TY - JOUR

T1 - Uniqueness of the interior plane strain time-harmonic viscoelastic inverse problem

AU - Zhang, Yixiao

AU - Barbone, Paul E.

AU - Harari, Isaac

AU - Oberai, Assad A.

PY - 2016/7/1

Y1 - 2016/7/1

N2 - Elasticity imaging has emerged as a promising medical imaging technique with applications in the detection, diagnosis and treatment monitoring of several types of disease. In elasticity imaging measured displacement fields are used to generate images of elastic parameters of tissue by solving an inverse problem. When the tissue excitation, and the resulting tissue motion is time-harmonic, elasticity imaging can be extended to image the viscoelastic properties of the tissue. This leads to an inverse problem for the complex-valued shear modulus at a given frequency. In this manuscript we have considered the uniqueness of this inverse problem for an incompressible, isotropic linear viscoelastic solid in a state of plane strain. For a single measured displacement field we conclude that the solution is infinite dimensional, and the data required to render it unique is determined by the measured strain field. In contrast, for two independent displacement fields such that the principal directions of the resulti.

AB - Elasticity imaging has emerged as a promising medical imaging technique with applications in the detection, diagnosis and treatment monitoring of several types of disease. In elasticity imaging measured displacement fields are used to generate images of elastic parameters of tissue by solving an inverse problem. When the tissue excitation, and the resulting tissue motion is time-harmonic, elasticity imaging can be extended to image the viscoelastic properties of the tissue. This leads to an inverse problem for the complex-valued shear modulus at a given frequency. In this manuscript we have considered the uniqueness of this inverse problem for an incompressible, isotropic linear viscoelastic solid in a state of plane strain. For a single measured displacement field we conclude that the solution is infinite dimensional, and the data required to render it unique is determined by the measured strain field. In contrast, for two independent displacement fields such that the principal directions of the resulti.

UR - http://www.scopus.com/inward/record.url?scp=84964515183&partnerID=8YFLogxK

U2 - 10.1016/j.jmps.2016.03.018

DO - 10.1016/j.jmps.2016.03.018

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AN - SCOPUS:84964515183

SN - 0022-5096

VL - 92

SP - 345

EP - 355

JO - Journal of the Mechanics and Physics of Solids

JF - Journal of the Mechanics and Physics of Solids

ER -