Artificial prostheses with preferred geometries

Implantable medical devices, such as intraluminally implantable stents and valves, are provided having certain preferred shapes. Preferably, a portion of the implantable medical device can define a sinus region having a preferred geometry. The sinus region can have one or more preferred geometric configurations described herein, for example to mitigate or prevent thrombosis within a body vessel. The medical device can include a valve means, such as one or more valve leaflets positioned within the sinus region. The implantable medical devices can be delivered from a catheter within a body vessel, and are preferably expandable from a compressed configuration to a radially expanded configuration. The implantable frames can be self-expanding or balloon expandable. Portions of the medical device, such as the implantable frame or a valve leaflet, are optionally coated with one or more bioactive materials.