Brain stem

The brain stem, or brainstem, was a part of the brain necessary for life. (TV: The Magician's Apprentice) Its neurological function involved memory storage or retrieval, (PROSE: Piecemeal) and respiratory function. (PROSE: Anachrophobia) Bio-computers had artificially cultured neural stems, acting as "rudimentary brainstem[s]". (PROSE: Piecemeal)

In the final stages of mental shutdown, when physical shutdown would commence, brainsteam death would be followed by complete respiratory collapse. This was closely followed by liver failure and renal collapse, the final signs of general systemic failure, leading to death within an hour. (PROSE: Anachrophobia)

suggested that Time Lords only had one brain stem, and that two snipers to it, as well as three for each heart, could take her out before she could initiate regeneration. (TV: The Magician's Apprentice) This was a lie, however, as Rafando revealed Time Lords had three; necessary steps to killing a Time Lord were stopping both hearts, all three brain stems, and delivering a cellular shockwave which would permanently disable regeneration. (TV: Extremis)

Florence Finnegan planned to use the Royal Hope Hospital's MRI machine, while on the Moon, amplified to 50,000 tesla, to "send out a magnetic pulse that'll fry the brain stems of every living thing within two hundred and fifty thousand miles", which would have included the whole side of the Earth facing the moon. (TV: Smith and Jones)

In the 1890s, a Clockwork Droid scanned the Twelfth Doctor, and listed organs they could harvest, as items on the menu at Mancini's Family Restaurant: liver, spleen, brain stem, eyes, lungs and skin.

In 2061, scientists analysed a Corporeal brain stem, raising, briefly, an interest in the Ethereal. (PROSE: The Ethereal)

Sister Casp said that the Sisters of Plenitude might need to review their brain stem policy, if another of the "flesh" they used as lab rats cried out again. She had not previously known they could develop sentience, indeed speech, yet Casp still opted to incinerate the man who cried for help, as "standard procedure". (TV: New Earth)