Implantable medical devices 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, a central region, and a covering material. The devices are endoscopically deployable and may include flange members having hinge members or variable properties such as length, angle, shape, material stiffness, and wire diameter.
