Prosthetic heart valve with pouch

Apparatus, comprising:

• a frame assembly that comprises a valve body that circumscribes a longitudinal axis and defines a lumen along the axis;
• a tubular liner that lines the lumen and has an upstream end and a downstream end;
• a plurality of prosthetic leaflets, disposed within the lumen, attached to the liner, and arranged to facilitate one-way upstream-to-downstream fluid flow through the lumen;
• a first sheet of flexible material, the first sheet having (i) a greater perimeter, and (ii) a smaller perimeter that defines an opening aligned with the lumen of the valve body;
• and
• a second sheet of flexible material:
• the second sheet having a first perimeter and a second perimeter,
• the first perimeter being attached to the greater perimeter of the first sheet around the greater perimeter of the first sheet, and
• the second sheet extending from the first perimeter radially inwards and downstream toward the second perimeter, the second perimeter circumscribing and attached to the valve body,
• wherein:
• the first sheet, the second sheet, and the liner define an inflatable pouch,
• the inflatable pouch defines an interior space therein,
• the first sheet defines an upstream wall of the pouch,
• the second sheet defines a radially-outer wall of the pouch,
• the liner defines a radially-inner wall of the pouch,
• the second sheet is in contact with the first sheet, and
• the pouch circumscribes the valve body.