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TECHNICAL PAPERS: Fluids/Heat/Transport

# Three-Dimensional Convective Alveolar Flow Induced by Rhythmic Breathing Motion of the Pulmonary Acinus

[+] Author and Article Information
Josué Sznitman1

Institute of Fluid Dynamics, ETH Zurich, CH-8092 Zurich, Switzerlandsznitman@ifd.mavt.ethz.ch

Fabian Heimsch, Thomas Heimsch, Daniel Rusch, Thomas Rösgen

Institute of Fluid Dynamics, ETH Zurich, CH-8092 Zurich, Switzerland

1

Corresponding author.

J Biomech Eng 129(5), 658-665 (Jan 29, 2007) (8 pages) doi:10.1115/1.2768109 History: Received November 15, 2005; Revised January 29, 2007

## Abstract

Low Reynolds number flows $(Re<1)$ in the human pulmonary acinus are often difficult to assess due to the submillimeter dimensions and accessibility of the region. In the present computational study, we simulated three-dimensional alveolar flows in an alveolated duct at each generation of the pulmonary acinar tree using recent morphometric data. Rhythmic lung expansion and contraction motion was modeled using moving wall boundary conditions to simulate realistic sedentary tidal breathing. The resulting alveolar flow patterns are largely time independent and governed by the ratio of the alveolar to ductal flow rates, $Q̇a∕Q̇d$. This ratio depends uniquely on geometrical configuration such that alveolar flow patterns may be entirely determined by the location of the alveoli along the acinar tree. Although flows within alveoli travel very slowly relative to those in acinar ducts, $0.021%⩽Ua∕Ud⩽9.1%$, they may exhibit complex patterns linked to the three-dimensional nature of the flow and confirm findings from earlier three-dimensional simulations. Such patterns are largely determined by the interplay between recirculation in the cavity induced by ductal shear flow over the alveolar opening and radial flows induced by wall displacement. Furthermore, alveolar flow patterns under rhythmic wall motion contrast sharply with results obtained in a rigid alveolus, further confirming the importance of including inherent wall motion to understand realistic acinar flow phenomena. The present findings may give further insight into the role of convective alveolar flows in determining aerosol kinematics and deposition in the pulmonary acinus.

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## Figures

Figure 1

Computational mesh of geometrical model of duct with alveolus (shown here at generation z′=1). The alveolus radius is given by ra, the airway duct diameter and length are, respectively, Dd and ld. The alveolus half-opening angle is denoted by α. Fine meshing is obtained within the alveolus and its near surroundings to solve accurately for the alveolar flow.

Figure 2

Cross-sectional view of alveolus and duct midplane, parallel to streamwise flow direction, illustrating streamlines with velocity field magnitude obtained in a rigid-wall (Q̇a∕Q̇d=0) alveolus of acinar generation z′=1(Re=0.47). Color bar on left denotes velocity magnitude along streamlines, in m∕s. The red line illustrates qualitatively the separation between the slow recirculating flow within the alveolus and the more rapid ductal flow. The line spanning from the proximal to distal corner denotes the intersection curve between the alveolus opening ring and the alveolar duct.

Figure 3

Cross-sectional view of alveolus and duct midplane, parallel to streamwise flow direction, illustrating streamlines with velocity field magnitude obtained at peak expiration at acinar generation z′=1 (Re=1.46, Q̇a∕Q̇d=0.009%). Color bar on left denotes velocity magnitude along streamlines, in m∕s. The line spanning from the proximal to distal corner denotes the intersection curve between the alveolus opening ring and the alveolar duct.

Figure 4

Illustration of instantaneous alveolar streamlines with velocity field magnitude obtained at peak inspiration at acinar generation z′=5 (Re=0.112, Q̇a∕Q̇d=0.82%). Color bar on left denotes velocity magnitude along streamlines, in m∕s. (a) Cross-sectional view of alveolus and duct midplane in streamwise flow direction: Note the slower recirculating flow within the alveolus compared to that flowing through the duct; the line spanning from the proximal to distal corner denotes the intersection curve between the alveolus opening ring and the alveolar duct. (b) Projection of streamlines with corresponding velocity magnitude in 3D space onto cross-sectional view of alveolus in spanwise direction.

Figure 5

Recirculation streamlines within alveolus, obtained from the projection in 3D space onto alveolus midplane in streamwise flow direction, and illustrating different instantaneous breathing times over a complete breathing cycle at generation z′=5(Q̇a∕Q̇d=0.82%). Each subfigure is annotated with the instantaneous breathing time (in s) and the ductal Reynolds number Re. Note that the location of the recirculation region remains essentially unchanged over the entire cycle along the proximal side of the alveolus. Resulting streamlines compare well with instantaneous alveolar flow patterns obtained in previous 2D simulations (Fig. 6 in Ref. 14).

Figure 6

Illustration of instantaneous alveolar streamlines with velocity field magnitude obtained at acinar generation z′=8 during inspiration with Re=0.008 and Q̇a∕Q̇d=24.25%. Color bar on left denotes velocity magnitude along streamlines, in m∕s. (a) Cross-sectional view of alveolar midplane in streamwise flow direction (flow is from left to right). (b) Corresponding view of alveolar radial streamlines and ductal streamlines in 3D space.

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