Electroencephalography (also known as EEG) was a medical test for measuring the electrical activity of the brain, such as theta waves.
In 2153, an EEG was performed as part of the collection of biometric data about a Borg drone by using electrode pads. The data was submitted to a computer monitor. (ENT: "Regeneration")
In 2365, a biobed performed an EEG scan on Commander William T. Riker. (TNG: "Shades of Gray")
In 2367, Nurse Ogawa monitored Riker's EEG while he was having the Trill symbiont Odan transplanted into his body. (TNG: "The Host")