A method of implanting a prosthetic heart valve includes advancing a distal end portion of a catheter shaft through a patient's vasculature. The distal end portion of the catheter shaft includes an expansion device. A prosthetic heart valve is mounted on the expansion device with the expansion device and the prosthetic heart valve in a compressed configuration. The method further includes positioning the distal end portion of the catheter shaft and the prosthetic heart valve to an implantation location, and expanding the prosthetic heart valve and the expansion device from the compressed configuration to an expanded configuration. The expansion device includes an inner expandable member and a plurality of outer expandable members. The outer expandable members are distributed such that there are gaps providing perfusion passageways between the expansion device and the prosthetic heart valve when the expansion device is in the expanded configuration.