An actuation mechanism for assisting the operation of the natural heart has a varying shape for deforming the heart. In one embodiment, a plurality of links articulates with respect to each other for varying the shape of the actuation mechanism. The plurality of links is configured for being positioned proximate to an outer surface of the heart for deforming the heart by varying the shape of the actuation mechanism. In another embodiment, a jacket for coupling with an outer surface of the heart has a tether coupled to successive sections of the jacket. The tether is operable to be translated with respect to the jacket sections to vary the shape of the jacket for deforming the heart. In another embodiment, a plurality of concentric ring structures are coupled together to move with respect to each other in a concentric fashion. A movement mechanism coupled to the rings is operable to vary their positions with respect to each other to vary the overall shape for deforming the heart.