Springdamper equivalents of the fractional, poroelastic, and poroviscoelastic models for elastography
Abstract
In MR elastography it is common to use an elastic model for the tissue's response in order to properly interpret the results. More complex models such as viscoelastic, fractional viscoelastic, poroelastic, or poroviscoelastic ones are also used. These models appear at first sight to be very different, but here it is shown that they all may be expressed in terms of elementary viscoelastic models. For a medium expressed with fractional models, many elementary springdamper combinations are added, each of them weighted according to a longtailed distribution, hinting at a fractional distribution of time constants or relaxation frequencies. This may open up for a more physical interpretation of the fractional models. The shear wave component of the poroelastic model is shown to be modeled exactly by a threecomponent Zener model. The extended poroviscoelastic model is found to be equivalent to what is called a nonstandard fourparameter model. Accordingly, the large number of parameters in the porous models can be reduced to the same number as in their viscoelastic equivalents. As long as the individual displacements from the solid and fluid parts cannot be measured individually the main use of the poro(visco)elastic models is therefore as a physics based method for determining parameters in a viscoelastic model.
 Publication:

arXiv eprints
 Pub Date:
 March 2017
 arXiv:
 arXiv:1703.09515
 Bibcode:
 2017arXiv170309515H
 Keywords:

 Physics  Biological Physics;
 Condensed Matter  Soft Condensed Matter
 EPrint:
 11 pages, 7 figures. Changed inconsistent notation in Eqs 1, 5, 8, 10 and corrected mistakes in Eqs 2, 4, 12, 30