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Coimbra Institute for Biomedical Image and Translational Research, Faculty of Medicine, University of Coimbra, Edifício do ICNAS, Polo 3 Azinhaga de Santa Comba 3000-548, Coimbra, Portugal

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1 Papers

On the Numerical Solution of the Inverse Elastography Problem for Time-harmonic Excitation

Topic: Elastography

Authors: Pedro Serranho ^{1

;

2} , Sílvia Barbeiro ³ , Rafael Henriques ³ , Ana Batista ¹ , Mário J. Santos ⁴ , Carlos Correia ¹ , José P. Domingues ⁵ , Custódio Loureiro ⁵ , João M. R. Cardoso ⁵ , Rui Bernardes ^{1

;

6} and Miguel Morgado ^{1

;

5}

Affiliations: ¹ Coimbra Institute for Biomedical Image and Translational Research, Faculty of Medicine, University of Coimbra, Edifício do ICNAS, Polo 3 Azinhaga de Santa Comba 3000-548, Coimbra, Portugal , ² Department of Science and Technology, Universidade Aberta, Rua da Escola Politécnica, 147, 1269-001, Lisbon, Portugal , ³ University of Coimbra, CMUC - Center of Mathematics, Department of Mathematics, Apartado 3008, EC Santa Cruz, 3001-501, Coimbra, Portugal , ⁴ University of Coimbra, Department of Electrical and Computer Engineering, Faculty of Science and Technology, Pólo II, 3030-290, Coimbra, Portugal , ⁵ Department of Physics, University of Coimbra, Rua Larga, 3004-516, Coimbra, Portugal , ⁶ University of Coimbra, CACC-Clinical Academic Center of Coimbra, Faculty of Medicine (FMUC), Coimbra, Portugal

Digital Object Identifier: 10.5220/0011125900003209

Proceedings of Imaging4OND 2022, ISBN: 978-989-758-563-0

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In this paper we address the numerical solution of the inverse elastography problem, from the knowledge of the excitation field on the boundary and the displacement field in a grid of points within the domain. We suggest using a representation of the solution by the method of fundamental solutions and using a Newton- type method to iteratively approximate the Lamé coefficients of the medium from elastography displacement measurements. We consider a toy model to illustrate the performance of the method.