A respiratory bypass system was a part of Gallifreyan physiology which allowed Time Lords to go without breathing for longer periods of time than most humans could. (BFA: Return of the Krotons) It also allowed them to filter out unpleasant smells. (NA: Cat's Cradle: Witch Mark)
The Doctor used it to survive more than once. The Doctor's fourth self used his respiratory bypass system to survive being strangled by an Osirian service robot. (DW: Pyramids of Mars) He later used it to avoid inhaling helium. (DW: The Robots of Death) The fifth incarnation used it to survive brief exposure to the vacuum of space (DW: Four to Doomsday) as well as being hanged. (ST: A Town Called Eternity) His sixth persona avoided hypoxia when he shut down atmospheric controls to the mines on the planet Onyakis to defeat the Krotons there. (BFA: Return of the Krotons) In his seventh body, the Doctor used his respiratory bypass system to avoid being overcome by ether. (NA: Timewyrm: Genesys) His eleventh incarnation survived the vacuum of low earth orbit long enough to find and put on an impact suit -- backwards. (DW: The Doctor, the Widow and the Wardrobe)
At least one human may have developed such a system: Timothy Dean, who gained one when he was infected with the Seventh Doctor's DNA. (NA: Human Nature)