The basal ganglia was a group of nuclei found in the Human brain. The basal ganglia is interconnected with the cerebral cortex, thalamus and brain stem, and associated with a variety of functions including motor control, cognition, emotions, and learning.
In 2372, The Doctor described the next step in his treatment of Danara Pel as creating "an axonal pathway between that (Klingon neural) tissue and your basal ganglia.", a procedure developed by Leonard McCoy in 2253. (VOY: "Lifesigns")
In 2373, Captain Benjamin Sisko's basil ganglia started to depolarize because of increased neural activity brought on by visions he had been experiencing. Doctor Bashir wanted to operate and repolarize the neural sheaths, but Sisko declined as it would have likely ended his visions. (DS9: "Rapture")