A vascular medical device is provided, which contains at least one phenolic compound. The medical device also contains at least one polymeric region, which regulate the release of the phenolic compound from the device. The polymeric region, in turn, contains at least one polymer species. In some embodiments, for example, the polymeric region contains a vinyl aromatic polymer species (e.g., a styrene homopolymer or copolymer). In other embodiments, for example, the polymeric region contains an alkene polymer species (e.g., an isobutylene homopolymer or copolymer). In still other embodiments, for example, the polymeric region contains a biostable polymer having at least one Tg below 25° C. (e.g., a homopolymer or copolymer containing one or more polyalkene polymer blocks).