In this paper, we model breathing at the level of a human alveolus by developing a novel mathematical framework that links pulmonary mechanics and gas exchange. Unlike previous models, the developed alveolar model comprises the alveolar gas mixture, capillaries perfused in the alveolar wall, pulmonary surfactant lining the alveolus and the pleural cavity. The inclusion of the multiple compartments affords interested researchers the chance to study the effect of several respiratory factors on breathing. Here, we investigate the effect of holding breath, breathing at different altitudes and frequencies, and varying cardiac output. The important role of pulmonary surfactant in breathing is also highlighted. In addition, we propose a new method to model the transport of oxygen and carbon dioxide between the alveolus and perfused capillaries, and provide a Lagrangian description of surfactant dynamics. Finally, the mechanical work of breathing at the level of the alveolus is derived and implemented to compare the required breathing effort in different scenarios. Numerical results are consistent with published experimental and computational work.

在本文中，我们通过开发将肺部力学和气体交换联系起来的新型数学框架，在人的肺泡水平上对呼吸进行建模。与以前的模型不同，已开发的肺泡模型包括肺泡气体混合物，在肺泡壁中灌注的毛细血管，在肺泡和胸膜腔内衬的肺表面活性物质。包含多个隔室为感兴趣的研究人员提供了研究几种呼吸因素对呼吸的影响的机会。在这里，我们研究屏住呼吸，在不同高度和频率下呼吸以及心输出量变化的影响。还强调了肺表面活性剂在呼吸中的重要作用。此外，我们提出了一种新的方法来模拟肺泡和灌注毛细血管之间氧气和二氧化碳的运输，并提供了表面活性剂动力学的拉格朗日描述。最后，得出并实施在肺泡水平的呼吸机械功，以比较不同情况下所需的呼吸努力。数值结果与已发表的实验和计算工作一致。