A biomedical polymer has a substantially linear base polymer; and branched polyethylene oxide covalently bonded to the base polymer as surface active end groups. The branched polyethylene oxide has at least two, more particularly at least four, and still more particularly at least six branches. Suitable base polymers include epoxies, polyurethanes, polyurethane copolymers, fluoropolymers, polyolefins and silicone rubbers. Biologically active agents may be attached to the branched polyethylene oxide. Suitable biologically active agents include microbial peptide agents, detergents, non-steroidal anti-inflammatory drugs, cations, amine-containing organosilicones, diphosphonates, fatty acids, fatty acid salts, heparin and glucocorticosteroids. The biological polymer may be used as a casing for a medical unit of an implantable medical device, such as a pacemaker. In this case, the casing at least partially encloses the medical unit.