The thin strands attached to the atrioventricular valves are called chordae tendineae. Chordae tendineae are fibrous cords that connect the papillary muscles of the heart to the tricuspid and mitral valves. When the ventricles contract, the papillary muscles also contract, which pulls on the chordae tendineae and helps to keep the valves from prolapsing or bulging back into the atria.