Shape optimization for tumor location

C. TURNER

Rio de Janeiro

Workshop; Non Linear waves; 2011

IMPA, CNPq

In this work an estimation methodology to determine unknown geometrical parameters of an embedded tumor is proposed. We defined a functional that represents the mismatch between a measured experimental temperature profile, may be obtained by infrared thermography, at the skin surface and the solution of an appropriate boundary problem. This functional is related with the geometrical parameters through the solution of the boundary problem, in such a way that finding the minimum of this functional form also means to find the unknown geometrical parameters of the embedded tumor. The Barzilai and Borwein gradient method was implemented to solve the optimization problem of finding the optimal geometric parameters and sensitivity analysis techniques couple with the adjoint method were considered to compute the shape derivative of the functional.