Our broad aim is to integrate experimental measurements (electro-cardiographic and MR) and cardiac computer models, for a better understanding of transmural wave propagation in individual hearts. In this paper, we first describe the acquisition and processing of the data provided to the EP simulation challenge organized at STACOM'11. The measurements were obtained in two swine hearts (i.e., one healthy and one with chronic infarction) and comprise in-vivo electro-anatomical CARTO maps (e.g., surfacic endo-/epicardial depolarization maps and bipolar voltage maps recorded in sinus rhythm), and high-resolution ex-vivo diffusion-weighted DW-MR images (voxel size <1mm 3). We briefly detail how we built anisotropic 3D MRI-based models for these two hearts, with fiber directions obtained using DW-MRI methods (which also allowed for infarct identification). We then focus on applications in cardiac modelling concerning propagation of depolarization wave, by employing forward mathematical approaches. Specifically, we present simulation results for the depolarization wave using a fast, macroscopic monodomain formalism (i.e., the two-variable Aliev-Panfilov model) and comparisons with measured depolarization times. We also include simulations obtained using the healthy heart and a simple Eikonal model, as well as a complex bidomain model. The results demonstrate small differences between computed isochrones using these computer models; specifically, we calculated a mean error ± S.D. of 2.8 ± 1.67 ms between Aliev-Panfilov and Eikonal models, and 6.1 ± 3.9 ms between Alie-Panfilov and bidomain models, respectively.