Computational models of heart electrophysiology achieved a great interest from the medical community since they represent a novel framework to study the mechanisms that underpin heart pathologies. The high demand of computational resources and the long computational times required to evaluate the model solution hamper the use of detailed computational models in clinical applications. In this paper, we propose a multi-front eikonal algorithm capable of adapting the conduction velocity (CV) to the activation frequency of the tissue substrate. We then couple the new eikonal model with a Mitchell-Schaeffer (MS) ionic model to determine the tissue electrical state. Compared to the standard eikonal model, this model introduces three novelties: first, the local value of the transmembrane potential and of the ionic variable are known from the solution of the ionic model; second, the action potential duration (AP D) and the diastolic interval (DI) are computed from the solution of the MS model and used to determine when a part of the tissue is re-excitable. Third, CV is locally adapted to the underpinning electrophysiological state through the analytical CV restitution expression and the computed local DI. We conduct series of simulations on a tissue slab and on 3D realistic heart geometry and compare results to the monodomain. Our results show that the new model is much more accurate than the standard eikonal model. This model enables the numerical simulation of the heart electrophysiology on a clinical time scale and thus constitutes a good model candidate for computer-guided cardiac therapy.Read less <