Topological asymptotic analysis for tumor identification problem

Article type: Research Article

Authors: Chorfi, Nejmeddine^{a; *} | Ghezaiel, Emna^b | Hassine, Maatoug^c

Affiliations: [a] Department of Mathematics, College of Sciences, King Saud University, Saudi Arabia | [b] ESSThs, Sousse University, Tunisia. E-mail: ghezaiel.emna@gmail.com | [c] FSM, Monastir University, Tunisia. E-mail: maatoug.hassine@enit.rnu.tn

Correspondence: [*] Corresponding author. E-mail: nchorfi@ksu.edu.sa.

Abstract: This work is concerned with the problem of identifying the shape, size and location of a small embedded tumor from measured temperature on the skin surface. The temperature distribution in the biological tissue is governed by the Pennes model equation. The proposed approach is based on the Kohn–Vogelius formulation and the topological sensitivity analysis method. The ill-posed geometric inverse problem is reformulated as a topology optimization. The temperature field perturbation, caused by the presence of a small anomaly, is analyzed and estimated. A topological asymptotic formula, describing the variation of the considered Kohn–Vogelius type functional with respect to the presence of a small anomaly is derived.

Keywords: Asymptotic analysis, topological sensitivity, inverse problem, Kohn–Vogelius formulation

DOI: 10.3233/ASY-201635

Journal: Asymptotic Analysis, vol. 123, no. 3-4, pp. 317-333, 2021