A prosthetic heart valve having a suture-permeable connecting band for securing the prosthetic heart valve to an anatomical cavity comprising:a flexible continuous connecting band having an inflow end and an outflow end, the connecting band having an undulating shape generally circumscribing a tube with alternating inflow cusps and outflow commissures, the cusps having large radii of curvatures relative to the commissures, an inflow edge of the connecting band substantially conforming to an outflow edge thereof and following the undulating shape such that axial gaps are created between adjacent cusps at the commissures, the gaps having a height of at least about 50% of the overall axial height of the connecting band, a sewing ridge being provided around the periphery of the connecting band that facilitates supra-annular attachment of the prosthetic valve, the sewing ridge being radially-outwardly directed at the commissures and larger and angled radially outward and toward the inflow end at the cusps.
