The groove running along the middle of a sword blade is known as a fuller, also called a blood groove or a groove. Contrary to a common misconception, the primary purpose of a fuller is not to allow blood to flow out of a wound. The main functions of a fuller are as follows:

1. Weight Reduction: By removing material from the blade, the fuller reduces the weight of the sword without compromising its structural integrity. This makes the sword lighter and more manageable, allowing for increased speed and maneuverability in combat.
2. Structural Reinforcement: Contrary to what some may believe, the fuller does not weaken the sword. In fact, it can increase the blade's strength and stiffness by redistributing the mass and reinforcing the central ridge. This can help prevent the sword from bending or breaking during combat or when striking objects.
3. Sound and Vibrations: When a sword is swung or strikes an object, it creates vibrations that can travel through the blade, handle, and hilt. The presence of a fuller can help dampen these vibrations and reduce the chances of discomfort or injury to the wielder's hands.
4. Symbolic and Aesthetic Purposes: In addition to its practical functions, the fuller can also have symbolic or decorative significance. It is often seen as an essential element of the overall design and craftsmanship of a sword, adding visual interest and complexity to the blade's appearance.

It's worth noting that the design and presence of a fuller can vary across different types of swords and historical periods. Some swords may have multiple fullers, while others may lack them entirely. The specific shape, depth, and length of the fuller can also vary depending on the sword's intended use, cultural influences, and the preferences of the swordsmith.