An extra-luminal ring (1200) includes a structural member (1202), which assumes a first elongate hollow shape (1206) when in a relaxed state; when deformed to a planar state (1208), generally defines a planar shape (1209) having two first sides (1220A, 1220B) parallel to each other, and two second sides (1222A, 1222B) parallel to each other; and when in the relaxed state, is configured such that the two first sides (1220A, 1220B) are generally straight and parallel with each other, and the two second sides (1222A, 1222B) are curved at least partially around a first longitudinal axis (1230) defined by the first elongate hollow shape (1206). The structural member (1202), when in a deformed state, has a second elongate hollow shape (1240), different from the first elongate hollow shape (1206), in which the two second sides (1222A, 1222B) are generally straight and parallel with each other, and the two first sides (1220A, 1220B) are curved at least partially around a second longitudinal axis (1250) defined by the second elongate hollow shape (1240).