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In MR elastography it is common to use an elastic model for the tissue'sresponse in order to properly interpret the results. More complex models suchas viscoelastic, fractional viscoelastic, poroelastic, or poroviscoelastic onesare also used. These models appear at first sight to be very different, buthere it is shown that they all may be expressed in terms of elementaryviscoelastic models.  For a medium expressed with fractional models, many elementary spring-dampercombinations are added, each of them weighted according to a long-taileddistribution, hinting at a fractional distribution of time constants orrelaxation frequencies. This may open up for a more physical interpretation ofthe fractional models.  The shear wave component of the poroelastic model is shown to be modeledexactly by a three-component Zener model. The extended poroviscoelastic modelis found to be equivalent to what is called a non-standard four-parametermodel. Accordingly, the large number of parameters in the porous models can bereduced to the same number as in their viscoelastic equivalents. As long as theindividual displacements from the solid and fluid parts cannot be measuredindividually the main use of the poro(visco)elastic models is therefore as aphysics based method for determining parameters in a viscoelastic model.

Spring-damper equivalents of the fractional, poroelastic, and poroviscoelastic models for elastography