Damping models in elastography

Current optimization based Elastography reconstruction algorithms encounter difficulties when the motion approaches resonant conditions, where the model does a poor job of approximating the real behavior of the material. Model accuracy can be improved through the addition of damping effects. These effects occur in-vivo due to the complex interaction between microstructural elements of the tissue; however reconstruction models are typically formulated at larger scales where the structure can be treated as a continuum. Attenuation behavior in an elastic continuum can be described as a mixture of inertial and viscoelastic damping effects. In order to develop a continuum damping model appropriate for human tissue, the behavior of each aspect of this proportional, or Rayleigh damping needs to be characterized. In this paper we investigate the nature of these various damping representations with a goal of best describing in-vivo behavior of actual tissue in order to improve the accuracy and performance of optimization based elastographic reconstruction. Inertial damping effects are modelled using a complex density, where the imaginary part is equivalent to a damping coefficient, and the effects of viscoelasticity are modelled through the use of complex shear moduli, where the real and imaginary parts represent the storage and loss moduli respectively. The investigation is carried out through a combination of theoretical analysis, numerical experiment, investigation of gelatine phantoms and comparison with other continua such as porous media models.