A simple viscoelastic model for soft tissues in the frequency range 6-20 MHz

IEEE Trans Ultrason Ferroelectr Freq Control. 2006 Aug;53(8):1404-11. doi: 10.1109/tuffc.2006.1665097.


In this paper, we present measurements of the shear properties of porcine skeletal muscle, liver, and kidney and a novel model describing them. Following a previously used method, shear mechanical impedances are measured, and complex shear moduli are obtained in the frequency range 6-20 MHz. As indicated in previous results, negative storage moduli are obtained in some measurements, which yield negative shear moduli in traditional linear viscoelastic models such as the Maxwell model, the Voigt model, and the Kelvin model. To resolve this problem, we propose a simple extension of the Voigt model. A mass is introduced into the model to account for the extra phase shift that apparently produces the negative moduli, and the shear stress thereby is related to the inertia of the material. The observed negative storage moduli are predicted by the new model when the relaxation time of the material is large and the working frequency is high. The model is fitted to experimental data to obtain values for material constants.

Publication types

  • Evaluation Study
  • Research Support, U.S. Gov't, Non-P.H.S.

MeSH terms

  • Animals
  • Computer Simulation
  • Connective Tissue / diagnostic imaging*
  • Connective Tissue / physiology*
  • Elasticity
  • Image Interpretation, Computer-Assisted / methods*
  • In Vitro Techniques
  • Models, Biological*
  • Radio Waves
  • Stress, Mechanical
  • Swine
  • Ultrasonography / methods*
  • Viscosity