The (human) respiratory rate at rest

TL;DR

This paper develops a simple, physiologically-based mathematical model to explain the resting breathing rate in humans and potentially other mammals, based on evolutionary efficiency principles and secondary school mathematics.

Contribution

It introduces a novel theoretical model linking respiratory rate to physiological parameters using basic mathematical principles, applicable across mammals.

Findings

Derived normal resting breathing rates for adults and newborns.

Explained higher breathing rate in newborns due to CO2 production and lung compliance.

Proposed model's potential application in pulmonary diagnostics and animal physiology.

Abstract

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 CO2-production rate of the organism, resistance, static compliance and dead space of the lungs, the inspiration duration: expiration duration - ratio and the end-expiratory CO2 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 CO2-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 for the spontaneous quiet breathing rate. In the absence of comparable animal data, this publication is intended to encourage further scientific tests.