This page contains information regarding Star Trek: Discovery, and thus may contain spoilers.
The respiratory system, or pulmonary system or oxy recyclatory system, was the organ system that involved in exchange of gases between an organism and its environment. The speed of one's respiration was referred to as respiratory rate or breathing rate. (ENT: "Terra Nova"; TOS: "The Naked Time"; Star Trek IV: The Voyage Home)
The Android Lieutenant Commander Data also had a functional respiratory system with the purpose to maintain thermal control of his main systems. Data explained this to Doctor Julian Bashir after he noticed that Data was breathing. (TNG: "Birthright, Part I")
In 2370, in the "Anatomical Scan - 9861" for Juliana Tainer, the oxy recyclatory system was listed under lungs coronal plane portion of the graphic. For her oxy recyclatory system, it was noted that it was below 27 bpm. (TNG: "Inheritance")
In 3189, an atomic scan was performed on the respiratory system of Philippa Georgiou. The results of the scan revealed that her blood base had a pH level of 7.41. She had a PaCO2 (partial pressure of carbon dioxide in arterial blood) of 42 millimeters of mercury (mmHG), a HCO3 of 24 millimoles of liter (mmol/l), and a P02 (partial pressure of oxygen in arterial blood) of 90. (DIS: "The Sanctuary")