Modeling Shear Wave Propagation in Biotissue: An Internal Variable Approach to Dissipation

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dc.contributor.advisor H.T. Banks, Committee Chair en_US
dc.contributor.advisor Negash Medhin, Committee Member en_US
dc.contributor.advisor Hien Tran, Committee Member en_US
dc.contributor.advisor Mansoor Haider, Committee Member en_US Luke, Nicholas Stephen en_US 2010-04-02T19:15:35Z 2010-04-02T19:15:35Z 2006-08-07 en_US
dc.identifier.other etd-08032006-134515 en_US
dc.description.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. en_US
dc.rights I hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to NC State University or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report. en_US
dc.subject nonlinear viscoelastic materials en_US
dc.subject shear wave propagation en_US
dc.subject mathematical modeling en_US
dc.subject inverse problem en_US
dc.title Modeling Shear Wave Propagation in Biotissue: An Internal Variable Approach to Dissipation en_US PhD en_US dissertation en_US Computational Mathematics en_US

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