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 pro...

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Bibliographic Details
Published in:SIAM journal on scientific computing Vol. 33; no. 3; pp. 1181 - 1211
Main Authors: Perego, Mauro, Veneziani, Alessandro, Vergara, Christian
Format: Journal Article
Language:English
Published: Philadelphia, PA Society for Industrial and Applied Mathematics 01.01.2011
Subjects:
Cardiovascular system
Compliance
Deformation
Displacement
Estimates
Estimating
Exact sciences and technology
Fluid-structure interaction
Inverse
Mathematical models
Mathematics
Methods of scientific computing (including symbolic computation, algebraic computation)
Modulus of elasticity
Numerical analysis
Numerical analysis in abstract spaces
Numerical analysis. Scientific computation
Sciences and techniques of general use
Studies
76Z05
Parameter estimation
Numerical analysis
fluid-structure interaction
Scientific computation
Numerical solution
inverse problems
Well posed problem
Sampling
65N21
vessel's rigidity
Inverse problem
ISSN:1064-8275, 1095-7197
Online Access:Get full text
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Summary: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. [PUBLICATION ABSTRACT]
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ISSN:1064-8275
1095-7197
DOI:10.1137/100808277