  We propose an immersed boundary scheme for the numerical resolution of the
Complete Electrode Model in Electrical Impedance Tomography, that we use as a
main ingredient in the resolution of inverse problems in medical imaging. Such
method allows to use a Cartesian mesh without accurate discretization of the
boundary, which is useful in situations where the boundary is complicated
and/or changing. We prove the convergence of our method, and illustrate its
efficiency with two dimensional direct and inverse problems.
