An apparatus for controlling a flow of blood in a lumen formed by a tissue wall of a patient's heart comprises an implantable constriction/compression device for gently compressing (i.e.- without substantially hampering the blood circulation in the tissue wall) at least one portion of the tissue wall to influence the flow in the lumen, and a stimulation device for stimulating the wall portion of the tissue wall. A control device controls the stimulation device to stimulate the wall portion, as the compression device constricts the wall portion, to cause contraction of the wall portion constricted by the compression device to further influence the flow in the lumen. The apparatus can be used for restricting or stopping the flow in the lumen, or for actively moving the blood in the lumen, with a low risk of injuring the heart.
