As part of a continuing effort by the scientific community to develop reliable models of the electrical waves that contracts the heart muscle, a combined approach is presented that includes an approximated deformation model for the moving heart using medical images of the heart muscle, a particle method for parabolic PDE's, and variational integrators for calculation of the deformation of the images. The electrical response of the myocardium will be approximated using a Monodomain model, and the motion of the heart will be initially interpolated following a diffeomorphic spline approach, solved using a gradient descent on the initial momentum. The meshless particle method developed involves the motion of the nodes (particles) by the time dependent vector field defined by the image registration, adding an extra difficulty to known electrophysiology meshless models.