Modeling Shear Wave Propagation in Biotissue: An Internal Variable Approach to Dissipation
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Date
2006-08-07
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Abstract
The ability to reliably detech artery disease based on the acoustic noises produced by a stenosis can provide a simple, non-invasive technique for diagnosis. Current research exploits the shear wave fields in body tissue to detect and analyze coronary stenoses. A mathematical model of this system, utilizing an internal strain variable approximation to the quasi-linear viscoelastic constitutive equation proposed by Fung, was previously presented. The methods an ideas outlined in that presentation are expanded upon in this work.
As an initial investigation, a homogeneous two-dimensional viscoelastic geometry is considered. Being uniform in theta, this geometry behaves as a one dimensional model, and the results generated from it are compared to the one dimensional results. Several variations of the model are considered, to allow for different assumptions about the elastic response. A statistical significance test is employed to determine if the extra parameters needed for certain variations of the model are necessary in modeling efforts.
After validating the model with the comparison to previous findings, more complicated geometries are developed. Simulations involving a heterogeneous geometry with a uniform ring running through the originam medium, a theta dependent model which considers a rigid occlusion formed along the inner radius of the geometry, and a model which combines the ring and occlusion are presented. In an attempt to move towards the ultimate goal of detecting the location of a stenosis from the data gathered at the chestwall, an inverse problem methodology is introduced and results from the inverse problem are shown.
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nonlinear viscoelastic materials, shear wave propagation, mathematical modeling, inverse problem
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Degree
PhD
Discipline
Computational Mathematics
