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Research Papers

# Respiratory Flow Phenomena and Gravitational Deposition in a Three-Dimensional Space-Filling Model of the Pulmonary Acinar Tree

[+] Author and Article Information
Josué Sznitman1

Institute of Fluid Dynamics, ETH Zurich, CH-8092 Zurich, Switzerlandsznitman@princeton.edu

Thomas Heimsch, Thomas Rösgen

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

Johannes H. Wildhaber

Department of Pediatrics, Cantonal Hospital, CH-1708 Fribourg, Switzerland

Akira Tsuda

Molecular and Integrative Physiological Sciences, Harvard School of Public Health, Boston, MA 02115

1

Corresponding author. Present address: Department of Mechanical and Aerospace Engineering, Princeton University, Princeton NJ 08544.

J Biomech Eng 131(3), 031010 (Jan 07, 2009) (16 pages) doi:10.1115/1.3049481 History: Received September 03, 2007; Revised August 05, 2008; Published January 07, 2009

## Abstract

The inhalation of micron-sized aerosols into the lung’s acinar region may be recognized as a possible health risk or a therapeutic tool. In an effort to develop a deeper understanding of the mechanisms responsible for acinar deposition, we have numerically simulated the transport of nondiffusing fine inhaled particles ($1 μm$ and $3 μm$ in diameter) in two acinar models of varying complexity: (i) a simple alveolated duct and (ii) a space-filling asymmetrical acinar branching tree following the description of lung structure by Fung (1988, “A Model of the Lung Structure and Its Validation  ,” J. Appl. Physiol., 64, pp. 2132–2141). Detailed particle trajectories and deposition efficiencies, as well as acinar flow structures, were investigated under different orientations of gravity, for tidal breathing motion in an average human adult. Trajectories and deposition efficiencies inside the alveolated duct are strongly related to gravity orientation. While the motion of larger particles $(3 μm)$ is relatively insensitive to convective flows compared with the role of gravitational sedimentation, finer $1 μm$ aerosols may exhibit, in contrast, complex kinematics influenced by the coupling between (i) flow reversal due to oscillatory breathing, (ii) local alveolar flow structure, and (iii) streamline crossing due to gravity. These combined mechanisms may lead to twisting and undulating trajectories in the alveolus over multiple breathing cycles. The extension of our study to a space-filling acinar tree was well suited to investigate the influence of bulk kinematic interaction on aerosol transport between ductal and alveolar flows. We found the existence of intricate trajectories of fine $1 μm$ aerosols spanning over the entire acinar airway network, which cannot be captured by simple alveolar models. In contrast, heavier $3 μm$ aerosols yield trajectories characteristic of gravitational sedimentation, analogous to those observed in the simple alveolated duct. For both particle sizes, however, particle inhalation yields highly nonuniform deposition. While larger particles deposit within a single inhalation phase, finer $1 μm$ particles exhibit much longer residence times spanning multiple breathing cycles. With the ongoing development of more realistic models of the pulmonary acinus, we aim to capture some of the complex mechanisms leading to deposition of inhaled aerosols. Such models may lead to a better understanding toward the optimization of pulmonary drug delivery to target specific regions of the lung.

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## Figures

Figure 1

Computational mesh of the simple alveolated duct structure at the fifth acinar generation. The alveolus radius is given by ra, the airway duct diameter and the length are Dd and ld, respectively. The alveolus half-opening angle is denoted by α.

Figure 2

Example of assembling order-2 polyhedra into an alveolar ductal tree, following Fig. 7b of Ref. 29. Two three-dimensional views ((a) and (b)) of the same geometry are illustrated here with corresponding acinar airway generation numbers. The entrance inlet for airflow is visible on the proximal side of generation 3 in (a). Scale of model is shown in meters.

Figure 3

Influence of gravity orientation (Cases (i)–(iii)) on deposition efficiency n(t)/N as a function of normalized time t/T for (a) 1 μm and (b) 3 μm diameter particles in the simple alveolated duct model (see Sec. 2).

Figure 4

1 μm particle trajectories, with velocity magnitude along trajectories (scale in m/s). (i)–(iii) (left and right columns) correspond to Cases (i)–(iii) in Fig. 3. (i) Deposition occurs only at the bottom of the duct. (ii) All particle trajectories are shown with alveolar flow pattern illustrated in the background (left). Trajectories are shown for deposited particles only (right). Note the complex trajectories inside the alveolus. (iii) All particle trajectories are shown with alveolar flow pattern in the background (left). Trajectories are shown for deposited particles only (right).

Figure 5

3 μm particle trajectories, with velocity magnitude along trajectories (in m/s). (i)–(iii) (left and right column) correspond to Cases (i)–(iii) in Fig. 3. (i) Deposition occurs only at the bottom of the duct. Trajectories are shown for deposited particles only (right). (ii) All trajectories are shown with alveolar flow pattern illustrated in the background (left). Trajectories are shown for deposited particles (right). (iii) All trajectories are shown with alveolar flow pattern in background (left). Trajectories are shown for deposited particles only (right). Deposition occurs around the opening ring.

Figure 6

(a) Profile of rms Re number versus acinar generation (rms Wo number is indicated and is constant over all generations). (b) Ratio of alveolar to ductal flow rate in the space-filling tree versus acinar generation (continuous line). Values are compared with previous investigations of alveolar flows (see details in text) and the simple alveolated duct model is indicated with an arrow. Following the space-filling assumption, Q̇a/Q̇d=1 at generation 8 (i.e., alveolar sac), since the alveolus and duct may not be distinguished between one another.

Figure 7

(a) 2D cross-sectional streamlines with velocity field magnitude obtained parallel to streamwise flow direction in generation 3 of the space-filling tree. Note the slower flow within alveoli compared with within the duct. (b) Close-up of 3D recirculating flow patterns observed in alveoli located in generation 3. 3D view of instantaneous radial streamlines at (c) airway generation 4 and (d) generations 7 and 8. (Velocity scale is logarithmic in m/s.)

Figure 8

Views of (a) 1 μm and (b) 3 μm particle trajectories in the space-filling acinar tree with velocity magnitude along trajectories (scale in m/s). Geometrical orientation with respect to gravity corresponds to configuration A (see Sec. 4). Views of (c) 1 μm and (d) 3 μm particle trajectories in configuration B.

Figure 9

Detail of sedimenting 3 μm diameter particle trajectories with velocity magnitude (scale in m/s). Left: Close-up of trajectories at the bifurcation of generation 3. Right: Alternative view of sedimenting trajectories.

Figure 10

Examples of distinct 1 μm particle trajectories for configuration A. Color code corresponds to particle residence time along trajectory (scale in seconds). Bottom row illustrates examples of particles leaving the computational domain during first exhalation phase.

Figure 11

Examples of distinct 1 μm particle trajectories for configuration B. Color code corresponds to particle residence time along trajectory (scale in seconds). Top row illustrates examples of particles, which settle in the shorter branch of generation 4, due to the specific orientation of gravity. Bottom row illustrates examples of particles leaving the computational domain during first exhalation phase.

Figure 12

Deposition efficiency n(t)/T in the space-filling geometry as a function of normalized time t/T for 1 μm (curves on the right) and 3 μm diameter particles (curves on the left) under configurations A and B (see text for details). Schematic corresponds to the orientation of generation 3 with respect to gravity.

Figure 13

Analytical and simulation results for the deposition efficiency n(t)/N during gravitational settling of 10 μm spherical particles in laminar horizontal pipe flow (Re=0.3)

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