The simultaneous role of an alveolus as flow mixer and flow feeder for the deposition of inhaled submicron particles

Abstract

In an effort to understand the fate of inhaled submicron particles in the small sacs, or alveoli, comprising the gas-exchange region of the lung, we calculated the flow in three-dimensional (3D) rhythmically expanding models of alveolated ducts. Since convection toward the alveolar walls is a precursor to particle deposition, it was the goal of this paper to investigate the streamline maps' dependence upon alveoli location along the acinar tree. On the alveolar midplane, the recirculating flow pattern exhibited closed streamlines with a stagnation saddle point. Off the midplane we found no closed streamlines but nested, funnel-like, spiral, structures (reminiscent of Russian nesting dolls) that were directed towards the expanding walls in inspiration, and away from the contracting walls in expiration. These nested, funnel-like, structures were surrounded by air that flowed into the cavity from the central channel over inspiration and flowed from the cavity to the central channel over expiration. We also found that fluid particle tracks exhibited similar nested funnel-like spiral structures. We conclude that these unique alveolar flow structures may be of importance in enhancing deposition. In addition, due to inertia, the nested, funnel-like, structures change shape and position slightly during a breathing cycle, resulting in flow mixing. Also, each inspiration feeds a fresh supply of particle-laden air from the central channel to the region surrounding the mixing region. Thus, this combination of flow mixer and flow feeder makes each individual alveolus an effective mixing unit, which is likely to play an important role in determining the overall efficiency of convective mixing in the acinus.

Fig. 1

Workflow to extract acinar duct: (a) Wide-field scanned sample of the tip of the right lower lung lobe of a Sprague-Dawley rat. (b) Region of interest (ROI) where we extracted one small acinus superimposed on sample (small cube with white border). (c) Rotated close-up view of the ROI, including two separate airways segments extracted using a threshold interval based region growing. Since the ROI is rotated in comparison to (b), the scale bars are of slightly different length. (d) Isosurfaces of extracted airway segments. A part of a single acinus (yellow, or light grey) and adjoining airway segment (green, or dark grey) in ROI. Several parts of the airway segment have been removed for clarity. The approximate path of the center of the airway may be discerned in the semitransparent rectangle, which marks the approximate region of one alveolar duct.

Fig. 2

Geometric model of a thoroughfare duct with partially alveolated walls imaged by SRXTM. The time-dependent, three-dimensional, Navier-Stokes equations were solved on a moving mesh using a finite element code that incorporated the arbitrary Lagrangian-Eulerian formulation for moving meshes. The geometrical model was developed using the C++ object oriented programming language and OpenGL graphic library [34]. The system of discrete equations was solved using a nonsymmetric Gaussian solver. About 400,000 eight-node, hexahedral, finite elements were employed with eight unknown velocities and constant pressure over the element. The actual pressure field was calculated at the post-processing stage. Mesh independence was reached at 400,000 to 600,000 finite elements with an error of less than 0.1% in an average difference for the velocity field. Time step independence was achieved at 400 time steps per cycle. A Laplacian smoothing technique was used in constructing the realistic alveolar model to create a smooth surface after the image reconstruction process. For each calculation, a parallel version of the solver required 24 h on 40 parallel Intel core2quad q6600, 2.4 GHz, processors. The size of the alveoli is 80 μm in diameter on average.

Fig. 3

Peak inspiration alveolar flow patterns at Re_duct = 1.5 in a geometric model of a thoroughfare duct with partially alveolated walls (Fig. 2). (a) and (b) Closed recirculating flows in the middle of alveolar cavity. (c) Spiral flow patterns from the midplane of the alveolus toward the expanding walls. (d) Incoming flow from the central channel. (e) Flows of (c) and (d) combined. The size of the alveoli is 80 μm in diameter on average.

Fig. 4

(a) Geometrical details of the idealized CFD model, where d is the diameter of the central duct and the alveolus, l is the duct length, and h = 3 d/4 for an opening angle θ = 120 deg. The main flow direction is aligned with the z direction and the midplane of thealveolusisa y-z plane at x = 0. (b) Typical grid with 80,327 tetrahedral cells.

Fig. 5

Axial velocity profile at maximum inspiratory flow at x = 0 and z = 0 over the top half of the model alveolus for three different grids (left) and three different time steps (right). (Grid 1, 2, and 3 = 41,625, 80,327, and 181,882 cells, respectively, and ndt = number of time steps over the breathing cycle.)

Fig. 6

Flow in the midplane of an idealized spherical alveolus showing the four distinct zones and the stagnation point. Zone I, the rotating flow, which has closed streamlines, in the middle of the alveolus. Zone II, the flow that enters the alveolus distally from the duct. Zone III, the small amount of flow that enters the alveolus from the duct proximally and is between the alveolar wall and the stagnation point. Zone IV, the duct flow that passes by the alveolus. (Note that this flow was produced using the same finite element CFD code used to compute the flow shown in Fig. 3.)

Fig. 7

Instantaneous streamlines originating off midplane of an idealized spherical alveolus at maximum inspiratory flow (t = T/4) for conditions typical of generation 18 (Q_A/Q_D = 0.0021 and Re_max = 0.25). Zones comparable to zones I, II, and IV are clearly discernible but the streamlines in zone I spiral towards the alveolar wall; one inside the other, like a Russian nesting doll. (The structure of the flow is such that zone III must exist but it was too small to be visualized in these figures.)

Fig. 8

Details of Russian-nesting-doll structure. Q_A/Q_D = 0.0003, Re_max = 2.0, t = T/4.

Fig. 9

Instantaneous streamlines at maximum inspiratory flow (t = T/4) for alveoli located in generations 15, 18, and 23. Q_A/Q_D and Re_max = 0.0003 and 2.0, 0.0021 and 0.25, and 0.25 and 0.008, for the mentioned generations, respectively. Lower right panel: Velocity magnitude along representative streamlines. Velocity normalized by the mean velocity in the duct and distance normalized by the duct diameter. Velocity curves represent the velocity along the outermost streamline, shown in red, in the upper panels.

Fig. 10

Instantaneous streamlines in zone I originating off midplane of an idealized spherical alveolus for conditions typical of generation 15 (Q_A/Q_D = 0.0003 and Re_max = 2.0). Left panel: Maximum inspiratory flow (t = T/4). Right panel: Maximum expiratory flow (t = 3 T/4).

Fig. 11

Four particles released at the beginning of inspiration near the distal corner of the alveolus near the symmetry plane (shown encircled by a small black rectangle in the top left panel and by a small black square in the top right panel) and tracked over multiple breaths (top panels). Q_A/Q_D = 0.0003, Re_max = 2.0, t = T/4. Each track is depicted in a different color. The final (deposited) positions of two selected tracks are shown by open circles in the middle and lower right panels. The small closed circles indicate the position of the particle at the end of each breathing cycle. (Geometry shown at minimum volume.)

Fig. 12

Four particles released at the beginning of inspiration in the center of the flow near the symmetry plane (shown encircled by small black rectangles in the top panels) and tracked over multiple breaths (top panels). Q_A/Q_D = 0.0003, Re_max = 2.0, t = T/4. Each track is depicted in a different color. The final (deposited) positions of two selected tracks are shown by open circles in the middle and lower right panels. The small closed circles indicate the position of the particle at the end of each breathing cycle. (Geometry shown at minimum volume.)