Computational modeling of airway closure

Capillary instability of a two-layer liquid film lining a rigid tube is studied computationally as a model for liquid plug formation and closure of human airways. The two-layer liquid consists of a serous layer, also called periciliary liquid layer (PCL), at the inner side and a mucus layer at the outer side. Together, they form the airway surface liquid (ASL) lining the airway wall and surrounding an air core. Liquid plug formation occurs due to the Plateau-Rayleigh instability when the liquid film thickness exceeds a critical value. Numerical simulations are performed for the entire closure process including the pre- and post-coalescence phases. The mechanical stresses and their gradients on the airway wall are investigated for physiologically-relevant ranges of the mucus-to-serous thickness ratio, the viscosity ratio, the air-mucus and serous-mucus surface tensions encompassing healthy and pathological conditions of a typical adult human lung. The growth rate of the two-layer model is found to be higher in comparison with a one-layer equivalent configuration. This leads to a much sooner closure in the two-layer model than in the corresponding one-layer model. Moreover, it is found that the serous layer generally provides an effective protection to the pulmonary epithelium against the high shear stress excursions and their gradients. Furthermore, a linear stability analysis using lubrication approximations is also performed, and the results are found to be in good qualitative agreement with the simulations. Airway mucus is a highly complex fluid, and displays a range of non-Newtonian characteristics. In order to take effects of elastoviscoplasticity and shear-thinning of the pulmonary mucus into account, the airway closure problem is studied by modeling the mucus as a single layer, i.e., PCL and ASL are considered as a homogeneous one-layer elastoviscoplastic (EVP) liquid, using the Saramito-HB model [Saramito (Journal of Non-Newtonian Fluid Mechanics (2009) 158(1-3), 154-161)]. Firstly healthy, asthma, cystic fibrosis (CF) and chronic obstructive pulmonary disease (COPD) mucus are represented by following a parameter fitting algorithm (similar to [Fraggedakis et al. (Soft Matter (2016) 12(24), 5378-5401)]) by using the experimental data of [Patarin et al. (Scientific Reports (2020) 10(1), 1-10)]. The obtained parameters show that CF mucus has the highest elastic modulus and the yield stress is the highest in COPD case. This generally confirms that the viscoelastic/viscoplastic features of the mucus increases in pulmonary diseases. Afterwards, extensive numerical simulations are performed to see the effects of these diseases on the airway closure. To that end, the diseased mucus parameters are used, and the surface tension and the initial non-dimensonal thickness are varied in a physiologically meaningful range. Then, the healthy case is chosen as the baseline to perform a parametric study. Here, the elastic modulus, the yield stress and the power-law index of the Saramito-HB model are varied to assess the individual effects of these parameters. The results indicate that increasing yield stress and elastic modulus may abate the airway closure. However, if the initial thickness of the liquid layer and the surface tension increase, which is a typical case in these obstructive pulmonary diseases, then the closure starts to occur for the high viscoelastic/viscoplastic cases as well.