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. 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. A delivery apparatus for delivering the support structure can include a first shaft that is allowed to move in a proximal direction relative to a second shaft, when the second shaft foreshortens as a result of an adjustment mechanism being actuated to increase the curvature of the second shaft.