A stabilizer for operations on a heart includes a fastening shaft and a tissue contact component with two elongated bearing elements provided on a base section and adapted to be arranged on two opposing sides of a blood vessel such that at least one section of the blood vessel runs between the two bearing elements, wherein the base section is affixed to one end of the fastening shaft. At least one bearing element has a slit extending longitudinally at least over a section thereof. The fastening shaft has an axially proceeding channel which extends at least over a section of the fastening shaft and is connected to at least one connecting channel in the region of the end of the fastening shaft on which the base section is mounted, the connection channel connecting the axially proceeding channel to the surroundings, wherein the axial end of the fastening shaft is closed.
