Estimation of shear modulus in media with power law characteristics

Ultrasonics. 2016 Jan:64:170-6. doi: 10.1016/j.ultras.2015.09.003. Epub 2015 Sep 9.

Abstract

Shear wave propagation in tissue generated by the radiation force is usually modeled by either a lossless or a classical viscoelastic equation. However, experimental data shows power law behavior which is not consistent with those approaches. It is well known that fractional derivatives results in power laws, therefore a time fractional wave equation, the Caputo equation, which can be derived from the fractional Kelvin-Voigt stress and strain relation is tested. This equation is solved using the finite difference method with experimental parameters obtained from the existing literature. The equation is characterized by a fractional order which is also the power law exponent of the frequency dependent shear modulus. It is shown that for fractional order between 0 and 1, the equation gives smaller shear modulus than the classical model. The opposite situation applies for fractional order greater than 1. The numerical simulation also shows that the shear wave velocity method is only reliable for small losses. In our case, this is only for a small fractional order. Based on the published values of fractional order from other studies, there is therefore a chance for biased estimation of the shear modulus.

Keywords: Attenuation; Fractional derivative; Shear wave.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Computer Simulation
  • Elastic Modulus* / physiology
  • Elasticity Imaging Techniques* / methods
  • Shear Strength / physiology