There is provided a method for controlling a flow of fluid and/or other bodily matter in a lumen formed by a tissue wall of a patients organ. The method comprises gently constricting (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 stimulating the constricted wall portion to cause contraction of the wall portion to further influence the flow in the lumen. The method can be used for restricting or stopping the flow in the lumen, or for actively moving the fluid in the lumen, with a low risk of injuring the organ. Such an organ may be the esophagus, stomach, intestines, urine bladder, urethra, ureter, renal pelvis, aorta, corpus cavernosum, exit veins of erectile tissue, uterine tube, vas deferens or bile duct, or a blood vessel.