The present invention is directed to an apparatus, system, and method for occluding or closing bodily passageways, including septal apertures in the heart, that employs a self-expanding shape-memory material to engage and conform to the lateral faces of the bodily passageways, wherein a structure comprising the self-expanding shape-memory material extends substantially around the periphery of a membrane or a membranous covering and is designed to hold the membrane or the membranous covering generally taut. The structure comprising a plurality of notches or cut-outs and assuming a variety of shapes and sizes suitable for occluding or closing various bodily passageways, including septal apertures located low in a heart or the septum. The present invention being specifically adapted for having a reduced propensity for tearing and rupturing, permitting post-deployment transseptal punctures and interatrial re-entry, and being designed to not interact or interfere with the tricuspid or mitral valves of the heart.
