Characteristics of airflow in a CT-based ovine lung: a numerical study

Characteristics of airflow in a CT-based ovine lung: a numerical study

Senthil Kabilan,1 Ching-Long Lin,2 and Eric A. Hoffman1

1Departments of Radiology and Biomedical Engineering, The University of Iowa, and2Department of Mechanical and Industrial Engineering and Iowa Institute of HydraulicResearch: Hydroscience and Engineering, The University of Iowa, Iowa City, Iowa

Submitted 28 September 2005; accepted in final form 28 October 2006

Kabilan S, Lin CL, Hoffman EA. Characteristics of airflow ina CT-based ovine lung: a numerical study. J Appl Physiol 102:1469 –1482, 2007. First published November 16, 2006; doi:10.1152/japplphysiol.01219.2005.—The transient airflow in a rigid,asymmetric monopodial sheep (ovine) tracheobronchial tree of up to13 generations was investigated numerically. The lung geometry wassegmented and reconstructed from computed-tomographic (CT) im-ages. The flow characteristics in the image-based sheep airway werecompared with the flow patterns produced by a Weibel-based modelat prime locations. Boundary conditions were prescribed 1) a velocityprofile from experimental data at the inlet and 2) zero pressure at thebronchial outlets. A mesh convergence study was carried out toestablish confidence in the model predictions, and gross left-rightventilation was validated against experimental xenon wash-in-wash-out data. Detailed flow characteristics were investigated at three pointsin the breathing cycle: 1) peak inhalation, 2) peak exhalation, and 3)transition. Simulation results revealed fundamental differences be-tween airflow in monopodial and bipodial branching airways. Com-pared with idealized bipodial flow, the flow in the sheep airway wasasymmetric and highly vortical, especially during exhalation andtransition. The streak lines during the inhalation phase suggest that theleft and right upper lobes are ventilated by airflow in the peripheralregion of the trachea. This work may contribute to understanding theinterplay between structure and function in the lung.

computational fluid dynamics; quantitative computed tomography;lung gas flow; monopodial bronchial geometry

LITTLE RESEARCH HAS BEEN CARRIED out on the flow characteris-tics of the monopodial lung airway tree seen in most nonhumanmammals. Briant and Cohen (4) compared the flow distributionin 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 caninebronchial tree, although the study was limited to steady-stateinhalation and exhalation. Their results also suggested thatmore flow is carried along the core through the bifurcationbecause of the inertial properties of the fluid. Cohen and Briant(7) also studied the flow distribution in human and caninetracheobronchial airway trees in an in vitro geometry derivedfrom casts. Their study suggested that the presence of smallerairways affected the flow distribution in the larger upstreamairways. Their results also suggested that the coupling of thelarynx with the tracheobronchial airway had little influence onairflow distribution in the human lung and even less influenceon airflow distribution in the canine lung. The presence of alarynx altered their predicted flow by �1% for most measure-ments and by �5% in others. They concluded that the greatestdifferences in airflow distribution between the human (bipo-

dial) and the canine (monopodial) lung were manifest in theupper lobes, where the airway branching pattern was mostdissimilar between the two species.

Although these early experimental findings suggested thatthe airflow in the distal lung affects the airflow of the proximallung, few computational studies have attempted to extend theiranalysis to several generations of airways. Most recent studieshave focused on small sections of lungs with simple bifurca-tions. For example, Kinsara et al. (14) and Balashazy et al.(1–3) focused on single-bifurcation models. Many of thesestudies, including the simulations by Gatlin et al. (11) of fluidflow and particle deposition in an asymmetric single bifurca-tion, were based on idealized elliptical cross sections. Despitethe admitted importance of these studies in investigating thelocal details of turbulent and particle flow, there is little doubtthat the complicated bifurcation patterns characteristic of realairway geometries result in disturbed flow, affecting the flowpatterns and particle deposition in subsequent bifurcations.This point was reinforced by Lee et al. (15) in their computa-tions of the velocity field, particle trajectories, and particledeposition efficiency for two- and three-dimensional single anddouble bifurcations. They concluded that the presence of asecond bifurcation alters the flow field and the particle trajec-tories. The limitation of the single-bifurcation model is furthersupported by Comer et al. (8), who studied aerosol transportand deposition in in-plane and 90° out-of-plane double-bifur-cation configurations. Their findings suggest that the localdeposition patterns differ with bifurcation level and orienta-tion.

Of the recent studies that have attempted to extend theircomputational analysis to a greater number of generations ofthe tracheobronchial tree, most have been two dimensionalor based on an idealized Weibel model, and none have beenmonopodial. The study by Wilquem and Degrez (20) onsteady inspiratory flow in a two-dimensional model of threegenerations of the human airways revealed a highly skewedvelocity profile downstream of the second junction. Thelimitation of a two-dimensional assumption was furtherillustrated later in the work of Caro (5), who showed thatvelocity profiles in daughter branches after a bifurcation arestrongly affected by the angle of rotation, the azimuthalangle, between consecutive bifurcations. In terms of recentthree-dimensional models, Comer et al. (9, 10) and Zhang etal. (21, 22) simulated airflow and particle deposition ingenerations 3– 6 of a Weibel-based model. Although theseinvestigations were important, numerical experiments byNowak et al. (17) demonstrated that the velocity fields in a

Address for reprint requests and other correspondence: E. A. Hoffman,Dept. of Radiology, Univ. of Iowa College of Medicine, 200 Hawkins Dr.,Iowa City, IA 52242 (e-mail: [email protected]).

The costs of publication of this article were defrayed in part by the paymentof page charges. The article must therefore be hereby marked “advertisement”in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

J Appl Physiol 102: 1469–1482, 2007.First published November 16, 2006; doi:10.1152/japplphysiol.01219.2005.

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CT-scan-based geometry are more complex than those in theWeibel-based model because of airway curvature and com-plex shapes at junctions.

We are unaware of studies involving computational fluiddynamics in a three-dimensional CT-based monopodial lungairway tree, which is the focus of the present study. Thespecific goals are fourfold: 1) to generate a topologicallyfaithful computational grid of nearly nine generations of themonopodial ovine tracheobronchial tree from CT images, 2) tostudy how the tree geometry influences flow characteristics inmonopodial branching airways, 3) to compare the flow patternsin the monopodial and bipodial branching airway trees, and 4)to investigate the effect of the upper right lobe on the flow fieldin the trachea, which is unique to the sheep.

METHODS

Lung Geometry

A three-dimensional image dataset from a multidetector-row CT(MDCT; Siemens Sensation 64) scan of the sheep airway was seg-mented as described by Tschirren et al. (19) and converted to a

stereolithography file, representing the outer surface of the tracheo-bronchial tree. Scan acquisition parameters followed a volumetricprotocol: 100 mA, 120 kV, 1 mm collimation, 1.3 mm effective slicethickness, 0.65 mm overlap, and 1.2 mm pitch. The slice parametermode was 32 � 0.6 mm. Images were reconstructed into 512 � 512slice matrices.

The airway surface was first smoothed globally using the weightedLaplacian smoothing algorithm in Magics (Materialise, Ann Arbor,MI) to filter hard edges resulting from limited image resolution. Theterminal branches were then trimmed, resulting in a surface that wasnearly perpendicular to the airway centerline. This procedure wasrepeated for the entire geometry, resulting in 451 outlet faces (Fig. 1).Because of the nature of CT scanning, our detection of airways is notbased on generation number but, rather, size (and, to some extent,orientation between the segment’s long axis and the CT slice orien-tation). Depending on the path, we found 7–13 generations. However,the average diameter of all the 451 outlets was computed to be 1.14mm, with a standard deviation of 0.34 mm. Gambit (Fluent, Lebanon,NH) was used to convert the final surface geometry to an unstructuredvolume mesh consisting of 792,915 nodes and 3,480,693 tetrahedralelements. The volume mesh was generated using the T-grid meshingscheme, which primarily consists of tetrahedral mesh elements butmay also contain, wherever appropriate, shapes, such as hexahedral,pyramidal, and wedge elements, as well. The algorithm works on theprinciple that if a boundary layer is attached to any of the faces on thevolume, it generates hexahedral or prism elements in the regionsadjacent to the boundary layers. If any quadrilateral face elementexists 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 theremainder of the volume. Then the rest of the volume is filled withtetrahedral elements.

Fig. 1. Sheep lung model and locations selected for probing flow fields.

Fig. 2. Profile of inlet velocity with respect to time measured using aresistance-based pneumotachometer during mechanical ventilation. Aver-age diameter of the trachea at the inlet was 19.34 mm. Measured flow anddiameter were used to calculate time-dependent average velocity at theinlet. Pause in velocity-time curve occurs when scanner is triggered for dataacquisition. Oscillations during inhalation are due to piston movement ofthe mechanical ventilator. Point A was used to investigate peak inhalationphase, point B to investigate peak exhalation phase, points C and D toinvestigate the effect of pause on the flow field, and point E to investigatethe transient phase of the flow.

1470 CT-BASED STUDY OF AIRFLOW IN THE OVINE AIRWAY

J Appl Physiol • VOL 102 • APRIL 2007 • www.jap.org

Numerical Methods

Airflow predictions were based on the three-dimensional, incom-pressible Navier-Stokes equations for fluid mass and momentum

� � u � 0 (1)

�u

�t� u � �u �

� �p

�� v�2u (2)

where � is the density, � is the kinematic viscosity, u is the fluidvelocity vector, and p is the pressure. The resulting system ofequations was solved with a fractional four-step characteristic Galer-kin finite-element method (16). This approach is second-order accu-rate and does not require any special treatment on the boundaryconditions of the intermediate velocity. Continuity is enforced bysolving the pressure-Poisson equation. The time (0.0005-s) step is

estimated by the Courant-Friedrichs-Levy condition, and the total runtime with the above-mentioned mesh size on an HP zx6000 Itaniumworkstation is �8 days (for a detailed description see Ref. 16).

For all calculations, air at room temperature was considered to bethe working fluid, with a density of 1.139 kg/m3 and a kinematicviscosity of 1.665 � 10�5 m2/s. The inlet boundary conditionconsisted of a prescribed velocity-time curve (Fig. 2) based onexperimental data. These data were acquired during the CT scanused to determine the lung geometry. At zero velocity points, thelung volume was held constant (Fig. 2). The outlet boundarycondition on all 451 faces was zero pressure. Because of therelatively uniform size of all terminal branches, this was consid-ered adequate. The no-slip condition was applied to the remainingairway boundaries, which were assumed to be rigid and imperme-able. Airflow was assumed to be laminar on the basis of a

Fig. 3. Nondimensional axial velocity (A), in-plane velocity vectors (B), and axial velocity vectors (C) at markers 1, 2, and 3.

1471CT-BASED STUDY OF AIRFLOW IN THE OVINE AIRWAY


computed Reynolds number of 1,500 at peak inhalation and peakexhalation.

Weibel Model

A Weibel model was generated to compare the flow patternsbetween the monopodial and bipodial branching patterns. It wasassumed that daughter branches began their separation at the bifurca-tion point as the frustum of a cone. The large diameter of the frustumwas set equal to the diameter of the parent branch, and the smalldiameter of the frustum was set equal to the diameter of the daughterbranch. The length of the frustum was assumed to be one-tenth of thelength of the daughter branch. These assumptions were necessary,because the Weibel model defines only one diameter for each gener-ation of airway (for detailed information about the geometry see Ref.17). The final model consisted of 73,280 nodes and 318,318 tetrahe-

dral elements. To validate this model, predictions of airflow werecompared with those of Nowak et al. (17).

Mesh Convergence Study and Validation

To verify that the solutions were independent of the mesh, the meshdensity was approximately doubled for the CT-based geometry. Oth-erwise, the same boundary conditions and solution parameters wereapplied. This mesh consisted of 1,457,646 nodes and 6,377,921tetrahedral elements. Flow fields were compared at three main loca-tions (markers 4–6 in Fig. 1).

To gain confidence in overall model predictions, the percent flowinto the right and the left lung was computed and compared with thepercent measured volume based on a xenon wash-in-washout 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 isnecessary that the average time constants (gas turnover rate) of the leftand right lungs be equal. A xenon study was performed, and the timeconstants for the xenon wash-in and washout curves were plottedfor the left and right lungs to calculate specific ventilation(ml �min�1 �ml�1) according to Tajik et al. (18) and Chon et al. (6).The regions of interest used for computing the regional ventilationwere 11 � 11 pixels throughout the left and right lungs, with eachlung studied independently.

Airflow Investigations

Airflows were examined in the normal airways and after theintroduction of an artificial blockage. The comparative analysis fo-cuses on three time points: 1) peak inhalation, 2) peak exhalation, and3) transition. Peak inhalation was taken to be the maximum of the

measured velocity profile (point A in Fig. 2), corresponding to 1.1895m/s, whereas peak exhalation was taken to be the minimum of themeasured velocity profile (point B in Fig. 2), corresponding to �2.1m/s. For open and obstructed airway trees, the flow fields werequeried at identical locations (see markers in Fig. 1).

Specifically, markers 1–3 were chosen to examine the effect of theupper right lobe on the flow field. Marker 4 was selected to study flowpattern in the trachea just before the first bifurcation. Similarly,markers 5 and 6 were chosen to study the flow patterns in the left andright lungs, respectively, after the flow in the trachea encounters thefirst flow divider and also for a direct comparison of flow features withthe Weibel model. Markers 7–9 were selected to study the effect of abranch with a �180° turn and the more rapid narrowing on the flowfield in the upper left lobe. Markers 10–13 were chosen to study thecharacteristics of flow fields deep in the lung. At all 13 markers, the




axial velocity was nondimensionalized with respect to the globalmaximum velocity for comparison.

To further refine our understanding of the three-dimensional struc-ture of flow in the monopodial lung, streak lines seeded in the sheeptrachea were traced into the lung during the inhalation phase usingTecplot (Tecplot, Bellevue, WA). The cross section of the trachea wasdivided into two general regions: 1) a peripheral region, which waswithin 1 mm from the external surface, and 2) a core region, whichwas everything inside the peripheral region. A total of 12 fluidsolution data files uniformly distributed at various time points duringthe inhalation phase are used for the streak-line analysis. For theperipheral region, 95 streak lines were seeded at the inlet and evenlydistributed in that layer. For the core region, 150 streak lines wereseeded at the inlet and evenly distributed. Ten sets of seeds wereintroduced into the flow stream between any two unsteady-state fluidsolution data files.

RESULTS

Mesh Convergence and Validation

At the three locations for comparison (markers 4–6 in Fig.1), there was no noticeable variation in the axial velocitycontours or in the secondary radial velocity (not shown). Thiswas true during all three time points examined: peak inhala-tion, peak exhalation, and transition. In addition, the flow rateat six different locations (markers 1, 4–6, 10, and 12 in Fig. 1)

was computed. At no time or location did the percent differ-ences exceed 0.41%. Because the time step is estimated by theCourant-Friedrichs-Levy condition and the difference betweenthe solutions of two different meshes is negligible, we couldinfer that the solution is independent of the time step.

The magnitude of the axial velocity and the in-plane flowwas larger in the right than in the left lung, and the percent flowinto the right and left lungs was computed to be 59.26 and40.74%, respectively. The measured right and left volumeswere 1,669.94 and 1,224.68 cm3, which translate to 57.69 and42.30% of total lung volume.

Measured right and left volume flow rates were assessed to be0.08 and 0.079 ml/min, with standard errors of 0.001 and 0.009,respectively. Thus, even though the right and left volume ratioswere 57.69 and 42.30%, the regional ventilation values (per unitvolume) in the right and left lungs were identical to the predictedvalues to within statistical significance.

Normal Airways: Peak Inhalation

Marker 1. The axial velocity at marker 1 was asymmetric(Fig. 3, A1 and C1), with a higher magnitude on the side of thefirst lobar bifurcation. Although the prescribed flow at thetrachea inlet was uniform, this asymmetry was already visiblea mere 2 mm downstream from the inlet (not shown). Two

Fig. 6. Streak lines during the inhalation phase withspherical markers (not particles) are color coded byabsolute velocity. A: peripheral streak lines at con-stant intervals along outer tracheal wall within �1mm from external surface. B: streak lines at constantintervals in core region of trachea at �1 mm fromexternal surface.



small underdeveloped vortices (circles in Fig. 3B1) were foundat the periphery of the wall, the first one closer to the posteriorwall and the second one closer to the anterior wall. The vortexcloser to the first lobe on the right lung moves the locationof the high-speed zone caused by the skewness of thevelocity profile further toward the wall. The counterrotatingvortex near the posterior wall is present in the low-speedflow zone and appears not to have a profound effect on theflow field.

Marker 2. The flow in the trachea enters the upper lobe atmarker 2 (Fig. 3, A2 and B2), producing a jet into an airwaybranch of smaller diameter. The majority of the air that flowsinto the upper lobe derives from the peripheral zone of thetrachea (Fig. 3A2). Although this location is halfway past the

upper lobe bifurcation, the high-speed zone is diminished butstill present, suggesting that the formation of the high-speedzone in the trachea may be due to the higher functional volumeof the right lung.

Marker 3. Downstream of the upper lobe bifurcation (Fig.3A3) the flow assumes a more flat profile with less asymmetry(Fig. 3C3). Little of the upstream vorticity is noticeable. Inaddition, the high-speed zone (crescent in Fig. 3A3) has movedcloser to the wall of the trachea with respect to the high-speedzone at marker 1. This is due to the flow of the peripheral airinto the first lobe (upstream), which pulls the high-speed zonecloser to the tracheal wall.

Marker 4. It is apparent at marker 4 (Fig. 4A1) that theflow is adjusting to the geometric transition from the trachea

Fig. 7. Nondimensional axial velocity (A), in-plane velocity vectors (B), and axial velocity vectors (C) for markers 3, 2, and 1.



to the daughter branches. The flow is once again asymmetrictoward the right lung bronchus (marker 6).

Markers 5 and 6. Immediately after the main trachealbifurcation, the flow in the left (marker 5) and right (marker 6)lungs is similar (Fig. 4, A2 and A3) but different from thatpredicted in Weibel bronchi. For both, the highest axial veloc-ity was adjacent to the inside wall of the bifurcation; however,neither exhibit any significant symmetrical or asymmetricvortices.

Marker 7. The flow at marker 7 (Fig. 5, A1, B1, and C1) isvery similar to that at marker 5, with similar off-axis compo-nents and a similar axial velocity profile. With respect to flowat marker 5, the high-speed zone is diminished.

Marker 8. At the 180° bronchus, the core region enters theairway branch, in contrast to the situation in the flow into the

upper lobe, which was fed by the peripheral region. The air inthe core region (Fig. 5, A2 and B2) first goes toward the bottomedge of the bronchus and then enters the airway branch.Because of this effect, a low axial velocity region is creatednear the outer wall of the main bronchus (arrow).

Marker 9. The upstream low-axial-velocity region (Fig.5A2) becomes more substantial at marker 9 (Fig. 5A3), andtwo counterrotating vortices form (Fig. 5B3). The 180°branch thus not only reduces the velocity of the high-speedzone but also pulls it toward the outer wall of the mainbronchus.

Markers 10–13. The high-speed zone, which upstream(markers 5 and 7) is located near the inner wall, moves towardthe core region (not shown) because of airway branching on theouter wall of the bronchi. This effect can also be seen on the




right lung at markers 12 and 13, although the magnitude of thevelocity is greater in the right than in the left lung at all thecorresponding cross sections.

Streak-line analysis. The fluid solution data files during theinspiratory phase were loaded into Tecplot for the streak-lineanalysis. The streak lines seeded within the outermost (�1 mm)layer, entered, and terminated in the apical portion of the lungabove the carina, with a few exceptions, i.e., those that entered thebasal portion of the right lung and also some branches in the leftlung (Fig. 6A). The peripheral region mainly ventilates the entireapical portion of the lung and the anterior portion of the basallung. By contrast, streak lines seeded in the core region ventilatedthe basal portion of the lung (Fig. 6B).

Normal Airways: Peak Exhalation

Flow during the peak exhalation phase through the sheepairway model is quite different from the peak inhalation flowand, in general, is much more complicated. The flow is lesscoherent, with asymmetric vortices. In-plane velocity (second-ary flow) is very important during exhalation, since it is theprimary factor governing the mixing of inhaled gas, aerosoltransport, and deposition in the lung.

Marker 3. The velocity consists predominantly of fourasymmetric vortices (Fig. 7B1) downstream of the trachealbranch or the first upper lobe. In addition, a high-speed zoneexists close to the center of the trachea (Fig. 7A1).




Markers 1 and 2. Flow from the first lobe enters the maintrachea. This flow moves the two vortices near the posterior ofthe trachea toward the inner core (Fig. 7, A2 and B2). The flowcontinues upstream, creating a faster high-speed zone (Fig. 7, A3,B3, and C3). Although there is an increase in the magnitude of thehigh-speed zone, the effect of the first lobe is to reduce thevelocity by inhibiting the flow development (see Blocked UpperLobe Simulation). Two additional vortices enhance the mixing ofthe gases in the upper tracheal region (Fig. 7B3). Thus it can beinferred that the right upper lobe has a major role in the mixing ofthe inhaled gases in the upper trachea during exhalation.

Markers 4–6. Because the flow rate is greater from the rightthan from the left bronchus, an asymmetric high-speed region

exists upstream of the tracheal bifurcation (Fig. 8A1). In thetrachea, the velocity vectors are less coherent, consisting offour vortices and, also, substantial radial flow (Fig. 8B1). Justbelow (markers 5 and 6) the first bifurcation (Fig. 8, A2, B2,C2, A3, B3, and C3) the flow in the two bronchi is quitedifferent. The flow in the left bronchus is characterized byskewness, with two fully developed asymmetric vortices. In theright bronchus, two vortices also exist; however, only one isfully developed. In addition, the magnitude of the averagevelocity is less on the left than on the right.

Marker 9. As the branches merge onto the main bronchus,they tend to accelerate the flow near the inner wall of the mainbronchus (Fig. 9C1).

Fig. 10. Nondimensional axial velocity (A), in-plane velocity vectors (B), and axial velocity vectors (C) at markers 4, 5, and 6 during transition. Note strongvortices in B.



Markers 7 and 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 ofthe bronchus (Fig. 9B2) and a low-velocity region near theposterior wall (Fig. 9A2). As the flow from the core region ofthe branch enters the main bronchus, it moves the two vorticesfarther toward the bottom of the main bronchus. Slightly abovethat bifurcation (marker 7), the flow returned from the branchaccelerates the fluid in the high-speed zone (Fig. 9A3). Also, atthis location, two fully developed vortices exist near the outerwall and one underdeveloped vortex exists near the apex of thebronchial wall (Fig. 9B3). This underdeveloped vortex degen-erates quickly (Fig. 8B2).

Markers 10–13. Below these major bifurcations, the flowcharacteristics (not shown) are quite random, with radial flows,vortices, and some local asymmetry due to the numerous sidebranches. The greater distribution of branches on the outer wallat these deeper locations tends to move the high-speed zonecloser to the inner wall for both bronchi.

Normal Airways: Transition

Flow was investigated at two flow rates between peakinhalation and peak exhalation. 1) Flow patterns were evalu-ated before and after the pause for triggering the scanner(points C and D in Fig. 2). 2) Flow patterns were evaluated atflow reversal (point E in Fig. 2).

Flow patterns were similar before and after breath hold, withslightly greater velocity at point D than at point C. For

example, the magnitude of the nondimensional axial velocitywas 15.4% greater at point D than at point C. During flowreversal (point E in Fig. 2), the fluid near the periphery of thetrachea (Fig. 10C1) has already changed the direction, whereasthe fluid in the core region is still moving in the forwarddirection because of the reduced inertia in the boundary.Beyond the main bifurcation (markers 5 and 6), the fluid closerto the outer wall has changed the direction but not the fluid nearthe inner wall (Fig. 10, C2 and C3) because of the greatervelocity near the inner wall than near the outer wall at theselocations. In addition, at these locations, strong vortices areformed moving in opposite directions (Fig. 10, B2 and B3).These vortices continue to be present throughout the expiratoryphase and are dominant during peak expiratory flow. Thus itcan be inferred that the transient phase of the flow is the maincause for strong vortices in the flow, which influence mixing ofthe inhaled gases.

Blocked Upper Lobe Simulation

To further investigate the hypothesis that the main cause forthe formation of the high-speed zone (the skewed velocityprofile) in the trachea may be the higher functional right lungvolume, a separate simulation was performed in which all theoutlets of the upper right lobe were closed (no flow). Except forthese changed boundary conditions, the simulations were iden-tical.

Under this scenario, during peak inspiratory flow, the high-speed zone persists in the upper trachea near the wall (marker

Fig. 11. Nondimensional axial velocity (A), in-plane velocity vectors (B), and axial velocity vectors (C) for markers 1 and 4 during peak inhalation for blockedupper lobe simulation.



1). In fact, the nondimensional axial velocities are indistin-guishable in the trachea (Figs. 11A1 and 3A1) and only slightlyhigher in the obstructed simulation just upstream of the mainbifurcation (Figs. 11A2 and 4A1). Additionally, there are fewdifferences in flow magnitude and direction in the left bronchus(not shown). Flow into the right bronchus is substantiallyhigher in the blocked case because of conservation of mass.

Analysis of the obstructed flow simulation also elucidatesthe influence of the upper lobe bronchus on the flow field. Atpeak exhalation, flow just above the main bifurcation is similarin the obstructed and normal unobstructed simulations, al-though the magnitude of the former is higher (Figs. 8A1 and12A2). In the upper trachea, the flow patterns differ in terms ofthe degree of vorticity (Figs. 7B3 and 12B1), with a fasterhigh-speed zone in the blocked mesh. Taken together, thesefindings suggest that the upper lobe bronchus enhances themixing of gases in the upper tracheal region but reduces thevelocity of the high-speed zone (see Normal Airways: PeakExhalation).

Monopodial vs. Bipodial Flow

In the bipodial-Weibel model, flow just above the mainbifurcation was nearly parabolic during inspiration (Fig. 13,A1, B1, and C1). As shown in Fig. 4, the monopodial profile atthis point is considerably blunter (Fig. 4C1) and asymmetric(Fig. 4A1). Furthermore, in the sheep lung simulation, incontrast to the Weibel model (Fig. 13, A2, B2, and C2), nosymmetrical or asymmetric vortices were noticed just down-

stream of the main bifurcation (markers 5 and 6). Duringexpiration, at these same locations, four symmetrical vorticeswere observed in the Weibel model (Fig. 14, A1, B1, and C1),where multiple asymmetric vortices are found in the monopo-dial lung.

DISCUSSION

In this study, airflow in the sheep lung was simulated on thebasis of experimentally measured flow conditions applied to atopologically faithful three-dimensional computational gridgenerated from CT images. It was hypothesized that the skew-ness in the velocity profile (namely, the location of the high-speed zone) was introduced in the trachea mainly due to thevolume difference between the right and left lung. This hy-pothesis was tested in two different monopodial grid configu-rations: a normal geometry and an obstructed geometry. Thisfinding is novel and suggests functional behavior in the airwaytree that may be important in the analysis of dosage andclearance. However, geometric features, such as wall curva-ture, may also play a role. This warrants further study.

Results from the obstructed upper lobe simulation supportevidence from the normal model that the upper lobe bronchusdoes not assist the formation of a high-speed zone in thetrachea. This suggests that the upper lobe bronchus reduces theoverall ventilation in both 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 theleft lung. Moreover, the magnitude of the velocity was consis-

Fig. 12. Nondimensional axial velocity (A), in-plane velocity vectors (B), and axial velocity vectors (C) at markers 1 and 4.



tently greater in the right than in the left lung at any corre-sponding cross section.

The streak-line analysis supported the notion that the periph-eral region of airflow mainly ventilates the entire apical portionof the right lung and the anterior portion of the basal lung, andthe basal region of the lung is ventilated by the airflow in thecentral portion of the trachea. It was hypothesized that thetransition between inhalation and exhalation is the main cause

for the formation of strong vortices present along the entireexpiratory curve. These vortices may play a major role in themixing of the inhaled gases during expiration. It was concludedfrom the comparison of the Weibel model with the sheep lungthat the flow in these models is completely different. There wasno agreement between the two models at any of the crosssections. These data demonstrate the profound effects causedby differences in airway geometry.

Fig. 13. Weibel model of nondimensional axial velocity (A), in-plane velocity vectors (B), and axial velocity vectors (C) during simulation of peak inhalation.

Fig. 14. Weibel model of nondimensional axial velocity (A), in-plane velocity vectors (B), and axial velocity vectors (C) during simulation of peak exhalation.



This work has provided a detailed assessment of the fluiddynamics in the monopodial branched airway tree through useof high-resolution, volumetric MDCT image data in conjunc-tion with high-fidelity computational fluid dynamics. Themethodologies outlined in this study form the basis for ourability to examine the effects of gas density and viscosity onthe regional distribution of ventilation. This becomes criticallyimportant as we seek to utilize xenon and helium gases inconjunction with MDCT and magnetic resonance imaging tounderstand determinants of ventilation heterogeneity in healthand disease.

Limitations

The limitations of the present study include the assumptionof a constant-pressure boundary condition for all 451 outlets.Although we believe that this is a reasonable first approxima-tion, since the diameters of all terminal outlets were similar, inreality, it is likely that the pressure varies with respect to lunglocation because of such factors as regional differences inpleural pressure gradients, lung mechanics, and path lengths.Since this is likely, in part, subject dependent, it becomes quitea complex problem if one wishes to correctly attribute variableboundary conditions. This will certainly be the topic of manyfuture studies. In addition, velocity profile from the mechanicalventilator does not represent the normal breathing pattern in alive animal. However, results shown here suggest that althoughthe pause in the inlet velocity profile alters the magnitude, theflow characteristics are unchanged. The flow in the model wasassumed to be laminar, whereas a turbulence model wouldhave been a more appropriate choice. The sheep in the presentstudy were intubated with a very smooth tube that reachesabout the area where the computational model begins. Thusthis model is valid for predictions to compare with the xenonand future helium data. The use of a turbulence model could beconsidered for future study without much difficulty. Presentlythe study compares airflow characteristics in a CT-based mo-nopodial geometry with an idealized bipodial geometry. Thecomparison between the two geometries shows the differencesin the flow characteristics because, basically, the bifurcationpatterns are immensely different between the monopodial andthe bipodial lungs. However, the difference in wall shapes ofthe CT-based monopodial airway tree and the idealized human-like bipodial model may also contribute to the differences inflow characteristics. Thus the use of CT-based geometry for thebipodial lung geometry could be considered for future study.The potential errors due to sampling artifacts introduced in theairway geometry by way of nonisotropic sampling via CTscanning would be addressed in future research.

ACKNOWLEDGMENTS

The authors thank M. Tawhai, G. McLennan, J. Tschirren, and D. Chon forassistance and discussion during the course of the study and the NationalCenter for Supercomputing Applications for allocating the computer time toperform the simulation.

GRANTS

This research was supported by National Heart, Lung, and Blood InstituteGrant HL-064368 and National Institute for Biomedical Imaging and Bioengi-neering Grant EB-005823 under the IMAG program for Multiscale Modeling.

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Characteristics of airflow in a CT-based ovine lung: a numerical study

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