Radial transport along the human acinar tree

Abstract

A numerical model of an expanding asymmetric alveolated duct was developed and used to investigate lateral transport between the central acinar channel and the surrounding alveoli along the acinar tree. Our results indicate that some degree of recirculation occurs in all but the terminal generations. We found that the rate of diffusional transport of axial momentum from the duct to the alveolus was by far the largest contributor to the resulting momentum in the alveolar flow but that the magnitude of the axial momentum is critical in determining the nature of the flow in the alveolus. Further, we found that alveolar flow rotation, and by implication chaotic mixing, is strongest in the entrance generations. We also found that the expanding alveolus provides a pathway by which particles with little intrinsic motion can enter the alveoli. Thus, our results offer a possible explanation for why submicron particles deposit preferentially in the acinar-entrance region.

Figure A1

Typical non-orthogonal grid cell

Figure A2

5-block grid. Broken lines indicates block boundaries

Figure A3

Wall boundary cell.

Figure 1

(a) Scanning electron micrograph of an alveolar duct surrounded by alveoli (From Gehr et al. [24], by permission). (b) Schematic of dichotomously bifurcating acinar airways.

Figure 2

Estimated variation of convective and diffusive radial transport of radial and axial momentum, over inspiration, normalized by diffusive radial transport of axial momentum. Included are the variations of Re at maximum inspirational flow rate and QA/QD.

Figure 3

(a) Three-alveoli solution domain: Q_A is the volume flow into the alveoli and Q_D is the volume flow in the duct. (b) 3D cross-sectional view of solution domain (with peaked top surface).

Figure 4

Prediction and analytical solution (Uchida and Aoki, [14]) of flow in an expanding tube.

Figure 5

Predicted streamlines for expanding (upper) and rigid (lower) model alveoli for generations 15, 19, 21 and 23. The broken line shown in the lower left panel indicates the line along which transport into all alveoli is calculated.

Figure 6

Rate of radial convective transport of axial momentum, per unit density, (u_ru_z) and rate of radial convective transport of radial momentum, per unit density, ( u_ru_r) along the alveolar opening (i.e., along the broken line in the lower left panel of Fig. 5) at maximum inspirational flow rate; i.e., t = T/4, for expanding (upper) and rigid (lower) model alveoli for generations 15, 19, 21 and 23.

Figure 7

Rate of radial diffusive transport of axial momentum, per unit density, (−ν∂u_z / ∂r) and rate of radial diffusive transport of radial momentum, per unit density, (−ν∂u_r /∂r) along the alveolar opening (i.e., along the broken line in the lower left panel of Fig. 5) at maximum inspirational flow rate; i.e., t = T/4, for expanding (upper) and rigid (lower) model alveoli for generations 15, 19, 21 and 23.

Figure 8

Predicted total radial transport over inspiration normalized by total radial diffusion of axial momentum over inspiration.

Figure 9

Typical paths taken by fluid elements over inspiration in model alveoli in each alveolar generation. Starting position denoted by the symbol ⊙.

Figure 10

Normalized distance traveled over inspiration by fluid elements in model alveoli in each generation. Distance (l) normalized by the alveolus width (w). Starting position of fluid elements in each alveolus as shown in Figure 9.

Figure 11

Area near the proximal alveolar septum (shaded) over which flow enters the expanding model alveolus. The lower (broken) line is the path taken by a fluid element in the rigid model. The upper (solid) line is the path taken by the same fluid element in the expanding model.

Figure 12

Path lines of a pair of fluid elements over ten breathing cycles (upper panels) and time history of the distance between the fluid elements, s, normalized by the alveolar width, w (lower panels). Initial position of fluid elements shown by the symbol ⊙. Initial value of normalized separation, s/w = 0.0001.