A plurality of structures that resiliently attract one another are provided for implanting in a patient around a body tissue structure of the patient. For example, the body tissue structure may be the esophagus, and the plurality of structures may be implanted in an annulus around the outside of the esophagus, the annulus being substantially coaxial with the esophagus. The attraction may be between annularly adjacent ones of the structures in the annulus, and it may be provided, for example, by magnets or springs. The array of structures is preferably self-limiting with respect to the smallest area that it can encompass, and this smallest area is preferably large enough to prevent the apparatus from applying excessive pressure to tissue passing through that area.