CHARACTERISTICS OF AIRFLOW IN A CT-BASED OVINE LUNG: A NUMERICAL STUDY

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1 Page 1 of 40 Articles in PresS. J Appl Physiol (November 16, 2006). doi: /japplphysiol CHARACTERISTICS OF AIRFLOW IN A CT-BASED OVINE LUNG: A NUMERICAL STUDY 1 Senthil Kabilan, Ching-Long Lin 2, and Eric A. Hoffman 1 Departments of Radiology and Biomedical Engineering, The University of Iowa College of Medicine, Iowa City, Iowa Department of Mechanical and Industrial Engineering and IIHR - Hydroscience & Engineering, The University of Iowa, Iowa City, Iowa Running Head: CT-Based Study of Airflow in the Ovine Airway. Send correspondence to : Eric A. Hoffman, Ph.D. Department of Radiology University of Iowa College of Medicine 200 Hawkins Drive Iowa City, IA USA (Voice) (Fax) eric-hoffman@uiowa.edu Copyright 2006 by the American Physiological Society. 1

2 Page 2 of 40 ABSTRACT The transient airflow in a rigid, asymmetrical monopodial sheep (ovine) tracheobronchial tree of up to 13 generations was investigated numerically. The lung geometry was segmented and reconstructed from Computed-Tomography (CT) images. The flow characteristics in the image-based sheep airway were compared with the flow patterns produced by a Weibel-based model at prime locations. Boundary conditions were prescribed 1) a velocity profile from experimental data at the inlet, and 2) zero pressure at the bronchial outlets. A mesh convergence study was carried out to establish confidence in the model predictions, and gross left-right ventilation were validated against experimental Xenon wash-in/wash-out data. Detailed flow characteristics were investigated at three points in the breathing cycle: i) at peak inhalation, ii) at peak exhalation, and iii) during the transition phase. Simulation results revealed fundamental differences between airflow in monopodial and bipodial branching airways. Compared to idealized bipodial flow, the flow in the sheep airway was asymmetric and highly vortical, especially during the exhalation and the transition phase. The streaklines during inhalation phase suggest that the left and right upper lobes are ventilated by airflow in the peripheral region of the trachea. This work may contribute towards understanding the interplay between structure and function in the lung. 2

3 Page 3 of 40 INTRODUCTION Little research has been carried out on the flow characteristics of the monopodial lung airway tree seen in most non-human mammals. Briant et al. (4) compared the flow distribution in up to five generations of the human (bipodial) and canine (monopodial) lung in an in vitro geometry derived from casts. They concluded that the effect of inertia is greater in the canine bronchial tree, though the study was limited to steady-state inhalation and exhalation. Their results also suggested that more flow is carried along the core through the bifurcation due to the inertial properties of the fluid. Cohen et al. (7) also studied the flow distribution in human and canine tracheobronchial airway trees in an in vitro geometry derived from casts. Their study suggested that the presence of smaller airways affected the flow distribution in the larger upstream airways. Their results also suggested that the coupling of the larynx with the tracheobronchial airway had little influence on the airflow distribution in the human lung and even less influence on the canine lung. The presence of a larynx altered their predicted flow by less than 1% for most measurements and by not more than 5% in others. They concluded that the greatest differences in airflow distribution between the human (bipodial) and the canine (monopodial) lung were manifest in the upper lobes where the airway branching pattern were most dissimilar between the two species. Though these early experimental findings suggested that the airflow in the distal lung affects that of the proximal lung, few computational studies have attempted to extend their analysis to several generations of airways. In fact, most recent studies have focused on small sections of lungs with simple bifurcations. For example, the work of Kinsara et al. (14), Balásházy et al. (2,3), and Balásházy (1), focused on single 3

4 Page 4 of 40 bifurcation models. Many of these studies, including the simulations by Gatlin et al. (11), of fluid flow and particle deposition in an asymmetric single bifurcation, were based on idealized elliptical cross-sections. In spite of the admitted importance of these studies in investigating the local details of turbulent and particle flow, there is little doubt that the complicated bifurcation patterns characteristic of real airway geometries result in disturbed flow, affecting the flow patterns and particle deposition in subsequent bifurcations. This point was reinforced by Lee et al. (15), in their computations of the velocity field, particle trajectories, and particle deposition efficiency for two-dimensional and three-dimensional single and double bifurcations. They concluded that the presence of a second bifurcation alters both the flow field and the particle trajectories. The limitation of the single bifurcation model is further supported by Comer et al. (8), who studied aerosol transport and deposition in both in-plane and 90 degree out-of-plane double bifurcation configurations. Their findings suggest that the local deposition patterns differ both with bifurcation level and orientation. Of the recent studies that have attempted to extend their computational analysis to a greater number of generations of the tracheobronchial tree, most have been either twodimensional or based on an idealized Weibel model, and none have been monopodial. For example, the study by Wilquem et al. (20) on steady inspiratory flow in a 2D model of three generations of the human airways revealed a highly skewed velocity profile downstream of the second junction. The limitation of a 2D assumption was further illustrated later in the work of Caro (5), who showed that velocity profiles in daughter branches after a bifurcation are strongly affected by the angle of rotation - the azimuthal angle - between consecutive bifurcations. In terms of recent 3D models, Comer et al. (9, 4

5 Page 5 of 40 10) and Zhang et al. (21, 22) have simulated airflow and particle deposition in generations 3-6 of a Weibel-based model. Though these investigations were important, numerical experiments by Nowak et al. (17) demonstrated that the velocity fields in a CT-scan-based geometry are more complex than those in the Weibel-based model due to airway curvature and complex shapes at junctions. We are unaware of studies involving computational fluid dynamics in a 3D CT-based monopodial lung airway tree, which is the focus of this present study. The specific goals are fourfold: i) generate a topologically faithful computational grid of nearly nine generations of the monopodial ovine tracheobronchial tree from CT images; ii) study how the tree geometry influences flow characteristics in monopodial branching airways; iii) compare the flow patterns in the monopodial and bipodial branching airway trees; and iv) investigate the effect of the upper right lobe on the flow field in the trachea which is unique to the sheep. METHODS Lung geometry: A three-dimensional image dataset from a multidetector-row MDCT (Siemens Sensation 64) scan of the sheep airway was segmented as per Tschirren et al. (19), and converted to a stereo-lithography file, representing the outer surface of the tracheobronchial tree. Scan acquisition parameters followed a volumetric protocol: 100mAs, 120kV, 1mm collimation, effective slice thickness of 1.3mm, overlap of.65mm, pitch of 1.2mm. The slice parameter mode was 32 x 0.6 mm. Images were reconstructed into 512x512 slice matrices. 5

6 Page 6 of 40 The airway surface was first smoothed globally using the weighted Laplacian smoothing algorithm in Magics (Materialise. Ann Arbor, MI) to filter hard edges resulting from limited image resolution. The terminal branches were then trimmed, resulting in a surface which was nearly perpendicular to the airway centerline. This procedure was repeated for the entire geometry, resulting in 451 outlet faces (Fig. 1). Because of the nature of CT scanning, our detection of airways is not based upon generation number but rather size (and to some extent orientation between the segment s long axis and the CT slice orientation). Depending upon the path, we found between 7 and 13 generations. However, the average diameter of all the 451 outlets was computed to be 1.14 mm with a standard deviation of 0.34 mm. The final surface geometry was converted to an unstructured volume mesh using Gambit (Fluent Inc. Lebanon, NH), consisting of 792,915 nodes and 3,480,693 tetrahedral elements. The volume mesh was generated using the T-grid meshing scheme, which primarily consists of tetrahedral mesh elements but may also contain wherever appropriate, shapes like hexahedral, pyramidal, and wedge elements as well. The algorithm works on the principle that if a boundary layer is attached to any of the faces on the volume, it generates hexahedral or prism elements in the regions adjacent to the boundary layers. If any quadrilateral face element exists on the volume faces, it generates pyramidal volume elements which in turn create a transition from the associated hexahedral/quadrilateral elements to the tetrahedral elements that will occupy the remainder of the volume. Then the rest of the volume is filled with tetrahedral elements. Numerical methods: Airflow predictions were based on the three-dimensional, incompressible Navier-Stokes equations for fluid mass and momentum: u v = 0 (1) 6

7 Page 7 of 40 v u v v + u u = t p 2 v + ν u ρ (2) where ρ is the density, ν is the kinematic viscosity, u v is the fluid velocity vector and p is the pressure. The resulting system of equations was solved with a fractional fourstep characteristic Galerkin finite element method (16). This approach is second-order accurate, and does not require any special treatment on the boundary conditions of the intermediate velocity. Continuity is enforced by solving the pressure-poisson equation. The time step ( sec) is estimated by the Courant-Friedrichs-Levy (CFL) condition, and the total run time with the above mesh size on a HP zx6000 Itanium workstation is about 8 days. A detailed description is given by Lin et al. (16). For all calculations, air at room temperature was considered to be the working fluid, with 3-5 a density of kg/m and a kinematic viscosity of m 2 /s. The inlet boundary condition consisted of a prescribed velocity-time curve (Fig. 2) based on experimental data. This data was acquired during the CT-scan used to determine the lung geometry. At zero velocity points, the lung volume was held constant (Fig. 2). The outlet boundary condition, on all 451 faces, was zero pressure. Because of the relatively uniform size of all terminal branches this was considered adequate. The no-slip condition was applied to the remaining airway boundaries, which were assumed to be rigid and impermeable. Airflow was assumed to be laminar based a computed Reynolds number of 1,500 at peak inhalation and peak exhalation. Weibel Model: A Weibel model was generated to compare the flow patterns between the monopodial and bipodial branching patterns. It was assumed that daughter branches began their separation at the bifurcation point as the frustum of a cone. The large diameter of the frustum was set equal to the diameter of the parent branch and the small 7

8 Page 8 of 40 diameter of the frustum was set equal to the daughter. The length of the frustum was assumed to be one tenth of the length of the daughter branch. These assumptions were necessary because the Weibel model defines only one diameter for each generation of airway. Detailed information about the geometry can be found in Nowak et al. (17). The final model consisted of 73,280 nodes and 318,318 tetrahedral elements. To validate this model, predictions of airflow were compared with those of Nowak et al. (17). Mesh convergence study and validation: To check that the solutions obtained were independent of the mesh, the mesh density was approximately doubled for the CT-based geometry. Otherwise, the same boundary conditions and solution parameters were applied. This mesh consisted of 1,457,646 nodes and 6,377,921 tetrahedral elements. Flow fields were compared at three main locations (4, 5 and 6 of Fig. 1). To gain confidence in overall model predictions, the percentage flow into the right and the left lung were computed and compared to the percentage measured volume based on a Xenon wash-in-wash-out study. First, left and right lung volumes were segmented with the in house developed software Pulmonary Analysis Software Suite (12, 13). For the predicted flow ratio to match the measured lung volumes, it is necessary that the average time constants (gas turnover rate) of the left and right lungs be equal. A Xenon study was performed and the time constants for the Xenon wash-in and wash-out curves were plotted for both the left and right lungs to calculate specific ventilation (ml/min/ml) according to Tajik et al. (18) and Chon et al. (6). The regions of interest used for computing the regional ventilation were pixels throughout the left and right lungs with each lung studied independently. 8

9 Page 9 of 40 Airflow investigations: Airflows were examined in both the normal airways and after the introduction of an artificial blockage. The comparative analysis focuses on three time points: i) peak inhalation, ii) peak exhalation, and iii) the transition. Peak inhalation was taken to be the maximum of the measured velocity profile (A in Figure 2), corresponding to m/s, while peak exhalation was taken to be the minimum of the measured velocity profile (B in Figure 2) corresponding to -2.1 m/s. For both open and obstructed airway trees, the flow fields were queried at identical locations (see markers in Figure 1). Specifically, markers 1, 2 and 3 were chosen to examine the effect of the upper right lobe on the flow field. Marker 4 was selected to study flow pattern in the trachea just before the first bifurcation. Similarly, markers 5 and 6 were chosen to study the flow patterns in the left and the right lung respectively after the flow in the trachea encounters the first flow divider and also for a direct comparison of flow features with the Weibel model. Markers 7, 8 and 9 were selected to study the effect of a branch with a nearly 180 turn and the more rapid narrowing on the flow field in the upper left lobe. Markers 10, 11, 12 and 13 were chosen to study the characteristics of flow fields deep in the lung. At all thirteen markers, the axial velocity was non-dimensionalized with respect to the global maximum velocity for comparison. To further refine our understanding of the three-dimensional structure of flow in the monopodial lung, streaklines seeded in the sheep trachea were traced into the lung during the inhalation phase using Tecplot (Tecplot Inc. Bellevue, WA). The cross section of the trachea was divided into two general regions: i) a peripheral region, which was within 1mm from the external surface, and ii) a core region, which was everything inside the peripheral region. A total of 12 fluid solution data files uniformly distributed at various 9

10 Page 10 of 40 time points during the inhalation phase are used for the streakline analysis. For the peripheral region, 95 streaklines were seeded at the inlet and evenly distributed in that layer. For the core region, 150 streaklines were seeded at the inlet and evenly distributed. Ten sets of seeds were introduced into the flow stream between any two unsteady state fluid solution data files. RESULTS Mesh Convergence and Validation At the three locations for comparison (4, 5 and 6 of Fig. 1), there was no noticeable variation in the axial velocity contours, nor in the secondary radial velocity (not shown). This was true during all three time points examined: peak inhalation, peak exhalation and transition. In addition, the flow rate at six different locations (1, 4, 5, 6, 10 & 12 in Fig. 1) was computed. At no time or locations were the percentage differences found to exceed 0.41%. Because the time step is estimated by the CFL condition and the difference between the solutions of two different meshes is negligible, we could infer that the solution is independent of the time step. The magnitude of the axial velocity and the in-plane flow in the right lung were larger than that in the left lung, and the percentage flow into the right and the left lung were computed to be 59.26% and 40.74%, respectively. The measured right and left volumes were found to be 1, cm 3 and 1, cm 3, which translate to percentages of % and 42.30% of total lung volume. Measured right and the left volume flow rates were assessed to be 0.08 ml/min and ml/min, with standard errors of and 0.009, respectively. Thus, even though the right and the left volume ratios were 57.69% and 42.30%, the regional ventilation (per 10

11 Page 11 of 40 unit volume) in the right and the left lung were identical to the predicted values to within statistical significance. Normal Airways - Peak Inhalation Marker 1: The axial velocity at marker 1 was asymmetrical (Figs. 3A 1 & 3C 1 ), with a higher magnitude on the side of the first lobar bifurcation. Though the prescribed flow at the trachea inlet was uniform, this asymmetry was already visible a mere 2 mm downstream from the inlet (not shown). Two small under-developed vortices (marked by the circles in Fig. 3B 1 ) were found at the periphery of the wall, the first one closer to the posterior wall and the second one closer to the anterior wall. The vortex closer to the first lobe on the right lung moves the location of the high speed zone caused by the skewness of the velocity profile further towards the wall. The counter-rotating vortex near the posterior wall is present in the low speed flow zone and appears not to have a profound effect on the flow field. Marker 2: The flow in the trachea enters the upper lobe at marker 2, (Fig. 3A 2 & 3B2), producing a jet into an airway branch of smaller diameter. The majority of the air that flows into the upper lobe derives from the peripheral zone of the trachea (Fig. 3A 2 ). Though this location is at halfway past the upper lobe bifurcation, the high speed zone is diminished though still present, suggesting that the formation of the high-speed zone in the trachea may be due to the higher functional lung volume of the right lung. Marker 3: Downstream of the upper lobe bifurcation (Fig. 3A 3 ) the flow assumes a more flat profile with less asymmetry (Fig. 3C 3 ). Little of the upstream vorticity is noticeable. In addition, the high-speed zone (crescent in Figure 3A 3 ) has moved closer to the wall of the trachea with respect to the high-speed zone at marker 1. This is due to the flow of the 11

12 Page 12 of 40 peripheral air into the first lobe (upstream), which pulls the high speed zone closer to the tracheal wall. Marker 4: It is apparent at marker 4 (Fig. 4A 1 ) that the flow is adjusting to the geometric transition from the trachea to the daughter branches. The flow is once again asymmetrical toward the right lung bronchus (marker 6). Markers 5 and 6: Immediately after the main tracheal bifurcation, the flow in the left lung (marker 5) and in the right lung (marker 6) is similar (Figs. 4A & 4A 2 3) but different from that predicted in Weibel bronchi. For both, the highest axial velocity was adjacent to the inside wall of the bifurcation; however neither exhibit any significant symmetrical or asymmetrical vortices. Marker 7: The flow at marker 7 (Fig. 5A 5B 5C 1, 1, 1) is very similar to that at marker 5, with similar off-axis components and a similar axial velocity profile. With respect to that at marker 5, the high-speed zone is diminished. Marker 8: At the 180 bronchus, the core region enters the airway branch unlike the situation in the flow into the upper lobe which was fed by the peripheral region. The air in the core region (Fig. 5A & 5B 2 2) first goes towards the bottom edge of the bronchus and then enters the airway branch. Because of this effect, there is a low axial velocity region created near the outer wall of the main bronchus (shown with an arrow). Marker 9: The upstream low axial velocity region (Fig. 5A 2 ) becomes more substantial at marker 9 (Fig. 5A 3), and two counter rotating vortices form (Fig. 5B3). The 180 branch thus not only reduces the velocity of the high-speed zone but also pulls it towards the outer wall of the main bronchus. 12

13 Page 13 of 40 Markers 10, 11, 12 &13: The high-speed zone, which in upstream (markers 5 & 7) is located near the inner wall, moves towards the core region (not shown) because of airway branching on the outer wall of the bronchi. This effect can also be seen on the right lung at markers 12 & 13, though the magnitude of the velocity in the right lung is greater than that of the left lung at all the corresponding cross sections. Streakline Analysis: The fluid solution data files during the inspiratory phase were loaded into Tecplot for the streakline analysis. The streaklines seeded within the outermost (<1 mm) layer, entered and terminated in the apical portion of the lung above the carina with a few exceptions that entered the basal portion of the right lung and also some branches in the left lung (Fig 6A). The peripheral region mainly ventilates the entire apical portion of the lung and the anterior portion of the basal lung. By contrast, streaklines seeded in the core region ventilated the basal portion of the lung (Fig 6B). Normal Airways - Peak Exhalation Flow during the peak exhalation phase through the sheep airway model is quite different from the peak inhalation flow, and in general is much more complicated. The flow is less coherent, with asymmetrical vortices. In-plane velocity (secondary flow) is very important during exhalation since it is the primary factor governing the mixing of inhaled gas, aerosol transport and deposition in the lung. Marker 3: The velocity consists predominantly of four asymmetrical vortices (Fig. 7B 1 ) downstream of the tracheal branch or the first upper lobe. In addition, a high-speed zone exists close to the center of the trachea (Fig. 7A 1 ). 13

14 Page 14 of 40 Markers 1 & 2: Flow from the first lobe enters the main trachea. This flow moves the two vortices near the posterior of the trachea towards the inner core (Figs. 7A 2 & 7B2). The flow continues upstream creating a faster high-speed zone exists (Figs. 7A 3, 7B 3 & 7C3). Although there is an increase in the magnitude of the high-speed zone, the effect of the first lobe is to reduce the velocity by inhibiting the flow development. The aforementioned inference will be discussed in detail later in the blocked upper lobe simulation section. Two additional vortices enhance the mixing of the gases in the upper tracheal region (Fig. 7B 3 ). Thus, it can be inferred that the right upper lobe has a major role in the mixing of the inhaled gases in the upper trachea during exhalation. Markers 4, 5 & 6: Due to large flow rate from the right bronchus compared to that of the left bronchus, an asymmetric high-speed region exists upstream of the tracheal bifurcation (Fig. 8A 1 ). In the trachea, the velocity vectors are less coherent, consisting of four vortices and also substantial radial flow (Fig. 8B 1 ). Just below (markers 5 & 6) the first bifurcation (Figs. 8A2, 8B2, 8C2 and 8A3, 8B3, 8C3) the flow in the two bronchi is quite different. The flow in the left bronchus is characterized by skewness, with two fullydeveloped asymmetrical vortices. In the right bronchus, two vortices also exist; however, only one of which is fully developed. In addition, the magnitude of the average velocity on the left is less than that on the right. Marker 9: As the branches merge on to the main bronchus, they tend to accelerate the flow near the inner wall of the main bronchus (Fig. 9C ). 1 Markers 7 & 8: At the branch with 180 turn on the left (marker 8 in Fig. 1), flow is returned to the main bronchus, with the formation of a strong vortex near the posterior wall of the bronchus (Fig. 9B ), and a low velocity region near the posterior wall (Fig. 2 14

15 Page 15 of 40 9A 2 ). As the flow from the core region of the branch enters the main bronchus, it moves the two vortices further towards the bottom of the main bronchus. Slightly above that bifurcation (marker 7) the flow returned from the branch accelerates the fluid in the highspeed zone (Fig. 9A 3 ). Also, at this location, two fully developed vortices exist near the outer wall and one underdeveloped vortex exists near the apex of the bronchial wall (Fig. 9B ). This underdeveloped vortex degenerates quickly (Fig. 8B ). 3 2 Markers 10, 11, 12 and 13: Below these major bifurcations, the flow characteristics (not shown) are quite random, with radial flows, vortices and some local asymmetry due to the numerous side branches. The greater distribution of branches on the outer wall at these deeper locations tends to move the high-speed zone closer to the inner wall for both bronchi. Normal Airways - Transition Flow was investigated at two flow rates between peak inhalation and peak exhalation. First, flow patterns were evaluated before and after the pause for triggering the scanner (C & D in Fig. 2). Second, the flow patterns were evaluated at flow reversal (E in Fig. 2). Flow patterns were similar before and after breath hold with the magnitude of velocity at D being slightly greater than that at C. For example the magnitude of the nondimensional axial velocity at D was 15.4% greater than at C. During flow reversal (E in Fig. 2), the fluid near the periphery of the trachea (Fig. 10C 1 ) has already changed the direction whereas the fluid in the core region is still moving in the forward direction due to the reduced inertia in the boundary. Beyond the main bifurcation (markers 5 and 6), the fluid closer to the outer wall has changed the direction but not the fluid near the inner wall (Fig. 10C & 10C ), due to the greater velocity near the inner wall with respect to

16 Page 16 of 40 that of the outer wall at these locations. In addition, at these locations strong vortices are formed moving in opposite directions (Fig. 10B & 10B 2 3). These vortices continue to be present throughout the expiratory phase and are dominant during peak expiratory flow. Thus, it can be inferred that the transient phase of the flow is the main cause for strong vortices in the flow which influence mixing of the inhaled gases. Blocked Upper Lobe Simulation To further investigate the hypothesis that the main cause for the formation of the highspeed zone (the skewed velocity profile) in the trachea may be the higher functional right lung volume, a separate simulation was performed, in which all the outlets of the upper right lobe were closed (no flow). Except for these changed boundary conditions, the simulations were identical. Under this scenario, during peak inspiratory flow, the high-speed zone persists in the upper trachea near the wall (marker 1). In fact, the non-dimensional axial velocities are indistinguishable in the trachea (Figs. 11A 1 & 3A 1 ), and only slightly higher in the obstructed simulation just upstream of the main bifurcation (Figs. 11A 2 & 4A1). Additionally, there are few differences in flow magnitude and direction in the left bronchus (not shown). Flow into the right bronchus is substantially higher in the blocked case, due to conservation of mass. Analysis of the obstructed flow simulation also elucidates the influence of the upper lobe bronchus on the flow field. At peak exhalation, flow just above the main bifurcation is similar in both the obstructed and normal unobstructed simulations, though the magnitude of the former is higher (Figs. 8A & 12A 1 2). In the upper trachea, the flow patterns differ in terms of the degree of vorticity (Figs. 7B 3 & 12B1), with a faster high- 16

17 Page 17 of 40 speed zone in the blocked mesh. Taken together, these findings suggest that the upper lobe bronchus enhances the mixing up of gases in the upper tracheal region, but reduces the velocity of the high-speed zone as mentioned in the Normal Airways - Peak Exhalation section. Monopodial vs. Bipodial Flow In the bipodial-weibel model, flow just above the main bifurcation was nearly parabolic during inspiration (Fig. 13A, 13B, and 13C 1 1 1). As we have seen, the monopodial profile at this point is considerably blunter (Fig. 4C 1 ) and asymmetric (Fig. 4A 1 ). Furthermore, in the sheep lung simulation, unlike the Weibel (Fig. 13A 2, 13B 2, and 13C2), no symmetrical or asymmetrical vortices were noticed just downstream of the main bifurcation (markers 5 & 6). During expiration, at these same locations, four symmetric vortices were observed in the Weibel model (Fig. 14A, 14B 1 1, and 14C 1 ), where multiple asymmetric vortices are found in the monopodial lung. DISCUSSION In this study, simulation of airflow in the sheep lung was performed based on experimentally measured flow conditions applied to a topologically faithful 3D computational grid generated from CT images. It was hypothesized that the skewness in the velocity profile (namely, the location of high speed zone) was introduced in the trachea mainly due to the volume difference between the right lung and the left lung. This hypothesis was tested in two different monopodial grid configurations: a normal geometry and an obstructed geometry. This finding is novel and suggests functional behavior in the airway tree that may be important in the analysis of dosage and clearance. 17

18 Page 18 of 40 It should be noted however that geometric features, such as wall curvature, may also play a role. This warrants further study. Results from the obstructed upper lobe simulation support evidence from the normal model that the upper lobe bronchus does not assist the formation of a high-speed zone in the trachea. This suggests that the upper lobe bronchus reduces the overall ventilation in both the lungs. It was found that the high-speed zone in the trachea enters the right lung bronchus, thereby ventilating the right lung to a greater degree than the left lung. Moreover, the magnitude of the velocity in the right lung was found to be consistently greater than that of the left lung at any corresponding cross section. The streakline analysis supported the notion that the peripheral region of airflow mainly ventilates the entire apical portion of the right lung and the anterior portion of the basal lung, and the basal region of the lung is ventilated by the airflow in the central portion of the trachea. It was hypothesized that the transition between inhalation and exhalation is the main cause for the formation of strong vortices, present along the entire expiratory curve. These vortices may play a major role in the mixing of the inhaled gases during expiration. It was concluded from the comparison between the Weibel model and the sheep lung that the flow in these models is completely different. There was no agreement between the two models at any of the cross sections. These data demonstrate the profound effects caused by differences in airway geometry. This work has provided a detailed assessment of the fluid dynamics in the monopodial branched airway tree through use of high-resolution, volumetric MDCT image data in conjunction with high-fidelity computational fluid dynamics. The methodologies outlined in this paper form the basis for our ability to study the effects of 18

19 Page 19 of 40 gas density and viscosity on the regional distribution of ventilation. This becomes critically important as we seek to utilize Xenon and Helium gases in conjunction with MDCT and MRI imaging to understand determinants of ventilation heterogeneity in health and disease. LIMITATIONS The limitations in this current study include the assumption of a constant pressure boundary condition for all 451 outlets. While we believe that this is a reasonable first approximation since the diameters of all terminal outlets were similar, in reality, it is likely that the pressure varies with respect to lung location due to regional differences in pleural pressure gradients, lung mechanics, path lengths etc. Since this is likely, in part, subject dependent, it becomes quite a complex problem if one wishes to correctly attribute variable boundary conditions. This will certainly be the topic of many future studies. In addition, velocity profile from the mechanical ventilator does not represent the normal breathing pattern in a live animal. However, results shown herein suggest that while the pause in the inlet velocity profile alters the magnitude, the flow characteristics are unchanged. The flow in the model was assumed to be laminar, whereas a turbulence model would have been a more appropriate choice. For the sheep in the current study, they were intubated with a very smooth tube that goes down about to the area where the computational model begins. Thus, this model is valid for predictions to compare with the Xenon and future He data. The use of a turbulence model could be considered for future study without much difficulty. Presently the study compares airflow characteristics in a CT based monopodial geometry with an idealized bipodial geometry. The comparison between the two geometry does show the differences in the flow 19

20 Page 20 of 40 characteristics due to the basic fact that the bifurcation patterns are immensely different between the monopodial and the bipodial lungs. However, the difference in wall shapes of the CT-based monopodial airway tree and the idealized human-like bipodial model may also contribute to the differences in flow characteristics. Thus, the use of CT based geometry for the bipodial lung geometry could be considered for future study. The potential errors due to sampling artifacts introduced in the airway geometry by way of non-isotropic sampling via CT scanning would be addressed in future research. 20

21 Page 21 of 40 ACKNOWLEDGEMENT The authors would like to thank M. Tawhai, G. McLennan, J. Tschirren, and D. Chon for assistance and discussion during the course of the study.. The financial support of the National Institutes of Health through NIH grant HL and NIH grant EB awarded through the National Institute for Biomedical Imaging and Bioengineering (NIBIB) under the IMAG program for Multiscale Modeling is acknowledged. The authors also thank the National Center for Supercomputing Applications (NCSA) for allocating the computer time to perform the above simulation. 21

22 Page 22 of 40 REFERENCE 1. Balásházy I. Simulation of particle trajectories in bifurcating tubes. J Comput Phys 110: 11-22, Balásházy I, and Hofmann W. Particle deposition in airway bifurcations - Inspiratory flow. J Aerosol Sci 24: , Balásházy I, and Hofmann W. Deposition of aerosols in asymmetric airway bifurcations. J Aerosol Sci 26: , Briant JK, and Cohen BS. Flow distribution through human and canine airways during inhalation and exhalation. J Appl Physiol 67(4): , Caro C. Swirling steady inspiratory flow in models of human bronchial airways. Ann Biomed Eng Supplement 1 29: S138, Chon, D., Simon, B.A., Beck, K.C., Shikata, H., Saba, O.I., Won, C., and Hoffman, E.A., Differences in regional wash-in and wash-out time constants for xenon-ct ventilation studies. Resp Physiol Neurobi 148: 65-83, Cohen BS, and Briant JK. Flow distribution in human and canine tracheobronchial airway casts. Health Phys Sup 1 57: 21-27, Comer JK, Kleinstreuer C, Hyun S, and Kim CS. Aerosol transport and deposition in sequentially bifurcating airways. ASME J Biomech Eng 122: , Comer JK, Kleinstreuer C, and Zhang Z. Flow structures and particle deposition patterns in double-bifurcation airway models. Part 1. Air flow fields. J Fluid Mech 435: 25-54,

23 Page 23 of Comer JK, Kleinstreuer C, and Zhang Z. Flow structures and particle deposition patterns in double-bifurcation airway models. Part 2. Aerosol transport and deposition. J Fluid Mech 435: 55-80, Gatlin B, Cuicchi C, Hammersley J, Olson D, Reddy R, and Burnside G. Particle path and wall deposition patterns in laminar flow through a bifurcation, ASME FEDSM Vancouver, British Columbia, Guo J, Reinhardt JM, Kitaoka H, Zhang L, Sonka M, McLennan G, and Hoffman EA. Integrated system for CT-based assessment of parenchymal lung disease. IEEE International Symposium on Biomedical Imaging , Hoffman EA, Clough AV, Christensen GE, Lin CL, McLennan G, Reinhardt JM, Simon BA, Sonka M, Tawhai MH, van Beek EJ, Wang G. The comprehensive imaging-based analysis of the lung: a forum for team science. Acad Radiol 11(12): , Kinsara AA, Tompson RV, and Loyalka SK. Computational flow and aerosol concentration profiles in lung bifurcations. Health Phys 64: 13-22, Lee JW, Goo JH, and Chung MK. Characteristics of Inertial Deposition in a Double Bifurcation. J Aerosol Sci 27: , Lin CL, Lee H, Lee T, and Weber LJ, A level set characteristic Galerkin finite element method for free surface flows. Int J Numer Meth Fluids 49(5): , Nowak N, Kakade PP, and Annapragada AV. Computational fluid dynamics simulation of airflow and aerosol deposition in human lungs. Ann Biomed Eng 31 (4): ,

24 Page 24 of Tajik JK, Kugelmass SD, and Hoffman EA. An automated method for relating regional pulmonary structure and function: integration of dynamic multislice CT and thin-slice high-resolution CT. SPIE Medical Imaging 1993 Proceedings 1905: , Tschirren, J, Hoffman EA, McLennan G, and Sonka M. Airway tree segmentation using adaptive regions of interest. Progress in Biomedical Optics and Imaging 5(23): , Wilquem F, and Degrez G. Numerical modeling of steady inspiratory airflow through a three-generation model of the human central airways. ASME J Biomech Eng 119: 59 65, Zhang Z, and Kleinstreuer C. Transient airflow structures and particle transport in a sequentially branching lung airway model. Phys Fluids 14(2): , Zhang Z and Kleinstreuer C, Kim CS, and Hickey AJ. Aerosol transport and deposition in a triple bifurcation bronchial airway model with local tumors. Inhal toxicol 14: ,

25 Page 25 of 40 FIGURE LEGENDS Fig.1: The sheep lung model and the locations selected for probing the flow fields are demonstrated. Fig.2: For the sheep used in this study, the inlet velocity with respect to time was measured using a resistance-based pneumotachometer during mechanical ventilation and the profile is demonstrated here. The average diameter of the trachea at the inlet was found to be mm. The measured flow and the diameter were used to calculate the time dependent average velocity at the inlet. The pause that can be noticed in the velocity time curve is when the scanner is triggered for acquiring the data. The oscillations seen during the inhalation is due to the piston movement of the mechanical ventilator. Point A was used for investigating the peak inhalation phase and point B was used for investigating the peak exhalation phase. Points C and D were used for investigating the effect of the pause on the flow field. Point E was used to investigate the transient phase of the flow. Fig.3: Non-dimensional axial velocity (left), in-plane velocity vectors (middle) and axial velocity vectors (right) are demonstrated at locations marked 1, 2 and 3. Fig.4: Non-dimensional axial velocity (left), in-plane velocity vectors (middle) and axial velocity vectors (right) are shown at locations marked 4, 5 and 6. Fig.5: Non-dimensional axial velocity (left), in-plane velocity vectors (middle) and axial velocity vectors (right) are shown at location marked 7, 8 and 9. Fig.6: Streaklines during the inhalation phase with spherical markers (not particles) are color-coded by absolute velocity. (Left) Peripheral streaklines at constant intervals along the outer tracheal wall within ~1mm from the external surface are demonstrated. (Right)

26 Page 26 of 40 Streaklines at constant intervals in the core region of the trachea at approximately 1mm from the external surface are demonstrated. Fig.7: Non-dimensional axial velocity (left), in-plane velocity vectors (middle) and axial velocity vectors (right) are shown for locations marked 3, 2 and 1. Fig.8: Non-dimensional axial velocity (left), in-plane velocity vectors (middle) and axial velocity vectors (right) are shown for locations marked 4, 5 and 6. Fig.9: Non-dimensional axial velocity (right), in-plane velocity vectors (middle) and axial velocity vectors (right) are shown for locations marked 9, 8 and 7. Fig.10: Non-dimensional axial velocity (right), in-plane velocity vectors (middle) and axial velocity vectors (right) at locations 4, 5 and 6 during the transition phase are demonstrated. Strong vortices are seen in the middle column. Fig.11: Non-Dimensional axial velocity (left), in-plane velocity vectors (middle) and axial velocity vectors (right) are shown for locations 1 and 4 during the peak inhalation for the blocked upper lobe simulation. Fig.12: Non-Dimensional axial velocity (left), in-plane velocity vectors (middle) and axial velocity vectors (right) are shown at locations 1 and 4. Fig.13: Non-Dimensional axial velocity (left), in-plane velocity vectors (middle) and axial velocity vectors (right) are shown using the Weibel model during simulation of peak inhalation. Fig.14: Non-Dimensional axial velocity (left), in-plane velocity vectors (middle) and axial velocity vectors (right) are shown using the Weibel model during simulation of peak exhalation.

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