According to one representative embodiment, a method of treating aortic insufficiency comprises delivering a support structure to a position around the leaflets of a native heart valve. The support structure comprises an annular body defining an interior and at least one projection extending radially inwardly from the annular body. An expandable prosthetic heart valve can be advanced into the native heart valve and into the interior of the annular body. The prosthetic heart valve can be expanded into contact with the leaflets of the native valve, thereby causing the leaflets of the native valve to be frictionally secured between an inner surface of the annular body and an outer surface of the prosthetic heart valve and causing the at least one projection and a portion of one of the leaflets contacted by the at least one projection to extend into an opening of the frame of the prosthetic valve.
