An intraluminal device replaces the mitral valve in the human heart without tissue insult or injury via catheter-based deployment and securement. By controlling radial force, a one-piece device in a substantially hyperboloid configuration is emplaced using a least one of a biological adhesive and a porous layer encapsulating the device, for example, ePTFE, to manage the potential for migration. Systems for emplacement are likewise disclosed.
