Electrical activity in the heart is associated with the propagation of waves with localized sharp fronts and strong gradients while for a large portion of the domain little variation is shown in all dependent variables. An other difficulty is the coupling of the electrical activity in the heart with the surrounding tissues in the torso. Anisotropic mesh adaptation has proved to be a powerful strategy to improve the accuracy and efficiency of finite element methods for solution with strong directional variations as seen with electrical waves in the heart. A main issue in our problem is the unsteady nature of the electrical waves which calls for time-dependant mesh adaptation strategies. We propose an anisotropic mesh adaptation method using a priori metric-based error estimate that is efficient for electrical waves in the heart-torso. A metric is built from metric intersection of all variables over consecutive time steps. Geometries in medical applications are often obtained from medical image segmentation, in our case using a level-set method. To deal with such level-set description of the heart-torso interface, we investigate the use of body fitted and non-body fitted meshes. An appropriate modification of the metric estimator is proposed to insure the accuracy of finite element solutions on non-body fitted meshes. In our talk, the methodology will be described in details and numerical results will show the efficiency of the approach for computing electrical waves propagation using a moving 2D heart-torso geometry.