ex vivo skeletal muscle over a frequency bandwidth of 100–600 Hz. We will describe this process where shear wave attenuation is modeled using a power law, and the shear wave velocity dispersion is predicted by applying the Kramers–Kronig relationships. In this study, we apply this method to shear wave propagation measurements made in different soft tissues such as ex vivo porcine skeletal muscle and kidney and in vivo porcine liver. The shear wave velocity predictions using the Kramers–Kronig relationships agree with the velocity measurements. The mean square error for these tissues ranged from 0.0024–0.0625 m2/s2. The Kramers–Kronig relationships can be used in shear wave propagation measurements in different types of soft tissues. [This work was supported in part by NIH Grants Nos. EB002167 and DK082408.]