A Variational Approach for Estimating the Compliance of the Cardiovascular Tissue: An Inverse Fluid-Structure Interaction Problem

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 the Young modulus estimation. In the case of arteries, no forced deformation is required, since vessels naturally move under the action of blood. Young modulus can be therefore 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 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.