We briefly present a new epicardial source model for the inverse problem of cardiac electrocardiography. It couples a surface equation on the epicardium with the three-dimensional torso, while incorporating heart-torso fluxes and possible anisotropic conductivities in the intracellular and extracellular domains. As this capability is new for a surface model, we investigate the impact of inserting epicardial fiber directions into the surface source model on inverse reconstructions, compared with isotropy-based reconstructions. Our results show that the epicardial fibers degrade the epicardial model based ECGi reconstructions, in particular the transmembrane voltage, whereas isotropic reconstructions demonstrate significantly higher accuracy for the extracellular potential and the transmembrane voltage. We believe that, due to interactions and compensations within the myocardial volume, the solutions of the bidomain model taken on a surface are more similar to isotropic solutions than strongly anisotropic ones. In this case, taking an isotropic assumption in a surface model based ECGi is a relevant choice.