A heart support system featuring a constraint sized to fit about at least a portion of an adult human heart in a living body, an expandable chamber disposed within the constraint so as to apply pressure against the heart when expanded and a connector system including a pneumatic connection port in hydraulic communication with the expandable chamber. The heart support system can include a supply unit with: a source of pressurized fluid and a pneumatic supply line extending from the pressurized fluid source. The pneumatic supply line is connectable to the pneumatic connection port.