Locating multiple tumors by moving shape analysis

A methodology to determine the unknown shape of an embedded tumor is proposed. A functional that represents the mismatch between a measured experimental temperature profile, which may be obtained by infrared thermography at skin surface, and the solution of an appropriate boundary problem is defined. Using the Pennes's bioheat transfer equations, the temperature in a section of healthy tissue with a tumor region is modeled by a boundary problem. The functional is related to the shape of the tumor through the solution of the boundary problem, in such a way that finding the minimum of the functional form also means finding the unknown shape of the embedded tumor. The shape derivative of the functional is computed in each node of an approximation of the solution by the method of Finite Elements using similar methods considered by Pironneau [7]. The algorithm presented include an adaptive strategy to improve the error of the objective function. Numerical results with multiple connected tumors are considered to illustrate the potential of the proposed methodology.