Probabilistic plugging of airways by sliding mucus films

TL;DR

Using reduced-order simulations of a large ensemble of randomly perturbed films, it is shown that the answer is not determined by just the film's volume, and that there are a range of intermediate films for which plugging is uncertain.

Abstract

When do mucus films plug lung airways? Using reduced-order simulations of a large ensemble of randomly perturbed films, we show that the answer is not determined by just the film's volume. While very thin films always stay open and very thick films always plug, we find a range of intermediate films for which plugging is uncertain. The fastest-growing linear mode of the Rayleigh-Plateau instability ensures that the film's volume is divided among multiple humps. However, the nonlinear growth of these humps can occur unevenly, due to spontaneous axial sliding -- a lucky hump can sweep up a disproportionate share of the film's volume and so form a plug. This sliding-induced plugging is robust and prevails with or without gravitational and ciliary transport.

Figures (4)

• Figure 1: (a) Schematic of the annular mucus film in a long axisymmetric airway, spanning multiple wavelengths of the fastest-growing mode $\Lambda$. (b-e) Kymographs of the evolution of the film, in representative randomly-initialized runs, for thick, thin, and intermediate films: (b) $1-d_0 = 0.13$, (c) $1-d_0 = 0.047$, (d-e) $1-d_0 = 0.081$. Panels (b-e) are animated in supplementary https://bighome.iitb.ac.in/index.php/s/nf9eqr2G5cbp9ZF, https://bighome.iitb.ac.in/index.php/s/w9X3o8BE4zwGdjE, https://bighome.iitb.ac.in/index.php/s/pgDxQAEHLz6wHpM and https://bighome.iitb.ac.in/index.php/s/S34zeEr7Bab76Xfsupplement
• Figure 2: (a) Probability of plugging as a function of the initial film thickness. The dashed vertical lines show the critical thickness beyond which unduloids do not exist, considering the film's volume in the full domain ($1-d^L_0 = 0.025$) and in the $\Lambda$ unit-cell ($1-d^\Lambda_0 = 0.117$). (b) The distance of the deepest hump from the farther of its two neighbors $\ell$, scaled by $\Lambda$ and plotted separately for open and closed realizations.
• Figure 3: (a) Evolution of the minimum interface position $d_{min}$ for randomly perturbed films (three realizations) of different initial thicknesses on a short domain with a single growing hump ($L = \Lambda$). (b) Time-trace of the axial position of $d_{min}$ for the realizations of the intermediate-thickness film; the semi-log inset shows the film's profile in one of these realizations (animated in https://bighome.iitb.ac.in/index.php/s/8Mj9NLDDPpN5XWosupplement) just before and after sliding.
• Figure 4: (a) Plugging fraction for simulations run with (i) no ciliary transport ($u_c = 0$) and (ii) with weak gravitational acceleration instead of ciliary transport. (b) Fraction of the wall occupied by mucus-depleted zones: the measurements from the ensemble of simulations are compared with the fastest-mode based prediction (solid black line) of Swarnaditya-particles.