Solution of the inverse elastography problem for parametric classes of inclusions with a posteriori error estimateстатья
Статья опубликована в высокорейтинговом журнале
Информация о цитировании статьи получена из
Web of Science,
Scopus
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 11 января 2018 г.
Аннотация: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’smodulus in an investigated specimen. Our goal is to detecthomogeneous 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.