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 |
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Rok vydání: | 2017 |
Předmět: |
medicine.diagnostic_test
Applied Mathematics 010102 general mathematics Mathematical analysis Inverse Young's modulus Inverse problem 01 natural sciences 010101 applied mathematics symbols.namesake medicine symbols A priori and a posteriori Elastography 0101 mathematics Parametric statistics Mathematics |
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 |
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