Shape optimization for tumor location

In non-invasive thermal diagnostics for the location of a tumor, accurate correlations between the thermal image on skin surface and interior human physiology are often desired, which require general solutions for the bioheat equation. In this paper we use sensitivity analysis in order to compute the shape derivative of the funtional that provides the minimum (the geometrical position of the tumnor). We minimize a functional that depends on the temperature of the body in a domain and on the temperature on the boundary of the domain obtained from the experimental data.