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Spatially Weighted Objective Function to Solve the Inverse Elasticity Problem for the Elastic Modulus

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Computational Biomechanics for Medicine

Abstract

We briefly review the iterative solution of the inverse problem in elasticity, which is posed as a constrained optimization method. The objective function minimizes the discrepancy between a measured and a computed displacement field in the L-2 norm and is subject to the static equations of equilibrium in elasticity. We realize that this inverse formulation is sensitive to Dirichlet and Neumann boundary conditions, i.e., sensitive to varying spatial deformations in the region of interest. This problem arises in particular, when solving the inverse problem for more than one inclusion in a homogeneous background, where the inclusions represent diseased tissues such as cysts, benign tumors, malignant tumors, etc. In order to address this issue, we propose to introduce a new formulation of the objective function, where the displacement correlation term is spatially weighted. We refer to this new formulation as the spatially weighted objective function and show that it improves the uniqueness of the inverse problem solution.

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Correspondence to Sevan Goenezen .

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Mei, Y., Goenezen, S. (2015). Spatially Weighted Objective Function to Solve the Inverse Elasticity Problem for the Elastic Modulus. In: Doyle, B., Miller, K., Wittek, A., Nielsen, P. (eds) Computational Biomechanics for Medicine. Springer, Cham. https://doi.org/10.1007/978-3-319-15503-6_5

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  • DOI: https://doi.org/10.1007/978-3-319-15503-6_5

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-15502-9

  • Online ISBN: 978-3-319-15503-6

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