An Augmented Lagrangian Method for Identifying Discontinuous Parameters in Elliptic Systems
SIAM Journal on Control and Optimization
Perspectives in Flow Control and Optimization
Perspectives in Flow Control and Optimization
SIAM Journal on Scientific Computing
Fluid-structure partitioned procedures based on Robin transmission conditions
Journal of Computational Physics
GNU Scientific Library Reference Manual - Third Edition
GNU Scientific Library Reference Manual - Third Edition
Fair: Flexible Algorithms for Image Registration
Fair: Flexible Algorithms for Image Registration
Optimal Control of Parameter-Dependent Convection-Diffusion Problems around Rigid Bodies
SIAM Journal on Scientific Computing
High resolution methods for scalar transport problems in compliant systems of arteries
Applied Numerical Mathematics
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Estimation of the stiffness of a biological soft tissue is useful for the detection of pathologies such as tumors or atherosclerotic plaques. Elastography is a method based on the comparison between two images before and after a forced deformation of the tissue of interest. An inverse elasticity problem is then solved for Young's modulus estimation. In the case of arteries, no forced deformation is required, since vessels naturally move under the action of blood. Young's modulus can therefore be estimated by solving a coupled inverse fluid-structure interaction problem. In this paper we focus on the mathematical properties of this problem and its numerical solution. We give some well posedness analysis and some preliminary results based on a synthetic data set, i.e., test cases where the exact Young's modulus is known and the displacement dataset is numerically generated by solving a forward fluid-structure interaction problem. We address the problem of the presence of the noise in the measured displacement and of the proper sampling frequency for obtaining reliable estimates.