Aerosol deposition in mucus-lined ciliated airways

TL;DR

The paper develops a two-phase, axisymmetric thin-film model for a mucus-lined airway using the weighted-residual integral boundary-layer (WRIBL) framework to couple air flow, mucus film dynamics, and ciliary forcing. It shows that capillary-driven Rayleigh-Plateau instabilities create hump-like mucus structures and wall-depleted zones, whose extent increases with mucus volume, and that particle deposition depends non-monotonically on size due to Brownian diffusion and inertia, with deposition patterns shaped by the mucus geometry. A key finding is that air flow and ciliary motion have minimal impact on the mucus film shape over breath timescales; a one-way coupled WRIBL model suffices for predicting deposition. The work highlights how mucus patterning can both hinder and promote wall deposition depending on particle size and turnover, with implications for optimizing inhaled drug delivery and understanding allergen/pathogen exposure risk in the respiratory tract.

Abstract

We study the transport and deposition of inhaled aerosols in a mid-generation, mucus-lined lung airway, with the aim of understanding if and how airborne particles can avoid the mucus and deposit on the airway wall -- an outcome that is harmful in case of allergens and pathogens but beneficial in case of aerosolized drugs. We adopt the weighted-residual integral boundary-layer model of Dietze and Ruyer-Quil (J. Fluid Mech., vol. 762, 2015, pp. 68-109) to describe the dynamics of the mucus-air interface, as well as the flow in both phases. The transport of mucus induced by wall-attached cilia is also considered, via a coarse-grained boundary condition at the base of the mucus. We show that the capillary-driven Rayleigh-Plateau instability plays an important role in particle deposition by drawing the mucus into large annular humps and leaving substantial areas of the wall exposed to particles. We find, counter-intuitively, that these mucus-depleted zones enlarge on increasing the mucus volume fraction. Particles spanning a range of sizes (0.1 to 50 microns) are modelled using the Maxey-Riley equation, augmented with Brownian forces. We find a non-monotonic dependence of deposition on size. Small particles diffuse across streamlines due to Brownian motion, while large particles are thrown off streamlines by inertial forces -- particularly when air flows past mucus humps. Intermediate-sized particles are tracer-like and deposit the least. Remarkably, increasing the mucus volume need not increase entrapment: the effect depends on particle-size, because more mucus produces not only deeper humps that intercept inertial particles, but also larger depleted-zones that enable diffusive particles to deposit on the wall.

Figures (15)

• Figure 1: (a) Illustration of a middle generation, mucus-lined, ciliated airway with inhaled aerosols being transported by the respiratory airflow. (b) Schematic of the simplified axisymmetric airway, corresponding to the mathematical model of § 2. The subscripts $a$ and $m$ denote the air and mucus phases, respectively, and $u_c$ is the spatio-temporally periodic, metachronal velocity (red arrows) imposed by the cilia on the base of the mucus film.
• Figure 2: Cilia translates the mucus film without altering the capillary-driven dynamics and the consequent emergence of humps and depleted zones. The top two rows present snapshots of the evolution of the film, with cilia (a-c) and without cilia, i.e., with $u_c = 0$ (d-f). Panel (g) compares the growth of the hump by tracing the evolution of the minimum of $d(z,t)$. Panel (h) compares the time-traces of the centre of mass of the entire film, clearly showing that cilia causes the film to translate; the inset subtracts out the net translation $\langle u_c \rangle t$ and reveals tiny lateral air-induced oscillations. Panel (i) presents the time-trace of the spatially-averaged root-mean-square mucus velocity, normalized with the mean cilia velocity; the inset zooms into the curve for the no-cilia case.
• Figure 3: The metrachronal cilia velocity \ref{['cilia_bc']} has the same effect on the flow as the constant cilia velocity \ref{['cilia_bc_const']}, as evidenced by the kymographs of the evolution of the film thickness $1-d(z,t)$ (panels a, c) and the snapshots of the streamlines in the air and mucus (panels b, d). The snapshot of the streamlines corresponds to the time of the second line profile drawn in the kymographs ($t \approx 15.6 \,T_b$).
• Figure 4: Comparison of the time traces of (a) the minimum position of the interface, (b) the centre-of-mass of the film, and (c) the root-mean-square mucus velocity, for the metrachronal and constant cilia velocities (given by \ref{['cilia_bc']} and \ref{['cilia_bc_const']} respectively). The curves overlap in each panel, showing perfect agreement.
• Figure 5: Comparison of the interface evolution predicted by the fully-coupled and the one-way coupled WRIBL models; in the latter, air does not affect the flow mucus film. (a) Evolution of the minimum interface position (main panel) and the centre of mass (inset). Kymographs of the film thickness are compared in panels (b-c).