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 (42a, 42b, 202, 204, 302, 304, 402, 404, 502, 504, 602, 604, 702, 703, 802, 804), a central portion (44, 206, 306, 406, 506, 606, 706, 806), and a covering material (112, 712). The devices are endoscopically deployable and may include open cells or undulating edges that facilitate a secure connection between the tissue structures.
