The major blood vessels that run through the heart (from right to left) =1 the pulmonary artery, vena cava, aorta, pulmonary vein. The vena cava delivers deoxygenated blood to the right atrium, the pulmonary artery carries blood away to the lungs, the pulmonary vein carries oxygenated blood back to the left atrium, and the aorta takes it away to the body. Semilunar valves at the base of the major arteries