An implantable medical device (30) for treating aortic dissections includes a stent graft part (34) having a bulbous section (48) of greater radial diameter than the radial diameter of first and second sections (60,62) of the stent graft part (34). The bulbous section (48) is able to close off the false lumen (10) of an aortic dissection, thereby to prevent any fluid backflow into the false lumen (10). Radiopaque markers (70) may be provided for orientation and deployment purposes. The device (30) is able to treat chronic dissections and reduce false lumen backflow, which remains otherwise an unresolved issue in the endovascular treatment of false lumen aneurysms.
