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.
Next to Magnet Resonance Elastography and Ultrasound Elastography, Digital Image Elasto-Tomography
(DIET) is a new imaging-technique, using only motion data available on the boundary, to reconstruct mechanical
material parameters, i.e. the interior sti.ness of a domain, in order to diagnose tissue related disease
such as breast cancer. Where classically Finite Element Methods have been employed to solve this inverse
problem, this paper explores a new approach to the reconstruction of mechanical material properties of tissue
and tissue defects by the use of Boundary Element Methods (BEM). Using the Boundary Integral Equations
for Linear Elasticity in two dimensions within a Conjugate Gradients based inverse solver, material properties
of healthy and malicious tissue could be determined from displacement data on the boundary. First simulation
results are presented.
A nonlinear inversion scheme formulated on small subzones of the total region of interest (ROI) is developed. The algorithm reconstructs the distribution of a linear elastic stiffness term and a Maxwellian damping parameter over the entire ROI through a least squares optimization. The subzones are generated in a hierarchical manner based on progressive error minimization and processed in an automated, sweeping fashion until certain performance criterion are met. Simulation results show that the algorithm works well to minimize global error and is capable of simultaneously reconstructing both property parameter distributions even in the presence of random noise, although initial experience suggests that the elastic property image is superior to its attenuation coefficient counterpart.