Fractional calculus in viscoelasticity: An experimental study

Abstract

Viscoelastic properties of soft biological tissues provide information that may be useful in medical diagnosis. Noninvasive elasticity imaging techniques, such as Magnetic Resonance Elastography (MRE), reconstruct viscoelastic material properties from dynamic displacement images. The reconstruction algorithms employed in these techniques assume a certain viscoelastic material model and the results are sensitive to the model chosen. Developing a better model for the viscoelasticity of soft tissue-like materials could improve the diagnostic capability of MRE. The well known “integer derivative” viscoelastic models of Voigt and Kelvin, and variations of them, cannot represent the more complicated rate dependency of material behavior of biological tissues over a broad spectral range. Recently the “fractional derivative” models have been investigated by a number of researchers. Fractional order models approximate the viscoelastic material behavior of materials through the corresponding fractional differential equations. This paper focuses on the tissue mimicking materials CF-11 and gelatin, and compares fractional and integer order models to describe their behavior under harmonic mechanical loading. Specifically, Rayleigh (surface) waves on CF-11 and gelatin phantoms are studied, experimentally and theoretically, in order to develop an independent test bed for assessing viscoelastic material models that will ultimately be used in MRE reconstruction algorithms.