The minimally invasive pulmonary artery band includes an elongate tube having a reservoir of inflation fluid attached at one end and a clamp head attached to the other end. The clamp head is a hexagonal clamp frame having a gap to facilitate wrapping the clamp frame around the pulmonary artery. The clamp frame includes at least one balloon element attached thereto. The balloon element is selectively inflatable from the inflation fluid provided by the reservoir. The balloon element is configured for inflation into predefined shapes, and the pulmonary artery band allows for fine adjustments to compression and the shape of compression of the pulmonary artery to gradually reach a predefined state of occlusion.