Streamline crossing: An essential mechanism for aerosol dispersion in the pulmonary acinus

Abstract

The dispersion of inhaled microparticles in the pulmonary acinus of the lungs is often attributed to the complex interplay between convective mixing, due to irreversible flows, and intrinsic particle motion (i.e. gravity and diffusion). However, the role of each mechanism, the exact nature of such interplay between them and their relative importance still remain unclear. To gain insight into these dispersive mechanisms, we track liquid-suspended microparticles and extract their effective diffusivities inside an anatomically-inspired microfluidic acinar model. Such results are then compared to experiments and numerical simulations in a straight channel. While alveoli of the proximal acinar generations exhibit convective mixing characteristics that lead to irreversible particle trajectories, this local effect is overshadowed by a more dominant dispersion mechanism across the ductal branching network that arises from small but significant streamline crossing due to intrinsic diffusional motion in the presence of high velocity gradients. We anticipate that for true airborne particles, which exhibit much higher intrinsic motion, streamline crossing would be even more significant.

Keywords: Inhaled aerosol; Lungs; Microfluidics; Particle dispersion; Pulmonary Acinus; Tracking velocimetry.

Fig. 1

Top view of the acinar tree model consisting of five acinar generations (numbered G1 to G5) that are lined with alveolar cavities. Flow within the device is controlled either by cyclically pressurizing the water chamber to deform the thin PDMS walls, or alternatively by leaving the chamber dry and connecting a syringe pump directly to the inlet. The inlet channel extends far beyond the shown field of view (FOV) to a distance of 2.2 cm and is used as a straight channel for comparative experiments (see Methods and Results and discussion).

Fig. 2

Trajectories of 1 μm particles suspended in 64% (v/v) glycerol within alveolar cavities located at generations 1 (left), 3 (middle) and 5 (right) of the microfluidic acinar model. Alveolar walls are marked with a white line for clarity. Note that trajectories are overlaid on the first image in the sequence used for particle tracking. Color coding represents normalized time where dark blue indicates the starting time and red encodes the end time (see left panel). Note that the overall tracking time varies between the shown trajectories, spanning 3 to 14 cycles. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article).

Fig. 3

Trajectories of 2 μm particles suspended in 16.5% (v/v) glycerol within alveolated ducts. Particle locations at the reversal between inhalation and exhalation are marked with circles and chronologically numbered according to cycle. Note that to maintain all particle trajectories within the FOV, experiments are limited to 4 cycles.

Fig. 4

Experimental time lapse images of bolus dispersion showing particle locations at t = 0, T, 2 T, 3 T and 4 T in the first generation of the alveolated tree model (left column) and in the straight channel (middle column); a total of n = 171 are shown in both cases where the particle ensembles correspond to the superposition of multiple independent experiments (as exemplified in SM Video 1 and 2). Numerical simulations for the straight channel are shown (right column) with n = 1024. Note that particles are colored according to particle index.

Fig. 5

(a) Mean square displacement (MSD) as a function of cumulative cycles for experiments in the acinar tree and in the straight channel, respectively. Statistics are extracted for a total of n = 171 tracked particles in each case. Inset: Corresponding experimental MSD curve for freely diffusing particles in the absence of flow (n = 500); also shown is the theoretical prediction following the Stokes–Einstein equation. (b) Histogram and box plot (inset) for the characteristic average step size in the acinar tree model (“tree”) and in the straight channel (“duct”); see text for details. The bar plot depicts average and SD for step sizes in the duct and tree. A Mann–Whitney U test was used to test for statistical significance (*p < 0.001).