What structure holds the chordae tendineae to the interior walls of the heart?

The chordae tendineae are fibrous strings that connect the papillary muscles to the tricuspid and mitral valves within the heart. The role of the papillary muscles is pivotal; they contract during heartbeats to pull on the chordae tendineae, helping to keep the valves closed when the ventricles contract. This action prevents the backflow of blood and maintains proper circulation through the heart's chambers.

The other choices do not fulfill the same function. The septum serves as a wall dividing the left and right sides of the heart, but it does not connect to the chordae tendineae. Auricles are small pouches that increase the capacity of the atria but are not involved with anchoring the chordae tendineae. Valves themselves are the structures that prevent backflow of blood, but they do not physically anchor the chordae tendineae to the heart. Thus, the correct answer underscores the essential role of the papillary muscles in maintaining the function and stability of the heart's valves through their connection with the chordae tendineae.