Application of the topological sensitivity method to the detection of breast cancer

Abstract

Abstract This paper is concerned with an approach based on the topological sensitivity notion to solve a geometric inverse problem for a linear wave equation. The considered inverse problem is motivated by elastography. More precisely, the modelli ng of our application system has been aimed toward the detection of a breast tumour, in particular, and to enable the calculation of the tumour size, location and type. We start our analysis by rephrasing the considered inverse problem as an optimization one minimizing an energy cost functional. We establish an estimation describing the asymptotic behaviour of the wave equation solution with respect to the presence of a small tumour in the breast, which plays an important role in the derivation of a topological asymptotic formula for the considered cost function. Based on the derived theoretical results, we have developed a numerical algorithm for solving our inverse problem, which requires only one iteration. Some numerical experiments are presented to point out the efficiency and accuracy of the proposed approach.