Viscoelastic Modulus Reconstruction Using Time Harmonic Vibrations

Habib Ammari, Jin Keun Seo, Liangdong Zhou

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)836-851
Number of pages16
JournalMathematical Modelling and Analysis
Issue number6
Publication statusPublished - 2015 Nov 2

Bibliographical note

Publisher Copyright:
© 2015 Vilnius Gediminas Technical University.

All Science Journal Classification (ASJC) codes

  • Analysis
  • Modelling and Simulation


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