Implantable medical devices (40, 300, 400) for connecting tissue layers, such as for connecting a gallbladder and a portion of a gastrointestinal tract to create an anastomosis, include a tubular structure having a plurality of apposition portions (302,304), a central region (306), and a covering material. The devices are endoscopically deployable and include flange members (308, 310) having hinge members (322) of variable properties such as length, angle, shape, material stiffness, and wire diameter.
