An implantable flow connector for fluidically coupling a source tissue-enclosed body space with a destination element, comprising: a conduit having a lumen terminating at an orifice at a first end of the conduit implantable in the source body space through an opening formed in a tissue wall of the source body space, and a second end of the conduit implantable in the destination element through an opening in a surface of the destination element; and a circumferential flange, radially extending from the conduit proximate the conduit first end, configured to be implanted in the source body space adjacent an opening in the tissue wall of the source body space such that the conduit extends through the opening, the flange comprising one or more circumferentially adjacent sections at least one of which has a rigidity that decreases in a radially-increasing direction.