Apparatus and methods for regulating the flow of fluids through a body vessel or organ are provided by a stent comprising a deformable mesh covered with a biocompatible material, the mesh having a conical portion and a constricted region. The stent may be percutaneously and transluminally delivered and deployed in a vessel. The constricted region may then be selectively enlarged employing a conventional dilatation device to adjust the flow impedance created by the constricted region. In an alternative embodiment, the constricted region is preferably formed from a shape-memory material, so that the maximum degree of constriction may be recovered by heating the shape-memory material. Methods of implanting the stent and adjusting and optimizing the degree of flow impedance are also provided.