Percutaneously-deliverable dual-frame valve

Apparatus for use at a native valve of a heart of a subject, the apparatus comprising a prosthetic valve, the prosthetic valve comprising:

• a first frame, defining an arrangement of cells;
• a second frame;
• a first protrusion;
• and
• a second protrusion,
• wherein:
• the prosthetic valve has a compressed state in which the prosthetic valve is transluminally deliverable to the heart, and an expanded state into which the prosthetic valve is expandable within the heart,
• in the expanded state, the first frame is generally cylindrical and has an expanded width, and the prosthetic valve defines a lumen having a first end and a second end,
• in the compressed state, the first frame and the second frame are both generally cylindrical, and the first frame has a compressed width that is smaller than the expanded width,
• in the expanded state, the prosthetic valve provides directional fluid flow through the lumen by opening and closing in response to changes in relative fluid pressure between the first end and the second end,
• the prosthetic valve defines a first coupling point, a second coupling point, and an axis therebetween, the axis lying on a transverse cross-section of the first frame, and
• in both the compressed state and the expanded state:
• at the first coupling point, the first protrusion couples the second frame to the first frame by protruding into a first slot defined by the first frame, and
• at the second coupling point, the second protrusion couples the second frame to the first frame by protruding into a second slot defined by the first frame.