TY - JOUR
T1 - Viscoelastic Modulus Reconstruction Using Time Harmonic Vibrations
AU - Ammari, Habib
AU - Seo, Jin Keun
AU - Zhou, Liangdong
N1 - Publisher Copyright:
© 2015 Vilnius Gediminas Technical University.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2015/11/2
Y1 - 2015/11/2
N2 - This paper presents a new iterative reconstruction method to provide high-resolution images of shear modulus and viscosity via the internal measurement of displacement fields in tissues. To solve the inverse problem, we compute the Fréchet derivatives of the least-squares discrepancy functional with respect to the shear modulus and shear viscosity. The proposed iterative reconstruction method using this Fréchet derivative does not require any differentiation of the displacement data for the full isotropic linearly viscoelastic model, whereas the standard algebraic inversion method requires at least double differentiation. Because the minimization problem is ill-posed and highly nonlinear, this adjoint-based optimization method needs a very well-matched initial guess. We find a good initial guess. For a well-matched initial guess, numerical experiments show that the proposed method considerably improves the quality of the reconstructed viscoelastic images.
AB - This paper presents a new iterative reconstruction method to provide high-resolution images of shear modulus and viscosity via the internal measurement of displacement fields in tissues. To solve the inverse problem, we compute the Fréchet derivatives of the least-squares discrepancy functional with respect to the shear modulus and shear viscosity. The proposed iterative reconstruction method using this Fréchet derivative does not require any differentiation of the displacement data for the full isotropic linearly viscoelastic model, whereas the standard algebraic inversion method requires at least double differentiation. Because the minimization problem is ill-posed and highly nonlinear, this adjoint-based optimization method needs a very well-matched initial guess. We find a good initial guess. For a well-matched initial guess, numerical experiments show that the proposed method considerably improves the quality of the reconstructed viscoelastic images.
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U2 - 10.3846/13926292.2015.1117531
DO - 10.3846/13926292.2015.1117531
M3 - Article
AN - SCOPUS:84947919118
VL - 20
SP - 836
EP - 851
JO - Mathematical Modelling and Analysis
JF - Mathematical Modelling and Analysis
SN - 1392-6292
IS - 6
ER -