Magnetic resonance elastography is a technique where mechanical properties of materials are estimated by fitting a mechanical model to an MRI-acquired displacement field. These models have been primarily limited to viscoelasticity and linear elasticity, and only recently has poroelasticity been utilized as an applied model. To validate these estimates, the same material is measured via an independent dynamic mechanical analysis device. However, these devices only apply analytic viscoelastic models. In some cases, there is a model mismatch if a viscoelastic mechanical analysis is being compared to a poroelastic model in elastography. Thus, a poroelastic dynamic mechanical analysis technique is needed to properly measure porous media and compare the results with the appropriate elastography technique. A finite element technique was implemented on a TA-Q800 Dynamic Mechanical Analysis machine similar to the algorithm used in the corresponding MR elastography method. A viscoelastic version of the finite element code was created to validate the theory and show results similar to those obtained by the analytic DMA solution. Also, differences were seen that can be attributed to inertial forces not accounted for by an analytical solution. A poroelastic algorithm was then applied, showing great promise in the ability to measure properties of porous tissues.
KEYWORDS: Motion models, Reconstruction algorithms, Tissues, Elastography, Data modeling, Optimization (mathematics), Magnetic resonance elastography, Matrices, 3D modeling, Algorithm development
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.
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