Artificial heart valve structures and methods of their fabrication are disclosed. The heart valve structures may be fabricated from a biocompatible polymer and include one or more heart valve leaflet structures incorporated within a conduit. The valve structures may incorporate one or more conduit sinuses, as well as a gap between the lower margin of the valve leaflets and the interior of the conduit. In addition, the valve structures may include one or more valve sinuses created in a space between the valve leaflets and the conduit inner surface. Computational fluid dynamics and mechanical modeling may be used to design the valve leaflets with optimal characteristics. A heart valve structure may also incorporate a biodegradable component to which cells may adhere. The incorporated cells may arise from patient cells migrating to the biodegradable component, or the component may be pre-seeded with cells prior to implantation in a patient.