Commun. Comput. Phys.,
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Volume 3.


Modelling of Propagating Shear Waves in Biotissue Employing an Internal Variable Approach to Dissipation

H. T. Banks 1*, Nicholas S. Luke 1

1 Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC 27695-8205, USA.

Received 7 February 2007; Accepted (in revised version) 28 July 2007
Available online 30 October 2007

Abstract

The ability to reliably detect coronary 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. The methods and ideas outlined in earlier efforts \cite{Banks2002a} including a mathematical model utilizing an internal strain variable approximation to the quasi-linear viscoelastic constitutive equation proposed by Fung in \cite{Fung} is extended here. 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 from \cite{Banks2002a}. To allow for different assumptions on the elastic response, several variations of the model are considered. A statistical significance test is employed to determine if the more complex models are significant improvements. After calibrating the model with a comparison to previous findings, more complicated geometries are considered. Simulations involving a heterogeneous geometry with a uniform ring running through the original medium, a $\theta$-dependent model which considers a rigid partial occlusion formed along the inner radius of the geometry, and a model which combines the ring and occlusion are presented.

AMS subject classifications: 74D10, 35L45, 62P10

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Key words: Viscoelasticity, partial differential equations, shear waves, biotissue.

*Corresponding author.
Email: htbanks@ncsu.edu (H. T. Banks), nsluke@ncsu.edu (N. S. Luke)
 

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