Finding consensus among rheological models for shear waves in soft tissues

Abstract

Shear wave viscoelastic properties of tissue are now measured by a wide variety of methods including elastography, imaging scanners, rheological shear viscometers, and a variety of calibrated stress-strain analyzers. Because absorption and sound speed can be strong functions of frequency, fitting the data to an viscoelastic model which best describes observed behavior is a common step in understanding and comparing data sets among tissues and disease states. Because the same data can be represented by different model constants, there is a need to reach consistency and consensus on the most effective models among different sub-fields in acoustics, biomechanics, and elastography. To this end, we examined many established rheological models as well as data sets. We argue that the long history of biomechanics, including the concept of the extended relaxation spectrum, and the theoretical framework of multiple relaxation models which model the multi-scale nature of physical tissues, consistent with power law data extending over several decades of frequency and time, all lead to the conclusion that fractional derivative models represent the most succinct and meaningful models of soft tissue viscoelastic behavior.