Viscoelastic Modulus Reconstruction Using Time Harmonic Vibrations

Mathematical Modelling and Analysis

Liangdong Zhou¹  Jin Keun Seo¹  Habib Ammari² 

[1] Department of Computational Science and Engineering, Yonsei University, 50 Yonsei-Ro, Seodaemun-Gu, 120-749 Seoul, Korea;Department of Mathematics and Applications Ecole Normale Superieure, 45 Rue d’Ulm, 75005 Paris, France;

关键词: inverse problem;    viscoelasticity;    ill-posed problem;    reconstruction formula;   

DOI  :  10.3846/13926292.2015.1117531

来源: DOAJ

【 摘 要 】

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 Frechet derivatives of the least-squares discrepancy functional with respect to the shear modulus and shear viscosity. The proposed iterative reconstruction method using this Fr´echet 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.

【 授权许可】

Unknown