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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.
所有的学童都知道他们呼吸的频率，但即使是专家也不知道确切的原因。本出版物的目的是使用生理、物理和数学方法，借助进化将生理学推向尽可能经济的方向这一原则，建立一个静息自主呼吸频率模型。呼吸频率可以通过一个方程式得出，该方程式的参数包括：[公式：见文本]-生物体的[公式：见文本]-产生率、阻力、肺静态顺应性和死腔、吸气时间：呼气时间比以及呼气末[公式：见文本]分数。该推导仅需要中学数学知识。然后，使用成人或新生儿的示例，从文献中得出他们在静息时正常的呼吸频率值。与成人相比，新生儿呼吸频率较高的原因是相对较高的[公式：见文本]-产生率，加上肺的顺应性相对较低。一个附带的结果是，整个肺部的常见肺泡压力和常见时间常数也是经济原则的结果。由于上述参数不是人类特有的，因此没有理由假设上述方程不能也适用于许多通过胸腔呼吸的动物，尤其是哺乳动物。不仅生理学和生物学，而且医学都可以从中受益：在包括病理生理学在内的肺功能诊断中，正在讨论其适用性。然而，本出版物仅声称是自主安静呼吸频率的理论概念。在没有可比的动物数据的情况下，本出版物旨在鼓励进一步的科学测试。
