Solution of the inverse elastography problem for parametric classes of inclusions with a posteriori error estimate

Autor: Anatoly G. Yagola, Alexander S. Leonov, Alexander N. Sharov
Rok vydání: 2017
Předmět:
Zdroj: Journal of Inverse and Ill-posed Problems. 26:493-499
ISSN: 1569-3945
0928-0219
DOI: 10.1515/jiip-2017-0043
Popis: This article presents the solution of a special inverse elastography problem: knowing vertical displacements of compressed biological tissue to find a piecewise constant distribution of Young’s modulus in an investigated specimen. Our goal is to detect homogeneous inclusions in the tissue, which can be interpreted as oncological. To this end, we consider the specimen as two-dimensional elastic solid, displacements of which satisfy the differential equations of the linear static theory of elasticity in the plain strain statement. The inclusions to be found are specified by parametric functions with unknown geometric parameters and unknown Young’s modulus. Reducing this inverse problem to the search for all unknown parameters, we solve it applying the modified method of extending compacts by V. K. Ivanov and I. N. Dombrovskaya. A posteriori error estimate is carried out for the obtained approximate solutions.
Databáze: OpenAIRE