Simulation of the effect of local obstructions and blockage on airflow and aerosol deposition in central human airways

Aerosol Science 38 (2007) 865 – 884 www.elsevier.com/locate/jaerosci

Simulation of the effect of local obstructions and blockage on airflow and aerosol deposition in central human airways Árpád Farkas∗ , Imre Balásházy Radiation and Environmental Physics Department, MTA KFKI Atomic Energy Research Institute, P.O. Box 49, H-1525 Budapest, Hungary Received 6 March 2007; received in revised form 12 June 2007; accepted 13 June 2007

Abstract Investigation of the effect of sidewall and carinal tumours, airway constrictions and airway blockage on the inspiratory airflow and particle deposition in the large central human airways was the primary objective of this study. A computational fluid and particle dynamics model was implemented, validated and applied in order to simulate the air and particle transport and to quantify the aerosol deposition in double airway bifurcation models. Our investigations revealed that surface abnormalities and tubular constrictions can significantly alter the airstreams and the related local aerosol deposition distributions. Sidewall tumours have lead to an enhanced deposition of large particles and caused lower deposition efficiency values of nano-particles compared to the deposition efficiency in healthy airways. Central tumours multiplied the deposition efficiency of large particles but hardly affected the deposition efficiency of nano-particles. Airway blockage caused a significant redistribution of particle deposition sites. The deposition efficiency of the inhaled aerosols in constricted airways was much higher than the same deposition efficiency in healthy airways. Current results might help in the understanding of the adverse health effects of the inhaled air-pollutants in patients with lung disease and might be integrated into future aerosol therapy protocols. 䉷 2007 Elsevier Ltd. All rights reserved. Keywords: Airflow and particle deposition; Computational fluid and particle dynamics; Diseased airways

1. Introduction Modelling of the airflow and particle transport within the respiratory system is essential in assessing adverse health effects of inhaled particles and in optimising the aerosol drug delivery. The continuously enhancing capacity of the computers and the commercially available codes help more and more scientists to contribute to this challenging area. The development of medical imaging techniques and sophisticated geometry reconstruction methods also promoted the emerging of this field. Several studies related to inhaled air and particle transport modelling were published in the last decades (Calay, Kurujareon, & Holdo, 2002; van Ertbruggen, Hirsch, & Paiva, 2005; Ferron & Edwards, 1996; Gradon & Orlicki, 1990; Jin, Fan, Zeng, & Cen, 2007; Kimbell et al., 2007; Liu, So, & Zhang, 2003; Luo, Hinton, Liew, &

∗ Corresponding author. Tel.: +36 1 3922222, 3923404; fax: +36 1 3922712.

E-mail address: [email protected] (Á. Farkas). 0021-8502/$ - see front matter 䉷 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.jaerosci.2007.06.004

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Tan, 2004; Moskal & Gradon, 2002; Nowak, Kakade, & Annapragada, 2003; Schroeter, Kimbell, & Asgharian, 2006; Shi, Kleinstreuer, & Zhang, 2007; Zhang, Kleinstreuer, Donohue, & Kim, 2005). Aerosol deposition models based on analytical formulas provided useful information regarding the total, regional and generation-number specific particle deposition efficiencies. However, these models cannot predict the local inhomogeneity of aerosol deposition. Such deposition models applicable to adults are for example the single-path model developed by Yeh and Schum (1980), improved later by Cassee et al. (1999) and referred to as the multiple-path particle deposition model or the stochastic lung model developed by Koblinger and Hofmann (1990). Asgharian, Menache, and Miller (2004) have recently developed a stochastic multiple-path deposition model for children. The resolution of the deposition models based on computational fluid dynamics (CFD) techniques is much higher than the resolution of analytical models. However, due to the high computational expenses they are restricted to a region (Grgic, Finlay, Burnell, & Heenan, 2004; Heenan, Finlay, Grgic, Pollard, & Burnell, 2004) or some units—like one alveolus and one or a few bifurcations—of the healthy lung (Balásházy, Hoffmann, & Heistracher, 2003; Darquenne & Paiva, 1996; Haber & Tsuda, 1998; Tsuda, Henry, & Butler, 1995; Zhang, Kleinstreuer, & Kim, 2002). Airflow, particle deposition and related health consequences might change in the presence of lung diseases. Some airway disorders, like chronic bronchitis, emphysema, asthma bronchiale, cystic fibrosis, bronchiectasia or bronchiolitis obliterans may alter the airstreams. Intraluminar tumours may also have important effect on the flow configuration and particle deposition patterns. For example, tumours can affect either the carinal ridge of the bifurcations or the tubular part of the airways (Strausz, 1996; Strausz, Pápai, & Szima, 1996). However, earlier histological studies (Auerbach, Stout, Hammond, & Garfinkel, 1961; Kotin & Falk, 1959) indicate that preneoplastic and neoplastic lesions predominate at bifurcation regions rather than in tubular ones. Based on the deposition measurements of Churg and Vedal (1996) and Schlesinger and Lippmann (1978) the reason for the preferential tumour occurrence can be the higher local deposition density of the inhaled carcinogen particles at the carinal ridges of the airway bifurcations. Later, experimental measurements (Kim & Fisher, 1999) and CFD simulations (Balásházy & Hofmann, 1993; Zhang & Kleinstreuer, 2001) demonstrated the existence of the carinal deposition “hot spots”. In vivo measurements have demonstrated increased tracheobronchial airway resistance in case of chronic obstructive pulmonary disease (COPD) patients. This increase of the airway resistance leads to a more intensive particle deposition (Kim & Kang, 1997; Segal, Martonen, Kim, & Shearer, 2002). Moreover, there might be cases (e.g. excessive local mucus accumulation) when aerosol deposition increases significantly with only a small increase in flow resistance (Brown & Benett, 2004; Kim & Eldridge, 1985). Computations regarding micron-size aerosol deposition in a wholelung model of asthma performed by Martonen, Fleming, Schroeter, Conway, and Hwang (2003) revealed that asthma also increases the particle filtering efficiency. The same conclusion was drawn by Chalupa, Morrow, Oberdorster, Utell, and Frampton (2004), who measured the ultrafine particle deposition efficiency in case of asthma patients. However, there are several ethical and technical difficulties related to in vivo experiments. In contrast, numerical simulations are non-invasive, cost effective and repeatable. Accurate computer simulations can reveal the effect of each morphometric and breathing parameter on the airway deposition of particles with any size distribution. However, relatively few efforts related to CFD based airflow and particle deposition modelling in the diseased lung can be found in the published literature. Musante and Martonen (2001) have investigated the effects of both sidewall and carinal tumours on the bifurcation airflow. Zhang, Kleinstreuer, Kim, and Hickey (2002) and Kleinstreuer and Zhang (2003) studied the airflow and deposition of micron-size particles in a triple lung bifurcation affected by sidewall tumours. The respiratory flow in the airways with local constrictions was studied recently by Yang, Liu, and Lou (2006). Consequences of uniform constrictions were also reported by Longest, Vinchurkar, and Martonen (2006), who analysed the flow characteristics and deposition of 1–7 m inhaled particles. As can be seen, these papers are restricted either to the modelling of the airflow in the diseased airways or to the simulation of particle deposition in case of a single type of disease and a restricted range of aerosol particle sizes. The authors of this work propose to study the effects of all characteristic types of morphological changes on both airflow and local aerosol deposition for a large range of respirable particle sizes. In this work, the effects of tumours, airway narrowing and occlusion on the airflow and particle transport and deposition was studied in the third–fifth generations of the human adult tracheobronchial tree (if trachea is regarded as generation zero). To thoroughly investigate the effect of airway disorders on the airflow and aerosol deposition only one flow rate was selected herein (18 l/min at the level of trachea). Particle deposition efficiencies and deposition fractions were calculated for a large range of particle sizes (aerodynamic diameter: 1 nm–30 m). Airflow and particle deposition results were compared to the corresponding data of healthy lung.

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2. Methods The proposed study required the construction of different airway geometries, the setup of the numerical model for the flow field and particle deposition computations and the development of some post-processing tools. The studied healthy airway geometry consisted in a symmetric “in plane” double bifurcation with morphometric data characteristic of the third–fifth airway generations in Weibel’s symmetric lung model (Weibel, 1963). The “in plane” configuration means that the second bifurcation units have the same symmetry plane as the first one. The addition of more, higher generation branches would enhance the accuracy of the computations. However, there are a few advantages of using a double bifurcation as well. One of them is the running time. Triple bifurcations require more cells, which would imply longer runtimes. In case of healthy airways, based on symmetry arguments, only a half of the geometry needs to be modelled. However, diseased airways are not always symmetric (see the cases of lateral tumour or blocked airways), thus a higher number of cells are needed. Another advantage is related to model validation. The three-generation symmetric model has been the subject of both velocity profile measurements (Raick, Ramuzat, Corieri, & Riethmuller, 2003) and particle deposition experiments (Kim & Fisher, 1999; Oldham, Phalen, & Heistracher, 2000). However, to our knowledge there is no experimental data available for the four-generation airways in the open literature. Nevertheless, the authors of this study are aware of the fact that the use of double bifurcations may induce some errors and plan to extend the geometrical model in the future, by the addition of the sixth generation branches. The geometry of healthy airways was then modified by the application of tumours, constrictions and occlusions, which are illustrated in Figs. 1 and 2. For this purpose the GAMBIT (Gambit User’s Guide, 2001) and UNIGRAPHICS (Samuel, 2003) computer design and pre-processing tools were used, taking into account the exact mathematical description of the so-called morphologically realistic bifurcation (MRB) model of Heged˝us, Balásházy, and Farkas (2004). In this study, changes in the airflow field and deposition patterns in the presence of sidewall and central tumours were analysed. The tumorous geometries were created by Boolean extraction of 2, 4 and 6 mm diameter spheres from the healthy airways. The resulted geometries are presented in Fig. 1, middle and bottom panels. Both planar and three-dimensional images are presented, with the sidewall (middle panel) and carinal (lower panel) tumours magnified. The two-dimensional representations depict the geometry in the main plane. As can be seen, sidewall tumours were hemispheres applied on the inner side of one of the fourth-generation tubes. The airway–tumour transitions were smoothed in order to avoid the morphologically unrealistic sharp edges. In case of carinal tumours the centre of the sphere was the peak of the carina, thus the tumour site was a surface larger than the surface of the corresponding hemisphere. Airway narrowing was modelled by decreasing the airway diameters linearly from the central part of the first bifurcation downstream to the end of the daughter branches of the second bifurcations so as to reduce them to the half of their normal diameter. Fig. 2 (upper panel) illustrates the two- and three-dimensional views of this constricted airway geometry. The cut plane is again the symmetry plane of the geometry. When including tumours (Fig. 1) only one side of the tree was considered, but for airway constriction both sides (all airways of the fifth generation) were shrunk (see Fig. 2). The explanation for this apparent discrepancy is that studying hundreds of pictures with tumorous bronchial airways (Strausz et al., 1996) we could not find any case when both daughter airways of the same bifurcation were affected by tumours. We had drawn the conclusion that such cases (if they exist) must be very rare. Thus we have not considered this scenario in our investigations. In contrast, both daughter airways of the same bifurcation can be constricted. This often happens during an asthma attack for example. Occluded airways were created by simply closing one or two branches (Fig. 2, middle and lower panels). Four scenarios were considered here, namely when one of the fourth-generation branches is blocked, one of the fifthgeneration lateral branches is occluded, one of the fifth-generation medial branches is blocked and when both lateral and medial fifth-generation branches on the same side are closed. The applied numerical method required the space discretisation of the presented geometries by meshing. The finite volume method incorporated in FLUENT does not require a certain type of cell. However, unstructured meshes are more flexible and the meshing process can be highly automated. While bifurcation geometries can be meshed relatively fast with tetrahedral cells, their meshing with hexahedral cells requires the decomposition of the geometry into subdomains, which is time consuming. Beyond the meshing time, important issues when deciding what kind of mesh to use are the accuracy and convergence. Numerical diffusion can be reduced by aligning the cells with the flow direction. This can be easily done with hexahedral cells in case of laminar parabolic flow in a straight tube. However,

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Fig. 1. Healthy and tumorous model airway geometries, generations third–fifth in the Weibel model (Weibel, 1963). Upper panel, left: three-dimensional healthy airways; upper panel, right: main plane of the geometry of healthy airways; middle panel, left: three-dimensional airway geometry with the sidewall tumour magnified; middle panel, right: symmetry plane of the tumorous airways with a sidewall tumour. Dtum denotes the tumour diameter; lower panel, left: three-dimensional representation of a tumorous airway geometry with the magnified tumour, affecting the carinal region of the first bifurcation; lower panel, right: symmetry plane of the tumorous airways with a central tumour. Dtum denotes the tumour diameter.

it is rather difficult to define a prevailing flow direction in complicated flows and geometries (e.g. flow in the central zone of lung bifurcations). To overcome the increased level of numerical diffusion related to the use of tetrahedral cells, mesh refinement based on flow parameters can also be performed. Longest and Vinchurkar (2007) have shown that a flow adapted tetrahedral mesh results in a reasonable grid convergence as well. Thus, in this study tetrahedral cells were employed and an unstructured computational grid consisting in about two million computational cells was generated. The grid was adapted based on velocity gradients. In addition, the numerical mesh was refined around the bifurcation points by a size function technique, incorporated in GAMBIT code (part of FLUENT programme package). Our validation results revealed that the mesh style chosen by us is appropriate for the modelling of airflow and particle deposition in the proposed healthy and diseased airways. Air and particle transport within the discretised computational domain was described by the application of a finite volume Navier–Stokes solver. An Euler–Lagrange method was applied, which involved the computation of individual particle trajectories in the carrying air, treated as a continuum.

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Fig. 2. Constricted and blocked bronchial airways. Upper panel, left: three-dimensional narrowed airways; upper panel, right: main plane of the geometry of constricted airways. The dashed lines mark the contours of a healthy geometry; middle panel, left: symmetry plane of the blocked airways with the blockage at one of the fourth-generation branches; middle panel, right: symmetry plane of the blocked airways with the blockage at one of the fifth-generation lateral branches; lower panel, left: symmetry plane of the blocked airways with the blockage at one of the fifth-generation medial branches; lower panel, right: symmetry plane of the blocked airways with both the lateral and medial fifth-generation branches on the same side closed.

In general, the flow field in airways can be laminar, transitional or turbulent depending upon the inlet flow rate and airway geometry (Dekker, 1961; Finlay, Stapleton, & Yokota, 1996; Katz & Martonen, 1999). While earlier studies were restricted to laminar flow modelling, a number of studies dealing with numerical simulation of turbulence in the airways appeared last years. LES (Jin et al., 2007; Luo et al., 2004), k– (Matida, Finlay, Lange, & Grgic, 2004; Moskal & Gradon, 2002; Stapleton, Guentsch, Hoskinson, & Finlay, 2000), standard k– (Longest & Vinchurkar, 2007) and LRN k– (Farkas, Balásházy, & Sz˝ocs, 2006; Zhang, Kleinstreuer, & Kim, 2002) turbulence models have been applied

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to resolve the flow in the highly complex geometry of the airways. Because of the respiratory disease, patients may not perform durable heavy physical exercise. Hence our computations were carried out for a relatively low flow rate (18 l/min at the level of trachea) corresponding to sedentary breathing (ICRP66, 1994). This flow rate corresponds to an inlet Reynolds number of 585. Thus, in this study the flow was assumed to be steady and laminar. The isothermal and incompressible Navier–Stokes and continuity equations were solved by the finite volume scheme of FLUENT CFD code (Fluent User’s Guide, 2001). The inlet air velocity profiles were parabolic and a no-slip condition was set at the walls. This condition assumes that the air velocity at the wall is equal to the wall velocity. Since the wall was non-moving, the air velocity was set to zero at the wall. Choosing of the outlet boundary conditions is one of the most critical steps of the modelling of air and particle transport within the airways. Actually, there are two plausible possibilities: (i) pressure conditions, where the pressure at each outlet is specified or (ii) outflow conditions, where the flow rates must be specified at the outlets. In the published literature, there are plenty of examples for both methods. Pressure outlet conditions were used among others by Oldham et al. (2000), Comer, Kleinstreuer, and Zhang (2001a), Zhang, Kleinstreuer, and Kim (2002), Liu et al. (2003), Luo et al. (2004), Cebral and Summers (2004) and Yang et al. (2006). The outflow condition was imposed for instance by Calay et al. (2002), Moskal and Gradon (2002), Nowak et al. (2003), van Ertbruggen et al. (2005) and Longest et al. (2006). The difficulty of choosing the appropriate outlet boundary condition comes from the fact that usually neither the exact pressure nor the realistic flow rate weighting is a priori known. Thus, most of the authors assume either uniform pressure or equally distributed flow rate boundary conditions at the flow outlets. Horsfield, Dart, Olson, Filley, and Cumming (1971) have published the branch specific flow rates for a given tracheobronchial tree. Those flow rate values were derived from measured anatomical data, admitting that the different regions of the lung are equally ventilated. van Ertbruggen et al. (2005) have reconstructed the same geometry and have used Horsfield’s flow rate distribution in their CFD computations. However, Horsfield’s data set cannot be used here from multiple reasons: (i) there are several third–fifth generation bifurcations in a tracheobronchial tree; (ii) in contrast to the Horsfield’s realistic airways the present airway segment is an idealised, symmetric system. In this study uniform pressure condition with zero gauge (relative) pressure at the outlets has been used. This boundary condition could induce significant errors in asymmetric systems, but in a symmetric geometry is a still reasonable condition. To see the effect of boundary conditions we have repeated our deposition efficiency computations assuming outlets with equally weighted airflow for the healthy lung case. There were no significant differences between the two boundary conditions in terms of deposition efficiency, although the deposition efficiency values for large particles were slightly higher assuming outflow boundary conditions than their values at uniform pressure condition. For ultrafine particles the tendency was opposite. However, the differences were not significant and could not affect the outcomes of this study. In this manner, inspiratory air velocity values, characteristic of each computational cell were computed. Starting from the calculated air velocities and velocity gradients, tracking of unit density monodisperse spherical particles has been performed by numerical integration of the force balance equation (Newton’s second law). The deposition mechanisms considered here were inertial impaction, gravitational settling and the Brownian diffusion. Interception could be neglected because the particle diameters were much smaller than the airway diameters. Diffusion was considered by adding a new, random force. Its values were selected from a Gaussian distribution, using the random number generator included in the FLUENT code. Other forces were discounted using order of magnitude arguments. The particle material is much denser than the air, thus, the buoyancy force, the virtual mass effect and the pressure force are very small. Some examinations led to the conclusion that the Saffman lift force (Saffman, 1965) can also be neglected. Inlet locations of the injected particles were selected from a distribution function based on the inlet air velocity profile. For this purpose a Monte Carlo selection–rejection technique was implemented. Initial velocities of the injected particles were equal to the air velocity characteristic of that location. Since a viscous mucus layer protects the bronchial airways, trapping walls were assumed, which resulted in instant deposition of the particles impacting the wall. The exact locations of particle incidences were stored for further processing. Hereon, we use the term deposition efficiency as the ratio of the number of particles deposited in a given airway segment to the number of particles entering the same segment. Similarly, we assume that the deposition fraction is the ratio of the number of particles deposited in a given airway segment to the number of particles entering the computational domain. In this work, we present the deposition efficiency for the whole computational domain and the deposition fractions either for individual bifurcations or for the tumour site. The related airway segments will be specified when deposition efficiency or deposition fraction results are presented or discussed.

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30

Deposition effciency (%)

Experiment (Kim & Fisher 1999) Simulation (Comer et al 2001)

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Deposition effciency (%)

35 30 25 20 25 10 5 0 1

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Particle diameter (nm) Fig. 3. Comparison of the computed deposition efficiency values with experimental and simulated data from the open literature. All deposition efficiency data refer to double bifurcation healthy airways. Upper panel: micro-particles; lower panel: nano-particles.

The numerical model was validated by the comparison of our computed flow profiles and deposition efficiencies with several measured and simulated data. Our axial velocity profiles compared well with the measured profiles of Schroter and Sudlow (1969) and Zhao and Lieber (1994), as well as with the simulated profiles of Liu, So, and Zhang (2002) and Comer et al. (2001a). Regarding particle deposition, we present a comparison of our micro-particle deposition efficiency results with similar data measured by Kim and Fisher (1999) and simulated by Comer, Kleinstreuer, and Zhang (2001b) in sequential double bifurcation tube models and a comparison of our nano-particle deposition results with those measured by Smith, Cheng, and Yeh (2001). The deposition efficiencies in Fig. 3 refer to the whole double bifurcation healthy lung geometry. As Fig. 3 demonstrates, present results are in line with the experimental data. The good agreement indicates that our model is basically appropriate for the characterisation of particle transport and deposition within the large central airways. 3. Results and discussions The discussion below is separated into two different sections. The first is on the airflow field characterisation by the study of flow partitioning, velocity isolines, velocity vectors and wall shear stresses. The second is on the

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Qout3 Qout4 Qout2 W1

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W2 W3

Qout1 Flow rate weighting

0.4

W4

Qin

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blocked at out1 and out 2

blocked at out2

blocked at out1

bilateral constriction

central tumour Dtum = 4 mm

sidewall tumour Dtum = 6 mm

sidewall tumour Dtum = 4 mm

sidewall tumour Dtum = 2 mm

healthy

0.1

Fig. 4. Splitting of the inspiratory airflow at the outlets of healthy and diseased airways. Qin (=2.25 l/ min) is the inlet flow rate, Qout1 , Qout2 , Qout3 , and Qout4 represent the outlet flow rates and W1 , W2 , W3 and W4 denote the flow rate weightings. Dtum is the symbol for tumour diameter.

computation of particle deposition patterns, deposition efficiencies and deposition fractions in the healthy and diseased airways. 3.1. Airflow fields The human lung is a complex air transporting system in which the energy losses caused by viscous dissipations are optimised. However, the presence of diseases may change the airway resistance, altering the breathing process. The resistance of an airway segment is related to the pressure drop and flow rate (Pedley, Schroter, & Sudlow, 1970). The rhythmically expanding–contracting alveoli overcome the pressure drops due to the viscous and other losses. In practice, it is quite difficult to measure pressure distribution in lung bifurcations. In contrast, CFD can be a powerful tool when determining pressure or pressure drop values (Comer et al., 2001b). However, this study is restricted to the computation of flow rate weightings in the different branches of healthy and diseased lungs. In addition, some important features of the airflow fields in diseased lungs are presented and compared to the healthy cases. For this purpose, numerical techniques presented in Section 2 were applied. 3.1.1. Flow splitting A parabolic velocity inlet profile in our symmetrical healthy airway model leads to equal flow rates in the fourthgeneration branches. However, an imbalance in flow partitioning due to the skewed axial velocity in fourth-generation airways can be observed at the level of fifth-generation branches. As a result, in medial branches flows more air than in lateral daughters. The presence of airway disorders can induce further imbalances. Fig. 4 compares the computed flow

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rate weightings (Wi ) in the case of the analysed diseased and healthy airways in the fifth-generation branches. All flow rates were scaled to the inlet flow rate, which was identical for all the studied geometries. The flow rate in the bronchi is defined as Wi =

Qouti , Qin

where Qin is the inlet flow rate and Qouti is the flow rate in the ith outlet. The results demonstrate significant flow redistributions in case of sidewall tumours. The flow rates in the branches down to the tumour decrease (especially in the medial branch) with the increase of tumour diameter. In case of central tumours and bilateral narrowing, the flow is still symmetrically distributed, but the ratio of median to the lateral flow rates is smaller when compared to the case of healthy airways. In case of bilateral airway constriction the flow was almost equally distributed in the four branches. The flow rate in a completely blocked branch is obviously zero. In the studied case the flow proved to be weighted almost equally in the three non-occluded fifth-generation ducts when one of the lateral branches (out1) was blocked. If one of the medial branches (out2) or both the lateral and medial branches (out1 and out2) are blocked, then the flow rate increases in the non-occluded branches in a more accentuated way. 3.1.2. Air velocities and shear stresses In order to see how the presence of different airway disorders can alter the flow, we compared the flow fields of healthy airways with those of affected by disease. The flow fields were characterised by velocity isolines, velocity vectors and wall shear stresses. A qualitative analysis can be performed by comparing the velocity isolines in the symmetry plane of the bifurcations. In this type of graphical representation, each line denotes a constant flow velocity. The increment between adjacent lines is constant, so regions with closely spaced lines are regions of high velocity gradients, whereas regions with widely spaced contour lines represent a relative flat velocity profile. Fig. 5 reveals that in case of sidewall tumour the flow is altered not only on the tumour side but also in the unobstructed airways and even in the first airway generation (third generation of the Weibel model). In Fig. 5 the 4 mm tumour case is presented. A significant difference between the airflow fields of healthy airways and airways with sidewall tumours is that the slow region present at the outer walls of the fourth-generation branches of the healthy airways, immediately after the onset of the central zone, becomes thinner on the unobstructed side and much thinner on the tumorous side of the diseased airways. In addition, a separation zone appears behind the tumour. Since the contours are based on velocity magnitudes, the recirculation induced downstream the tumour cannot be seen in Fig. 5a, but it can be detected from the vector representation in Fig. 5b. Central tumours seem to have smaller effect on the overall flow field, the disturbances being localised within the bifurcation zone (Fig. 5c). It is known (Balásházy, Heistracher, & Hoffmann, 1996) that the shape of central zone of the bifurcations influences the air velocity field and particle deposition patterns. It was experimentally (Pedley, Schroter, & Sudlow, 1971) and numerically (Comer et al., 2001a; Martonen, Yang, & Xue, 1994) demonstrated that the carinal shape strongly influences the secondary motions (Fig. 5e) and related particle deposition. Since the carinal ridge shape is modified by the central tumours, it is worth studying in what extent the flow field will be affected. Our investigations showed that the airflow impacts the tumour, generating strong secondary motions in daughter tubes. The secondary motions are related to the increased shear stresses close to the carina (Cebral & Summers, 2004). Therefore, we analysed the wall shear stresses, which are proportional to the normal derivative of the air velocity at the wall, giving the forces acting tangential to the surface due to friction, measured in pressure units. The shear stress values along the tumour edge in the main plane are presented in Fig. 5f. The figure demonstrates that shear stresses and related secondary motions are sensitive to the tumour size, having maximal values at 45◦ and 135◦ azimuthal orientations (marked with A and B). The secondary motions may strongly influence the deposition of the inhaled aerosols as well (Broday, 2004). However, for the quantification of particle deposition exact numerical analysis is necessary. Such investigations are presented in the next section. Airway narrowing accelerates the air, inducing high velocity values at the outlets. The outlet velocities in the nonoccluded branches are also enhanced in the case of airway blockage shown in Fig. 6 (right panel). Airway blockage produced upstream effects as well. As a result of the blocked fifth-generation lateral branch the velocity gradients became lower at the outer side and higher at the inner side of the fourth-generation upstream branch. To see in what extent the airflow disturbances mentioned above can influence the particle deposition discrete particles were injected

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10 m/s

A

B α

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1.5

1.0

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0.0 0

20

40

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80 100 120 140 160 180

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Fig. 5. Inspiratory velocity isolines, velocity vectors and wall shear stresses in the airway geometries shown in Figs. 1 and 2, assuming 18 l/min tracheal flow rate. (a) Velocity isolines in case of a 4 mm sidewall tumour; (b) velocity vectors in the vicinity of the tumour in the window shown on the left, magnified 8 times and rotated by 35◦ clockwise; (c) velocity isolines in case of a 4 mm central tumour; (d) velocity isolines in healthy airways; (e) secondary velocity vector field near the carinal tumour; (f) wall shear stresses along a central tumour as a function of the azimuthal angle (, presented on the left) from three different tumour sizes at 18 l/min inspiratory tracheal flow rate. Dtum denotes the tumour diameter.

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Fig. 6. Left panel: velocity isolines in case of narrowed airways; right panel: velocity isolines in case of bronchial airways with one of the fifth-generation lateral airways blocked.

Fig. 7. Segmentation of the airways studied in this work. B1, B2 and B3 are the three airway bifurcation units and G3, G4,1, G4,2, G5,1, G5,2, G5,3 and G5,4 denote the individual airways, where the first number is the generation number, the second one is the serial number within a generation.

and tracked in the analysed healthy and diseased airways by implementing the techniques presented in Section 2. The outcomes of these simulations are presented below. 3.2. Particle deposition results In this section, we shall analyse the effect of intraluminar tumours, airway narrowing and airway blockage on the aerosol deposition distribution. For the sake of clarity, the segmentation of the studied airways is presented in Fig. 7. 3.2.1. Healthy versus tumorous airways Tumours affect either the carinal zone of the bifurcations or the tubular part of the airways. According to our investigations these two types of tumours affect the local particle deposition in a very different way. Sidewall tumours decreased the deposition efficiency of nano-particles and increased the deposition efficiency of large, micron-size particles. For example, in case of a 6 mm sidewall tumour the deposition efficiency of 1 nm particles decreased by a factor of 5 compared to the deposition of the same particles in healthy airways. The same tumour increased the deposition efficiency of 10 m aerodynamic diameter particles by a factor of 1.6. The less intensive deposition of very small particles in the tumorous airways can be attributed to the variations of branch air/particle flow rates. At the same time the deposition by impaction of large particles increases and high particle accumulations appear, especially before the indentation of the tumour. The dependence of the deposition efficiency on the particle size for the studied whole size-range is plotted in Fig. 8, upper panel. From the health effects point of view local particle accumulations can be more important than the overall deposition efficiency. Thus, deposition fractions on the tumour surface were computed for the three studied tumour sizes. It is somewhat puzzling at first glance that according to Fig. 8, middle panel the deposition fraction of both nano- and micro-particles is increasing when the tumour diameter changes from 2 to 4 mm, but it decreases with further increase of the tumour size. The same deposition fraction as a function of tumour diameter is plotted in the bottom panel of Fig. 8 for three characteristic particle sizes. As the figure reveals, the phenomenon presented above is more accentuated for large particles. The explanation for this interesting behaviour is the existence of two competing effects: the increase of the number of particles depositing on the tumour with the increase of tumour diameter and the decrease of the number of

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30 Dtum = 6 mm Dtum = 4 mm Dtum = 2 mm healthy

Deposition fraction (%)

25 20 15 10 5 0 1E-3

0.01

0.1

1

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Particle diameter (μm) 7

Deposition fraction (%)

6 Dtum = 6 mm Dtum = 4 mm Dtum = 2 mm

5 4 3 2 1 0 1E-3

0.01

0.1

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Particle diameter (μm) 6 dp = 10 μm dp = 0.01 μm dp = 0.001 μm

Deposition fraction (%)

5 4 3 2 1 0 0

1

2

3

4

5

6

7

Tumour diameter (mm) Fig. 8. Deposition efficiencies and deposition fractions of the inhaled particles in airways affected by sidewall tumours. Upper panel: deposition efficiency computed for the whole geometry; middle panel: deposition fraction on the tumour site for different sidewall tumour sizes as a function of particle diameter; lower panel: deposition fraction on the tumour site for three characteristic particle sizes as a function of tumour size. Dtum and dp denote the tumour and particle diameters, respectively.

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Fig. 9. Deposition efficiencies and deposition fractions of the inhaled particles in central airways affected by carinal tumours. Upper panel: deposition efficiency computed for the whole system of healthy airways and in the presence of 4 and 6 mm central tumours; bottom panel: deposition fraction on the tumour surface. In the lower panel of the figure the healthy lung is missing because it has no tumour, thus the deposition fraction on the tumour site (ratio between the number of particles deposited on the tumour surface to the number of injected particles) is zero. dp denotes the particle diameter.

particles entering the occluded branch with the increase of tumour size. Indeed, the number of nano-particles depositing on the tumour surface due to diffusion should be higher when the tumour surface is larger. Similarly, the impaction driven deposition of large particles should rise with the increase of tumour size. However, this effect can predominate until the tumour reaches a critical size. From this point, due to the fewer and fewer particles entering the tumorous branch fewer particles can deposit on the tumour surface. This observation is in accordance with the conclusions of Zhang, Kleinstreuer, Kim, et al. (2002), who stated that the deposition fraction of micron-size particles increases up to a moment when the tumour blocks about a half of the lumen, then it decreases. In contrast to the sidewall tumours the presence of central ones hardly affects the deposition efficiency of nanoparticles (see Fig. 9). The increase of the tumour surface area allows the deposition of more nano-particles on the tumour site, but at the same time the enhanced air velocity in the branches downstream the tumour results in less particles deposited here by diffusion. As a result of these two effects the changes in the overall deposition efficiency of nano-particles in the presence of tumours are not significant. However, both the overall deposition efficiency and the deposition fraction on the tumour surface of large particles increased significantly when central tumours were present.

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Deposition efficiency (%)

100

constricted healthy 10

1

1E-3

0.01

0.1

1

10

Particle diameter (μm) Fig. 10. Comparison of deposition efficiencies computed for the whole geometry of healthy and constricted airways as a function of aerosol diameter.

For instance, the deposition efficiency of 10 m particles increased by a factor of 1.9 and 3.4 at the presence of 4 and 6 mm central tumours, respectively. The fraction of nano-particles deposited on the tumour surface was small in comparison with the number of nano-particles deposited in the whole geometry. As Fig. 9 demonstrates, an opposite behaviour can be observed in case of 10 m particles where the number of particles deposited on the tumour site is much higher than the number of particles deposited elsewhere, the most exposed area being the centre of the tumour. 3.2.2. Healthy versus constricted airways In order to study the effect of asthma or COPD induced broncho-constrictions on aerosol deposition we simulated the particle deposition patterns in symmetrically narrowed airways. The aerosol deposition efficiency in such airways proved to be quite different from the deposition efficiency in healthy airways. The comparison between the healthy and constricted deposition efficiencies calculated for the entire healthy and constricted geometries is shown in Fig. 10. As the figure demonstrates, the relative difference between the deposition efficiency in constricted and in healthy airways is the highest in case of micron-size particles reaching a value of 7.4 in case of 7 m particles. In terms of bifurcation specific deposition fractions the differences are even higher. This is demonstrated in Fig. 11, where deposition patterns of 3 m particles in case of healthy and narrowed airways are presented. Beside the deposition efficiency values computed for the whole geometries, the bifurcation specific deposition fractions were also compared. It can be seen that in bifurcations B1 and B2 these DF (deposition fraction in one bifurcation) values increased by a factor of 14 compared to the values in healthy airways. These results are in good agreement with those observed by Sbirlea-Apiou et al. (2004) and Longest et al. (2006). The outcome of this investigation, that is, the filtering of environmental pollutants and other hazardous materials can be up to one order of magnitude more efficient in the presence of broncho-constrictions, indicates an increased health risk associated with the inhalation of particulate matter in cases of asthma, bronchitis or COPD in general. Although only the laminar case and a single flow rate was considered, present results might help in the understanding of the complex therapeutic aerosol dynamics in the lung with local obstructions and provide useful quantitative information in the field of the optimisation of aerosolised drug administration. Further studies are necessary to investigate how the present results would change if subject activity induced turbulence will be apparent. Longest et al. (2006) have studied the deposition of micro-particles at different activity levels in constricted airways using laminar and LRN turbulence models. They stated that the filtering efficiency of the narrowed airways is significantly higher than the filtering efficiency of the corresponding healthy airways regardless the flow rate. Our results obtained for sedentary breathing are in line with the similar results from the mentioned paper. It is expected that the general trends presented in this study would not change at higher flow rates, at least in case of micro-particles. However, additional

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healthy DE = 0.67 %

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constricted DE = 3.18 % DF1 = 0.36 %

DF1 = 0.33 %

DF3 =1.4 %

DF3 = 0.1 % DF2 = 0.1 % DF2 = 1.4 %

dp = 3 μm

dp = 3 μm

Fig. 11. Overall deposition efficiencies and deposition fractions of 3 m particles in bifurcations B1, B2 and B3 in a healthy (left panel) and in a narrowed (right panel) system. DE denotes the deposition efficiency for the entire geometry and DF1, DF2 and DF3 are the deposition fractions for bifurcations B1, B2 and B3, respectively.

investigations are needed to clarify the effect of flow rate rise on the deposition of nano-particles in the constricted airways. Further efforts in this direction are in progress. 3.2.3. Healthy versus blocked airways In general, aerosol deposition is highly influenced by the airway geometry. In order to study the effect of airway blockage on the particle deposition we computed the deposition fractions in three individual bifurcations (B1, B2 and B3, see Fig. 12) in case of four specific occlusions, namely when one of the fourth-generation airways (G4,1) is blocked, one of the lateral branches of the fifth-generation airways (G5,1) is blocked, one of the medial branches of the fifth-generation airways is blocked (G5,2), and when the lateral (G5,1) and the medial (G5,2) fifth-generation ducts are simultaneously blocked. Fig. 12 presents a comparison of deposition fraction values computed for blocked and healthy airways in the three individual bifurcations. The deposition of aerosols in the first bifurcation (B1) does not seem to be affected by airway blockage, except when branch G4,1 is blocked. In this case, the deposition fractions are slightly lower. However, the deposition fractions in bifurcations B2 and B3 are strongly influenced by the occlusions. The deposition fraction in B2 is obviously zero when G4,1 is blocked. However, when both G5,1 and G5,2 are blocked some very small particles can enter B2 and deposit there due to Brownian diffusion. For example, the deposition fraction for 1 nm particles in B2 is not zero but 0.07%. If only one of the branches (G5,1 or G5,2) is blocked, the deposition fraction decreases in bifurcation B2 and it is enhanced in bifurcation B3. The reason for this behaviour can be the flow distribution. For example, when branch G5,1 is blocked only one third of the air volume entering bifurcation B1 flows into bifurcation B2 (see Fig. 4). As a consequence the number of particles entering bifurcation B3 and the number of particles depositing there is also higher. At the same time the deposition fraction values observed in bifurcation B2 are systematically lower. An interesting feature of the deposition fraction curves, including the one characteristic of the healthy airways, shown in middle and lower panels of Fig. 12 is that the curves have a peak regularly between 10 and 20 m, then strongly decline at higher particle sizes. The explanation for this shape is the very intensive filtering of large particles by bifurcation B1, which do not reach B2 and B3, thus do not deposit there. In conclusion, the numerical particle transport and deposition simulations proved that airway blockages may cause significant redistributions of the deposition sites. Although the applied computational method allows the characterisation of air and particle transport and deposition basically at a local level, starting from present results some regional and whole-lung effects can also be predicted. As Figs. 8 and 9 demonstrate, the effect of tumours on particle deposition depends on the tumour size and particle size. If a sidewall tumour is small, the deposition of nano-particles hardly changes when compared to their deposition in the healthy airways. However, with the increase of the tumour size the number of particles entering the deeper regions of

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Fig. 12. Deposition fractions computed in bifurcations B1 (upper panel), B2 (middle panel) and B3 (lower panel) versus particle aerodynamic diameter in case of healthy and occluded airways.

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the lung is decreasing downstream the tumour (down to zero, when the lumen is totally blocked) and increasing on the other side. In addition, on the non-tumorous side the air velocities are higher and the air transports the nano-particles deeper in the lung. At a global scale the effect of a central tumour is similar to the effect of a sidewall tumour. According to Fig. 9 the deposition efficiency of nano-particles in the modelled geometry does not change significantly with the increase of the tumour size. However, at a larger scale the upstream effects manifest as well. Because the tumour blocks a part of the lumen the airflow rate will be lower here than in a healthy system. Thus, less nano-particle enters and deposit in the diseased airway segment and downstream. At the same time, in other branches more nano-particles are transported by faster airstreams. Both sidewall and central tumours increased the deposition efficiency of large particles. The same increase could be observed in case of bilateral constriction. This finding is in agreement with earlier simulation results (Longest et al., 2006) and in vivo observations (Kim & Kang, 1997). At the same time, due to the high impactional deposition on the tumour surface or narrowed branches, less micro-particle will penetrate in the deeper airways downstream the tumour or narrowing. It seems that the different types of pathological changes considered in this work have different local effects but induce very similar global changes in air and particle transport, because in the latter case the degree of airway lumen reduction and not its shape is essential. Thus, while studying the cellular effects of the inhaled PM the CFD models, like the one applied in this work, are the most appropriate tool, exact regional deposition data can be obtained only by applying whole-lung models (Segal et al., 2002).

4. Conclusions This study demonstrated that computational fluid and particle dynamics (CFPD) methods can be a powerful tool for the characterisation of airflow and quantification of aerosol deposition in the airways with pathological changes. Using a finite volume based CFPD model the effects of tumours, airway narrowing and occlusion on the airstreams and particle deposition distributions have been investigated. Our numerical simulations revealed that the airflow and particle deposition patterns may be significantly changed by airway disorders. Regarding air flow distribution among the branches of the diseased airways it has been shown that sidewall tumours cause significant flow redistribution, decreasing the flow rate in the downstream branches on the tumour side and increasing it in the downstream branches on the opposite side. The bigger the sidewall tumour is the more this tendency is manifested. However, central tumours hardly affect the airflow weightings. Bilateral airway narrowing decreased the flow rate in the fifth-generation medial branches and increased it in the lateral branches. Occlusions have lead to enhanced flow rates in the non-occluded branches. Based on our aerosol transport and deposition modelling results sidewall tumours lead to an enhanced deposition of large particles and cause lower deposition efficiency values of nano-particles compared to the deposition efficiency in healthy airways. A sidewall tumour having a diameter of 6 mm decreased the nano-particle deposition efficiency by a factor of 5 and increased the deposition efficiency of large particles by a factor with a maximum value of 2. In addition, deposition increased at the tumour site until the tumour occupied about half of the airway lumen and then decreased with the further increase of the tumour. Central tumours hardly affected the deposition efficiency of nano-particles but enhanced the deposition efficiency of large particles. The deposition fraction on the tumour was again particle size dependent and increased with the increase of the size of the tumour. When one or two daughter branches of the second bifurcation were blocked the deposition fractions decreased in the blocked bifurcation and increased in the non-blocked second bifurcation. The extent of these changes was very sensitive to the particle size. The deposition efficiency of the inhaled aerosols in constricted airways was much higher than the deposition efficiency in the normal lung, their relative difference reaching 7.4 for particles with 7 m aerodynamic diameter. Beside the scientific values, the findings of this study may have practical importance, as well. Current results might help to understand the adverse health effects of the inhaled air-pollutants in patients with lung disease. For example, in case of inhalation of toxic or radioactive aerosols, changes in local deposition patterns due to the studied diseases may have significant health consequences, having altered the burden at cellular level (Farkas, Hofmann, Balásházy, ˝ 2007). Since the aerosol therapy is a potential alternative to treat lung diseases and even other disorders by & Szoke, delivering the medication to the systemic circulation via the lung, current model could also be applied in the field of aerosol drug delivery optimisation (Farkas et al., 2006). The present results might be integrated into future aerosol therapy protocols.

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