A mathematical model of a four-layer medium (muscle+fat+skin+air) is investigated. The system is studied in cartesian coordinates with the hypotheses of muscle anisotropy and isotropy of the fat and skin layers, assuming the fat to be less conductive than the skin. Determination of the potential distribution over the skin, due to sources in the muscle, is based on the solution of the Poisson equation in the spatial frequency domain in the different media. The arbitrary constants are determined imposing the boundary conditions. In this way the transfer function of the fat and skin layers is found and can be used to compute the potential distribution of the muscle-fat interface. The physiological parameters were obtained from literature. The results of simulation studies are proposed; it is clear that the subcutaneous tissue layers produce an attenuation and widening of the potential distribution present at the muscle surface. These effects can be partially compensated using high-pass spatial filters as proposed in the literature. A new class of bidimensional spatial filters is proposed; the filters are defined on the basis of the information about the isotropic layers rather than being general filters. An approximation of the ideal inverse transfer function of the sub-cutaneous layers is proposed as a discrete spatial filter that can be implemented with matrices with a small number of electrodes (maximum of 25 electrodes) and practicable interelectrode distance. A simulated evaluation of the new filter and the limitations of the approach are presented.