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In this paper, we analyze the use of simple models for solving the inverse problem in electrocardiography (IPE), which aims at recovering the heart condition from a set of remote voltages measurements. Specifically, we consider here the problem of estimating the shape, size and location of cardiac ischemic regions. The forward problem to generate the data (voltage measurements) is formulated by using the Luo-Rudy model, which provides a detailed description of the electrical behavior of cardiac cells. As for the inversion process, we use the two-current phenomenological model. The inversion procedure also incorporates a semi-automatic stage to characterize the conduction properties of the cardiac tissue. The ischemic regions are modeled by using standard level set techniques. Numerical results show that the algorithm is capable of estimating the position, size and shape of cardiac ischemic regions from noisy voltage measurements, for both 2D and 3D geometries. Our inverse procedure is benchmarked against zero-order Tikhonov regularization. This work is a proof of principle demonstrating the possibility of using simple models in the IPE towards realistic situations.