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Numerical simulation of airflow and microparticle deposition in a synchrotron micro-CT-based pulmonary acinus model a
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Toshihiro Sera , Kentaro Uesugi , Naoto Yagi & Hideo Yokota
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The Center for Advanced Medical Engineering and Informatics, Osaka University, 2-15, Yamadaoka, Suita, Osaka 565-0871, Japan b
Research & Utilization Division, SPring-8/JASRI, 1-1-1, Kouto, Sayo-cho, Sayo-gun, Hogyo 679-5198, Japan
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Image Processing Research Team, Center for Advanced Photonics, RIKEN, 2-1, Hirosawa, Wako, Saitama 351-0198, Japan Published online: 13 May 2014.
To cite this article: Toshihiro Sera, Kentaro Uesugi, Naoto Yagi & Hideo Yokota (2015) Numerical simulation of airflow and microparticle deposition in a synchrotron micro-CT-based pulmonary acinus model, Computer Methods in Biomechanics and Biomedical Engineering, 18:13, 1427-1435, DOI: 10.1080/10255842.2014.915030 To link to this article: http://dx.doi.org/10.1080/10255842.2014.915030
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Computer Methods in Biomechanics and Biomedical Engineering, 2015 Vol. 18, No. 13, 1427–1435, http://dx.doi.org/10.1080/10255842.2014.915030
Numerical simulation of airflow and microparticle deposition in a synchrotron micro-CT-based pulmonary acinus model Toshihiro Seraa*, Kentaro Uesugib, Naoto Yagib and Hideo Yokotac a
The Center for Advanced Medical Engineering and Informatics, Osaka University, 2-15, Yamadaoka, Suita, Osaka 565-0871, Japan; b Research & Utilization Division, SPring-8/JASRI, 1-1-1, Kouto, Sayo-cho, Sayo-gun, Hogyo 679-5198, Japan; cImage Processing Research Team, Center for Advanced Photonics, RIKEN, 2-1, Hirosawa, Wako, Saitama 351-0198, Japan
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(Received 14 May 2013; accepted 10 April 2014) The acinus consists of complex, branched alveolar ducts and numerous surrounding alveoli, and so in this study, we hypothesized that the particle deposition can be much influenced by the complex acinar geometry, and simulated the airflow and particle deposition (density ¼ 1.0 g/cm3, diameter ¼ 1 and 3 mm) numerically in a pulmonary acinar model based on synchrotron micro-CT of the mammalian lung. We assumed that the fluid – structure interaction was neglected and that alveolar flow was induced by the expansion and contraction of the acinar model with the volume changing sinusoidally with time as the moving boundary conditions. The alveolar flow was dominated by radial flows, and a weak recirculating flow was observed at the proximal side of alveoli during the entire respiratory cycle, despite the maximum Reynolds number at the inlet being 0.029. Under zero gravity, the particle deposition rate after single breathing was less than 0.01, although the particles were transported deeply into the acinus after inspiration. Under a gravitational field, the deposition rate and map were influenced strongly by gravity orientation. In the case of a particle diameter of 1 mm, the rate increased dramatically and mostly non-deposited particles remained in the model, indicating that the rate would increase further after repeated breathing. At a particle diameter of 3 mm, the rate was 1.0 and all particles were deposited during single breathing. Our results show that the particle deposition rate in realistic pulmonary acinar model is higher than in an idealized model. Keywords: computational fluid dynamics; particle deposition; pulmonary acinus; synchrotron radiation-CT
Introduction The deposition of inhaled particles in lung is a key factor in any assessment of the toxic effects of pollutant particles and evaluation of delivery of pharmacological agents. Particle deposition patterns are affected mainly by particle size and the flow characteristics within the complex respiratory tract. The pulmonary airway tree consists of a commonly constructed system of multiple branching tubes originating with the trachea, dividing by asymmetrical dichotomy into progressively shorter and smaller diameter bronchi, and then bronchioles as far as the terminal bronchioles (TBs). The TBs then divide, again by asymmetrical dichotomy, into a branched series of alveolar ducts (ADs) and associated surrounding alveoli, with the ductal paths terminating in groups of alveolar sacs (ASs). The groups of structures peripheral to each TB constitute a pulmonary acinus, which may be defined functionally as the largest lung unit in which all airways participate in gas exchange (Rodriguez et al. 1987). In the acinar region, individual branch diameter decreases rapidly with increasing branch generation, but the corresponding value of the summed branch cross-sectional area increases rapidly. As a result, the velocity is reduced markedly and Reynolds number also decreases. This low Re flow is much related to the pulmonary functions and dynamics in the deep lung.
*Corresponding author. Email: [email protected] q 2014 Taylor & Francis
According to a previous report (Elder et al. 2009), the inhaled particles greater than 10 mm diameter are mainly filtered at upper airways, and the small particles with a diameter of less than 10 mm can reach the alveolar region. Their particle transport in acinar region may be determined by the balance between aerodynamic and gravitational force, as these particles are too large to be influenced by Brownian force and too light to be substantially affected by inertia. The pulmonary acinus comprises the branched complex of alveolated airways that are connected to the same first-order respiratory or transitional bronchiole (Weibel et al. 2005). Exploring the depth of the lung is significant for the characterization of the respiratory functions. To better understand respiratory functions and dynamics, flow phenomena should be simulated using a realistic pulmonary acinar model. Analyzing the 3D structure of alveoli is difficult; therefore, alveolar geometry is measured using various techniques. Stereological analysis is a useful tool for quantitative characterization of the geometry of irregular 3D fixed samples based on continuous measurements of 2D planar sections with a light microscope. Parameswaran et al. (2009) stained fixed lungs of rat and mouse with silver complex solution (Merril et al. 1981), and visualized ADs and alveoli using a microfocal computed tomography system
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(micro-CT). Fixed rat lung tissue samples were visualized using synchrotron radiation-based X-ray tomographic microscopy (Ikura et al. 2004; Tsuda et al. 2008). However, obtaining the whole acinus based on CT images is problematic because it consists of complex, branched ADs and numerous surrounding alveoli with a thin alveolar wall. To overcome the challenges of imaging the whole acinus, several researchers have proposed an idealized pulmonary acinar model, and investigated flow phenomena and particle transport therein both numerically and experimentally. Tsuda et al. (1995) generated a 2D central thorough fare channel surrounded by a torus as the pulmonary duct and examined the effects of rhythmical expanding and contracting breathing in a sinusoidal manner. Haber et al. (2003) applied this 2D model to a 3D model and investigated the gravitational particle deposition with rhythmical airway motion. Sznitman et al. (2007, 2009) also simulated the alveolar flow and particle deposition in a 3D simple AD, such as a cylindrical channel mounted with an isolated spherical cavity and assemblages of polyhedra to form a space-filling asymmetrical acinar branching tree. According to these computational simulations using the moving boundary problem, the alveolar flows induced by rhythmical airway motion were kinematically irreversible and dominated by recirculating and radial flows, in contrast to the results from the rigid alveoli model (Davidson and Fitz-Gerald 1972). In addition, van Ertbruggen et al. (2008) measured experimentally the flow structures in a 3D scaled-up model of an alveolated bend with rigid walls. These idealized acinar models have been used to simulate not only flow, but also the viscoelastic behavior of the finite element method (Denny and Schroter 1997, 2000, 2006). The acinus consists of complex, branched ADs and numerous surrounding alveoli, and so we hypothesized that the particle deposition can be much influenced by the complex acinar geometry. In the current study, we simulated the flow patterns and particle deposition (diameter ¼ 1 and 3 mm) in a realistic 3D pulmonary acinar model based on CT images of the mammalian lung using computational fluid dynamics (CFD). The geometry was obtained using a high-resolution synchrotron CT system that enables visualization of the alveoli of a closedchest mouse with a voxel size of 3.3 mm3. In our simulation of airflow and particle deposition, we assumed that the fluid – structure interaction was neglected and that alveolar flow was induced by the expansion and contraction of the acinar model with the volume changing sinusoidally with time as the moving boundary conditions (Tsuda et al. 1995; Haber et al. 2003; Sznitman et al. 2007; Sznitman et al. 2009). In particular, we investigated the effect of gravity orientation on particle transport and deposition. In particular, under gravity field, our results indicated that the particle deposition rate in realistic pulmonary acinar model is higher than in an idealized model.
Pulmonary acinar model The pulmonary acinar model was based on CT images of a closed-chest mouse. All experimental protocols were approved by the SPring-8 Experimental Animals Care and Use Committee. SPring-8 is the third-generation synchrotron radiation source in Hyogo, Japan, which offers a higher flux X-ray than a laboratory X-ray source, resulting in higher contrast resolution (Goto et al. 2001). To reconstruct the CT images using the convolution back projection method, a summed projection was acquired at 2250 rotational positions around 1808 in 10 min. Because the X-ray beam is parallel, each horizontal line corresponds to a slice position along the rotation axis, and multiple slices (slice pitch was equal to the pixel size: ‘cubic voxel’) were readily obtained in one rotation (3D CT). The isotopic voxel size was 3.3 mm. A healthy male mouse (A/J, 9 weeks) was euthanized with diethyl ether and then mounted on the rotation stage. Figure 1 shows representative continuous CT images, and the TB and ADs can be visualized clearly. We identified cross-sections of the AD and alveoli using a thresholdbased 3D region-growing algorithm, in which the threshold value is preselected, leading to an optical segmentation result. Generally, the pixel intensity of air is less than that of lung tissues. Starting from a seeding voxel defined by the user, the algorithm accumulates all low-intensity voxels below the defined threshold. We measured the histogram of pixel intensity around the target airway, and defined the optimum threshold as the nadir of the saddle-like CT brightness histogram of an objective selection criterion. The interactive correction of the defined threshold value was carried out preliminarily. The segmented regions were overlaid on the CT images (black area in Figure 1). Figure 2 depicts the realistic pulmonary acinar model reconstructed from segmented CT images (Figure 1). To avoid any influences of the boundary conditions and achieve
Figure 1. Representative synchrotron CT images. The slice pitch (A– B, and B– C) is 9.9 mm. TB, terminal bronchiole; AD, alveolar duct; AS, alveolar sac.
Computer Methods in Biomechanics and Biomedical Engineering
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›u þ u7u ¼ 27p þ m72 u; r ›t
Figure 2. The realistic pulmonary acinar model based on synchrotron CT images (Figure 1). To avoid any influence of the boundary conditions on the computer simulation, the inlet was artificially lengthened using a straight tube of 130 mm diameter. As the initial condition of numerical simulation of particle deposition, the particles were located at the x – y plane perpendicular to the inlet indicated by the white arrow. The streamlines in proximal (A) and distal (B) alveoli indicated by black arrows are shown in Figure 3.
fully developed inflow at the inlet of the acinus, the inlet was artificially lengthened with a straight tube in the direction of the skeleton, as calculated by a 3D thinning algorithm. This algorithm performs a Euclidean distance (the distance from background) transformation and repeatedly checks that the Euclidean distance value is small as the voxels are deleted in sequence. Finally, it finds the middle line and the branching point of the airway network without altering the topology. The volume size was 1.9 mm £ 1.2 mm £ 0.8 mm3, and the inlet was of 130 mm diameter. CFD simulation Mesh generation The computational mesh was generated using ICEM CFD (ANSYS, Inc., Tokyo, Japan). We created an unstructured mesh with tetrahedron volume elements for the core. Three subsurface layers with prism volume elements were inserted along the walls to increase the accuracy of the simulation where the velocity gradients were the highest. The mesh comprised 2,410,584 cells. The mesh dependency of the solution was examined by solving the flow fields for various mesh configurations comprising 794,909– 8,105,172 cells. Velocity profiles were compared in several sections for all mesh configurations. The differences in the maximum velocity over 2,410,584 cells were less than 0.5%.
Numerical methods Assuming laminar and incompressible airflow, the governing equations are expressed as 7u ¼ 0;
ð1Þ
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where u represents the velocity, p is the pressure, m is the dynamic viscosity, and r is the density. To obtain the timedependent flow fields during rhythmic motion, these equations are solved numerically on a moving grid using a commercial finite-volume method CFX 11.0 (ANSYS, Inc.). Our model is designed to expand and construct selfsimilarly in a simple sinusoidal manner with a breathing period, T and origin, m. In this study, m is defined as the center of the artificial inlet. In normal breathing, breathhold occurs at end of expiration (Miller et al. 2005). In this study, however, we assumed that the acinar model was designed to expand and construct in a simple sinusoidal manner in order to compare the previous results (Tsuda et al. 1995; Haber et al. 2003; Sznitman et al. 2007; Sznitman et al. 2009). For geometrically self-similar motion, the volume expansion factor, W and length expansion factor, a are given by: V max 2 V min ; V min
ð3Þ
a ¼ ðW þ 1Þ1=3 21;
ð4Þ
W¼
where Vmax and Vmin represent the maximum and minimum volumes of the small airway model, respectively. The mesh displacement factor, b(t) is expressed as
bðtÞ ¼ 1 þ
a a p þ sin ft 2 ; 2 2 2
ð5Þ
where f ¼ 2p/T is the breathing frequency. In this model, to deform the airway model uniformly, the origin is set at the center of the inlet, M. Therefore, the distance of each node, L(t) from M and the maximum distance are then given by LðtÞ ¼ bðtÞL0 ;
ð6Þ
where L0 is the distance at t ¼ 0. In this study, the rate of mesh deformation is solved using the CFD software. The dynamics mesh was incorporated as a user-defined function, where the deforming wall was defined as selfsimilar expansion and construction in a sinusoidal manner. In each time step, the mesh convergence was confirmed.
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In particle deposition in the alveolar region, the governing equations are expressed as
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p 3 dU p p D p rp ¼ C D rD2P jU 2 U P j U 2 U p 6 dt 8 p þ d3p ðrp 2 rÞg; 6 24 CD ¼ 1 þ 0:15Re0:687 ; p Rep
ð7Þ ð8Þ
where rp is the particle density, Dp is the particle diameter, CD is the drag coefficient, and Rep is the particle Reynolds number (Schiller and Neumann 1933). In this simulation, we focused on the effects of convection and gravity and neglected Brownian forces. In particular, to investigate the effects of gravity on particle transport and deposition, we assumed that the gravity direction was negligible (zero gravity; case 1), parallel (x direction in Figure 2; case 2), and perpendicular to the artificial inlet (y direction in Figure 2; case 3). Furthermore, the numerical simulations were one-way coupled, i.e., the flow was assumed not to be influenced by the particles, with the particles being transported passively by airflow. For particle diameters of Dp ¼ 1 and 3 mm, rp was set equal to the density of water (1.0 g/cm3). In this study, the differences in velocity profiles after seven cycles were less than 1%, and then the particles were introduced in the model at the beginning of the 8th cycle. A uniform 2D grid was superimposed at the inlet of the acinus and behind the artificial inlet in Figure 2, and the particles (N ¼ 36,001) were released from these grid points. The particles were introduced into the flow field with initial velocity equal to the velocity at their grid points. At the boundaries, the perpendicular and parallel restitution coefficients of the particles at the wall were both set to 0, i.e., when a particle strikes a wall, it is assumed to be stuck at the wall. Furthermore, particles that exited the computational model were not reintroduced. Under physiological breathing of a human adult, the residual functional capacity and total lung capacity are approximately 3 and 6 l, respectively. In this study, we set W and T as 0.5 and 4.0 s, respectively. As the boundary condition, the pressure at the inlet was zero. The no-slip condition was assumed at the airway walls such that the fluid velocity matched the wall velocity at the interface in the case of a moving wall, as expressed by the previous equations.
Results and discussion In our simulation, the maximum Reynolds number, Remax, was 0.029 at the inlet and 0.0004 at the terminal AS. Figure 3 depicts the streamlines in proximal (Figure 3(A)) and distal (Figure 3(B)) alveoli during deep breathing. The Re of each AD flow was low (Remax ¼ 0.0038 and 0.0013 at
Figure 3. The streamlines in proximal (A) and distal (B) alveoli. Remax in the connecting AD was 0.0038 in (A) and 0.0013 in (B).
each connecting AD). In both alveoli, the flow was dominated by radial flow, and a weak recirculating flow was observed at the proximal side. These recirculating zones remained almost completely still during the breathing cycle. These flow patterns are similar to previous results using an ideal AD model (Sznitman et al. 2007), which was designed as a spherical cap connected to a cylindrical shell with open ends (Weibel 1986). In previous studies of a nowall-motion alveolus, the AD flow generated a recirculating region filling the entire alveolus and the convective exchange between the duct and alveolus was prohibited; in contrast, alveolar wall motion induced complex flow patterns in the alveolus(Tsuda et al. 1995; Sznitman et al. 2007; van Ertbruggen et al. 2008). In proximal acinar generation (Re at the AD ¼ 0.112), the alveolar flow was dominated by recirculation patterns that shifted to the
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Figure 4. The particle (Dp ¼ 1 mm) transport. Arrows indicate the gravity direction (A, case 1; B, case 2; C, case 3). The deposited particles are not shown.
proximal corner of the alveolus, and in deeper generations the recirculation zone gradually decreased the alveolar flow, which became largely radial (Sznitman et al. 2007). In particular, in the idealized terminal AS (Re at AD ¼ 0.008), the recirculation region vanished. In our realistic acinar model, however, a weak recirculating flow was observed in the distal alveolus despite the lower Re (Figure 3(B)). Tsuda et al. (1995) suggested that during flow in an expanding and
contracting alveolus, a stagnation saddle point exists, which induces highly complex and irreversible particle trajectories. Figures 4 and 5 present the transport of Dp ¼ 1 and 3 mm particles during single breathing, respectively. Figure 6 illustrates the particle depositions of Dp ¼ 1 and 3 mm after single breathing. In this study, the particle deposition rate during single breathing was defined as the
Figure 5. The particle (Dp ¼ 3 mm) transport. Arrows indicate the gravity direction (A, case 1; B, case 2; C, case 3). The deposited particles are not shown.
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Figure 6. Side view of particle deposition map (red area) after single breathing. Arrows indicate the gravity direction (A and D, case 1; B and E, case 2; C and F, case 3). Dp ¼ 1 mm (A –C), and 3 mm (D– F).
ratio of the number of deposited particles to the initial number of particles (Figure 7). In the case of zero gravity (case 1), both particles (Dp ¼ 1 and 3 mm) are transported deeply into the model after inspiration (Figures 4(A2) and 5(A2)). After expiration, the particles are dispersed widely around the initial positions (Figures 4(A4) and 5(A4)). The deposition rates for both particle diameters were less than 0.01 (Figure 7), and the particles were deposited not in the model but around the initial position (Figures 6(A) and (D)), despite being transported deeply into the model. These results show that there were no significant differences in particle transport and deposition between 1 and 3 mm particles under zero gravity. However, the
Figure 7.
gravity orientation exerted a marked effect on particle transport and deposition. In the case in which the gravity direction was parallel to the parent tube (case 2), the 1 mm particles were also transported deeply into the model after inspiration (Figure 4(B2)) and dispersed widely after expiration (Figure 4(B4)). Also, the particles were deposited in the model, in particular at the alveolar mouth and edge of the middle region (Figure 6(B)). The deposition rate was 0.22 (Figure 7). Gravity exerted a greater effect on the 3 mm particles. Many particles reached the end of the model after inspiration (Figure 5 (B3)) and all particles were deposited during expiration, in particular at the distal region (Figures. 6(E) and 7). In the
The deposition rates of particles (Dp ¼ 1 and 3 mm) during single breathing.
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Computer Methods in Biomechanics and Biomedical Engineering case in which the gravity direction was perpendicular to the parent tube (case 3), the 1 mm particles were transported deeply into the model and were sedimented and deposited by gravity (Figures 4(C4) and 6(C)). The deposition rate was 0.68, which was higher for case 3 than case 2 (Figure 7). The 3 mm particles were sedimented by gravity soon after the beginning of inspiration (Figures 5 (C1), 5(C2), and 5(C3)), and all particles were deposited behind the initial position during inspiration (Figures. 6(F) and 7). Ma et al. (2009) validated CFD predictions of flow field and particle trajectory with experiments within a scaled-up model of idealized alveolated airways, and showed that air flow and aerosol transport in the alveolated airways model can be simulated by CFD techniques with reasonable accuracy. In this study, however, our acinar model was based on synchrotron CT images, and so it is difficult to validate our numerical simulation. Ma and Darquenne (2011) developed a multigenerational 3D idealized model of alveolated airways with arbitrary bifurcation angles and spherical alveolar shape, and simulated the deposition of 1 and 3 mm aerosol particles. Our model is based on a single acinus, and on the other hand, their idealized model is based on three generation duct. In qualitative comparison, the tendencies of aerosol transport and deposition are strongly dependent on gravity orientation in both models. However, not only the model scale but also the model complexity are different, therefore the quantitative comparison is very difficult. In the idealized model, the deposition rate during the first cycle was 20 – 23% for 1 mm particles and 71 –73% for 3 mm particles, which are smaller than our results. The aforementioned results indicate that particle depositions are influenced strongly by gravity orientation. In the case of no gravity (case 1), the deposition efficiency of 1 and 3 mm particles was negligible (Figure 7), even though they were transported deeply into the alveolar region. However, the particle deposition rate was higher dramatically when gravity was not zero (cases 2 and 3). In the case in which the gravity direction was parallel to the parent tube (case 2), the deposition rate was higher than that in case 1 (Figure 7). The 3 mm particles were transported to the end of model during single breathing, and so the deposition rate reached 1.0. Although the 1 mm particles were transported after inspiration as deeply as those in case 1 (Figure 4(B2)), they were deposited at the alveolar mouth and edge; moreover, the deposition rate was higher. Furthermore, the rate increased during expiration rather than inspiration because of the complicated acinar geometry (Figure 7). After single breathing, many particles were still detected in the alveolar model (Figure 4(B4)), suggesting that the deposition rate may increase further after several breathings. In the case in which the gravity direction was perpendicular to the parent tube (case 3), the deposition rate for the same diameter size was higher than those in cases 1 and 2 (Figure 7). The
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1 mm particles were also transported after inspiration as deeply as those in cases 1 and 2 (Figure 4(C2)), and sedimented widely in the model after single breathing (Figure 6(C)). Similar to case 2, after single breathing, many particles were still detected in the alveolar model (Figure 4(C4)), suggesting that the deposition rate may increase after several breathings. The 3 mm particles were sedimented soon after the beginning of, and all particles were deposited earlier than in case 2. The Stokes numbers (St) correspond to the behavior of particles suspended in a flow. St is defined as the ratio of the response time of a particle to the characteristic time of the flow field. When St . 1, particles can detach from a flow, especially if the flow decelerates abruptly, whereas when St , 1, particles follow fluid streamlines closely. In this study, the St values of particles with Dp ¼ 1 and 3 mm were 1.39 £ 10 – 5 and 1.25 £ 10 – 4, respectively, indicating that the particles follow the fluid streamline. The terminal velocities of the particles when the acceleration of the particle is zero and the drag force equals the gravity force were 30 and 269 mm/s, respectively. Compared with the flow velocity at the AD (Figure 3), the terminal velocities were nonnegligible. In particular, the terminal velocity of 3 mm particles was higher than the maximum velocity at the AD. Therefore, particle deposition is greatly influenced by gravity. Alveolar kinematics is also essential for gas exchange in the deep lung. Various investigative techniques have been proposed, such as the light-scattering technique (Butler et al. 2002), optical coherence tomography (Popp et al. 2006; Hou et al. 2011), and in vivo microscopy (DiRocco et al. 2007; Pavone et al. 2007). In addition, Namati et al. (2008) evaluated alveolar dynamics in fresh lung ex vivo using confocal laser scanning microscopy, although this technique is limited to imaging to a depth of 50 mm. The details of the 3D kinematics of pulmonary acinus are not yet understood. Therefore, in this study, we assumed that the moving wall represents self-similar deformation. Microscopically, the lung expands and contracts self-similarly during respiration cycles (Ardila et al. 1974), and the alveolar flows and particle transport during self-similar and sinusoidal airway motion have been reported (Tsuda et al. 1995; Haber et al. 2003; Sznitman et al. 2007; Sznitman et al. 2009). In this study, the acinar model is reconstructed based on mammalian lung; on the other hand, the lung and flow conditions are based on human lung. This is the limitation of this study. The acinar models in previous studies (Tsuda et al. 1995; Haber et al. 2003; Sznitman et al. 2007; Sznitman et al. 2009; Ma and Darquenne 2011) are idealized in spite of the complex geometry. In this study, we hypothesized that the particle deposition can be much influenced by the complex acinar geometry. However, it is very difficult to obtain whole acinus of human lung even by micro-CT because the alveolar wall is very thin.
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Additionally, the acinus consists of complex, branched ADs and numerous surrounding alveoli. Recently, the synchrotron micro-CT can be used for mammalian lung and the alveolar wall can be detected due to the higher flux X-ray. The geometry differences between mammalian and human acinus are not well known; however, the mammalian acinus also consists of some branched ADs and numerous alveoli, like human acinus. It is intended that the simulation of airflow and microparticle deposition in realistic mammalian-based model will further contribute to the initial steps in the development toward an accurate understanding of airflow and particle deposition in a realistic human acinus.
Conclusion In this study, we simulated the airflow and particle deposition in a realistic pulmonary acinar model reconstructed from the mammalian lung during rhythmical self-similar breathing motion. The alveolar flows were dominated by radial flows, and a weak recirculating flow was observed at the proximal side of alveoli during the entire respiratory cycle, despite the maximum Re at the inlet being 0.029. Further, we investigated the effect of gravity on particle deposition (rp ¼ 1.0 g/cm3, Dp ¼ 1 and 3 mm). Under zero gravity, although both 1 and 3 mm particles reached the deep acinus after inspiration, the deposition rate after single breathing was less than 0.01. Under a gravitational field, both the deposition rate and map were influenced strongly by the gravity orientation. In the case of particles with Dp ¼ 1 mm, the rate increased dramatically and mostly non-deposited particles remained in the model, indicating that the rate would increase further after several breathings. In the case of particles with Dp ¼ 3 mm, the rate was 1.0 and all particles were deposited during single breathing. Our results show that the particle deposition rate in realistic pulmonary acinar model is higher than in idealized model.
Funding The experiments were carried out at the Program Review of SPring-8 (Proposal Number: 2007A2071). The work was supported by a Grant-in-Aid for Young Scientists (B) (19700394) from the Japan Society for the Promotion of Science.
References Ardila R, Horie T, Hildebrandt J. 1974. Macroscopic isotropy of lung expansion. Respir Physiol. 20:105 –115. Butler JP, Brown RE, Stamenovic´ D, Morris JP, Topulos GP. 2002. Effect of surface tension on alveolar surface area. J Appl Physiol. 93:1015– 1022. Davidson MR, Fitz-Gerald JM. 1972. Flow patterns in models of small airway units of the lung. J Fluid Mech. 52:61 –177.
Denny E, Schroter RC. 2006. A model of non-uniform lung parenchyma distortion. J Biomech. 39:652– 663. Denny E, Schroter RC. 1997. Relationships between alveolar size and fibre distribution in a mammalian lung alveolar duct model. J Biomech Eng. 119:289 – 297. Denny E, Schroter RC. 2000. Viscoelastic behavior of a lung alveolar duct model. J Biomech Eng. 122:143 –151. DiRocco JD, Carney DE, Nieman GF. 2007. Correlation between alveolar recruitment/derecruitment and inflection points on the pressure – volume curve. Intensive Care Med. 33:1204 – 1211. Elder A, Vidyasagar S, DeLouise L. 2009. Physicochemical factors that affect metal and metal oxide nanoparticle passage across epithelial barriers. Wiley Interdiscip Rev Nanomed Nanobiotechnol. 1:434 – 450. Goto S, Takeshita K, Suzuki Y, Ohashi H, Asano Y, Kimura H, Matsushita T, Yagi N, Isshiki M, Yamazaki H, et al. 2001. Construction and commissioning of a 215-m-long beamline at SPring-8. Nucl Instrum Meth Phys Res A. 467:682– 685. Haber S, Yitzhak D, Tsuda A. 2003. Gravitational deposition in a rhythmically expanding and contracting alveolus. J Appl Physiol. 95:657 – 671. Hou R, Le T, Murgu SD, Chen Z, Brenner M. 2011. Recent advances in optical coherence tomography for the diagnoses of lung disorders. Expert Rev Respir Med. 5:711 – 724. Ikura H, Shimizu K, Ikezoe J, Nagareda T, Yagi N. 2004. In vitro evaluation of normal and abnormal lungs with ultra-highresolution CT. J Thorac Imaging. 19:8 – 15. Ma B, Darquenne C. 2011. Aerosol deposition characteristics in distal acinar airways under cyclic breathing conditions. J Appl Physiol. 110:1271 – 1282. Ma B, Ruwet V, Corieri P, Theunissen R, Riethmuller M, Darquenne C. 2009. CFD Simulation and experimental validation of fluid flow and particle transport in a model of alveolated airways. J Aerosol Sci. 40:403 – 141. Merril CR, Goldman D, Sedman SA, Ebert MH. 1981. Ultrasensitive stain for proteins in polyacrylamide gels shows regional variation in cerebrospinal fluid proteins. Science. 211(4489):1437 –1438. Miller JD, Pegelow DF, Jacques AJ, Dempsey JA. 2005. Skeletal muscle pump versus respiratory muscle pump: modulation of venous return from the locomotor limb in humans. J Physiol. 15(563 Pt 3):925– 943. Namati E, Thiesse J, De Ryk J, McLennan G. 2008. Alveolar dynamics during respiration: are the pores of Kohn a pathway to recruitment? Am J Respir Cell Mol Biol. 38:572 – 578. Parameswaran H, Bartola´k-Suki E, Hamakawa H, Majumdar A, Allen PG, Suki B. 2009. Three-dimensional measurement of alveolar airspace volumes in normal and emphysematous lungs using micro-CT. J Appl Physiol. 107:583– 592. Pavone LA, Albert S, Carney D, Gatto LA, Halter JM, Nieman GF. 2007. Injurious mechanical ventilation in the normal lung causes a progressive pathologic change in dynamic alveolar mechanics. Crit Care. 11:R64. Popp A, Wendel M, Knels L, Koch T, Koch E. 2006. Imaging of the three-dimensional alveolar structure and the alveolar mechanics of a ventilated and perfused isolated rabbit lung with Fourier domain optical coherence tomography. J Biomed Opt. 11:014015. Rodriguez M, Bur S, Favre A, Weibel ER. 1987. Pulmonary acinus: geometry and morphometry of the peripheral airway system in rat and rabbit. Am J Anat. 180:143– 155. Schiller L, Neumann A. 1933. Uber die grundlegenden Berechungen bei der Schwer kraftaufbereitung. Ver Dtsch Ingenieure. 77:318– 320.
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Sznitman J, Heimsch F, Heimsch T, Rusch D, Ro¨sgen T. 2007. Three-dimensional convective alveolar flow induced by rhythmic breathing motion of the pulmonary acinus. J Biomech Eng. 129:658– 665. Sznitman J, Heimsch T, Wildhaber JH, Tsuda A, Ro¨sgen T. 2009. Respiratory flow phenomena and gravitational deposition in a three-dimensional space-filling model of the pulmonary acinar tree. J Biomech Eng. 131:031010. Tsuda A, Filipovic N, Haberthu¨r D, Dickie R, Matsui Y, Stampanoni M, Schittny JC. 2008. Finite element 3D reconstruction of the pulmonary acinus imaged by synchrotron X-ray tomography. J Appl Physiol. 105: 964– 976.
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Tsuda A, Henry FS, Butler JP. 1995. Chaotic mixing of alveolated duct flow in rhythmically expanding pulmonary acinus. J Appl Physiol. 79:1055– 1063. Van Ertbruggen C, Corieri P, Theunissen R, Riethmuller ML, Darquenne C. 2008. Validation of CFD predictions of flow in a 3D alveolated bend with experimental data. J Biomech. 41:399 – 405. Weibel ER. 1986. Functional morphology of lung parenchyma. In: Fishman AP, editor. Handbook of physiology: the respiratory System. Sec. 3, Vol. III, Chap. 8. Bethesda (MD): American Physiological Society; p. 89 – 111. Weibel ER, Sapoval B, Filoche M. 2005. Design of peripheral airways for efficient gas exchange. Respir Physiol Neurobiol. 148:3 –21.
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Numerical simulation of airflow and microparticle deposition in a synchrotron micro-CT-based pulmonary acinus model a
b
b
Toshihiro Sera , Kentaro Uesugi , Naoto Yagi & Hideo Yokota
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a
The Center for Advanced Medical Engineering and Informatics, Osaka University, 2-15, Yamadaoka, Suita, Osaka 565-0871, Japan b
Research & Utilization Division, SPring-8/JASRI, 1-1-1, Kouto, Sayo-cho, Sayo-gun, Hogyo 679-5198, Japan
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c
Image Processing Research Team, Center for Advanced Photonics, RIKEN, 2-1, Hirosawa, Wako, Saitama 351-0198, Japan Published online: 13 May 2014.
To cite this article: Toshihiro Sera, Kentaro Uesugi, Naoto Yagi & Hideo Yokota (2015) Numerical simulation of airflow and microparticle deposition in a synchrotron micro-CT-based pulmonary acinus model, Computer Methods in Biomechanics and Biomedical Engineering, 18:13, 1427-1435, DOI: 10.1080/10255842.2014.915030 To link to this article: http://dx.doi.org/10.1080/10255842.2014.915030
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Computer Methods in Biomechanics and Biomedical Engineering, 2015 Vol. 18, No. 13, 1427–1435, http://dx.doi.org/10.1080/10255842.2014.915030
Numerical simulation of airflow and microparticle deposition in a synchrotron micro-CT-based pulmonary acinus model Toshihiro Seraa*, Kentaro Uesugib, Naoto Yagib and Hideo Yokotac a
The Center for Advanced Medical Engineering and Informatics, Osaka University, 2-15, Yamadaoka, Suita, Osaka 565-0871, Japan; b Research & Utilization Division, SPring-8/JASRI, 1-1-1, Kouto, Sayo-cho, Sayo-gun, Hogyo 679-5198, Japan; cImage Processing Research Team, Center for Advanced Photonics, RIKEN, 2-1, Hirosawa, Wako, Saitama 351-0198, Japan
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(Received 14 May 2013; accepted 10 April 2014) The acinus consists of complex, branched alveolar ducts and numerous surrounding alveoli, and so in this study, we hypothesized that the particle deposition can be much influenced by the complex acinar geometry, and simulated the airflow and particle deposition (density ¼ 1.0 g/cm3, diameter ¼ 1 and 3 mm) numerically in a pulmonary acinar model based on synchrotron micro-CT of the mammalian lung. We assumed that the fluid – structure interaction was neglected and that alveolar flow was induced by the expansion and contraction of the acinar model with the volume changing sinusoidally with time as the moving boundary conditions. The alveolar flow was dominated by radial flows, and a weak recirculating flow was observed at the proximal side of alveoli during the entire respiratory cycle, despite the maximum Reynolds number at the inlet being 0.029. Under zero gravity, the particle deposition rate after single breathing was less than 0.01, although the particles were transported deeply into the acinus after inspiration. Under a gravitational field, the deposition rate and map were influenced strongly by gravity orientation. In the case of a particle diameter of 1 mm, the rate increased dramatically and mostly non-deposited particles remained in the model, indicating that the rate would increase further after repeated breathing. At a particle diameter of 3 mm, the rate was 1.0 and all particles were deposited during single breathing. Our results show that the particle deposition rate in realistic pulmonary acinar model is higher than in an idealized model. Keywords: computational fluid dynamics; particle deposition; pulmonary acinus; synchrotron radiation-CT
Introduction The deposition of inhaled particles in lung is a key factor in any assessment of the toxic effects of pollutant particles and evaluation of delivery of pharmacological agents. Particle deposition patterns are affected mainly by particle size and the flow characteristics within the complex respiratory tract. The pulmonary airway tree consists of a commonly constructed system of multiple branching tubes originating with the trachea, dividing by asymmetrical dichotomy into progressively shorter and smaller diameter bronchi, and then bronchioles as far as the terminal bronchioles (TBs). The TBs then divide, again by asymmetrical dichotomy, into a branched series of alveolar ducts (ADs) and associated surrounding alveoli, with the ductal paths terminating in groups of alveolar sacs (ASs). The groups of structures peripheral to each TB constitute a pulmonary acinus, which may be defined functionally as the largest lung unit in which all airways participate in gas exchange (Rodriguez et al. 1987). In the acinar region, individual branch diameter decreases rapidly with increasing branch generation, but the corresponding value of the summed branch cross-sectional area increases rapidly. As a result, the velocity is reduced markedly and Reynolds number also decreases. This low Re flow is much related to the pulmonary functions and dynamics in the deep lung.
*Corresponding author. Email: [email protected] q 2014 Taylor & Francis
According to a previous report (Elder et al. 2009), the inhaled particles greater than 10 mm diameter are mainly filtered at upper airways, and the small particles with a diameter of less than 10 mm can reach the alveolar region. Their particle transport in acinar region may be determined by the balance between aerodynamic and gravitational force, as these particles are too large to be influenced by Brownian force and too light to be substantially affected by inertia. The pulmonary acinus comprises the branched complex of alveolated airways that are connected to the same first-order respiratory or transitional bronchiole (Weibel et al. 2005). Exploring the depth of the lung is significant for the characterization of the respiratory functions. To better understand respiratory functions and dynamics, flow phenomena should be simulated using a realistic pulmonary acinar model. Analyzing the 3D structure of alveoli is difficult; therefore, alveolar geometry is measured using various techniques. Stereological analysis is a useful tool for quantitative characterization of the geometry of irregular 3D fixed samples based on continuous measurements of 2D planar sections with a light microscope. Parameswaran et al. (2009) stained fixed lungs of rat and mouse with silver complex solution (Merril et al. 1981), and visualized ADs and alveoli using a microfocal computed tomography system
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(micro-CT). Fixed rat lung tissue samples were visualized using synchrotron radiation-based X-ray tomographic microscopy (Ikura et al. 2004; Tsuda et al. 2008). However, obtaining the whole acinus based on CT images is problematic because it consists of complex, branched ADs and numerous surrounding alveoli with a thin alveolar wall. To overcome the challenges of imaging the whole acinus, several researchers have proposed an idealized pulmonary acinar model, and investigated flow phenomena and particle transport therein both numerically and experimentally. Tsuda et al. (1995) generated a 2D central thorough fare channel surrounded by a torus as the pulmonary duct and examined the effects of rhythmical expanding and contracting breathing in a sinusoidal manner. Haber et al. (2003) applied this 2D model to a 3D model and investigated the gravitational particle deposition with rhythmical airway motion. Sznitman et al. (2007, 2009) also simulated the alveolar flow and particle deposition in a 3D simple AD, such as a cylindrical channel mounted with an isolated spherical cavity and assemblages of polyhedra to form a space-filling asymmetrical acinar branching tree. According to these computational simulations using the moving boundary problem, the alveolar flows induced by rhythmical airway motion were kinematically irreversible and dominated by recirculating and radial flows, in contrast to the results from the rigid alveoli model (Davidson and Fitz-Gerald 1972). In addition, van Ertbruggen et al. (2008) measured experimentally the flow structures in a 3D scaled-up model of an alveolated bend with rigid walls. These idealized acinar models have been used to simulate not only flow, but also the viscoelastic behavior of the finite element method (Denny and Schroter 1997, 2000, 2006). The acinus consists of complex, branched ADs and numerous surrounding alveoli, and so we hypothesized that the particle deposition can be much influenced by the complex acinar geometry. In the current study, we simulated the flow patterns and particle deposition (diameter ¼ 1 and 3 mm) in a realistic 3D pulmonary acinar model based on CT images of the mammalian lung using computational fluid dynamics (CFD). The geometry was obtained using a high-resolution synchrotron CT system that enables visualization of the alveoli of a closedchest mouse with a voxel size of 3.3 mm3. In our simulation of airflow and particle deposition, we assumed that the fluid – structure interaction was neglected and that alveolar flow was induced by the expansion and contraction of the acinar model with the volume changing sinusoidally with time as the moving boundary conditions (Tsuda et al. 1995; Haber et al. 2003; Sznitman et al. 2007; Sznitman et al. 2009). In particular, we investigated the effect of gravity orientation on particle transport and deposition. In particular, under gravity field, our results indicated that the particle deposition rate in realistic pulmonary acinar model is higher than in an idealized model.
Pulmonary acinar model The pulmonary acinar model was based on CT images of a closed-chest mouse. All experimental protocols were approved by the SPring-8 Experimental Animals Care and Use Committee. SPring-8 is the third-generation synchrotron radiation source in Hyogo, Japan, which offers a higher flux X-ray than a laboratory X-ray source, resulting in higher contrast resolution (Goto et al. 2001). To reconstruct the CT images using the convolution back projection method, a summed projection was acquired at 2250 rotational positions around 1808 in 10 min. Because the X-ray beam is parallel, each horizontal line corresponds to a slice position along the rotation axis, and multiple slices (slice pitch was equal to the pixel size: ‘cubic voxel’) were readily obtained in one rotation (3D CT). The isotopic voxel size was 3.3 mm. A healthy male mouse (A/J, 9 weeks) was euthanized with diethyl ether and then mounted on the rotation stage. Figure 1 shows representative continuous CT images, and the TB and ADs can be visualized clearly. We identified cross-sections of the AD and alveoli using a thresholdbased 3D region-growing algorithm, in which the threshold value is preselected, leading to an optical segmentation result. Generally, the pixel intensity of air is less than that of lung tissues. Starting from a seeding voxel defined by the user, the algorithm accumulates all low-intensity voxels below the defined threshold. We measured the histogram of pixel intensity around the target airway, and defined the optimum threshold as the nadir of the saddle-like CT brightness histogram of an objective selection criterion. The interactive correction of the defined threshold value was carried out preliminarily. The segmented regions were overlaid on the CT images (black area in Figure 1). Figure 2 depicts the realistic pulmonary acinar model reconstructed from segmented CT images (Figure 1). To avoid any influences of the boundary conditions and achieve
Figure 1. Representative synchrotron CT images. The slice pitch (A– B, and B– C) is 9.9 mm. TB, terminal bronchiole; AD, alveolar duct; AS, alveolar sac.
Computer Methods in Biomechanics and Biomedical Engineering
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›u þ u7u ¼ 27p þ m72 u; r ›t
Figure 2. The realistic pulmonary acinar model based on synchrotron CT images (Figure 1). To avoid any influence of the boundary conditions on the computer simulation, the inlet was artificially lengthened using a straight tube of 130 mm diameter. As the initial condition of numerical simulation of particle deposition, the particles were located at the x – y plane perpendicular to the inlet indicated by the white arrow. The streamlines in proximal (A) and distal (B) alveoli indicated by black arrows are shown in Figure 3.
fully developed inflow at the inlet of the acinus, the inlet was artificially lengthened with a straight tube in the direction of the skeleton, as calculated by a 3D thinning algorithm. This algorithm performs a Euclidean distance (the distance from background) transformation and repeatedly checks that the Euclidean distance value is small as the voxels are deleted in sequence. Finally, it finds the middle line and the branching point of the airway network without altering the topology. The volume size was 1.9 mm £ 1.2 mm £ 0.8 mm3, and the inlet was of 130 mm diameter. CFD simulation Mesh generation The computational mesh was generated using ICEM CFD (ANSYS, Inc., Tokyo, Japan). We created an unstructured mesh with tetrahedron volume elements for the core. Three subsurface layers with prism volume elements were inserted along the walls to increase the accuracy of the simulation where the velocity gradients were the highest. The mesh comprised 2,410,584 cells. The mesh dependency of the solution was examined by solving the flow fields for various mesh configurations comprising 794,909– 8,105,172 cells. Velocity profiles were compared in several sections for all mesh configurations. The differences in the maximum velocity over 2,410,584 cells were less than 0.5%.
Numerical methods Assuming laminar and incompressible airflow, the governing equations are expressed as 7u ¼ 0;
ð1Þ
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where u represents the velocity, p is the pressure, m is the dynamic viscosity, and r is the density. To obtain the timedependent flow fields during rhythmic motion, these equations are solved numerically on a moving grid using a commercial finite-volume method CFX 11.0 (ANSYS, Inc.). Our model is designed to expand and construct selfsimilarly in a simple sinusoidal manner with a breathing period, T and origin, m. In this study, m is defined as the center of the artificial inlet. In normal breathing, breathhold occurs at end of expiration (Miller et al. 2005). In this study, however, we assumed that the acinar model was designed to expand and construct in a simple sinusoidal manner in order to compare the previous results (Tsuda et al. 1995; Haber et al. 2003; Sznitman et al. 2007; Sznitman et al. 2009). For geometrically self-similar motion, the volume expansion factor, W and length expansion factor, a are given by: V max 2 V min ; V min
ð3Þ
a ¼ ðW þ 1Þ1=3 21;
ð4Þ
W¼
where Vmax and Vmin represent the maximum and minimum volumes of the small airway model, respectively. The mesh displacement factor, b(t) is expressed as
bðtÞ ¼ 1 þ
a a p þ sin ft 2 ; 2 2 2
ð5Þ
where f ¼ 2p/T is the breathing frequency. In this model, to deform the airway model uniformly, the origin is set at the center of the inlet, M. Therefore, the distance of each node, L(t) from M and the maximum distance are then given by LðtÞ ¼ bðtÞL0 ;
ð6Þ
where L0 is the distance at t ¼ 0. In this study, the rate of mesh deformation is solved using the CFD software. The dynamics mesh was incorporated as a user-defined function, where the deforming wall was defined as selfsimilar expansion and construction in a sinusoidal manner. In each time step, the mesh convergence was confirmed.
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In particle deposition in the alveolar region, the governing equations are expressed as
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p 3 dU p p D p rp ¼ C D rD2P jU 2 U P j U 2 U p 6 dt 8 p þ d3p ðrp 2 rÞg; 6 24 CD ¼ 1 þ 0:15Re0:687 ; p Rep
ð7Þ ð8Þ
where rp is the particle density, Dp is the particle diameter, CD is the drag coefficient, and Rep is the particle Reynolds number (Schiller and Neumann 1933). In this simulation, we focused on the effects of convection and gravity and neglected Brownian forces. In particular, to investigate the effects of gravity on particle transport and deposition, we assumed that the gravity direction was negligible (zero gravity; case 1), parallel (x direction in Figure 2; case 2), and perpendicular to the artificial inlet (y direction in Figure 2; case 3). Furthermore, the numerical simulations were one-way coupled, i.e., the flow was assumed not to be influenced by the particles, with the particles being transported passively by airflow. For particle diameters of Dp ¼ 1 and 3 mm, rp was set equal to the density of water (1.0 g/cm3). In this study, the differences in velocity profiles after seven cycles were less than 1%, and then the particles were introduced in the model at the beginning of the 8th cycle. A uniform 2D grid was superimposed at the inlet of the acinus and behind the artificial inlet in Figure 2, and the particles (N ¼ 36,001) were released from these grid points. The particles were introduced into the flow field with initial velocity equal to the velocity at their grid points. At the boundaries, the perpendicular and parallel restitution coefficients of the particles at the wall were both set to 0, i.e., when a particle strikes a wall, it is assumed to be stuck at the wall. Furthermore, particles that exited the computational model were not reintroduced. Under physiological breathing of a human adult, the residual functional capacity and total lung capacity are approximately 3 and 6 l, respectively. In this study, we set W and T as 0.5 and 4.0 s, respectively. As the boundary condition, the pressure at the inlet was zero. The no-slip condition was assumed at the airway walls such that the fluid velocity matched the wall velocity at the interface in the case of a moving wall, as expressed by the previous equations.
Results and discussion In our simulation, the maximum Reynolds number, Remax, was 0.029 at the inlet and 0.0004 at the terminal AS. Figure 3 depicts the streamlines in proximal (Figure 3(A)) and distal (Figure 3(B)) alveoli during deep breathing. The Re of each AD flow was low (Remax ¼ 0.0038 and 0.0013 at
Figure 3. The streamlines in proximal (A) and distal (B) alveoli. Remax in the connecting AD was 0.0038 in (A) and 0.0013 in (B).
each connecting AD). In both alveoli, the flow was dominated by radial flow, and a weak recirculating flow was observed at the proximal side. These recirculating zones remained almost completely still during the breathing cycle. These flow patterns are similar to previous results using an ideal AD model (Sznitman et al. 2007), which was designed as a spherical cap connected to a cylindrical shell with open ends (Weibel 1986). In previous studies of a nowall-motion alveolus, the AD flow generated a recirculating region filling the entire alveolus and the convective exchange between the duct and alveolus was prohibited; in contrast, alveolar wall motion induced complex flow patterns in the alveolus(Tsuda et al. 1995; Sznitman et al. 2007; van Ertbruggen et al. 2008). In proximal acinar generation (Re at the AD ¼ 0.112), the alveolar flow was dominated by recirculation patterns that shifted to the
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Figure 4. The particle (Dp ¼ 1 mm) transport. Arrows indicate the gravity direction (A, case 1; B, case 2; C, case 3). The deposited particles are not shown.
proximal corner of the alveolus, and in deeper generations the recirculation zone gradually decreased the alveolar flow, which became largely radial (Sznitman et al. 2007). In particular, in the idealized terminal AS (Re at AD ¼ 0.008), the recirculation region vanished. In our realistic acinar model, however, a weak recirculating flow was observed in the distal alveolus despite the lower Re (Figure 3(B)). Tsuda et al. (1995) suggested that during flow in an expanding and
contracting alveolus, a stagnation saddle point exists, which induces highly complex and irreversible particle trajectories. Figures 4 and 5 present the transport of Dp ¼ 1 and 3 mm particles during single breathing, respectively. Figure 6 illustrates the particle depositions of Dp ¼ 1 and 3 mm after single breathing. In this study, the particle deposition rate during single breathing was defined as the
Figure 5. The particle (Dp ¼ 3 mm) transport. Arrows indicate the gravity direction (A, case 1; B, case 2; C, case 3). The deposited particles are not shown.
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Figure 6. Side view of particle deposition map (red area) after single breathing. Arrows indicate the gravity direction (A and D, case 1; B and E, case 2; C and F, case 3). Dp ¼ 1 mm (A –C), and 3 mm (D– F).
ratio of the number of deposited particles to the initial number of particles (Figure 7). In the case of zero gravity (case 1), both particles (Dp ¼ 1 and 3 mm) are transported deeply into the model after inspiration (Figures 4(A2) and 5(A2)). After expiration, the particles are dispersed widely around the initial positions (Figures 4(A4) and 5(A4)). The deposition rates for both particle diameters were less than 0.01 (Figure 7), and the particles were deposited not in the model but around the initial position (Figures 6(A) and (D)), despite being transported deeply into the model. These results show that there were no significant differences in particle transport and deposition between 1 and 3 mm particles under zero gravity. However, the
Figure 7.
gravity orientation exerted a marked effect on particle transport and deposition. In the case in which the gravity direction was parallel to the parent tube (case 2), the 1 mm particles were also transported deeply into the model after inspiration (Figure 4(B2)) and dispersed widely after expiration (Figure 4(B4)). Also, the particles were deposited in the model, in particular at the alveolar mouth and edge of the middle region (Figure 6(B)). The deposition rate was 0.22 (Figure 7). Gravity exerted a greater effect on the 3 mm particles. Many particles reached the end of the model after inspiration (Figure 5 (B3)) and all particles were deposited during expiration, in particular at the distal region (Figures. 6(E) and 7). In the
The deposition rates of particles (Dp ¼ 1 and 3 mm) during single breathing.
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Computer Methods in Biomechanics and Biomedical Engineering case in which the gravity direction was perpendicular to the parent tube (case 3), the 1 mm particles were transported deeply into the model and were sedimented and deposited by gravity (Figures 4(C4) and 6(C)). The deposition rate was 0.68, which was higher for case 3 than case 2 (Figure 7). The 3 mm particles were sedimented by gravity soon after the beginning of inspiration (Figures 5 (C1), 5(C2), and 5(C3)), and all particles were deposited behind the initial position during inspiration (Figures. 6(F) and 7). Ma et al. (2009) validated CFD predictions of flow field and particle trajectory with experiments within a scaled-up model of idealized alveolated airways, and showed that air flow and aerosol transport in the alveolated airways model can be simulated by CFD techniques with reasonable accuracy. In this study, however, our acinar model was based on synchrotron CT images, and so it is difficult to validate our numerical simulation. Ma and Darquenne (2011) developed a multigenerational 3D idealized model of alveolated airways with arbitrary bifurcation angles and spherical alveolar shape, and simulated the deposition of 1 and 3 mm aerosol particles. Our model is based on a single acinus, and on the other hand, their idealized model is based on three generation duct. In qualitative comparison, the tendencies of aerosol transport and deposition are strongly dependent on gravity orientation in both models. However, not only the model scale but also the model complexity are different, therefore the quantitative comparison is very difficult. In the idealized model, the deposition rate during the first cycle was 20 – 23% for 1 mm particles and 71 –73% for 3 mm particles, which are smaller than our results. The aforementioned results indicate that particle depositions are influenced strongly by gravity orientation. In the case of no gravity (case 1), the deposition efficiency of 1 and 3 mm particles was negligible (Figure 7), even though they were transported deeply into the alveolar region. However, the particle deposition rate was higher dramatically when gravity was not zero (cases 2 and 3). In the case in which the gravity direction was parallel to the parent tube (case 2), the deposition rate was higher than that in case 1 (Figure 7). The 3 mm particles were transported to the end of model during single breathing, and so the deposition rate reached 1.0. Although the 1 mm particles were transported after inspiration as deeply as those in case 1 (Figure 4(B2)), they were deposited at the alveolar mouth and edge; moreover, the deposition rate was higher. Furthermore, the rate increased during expiration rather than inspiration because of the complicated acinar geometry (Figure 7). After single breathing, many particles were still detected in the alveolar model (Figure 4(B4)), suggesting that the deposition rate may increase further after several breathings. In the case in which the gravity direction was perpendicular to the parent tube (case 3), the deposition rate for the same diameter size was higher than those in cases 1 and 2 (Figure 7). The
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1 mm particles were also transported after inspiration as deeply as those in cases 1 and 2 (Figure 4(C2)), and sedimented widely in the model after single breathing (Figure 6(C)). Similar to case 2, after single breathing, many particles were still detected in the alveolar model (Figure 4(C4)), suggesting that the deposition rate may increase after several breathings. The 3 mm particles were sedimented soon after the beginning of, and all particles were deposited earlier than in case 2. The Stokes numbers (St) correspond to the behavior of particles suspended in a flow. St is defined as the ratio of the response time of a particle to the characteristic time of the flow field. When St . 1, particles can detach from a flow, especially if the flow decelerates abruptly, whereas when St , 1, particles follow fluid streamlines closely. In this study, the St values of particles with Dp ¼ 1 and 3 mm were 1.39 £ 10 – 5 and 1.25 £ 10 – 4, respectively, indicating that the particles follow the fluid streamline. The terminal velocities of the particles when the acceleration of the particle is zero and the drag force equals the gravity force were 30 and 269 mm/s, respectively. Compared with the flow velocity at the AD (Figure 3), the terminal velocities were nonnegligible. In particular, the terminal velocity of 3 mm particles was higher than the maximum velocity at the AD. Therefore, particle deposition is greatly influenced by gravity. Alveolar kinematics is also essential for gas exchange in the deep lung. Various investigative techniques have been proposed, such as the light-scattering technique (Butler et al. 2002), optical coherence tomography (Popp et al. 2006; Hou et al. 2011), and in vivo microscopy (DiRocco et al. 2007; Pavone et al. 2007). In addition, Namati et al. (2008) evaluated alveolar dynamics in fresh lung ex vivo using confocal laser scanning microscopy, although this technique is limited to imaging to a depth of 50 mm. The details of the 3D kinematics of pulmonary acinus are not yet understood. Therefore, in this study, we assumed that the moving wall represents self-similar deformation. Microscopically, the lung expands and contracts self-similarly during respiration cycles (Ardila et al. 1974), and the alveolar flows and particle transport during self-similar and sinusoidal airway motion have been reported (Tsuda et al. 1995; Haber et al. 2003; Sznitman et al. 2007; Sznitman et al. 2009). In this study, the acinar model is reconstructed based on mammalian lung; on the other hand, the lung and flow conditions are based on human lung. This is the limitation of this study. The acinar models in previous studies (Tsuda et al. 1995; Haber et al. 2003; Sznitman et al. 2007; Sznitman et al. 2009; Ma and Darquenne 2011) are idealized in spite of the complex geometry. In this study, we hypothesized that the particle deposition can be much influenced by the complex acinar geometry. However, it is very difficult to obtain whole acinus of human lung even by micro-CT because the alveolar wall is very thin.
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Additionally, the acinus consists of complex, branched ADs and numerous surrounding alveoli. Recently, the synchrotron micro-CT can be used for mammalian lung and the alveolar wall can be detected due to the higher flux X-ray. The geometry differences between mammalian and human acinus are not well known; however, the mammalian acinus also consists of some branched ADs and numerous alveoli, like human acinus. It is intended that the simulation of airflow and microparticle deposition in realistic mammalian-based model will further contribute to the initial steps in the development toward an accurate understanding of airflow and particle deposition in a realistic human acinus.
Conclusion In this study, we simulated the airflow and particle deposition in a realistic pulmonary acinar model reconstructed from the mammalian lung during rhythmical self-similar breathing motion. The alveolar flows were dominated by radial flows, and a weak recirculating flow was observed at the proximal side of alveoli during the entire respiratory cycle, despite the maximum Re at the inlet being 0.029. Further, we investigated the effect of gravity on particle deposition (rp ¼ 1.0 g/cm3, Dp ¼ 1 and 3 mm). Under zero gravity, although both 1 and 3 mm particles reached the deep acinus after inspiration, the deposition rate after single breathing was less than 0.01. Under a gravitational field, both the deposition rate and map were influenced strongly by the gravity orientation. In the case of particles with Dp ¼ 1 mm, the rate increased dramatically and mostly non-deposited particles remained in the model, indicating that the rate would increase further after several breathings. In the case of particles with Dp ¼ 3 mm, the rate was 1.0 and all particles were deposited during single breathing. Our results show that the particle deposition rate in realistic pulmonary acinar model is higher than in idealized model.
Funding The experiments were carried out at the Program Review of SPring-8 (Proposal Number: 2007A2071). The work was supported by a Grant-in-Aid for Young Scientists (B) (19700394) from the Japan Society for the Promotion of Science.
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