Advection and Deposition of Microscale Droplets in Respiratory Airways

由呼吸道液滴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进治疗和保护战略。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对流感和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训研究生和本科生。该项目的主要重点是开发数学模型，描述受感染者咳嗽或打喷嚏产生的含有病原体的呼吸道液体液滴的运输和沉积。使用多尺度框架，一个单独的液滴及其与气道壁的相互作用的动力学进行了研究，然后纳入到一个全球模型的基础上Vlasov型方程的液滴传输的几何形状代表呼吸道。考虑了蒸发和冷凝等相变对液滴尺寸分布及其与壁面相互作用性质的影响。呼吸液模型解释了蛋白质、表面活性剂和盐等成分的存在。解决的关键问题是沉积位置和液滴的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NSF的法定使命，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

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.