The (human) respiratory rate at rest

J Math Biol. 2022 Oct 25;85(5):60. doi: 10.1007/s00285-022-01790-8.


All schoolchildren know how often they breathe, but even experts don't know exactly why. The aim of this publication is to develop a model of the resting spontaneous breathing rate using physiological, physical and mathematical methods with the aid of the principle that evolution pushes physiology in a direction that is as economical as possible. The respiratory rate then follows from an equation with the parameters [Formula: see text]-production rate of the organism, resistance, static compliance and dead space of the lungs, the inspiration duration: expiration duration - ratio and the end-expiratory [Formula: see text] fraction. The derivation requires exclusively secondary school mathematics. Using the example of an adult human or a newborn child, data from the literature then result in normal values for their breathing rate at rest. The reason for the higher respiratory rate of a newborn human compared to an adult is the relatively high [Formula: see text]-production rate together with the comparatively low compliance of the lungs. A side result is the fact that the common alveolar pressure throughout the lungs and the common time constant is a consequence of the economical principle as well. Since the above parameters are not human-specific, there is no reason to assume that the above equation could not also be applicable to many animals breathing through lungs within a thorax, especially mammals. Not only physiology and biology, but also medicine, could benefit: Applicability is being discussed in pulmonary function diagnostics, including pathophysiology. However, the present publication only claims to be a theoretical concept of the spontaneous quiet breathing rate. In the absence of comparable animal data, this publication is intended to encourage further scientific tests.

Keywords: -production rate; Airway resistance; Alveolar pressure; End-expiratory fraction; Evolutionary economy; Respiratory physiology; Respiratory rate; Static compliance; Time constant; Volume flow pattern.

MeSH terms

  • Adult
  • Animals
  • Child
  • Humans
  • Infant, Newborn
  • Lung*
  • Mammals
  • Respiratory Rate*