Advection and Deposition of Microscale Droplets in Respiratory Airways

通过呼吸道液体的微小飞沫传播的传染病影响着全世界数千万人。更好地了解感染的传播机制可以改善治疗和保护策略。虽然该项目的主要重点是结核病的传播，但其更广泛的社会影响包括流感和COVID-19等其他传染病的潜在应用。该项目的教育影响包括在应用数学家和生物医学研究人员之间密切互动的跨学科环境中培养研究生和本科生。该项目的主要重点是发展数学模型，以描述受感染者咳嗽或打喷嚏时产生的含有致病因子的呼吸道液体飞沫的运输和沉积。利用多尺度框架，研究了单个液滴的动力学及其与气道壁的相互作用，然后将其纳入基于vlasov型液滴传输方程的全局模型中。考虑了蒸发和冷凝等相变对液滴尺寸分布的影响及其与壁面相互作用的性质。呼吸道液体的模型说明了诸如蛋白质、表面活性剂和盐等成分的存在。解决的关键问题是液滴的沉积位置和大小分布作为初始分布的函数，以及环境参数，如温度和湿度。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Infectious diseases transmitted by tiny droplets of respiratory fluids affect tens of millions of people worldwide. Better understanding of the mechanism of transmission of infections can lead improvements in both treatment and protection strategies. While the main focus of the project is on transmission of tuberculosis, its broader societal impacts include potential applications to other infectious diseases such as influenza and COVID-19. Educational impacts of the project include training both graduate and undergraduate students in an interdisciplinary environment with close interaction between applied mathematicians and biomedical researchers. The main focus of the project is on the development of mathematical models describing transport and deposition of droplets of respiratory fluids containing the disease agent produced by cough or sneezing of an infected individual. Using a multiscale framework, dynamics of an individual droplet and its interaction with the airway wall is investigated and then incorporated into a global model based on Vlasov-type equation for droplet transport in a geometry representing respiratory airways. The effects of phase change such as evaporation and condensation on the size distribution of the droplets and the nature of their interaction with the wall are considered. A model of respiratory liquid accounts for the presence of components such as proteins, surfactants, and salts. The key questions addressed are the deposition location and size distributions of the droplets as functions of the initial distribution, as well as environmental parameters such as temperature and humidity.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.