Modelling of Propagating Shear Waves in Biotissue Employing an Internal Variable Approach to Dissipation (Communications in Computational Physics, 2008)
The ability to reliably detect coronary artery disease based on the acousticnoises 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 andanalyze coronary stenoses. The methods and ideas outlined in earlier efforts [6] including a mathematical model utilizing an internal strain variable approximation tothe quasi-linear viscoelastic constitutive equation proposed by Fung in [19] is extendedhere. As an initial investigation, a homogeneous two-dimensional viscoelastic geometry is considered. Being uniform in θ, this geometry behaves as a one dimensionalmodel, and the results generated from it are compared to the one dimensional resultsfrom [6]. To allow for different assumptions on the elastic response, several variationsof the model are considered. A statistical significance test is employed to determine ifthe more complex models are significant improvements. After calibrating the modelwith a comparison to previous findings, more complicated geometries are considered.Simulations involving a heterogeneous geometry with a uniform ring running throughthe original medium, a θ-dependent model which considers a rigid partial occlusionformed along the inner radius of the geometry, and a model which combines the ringand occlusion are presented.