Department of Mathematics, North Carolina A & T State University, Greensboro, NC 27411, USA.
Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30303, USA.
Cells. 2019 Jul 18;8(7):736. doi: 10.3390/cells8070736.
Mucociliary clearance is an important innate host defense of the mammalian respiratory system, as it traps foreign substances, including pollutants, pathogens, and allergens, and transports them out of the airway. The underlying mechanism of the actuation and coordination of cilia, the interplay between the cilia and mucus, and the formation of the metachronal wave have been explored extensively both experimentally and mathematically. In this mini-review, we provide a survey of the mathematical models of mucociliary clearance, from the motion of one single cilium to the emergence of the metachronal wave in a group of them, from the fundamental theoretical study to the state-of-the-art three-dimensional simulations. The mechanism of cilium actuation is discussed, together with the mathematical simplification and the implications or caveats of the results.
黏液纤毛清除是哺乳动物呼吸系统重要的先天防御机制，它能捕获包括污染物、病原体和过敏原在内的异物，并将其运出气道。纤毛的驱动和协调、纤毛和黏液的相互作用以及蠕动波的形成的潜在机制已经在实验和数学两个方面得到了广泛的研究。在这篇迷你综述中，我们提供了黏液纤毛清除的数学模型的调查，从单个纤毛的运动到一组纤毛中蠕动波的出现，从基础理论研究到最新的三维模拟。讨论了纤毛驱动的机制，以及数学简化和结果的意义或注意事项。
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