Simulation of Fiber Deposition in Bronchial Airways

Inhalation Toxicology, 17:717–727, 2005Copyright c© Taylor and Francis Inc.ISSN: 0895-8378 print / 1091-7691 onlineDOI: 10.1080/08958370500224565

Simulation of Fiber Deposition in Bronchial Airways

Imre BalashazyHealth and Environmental Physics Department, KFKI Atomic Energy Research Institute, Budapest,Hungary, and Respirisk Co., Budapest, Hungary

Mona MoustafaPhysics Department, Faculty of Science, El-Minia University, El-Minia, Egypt, and Division of Physicsand Biophysics, Department of Molecular Biology, University of Salzburg, Salzburg, Austria

Werner HofmannDivision of Physics and Biophysics, Department of Molecular Biology, University of Salzburg,Salzburg, Austria

Reka SzokeMaterials Department, KFKI Atomic Energy Research Institute, Budapest, Hungary

Amer El-Hussein and Abdel-Rahman AhmedPhysics Department, Faculty of Science, El-Minia University, El-Minia, Egypt

Penetration probabilities of inhaled man-made mineral fibers to reach central human airwayswere computed by a stochastic lung deposition model for different flow rates and equivalentdiameters. Results indicate that even thick and long fibers can penetrate into the central airwaysat low flow rates. Deposition efficiencies and localized deposition patterns were then computedfor man-made fibers with variable lengths in a three-dimensional physiologically realistic bifur-cation model of the central human airways by computational fluid dynamics (CFD) techniquesfor characteristic breathing patterns. The results obtained for inspiratory flow conditions in-dicate that deposition efficiencies were highest for parallel orientation of the fibers, increasingwith rising flow rate, branching angle, and fiber length at all orientations. Furthermore, depo-sition patterns were highly inhomogeneous and their localized distributions showed hot spotsin the vicinity of the carinal ridge and at the inner sides of the daughter airways. Comparisonswith other theoretical results demonstrate that the equivalent diameter concept, if includinginterception, presents a reasonable approximation for the parameter ranges employed in thepresent study.

Upon inhalation of ambient aerosols, initial deposition of in-haled particles in the human respiratory tract may have a signif-icant role in the development of lung diseases if the particles arenot sufficiently removed from the lung. In addition, the initial de-

Received 17 March 2005; accepted 26 May 2005.This research was supported by the Austrian-Egyptian Channel

System, the Hungarian NKFP-1/B-047/2004 and NKFP-3/A-089/2004projects, the Hungarian-EU GVOP-3.1.1-2004-05-0432/3.0 project,and the bilateral Hungarian-Austrian TeT A-03/02 project.

Address correspondence to Imre Balashazy, Health and Environ-mental Physics Department, KFKI Atomic Energy Research Insti-tute, PO Box 49, H-1525 Budapest, Hungary. E-mail: [email protected]

position characterizes the burden without clearance. Comparedto spherical particles, inhaled fibrous particles may cause addi-tional adverse health effects because of their specific shape, thusacting as so-called physical carcinogens. They may either piercethe lung tissue if deposited, or they may penetrate quite deeplyinto the airway system if aligned to the air streamlines. The localdistribution of deposited particles in the lungs depends on thegeometric dimensions of the airways, on the complex flow fieldwithin the respiratory system, and on the size and shape of par-ticles. Fibers may reach a preferred orientation when travelingin the airways and may become independent of initial orienta-tion (Timbrell, 1965; Harris & Fraser, 1976; Harris & Timbrell,1977). Fibrous particles may align with the streamlines or followa tumbling movement.

717

718 I. BALASHAZY ET AL.

Inhalation of asbestos fibers, especially crocidolite, mayinduce DNA damage, bronchial remodeling, and malignantbronchial epithelial proliferations (Marczynski et al., 1994; Vosset al., 2000). Asbestos substitutes, such as glass and otherman-made mineral fibers (MMMFs), are much less carcino-genic than the natural mineral fibers, primarily because of theirgreater diameters and hence correspondingly smaller inhala-bility. Based on our measurements, about 80% of glass fibershave about 3 µm diameter and about 20% have larger diameters(Szoke et al., 2004). The applied measurement techniques aredetailed, for example, in Szymanski et al. (2002), Nagy et al.(2001a, 2001b), Alfoldy et al. (1999), and Czitrovszky et al.(1999).

Although MMMFs were developed as substitutes for asbestosfibers, several publications indicate that glass fibers may inducelung lesions comparable to asbestos and should be consideredto be carcinogenic for humans. For example, the InternationalAgency for Research on Cancer (1988) stated that “at least 13studies demonstrate biologically plausible and statistically sig-nificant increases in the incidence of lung cancer and mesothe-lioma in rats and hamsters exposed to glasswool” (p. 232). Inaddition, epidemiological studies in Canada, the United States,and Europe allow the conclusion that glass wool fibers play arole in causing an excess of lung cancer risk observed amongthose employees (e.g., Shannon et al., 1987).

The deposition pattern of aerosol particles within the airwaysystem is strongly inhomogeneous and so-called hot spots canbe found within the bifurcations of the large conducting airways(Gradon & Orlicki, 1990; L. Zhang et al., 1996; Z. Zhang et al.,2002). These concentrated deposits are mainly located in thevicinity of the carinal ridges of the airway branchings (Ahmedet al., 1997), consistent with the sites of preferential tumor occur-rences (Schlesinger & Lippmann, 1978). Similar hot spots werealso found for fiber deposition in casts of the human tracheo-bronchial tree (Sussman et al., 1991) and in a model of bifurcat-ing tubes (Myojo, 1990, 1997; Myojo & Takaya, 2001). Suchconcentrated local deposition enhancements can be attributedto the physical mechanisms governing fiber transport and de-position in the lungs. Asgharian and Anjilvel (1995) derivedequations of motion for fiber transport in arbitrary flow fields.

The fundamental physical mechanisms causing the deposi-tion of approximately spherical particles in the respiratory tractare inertial impaction, gravitational settling (sedimentation), andBrownian motion (diffusion). The elongated geometric shapesof fibers result in the introduction of another effective deposi-tion mechanism, termed interception. Deposition by interceptionoccurs when a particle contacts and is then retained by the sur-rounding surface of an airway, even though the center of massof the particle remains on a fluid streamline.

The equivalent diameter concept used in this study maypresent only a crude approximation for single trajectories whenthe inertia of the particle is high and when the shear rate is ap-preciable (Broday et al., 1998), for example, at high flow rates inthe largest airways. However, for the calculation of deposition

patterns of many particles, this simple method together withthe computation of interception may represent an appropriateapproximation.

In the present computations, the fiber was assumed to be 4 µmin diameter and ranging in length from 4 to 200 µm, which areassumed to be characteristic of the glass and other man-madefiber deposits in the central airways. They have relatively highdeposition efficiencies, thereby ensuring proper statistics for theanalysis of individual deposition mechanisms. This diameterwas selected for two reasons: (1) The same diameter was usedin the simulations of the motion of fibers in the central humanairways by computational fluid dynamics (CFD) techniques byZhang et al. (1996), and (2) man-made-mineral fibers are usu-ally polydisperse with a considerable fraction around 4 µm di-ameter, and fibers with this size can penetrate to the centralairways.

Animal experimental studies, either by inhalation or intra-bronchial instillation, indicated that the most important param-eters to determine the toxicity and carcinogenity of fibers arethe local dose, the dimension, and the particle biopersistance(Vanessa & David, 1997; Oberdorster, 2002). The local dose isthe result of the primary deposition and clearance, thus, it is theretained fraction. Biopersistence describes the potential of par-ticles to dissolve or lose elements in the secretions and tissuefluid, either fragmented or mechanically cleared from the lungby tissue movement and macrophages (Ohyama et al., 2001).

The present study consists of two parts. In the first part, pen-etration probabilities were computed by the stochastic lung de-position model for man-made fibrous particles in order to deter-mine the fraction of inhaled particles, which may eventually bedeposited in central airway bifurcations. Penetration probabilityhere means the fraction of inhaled particles that leave the exam-ined section without deposition during inhalation. The inlet ofthese sections is either the entrance of the nose or the mouth. Inthe second part, deposition efficiencies and deposition patternswere simulated by computational fluid dynamics techniques forthose fibers, which could reach the central airway bifurcations.Deposition efficiency means here the deposited fraction of theparticles that enter into the central airway bifurcations analyzedby computational fluid dynamics technique.

By the application of the stochastic lung deposition model itwas possible to analyze the penetration probabilities of differ-ent glass wools or glass wool components into a given depth ofthe respiratory system. This type of analysis can be highly im-portant to estimate the inhalable fraction of a measured polydis-perse fiberglass. The smaller pathogenicity of man-made mineralfibers as compared to asbestos is due to their decreased abilityto produce inhalable dust, as diameters are too high for to reachthe lungs upon inspiration. The carcinogenicity of glass wool isfurther reduced because of its biosolubility.

The applied computational fluid dynamics models character-ize the local inhomogeneity of deposition and the local maximaof deposition densities even in cellular dimensions. These mayhave significance with respect to the health effects that mainly

DEPOSITION OF INHALED FIBERS 719

depend on the local, cellular doses and not on average lung tissuevalues. The results of these computations help us to understandthe pathological finding that most of the bronchial neoplastic le-sions caused by micrometer-size fibers originate in the vicinityof the carina ridges of the airway bifurcations.

METHODS

Stochastic Lung Deposition ModelAn updated version of the stochastic lung deposition model

(Hofmann et al., 1999) was applied to compute the penetra-tion probabilities of fibers up to the end of airway generation 3,where the trachea is airway generation 1, during both nose andmouth breathing at different breathing conditions. The equiva-lent diameter concept has been applied at these computations;that is, the model developed for spherical particles has beenused but the deposition of particles was calculated having sim-ulated the proper equivalent diameters. The interception depo-sition mechanism was not built into the stochastic lung deposi-tion model, only to the computational fluid dynamics model. Asshown later, the role of interception is not significant in the up-per and large central airways at the computed parameter valueseven in airway generations 4–5. In the present calculations, thestochastic lung deposition model is applied only up to airwaygeneration 3.

The philosophy of computing particle transport and depo-sition in a stochastic, asymmetric lung structure has been de-scribed in detail in the initial papers of Koblinger and Hofmann(1990) and Hofmann and Koblinger (1990). Thus, for the sakeof brevity, only those features of the model that are pertinent tothe present calculations are briefly described here.

The Monte Carlo transport and deposition model is basedon a stochastic morphometric model of the human lung, whichdescribes the inherent asymmetry and variability of the humanairway system. This variability of airway diameters, lengths,branching, and gravity angles, constrained by correlation amongsome of these parameters, is described mathematically by proba-bility density and correlation functions (Koblinger & Hofmann,1985). For the simulation of particle transport through thisstochastic lung structure, individual paths of inspired particlesare randomly selected by Monte Carlo methods from these math-ematical functions. That is, the computed geometric parametersin the case of each of the selected particle paths, such as airwaydiameters, lengths, branching angles, and gravity angles of thepath of the particle from airway generation to airway genera-tion, are randomly selected from probability density functionsof these parameters received by the statistical evaluation of theLovelace Foundation data (Raabe et al., 1977).

As a result of this variability, particles reach the central air-ways along different paths with different probabilities. The ran-dom walk, that is, the randomly selected path, of individual in-haled particles upon inspiration and expiration is simulated byMonte Carlo methods. Flow splitting in an airway bifurcationbetween the two asymmetric daughter airways is in the ratio of

the two cross sections of the daughter airways. This assumptionis well related to the peripheral air volume supported by each ofthe two daughter airways in case of the human lung (Koblinger& Hofmann, 1990). Deposition of particles in a given airwaygeneration is computed by analytical equations describing theaverage deposition of many particles in cylindrical airways forinertial and gravitational forces (Koblinger & Hofmann, 1990).Brownian motion of the particles was not taken into considera-tion because the effect of diffusion is negligible at the applied di-mensions of the particles. In the oro- and nasopharyngeal region,particle deposition is computed by empirical equations derivedfrom measurements in human volunteers (Cheng, 2003). Due tothe variability of the airway geometry and related flows, parti-cle deposition may vary along different paths. Thus penetrationprobability to a given airway generation, that is, the probabil-ity of inhaled fibrous particles to reach that airway generation,exhibits significant fluctuations, depending on the individual his-tory of each particle in upstream airways.

Computational Fluid Dynamics ModelExperimental fiber deposition results commonly refer to seg-

mental and subsegmental bronchial airway models (Myojo,1990, 1997; Myojo & Takaya, 2001). Hence the physiologi-cally realistic bifurcation geometry model of Heistracher andHofmann (1995) was applied to simulate airway generations 4–5 (trachea = generation 1). The three-dimensional airflow fieldwithin the bifurcation model was calculated by the FIRE compu-tational fluid dynamics (CFD) program package (AVL

©R , Graz,Austria), using finite volume techniques, for stationary inspira-tory flow conditions with a parabolic velocity entrance profile.The trajectories of straight, rigid fibers were analyzed by thetrajectory code of Balashazy (1994), applying the equivalent di-ameter concept and the effective length of interception under thesimultaneous action of inertial impaction, gravitational settling,Brownian motion, and interception deposition mechanisms. Thisstudy is focused on man-made-mineral fibers where the effectof difussion is negligible. Thus here only impaction and grav-itation are taken into consideration as deposition mechanisms.The motion of particles in a fluid under the influence of inertialforces is described by the Basset–Boussinesq–Qseen equation.Incorporating the additional effect of gravity, the equation ofmotion adopts the following form if the fluid density is muchsmaller than that of the particles:

md�udt

=(

1 − ρ

σ

)m�g + �v − �u

B[1]

where m is the mass of the fiber, �u and �v are the velocity vectorsof fiber and air, respectively, B = Cm/(3πµde), where B is themechanical mobility of the fiber, Cm is the Cunningham slipcorrection factor, µ is the absolute viscosity of air, and de is anequivalent diameter of the fiber, which is the Stokes diameterfor micrometer size fibers. In this article, it is approximated withthe impaction equivalent diameter, σ and ρ are the densitiesof fiber and air, respectively, �g is the gravitational acceleration


vector, and t is the time. The drag force on a fiber and the slipcorrection factor depend on fiber orientation (see later discussionand Asgharian et al., 1988). The Stokes number of fibers (St) issimilarly defined as for compact particles, but with the Stokesdiameter of the fiber. Thus, St = uτ/R, where τ = m B is therelaxation time of the fiber and R is the airway radius (Asgharianet al., 1988).

This trajectory code solves Eq. (1) under the condition thatthe air velocity gradient is constant during the elementary timestep of the particle’s trajectory. Details of this mathematical pro-cedure are described in Balashazy (1994). Note that the availablecommercial computational fluid dynamics codes can solve themotion equation of particles only with the assumption that theair velocity and not its gradient is constant during the elemen-tary time step. The former method may imply a too crude ap-proximation of impaction and thus result in incorrect depositionpatterns.

The starting points of the trajectories at the inlet of the parentbranch were selected randomly by a Monte Carlo technique inaccordance with the parabolic inlet velocity distribution of air.The intersection of the particle trajectories with the surround-ing wall surfaces finally determined the resulting deposition pat-terns. The number of randomly selected particles varied between1000 and 10000, depending on the magnitude of the resultingdeposition efficiencies and statistical errors.

A relatively simple approach to model the behavior of fibersin airways is the application of “equivalent particle diameters.”The deposition of fibrous particles can then be computed as thatof spherical particles, but substituting the geometric diameterwith the appropriately selected equivalent particle diameters.The equivalent particle diameter depends on a number of pa-rameters. Before all, it depends on the force field, for example,impaction versus gravity. Thus, the equivalent particle diametersof fibers are not necessarily the same for the different depositionmechanisms and may depend on the orientation of the fibersto the main air streamlines (Balashazy et al., 1990). Likewise,the interception length is also a function of the fiber orientation.In the present study, parallel, perpendicular, and random fiberorientations were analyzed. The first two represent limiting orextreme values regarding deposition.

The equivalent diameter approach is a simplification of thecalculation of the real complex trajectories of fibers. However,according to Broday et al. (1998), the deposition efficiency of aswarm of noninteracting spheroidal particles in vertical stagna-tion flows is the same as that of the equivalent spherical particleswith the same settling velocity. This observation holds for parti-cles uniformly dispersed far above the collector surface, and aslong as the interception capture mechanism does not affect thedeposition. In the present calculations, fibers are randomly andindependently selected at the inlet and they are far enough fromthe surface of the airways; in addition, interception is computedsimultaneously with the trajectories.

The sedimentation equivalent diameter (des) for fibers settlingwith their longitudinal axes parallel to the direction of gravity

can be approximated as (Balashazy et al., 1990):

des|| = 3

2df

√σ

σoln[(2β) − 0.5] [2]

where df is the diameter of the substitute cylinder, β is the aspectratio (length per diameter) of the fiber, σ is the material densityof the particle, and is σo the unit density.

Fibers settling with their longitudinal axes normal to the di-rection of gravity have sedimentation equivalent diameters of:

des⊥ = 3

4df

√2σ

σoln[(2β) + 0.5] [3]

and fibers of random orientation have sedimentation equivalentdiameters of

desr = 3

2df

√σ/σo

0.385ln(2β)−0.5 + 1.230

ln(2β)+0.5

[4]

According to the theoretical considerations of Harris andFraser (1976) and Yu et al. (1986), the following inertial im-paction equivalent diameters (dei) were assumed regarding fiberorientations with respect to the primary direction of airflow inairway bifurcations:

(a) parallel alignment, dei|| = des|| .(b) perpendicular alignment, dei⊥ = des⊥ .(c) random alignment, deir = desr .

The inertial impaction equivalent diameter (dei) is defined asthe diameter of a sphere of unit density that has the same Stokesnumber as the fiber considered, under the same flow conditions.

If fibers are aligned with the air streamlines in a horizontallypositioned airway bifurcation, then des = des⊥ and dei = dei‖.

For interception, it is particularly important to know the mag-nitude of the effective dimension for deposition, the interceptionlength, li, that is the interception cross section (Balashazy et al.,1990). In the case of particles oriented in a parallel fashion tothe streamlines, li is:

li = df

2[5]

and for a perpendicular orientation, li is

li = lf

2[6]

where lf is the fiber’s length.For randomly oriented fibers, li is one-half of the average

projected length that is determined by the equation:

li = 1

2

∫ lf

0

∫ √l2f −x2

0

√l2f − x2 − y2 dy dx

∫ lf

0

∫ √l2f −x2

0 dy dx= lf

3[7]

where x and y are the coordinates of a Cartesian referencesystem.


In case of diffusion, which is significant only for small par-ticles and mainly in small airways and alveoli, the continuousimpact with gas molecules will result in a coupled translationaland rotational Brownian motion of the fiber. Moreover, the dragforce on a fiber and the slip correction factor depend on the fiberorientation (Asgharian et al., 1988). This article is focused onglass fibers. In their size range, the effect of diffusion and slipcorrection is negligible; thus, here these effects are not detailed.

The trajectory of fibrous particles is given by a series of cylin-ders, where the radius of a cylinder is the interception cross sec-tion and its length is the distance that the particle flies during �t,that is during the time step of the numerical process. In the caseof the following simulations, the main plane of the bifurcationwas horizontally positioned.

FIG. 1. Oral and nasal penetration probabilities, that is, the probability to reach a given airway generation via the nose or themouth for different equivalent fiber diameters (σ = 2.6 g/cm3) under different breathing conditions. ET, extrathoracic region;GEN1, airway generation 1, that is the trachea; GEN2, airway generation 2; GEN3, airway generation 3; Q, tracheal flow rate; de,equivalent diameter; ds, diameter of spherical particle; lf, fiber length.

RESULTSIn the first part of this section, the penetration probabilities of

glass fibers to the entrance of airway generation 4 are computedfor three different flow rates under both nasal and oral breathingconditions by the stochastic lung deposition model, applyingthe equivalent diameter concept for randomly oriented fibers.Penetration probability here means the fraction of inhaled fiberswhich enter airway generation 4 without earlier airway deposi-tion following either nasal or oral breathing during inhalation.Figure 1 presents the results of these simulations for inhaled4 µm spherical and 25, 50, 100, and 200 µm long randomlyoriented glass fiber particles with a diameter of 4 µm and adensity of 2.6 g/cm3. Tracheal flow rates, Q, are 10 L/min (rest-ing), 60 L/min (light physical activity), and 120 L/min (heavy


exercise). For all flow rates employed, the filtration efficiency ofthe nose is much higher than that of the mouth. However, evenfor nasal breathing, the penetration probabilities of large fibersare a few percent at resting breathing conditions. For mouthbreathing at intermediate flow rates, the penetration probabil-ity of 25 µm long and 4 µm diameter glass fibers to airwaygeneration 4 is higher than 1%. At resting breathing condi-tions, the penetration probability of a 200 µm long glass fiberis 20% and that of a 25 µm long glass fiber is 40%. The den-sities of the other man-made mineral fibers are similar, thus theresults characterize the penetration probabilities of other man-made fibers, as well. These simulations demonstrate that thecarinal ridges of the central airway bifurcations can be reachedeven by large fibers, which may explain the epidemiologicallyobserved carcinogenicity of large man-made glass and mineralfibers.

In the second part of this study, deposition patterns and depo-sition efficiencies of these large man-made fibers were computedin a horizontally positioned airway bifurcation characteristic ofairway generation 4–5 dimensions, with a standard branchingangle of 35◦. The three-dimensional physiologically realisticbifurcation geometry assures smooth transitions between theparent and daughter and between the two daughter airways withrealistic curvature radii.

FIG. 2. Relationship between impaction equivalent diameter and fiber length (upper left panel) and effect of fiber orientation onthe deposition efficiency as a function of fiber length for the simultaneous action of impaction and interception (upper right panel),considering only inertial impaction (lower left panel), or only interception (lower right panel). The inspiratory tracheal flow rate is60 L/min.

The behavior and fate of inhaled fibers in the airways dependson flow and particle parameters. In laminar flow, long fibers (as-pect ratio greater than 5) usually align with the streamlines, whileshort fibers make tumbling movements. Due to the corrugatednature of the airway system and the complex form of naturalfibers, we analyzed the deposition efficiencies and localized de-position patterns of rigid fibers with parallel, perpendicular, andrandom orientations to the main airflow direction. The deposi-tion efficiencies were determined by the ratio of the number ofdeposited particles to the total number of simulated particles atthe inlet of airway generation 4.

Figure 2 illustrates the relationship between fiber length andinertial impaction equivalent diameter (left upper panel), and thedeposition efficiencies that originate from the simultaneous con-tribution of impaction, gravitation, and interception (right upperpanel), from inertial impaction (left bottom panel), and from in-terception (right bottom panel) as a function of fiber length atthe three orientations of the fibers (parallel, random, and per-pendicular) for light physical activity breathing condition. Atthese parameter values, the effect of gravitation can safely beneglected. The plots demonstrate that inertial impaction is thedominant deposition mechanism for this parameter combination.The shapes of the deposition efficiency curves are similar to thatof the inertial impaction0 equivalent diameter with rising fiber


length. Deposition in both cases is highest for parallel orienta-tion, which also demonstrates the dominant effect of impactionbecause of the impaction equivalent diameter being highest incase of parallel orientation. In contrast, deposition by intercep-tion is most efficient for perpendicular orientation, where theinterception cross section adopts its highest value.

Interception without the other deposition mechanisms wascomputed by switching off inertial impaction and gravitationalsettling in the motion equation of the particle, that is, interceptionpractically was described by following an air particle with aradius of the actual interception cross section.

Deposition efficiency was defined as the number of depositedfibers in the examined bifurcation, that is in airway generations4–5, divided by the number of fibers entered into this bifurcation.

The effect of flow rate on deposition efficiency for simulta-neous and single deposition mechanisms is analyzed in Figure 3as a function of fiber length for randomly oriented fibers at threedifferent inspiratory flow rates. The deposition efficiencies of thelongest (200 µm) fibers for the simultaneous action are about95% at 120 L/min, 83% at 60 L/min, and 16% at 10 L/mininspiratory flow rates. These data also prove that impaction isthe dominant mode of deposition in the central human airwaysunder the assumed exposure conditions.

The effect of branching angle on the deposition efficiency wasalso analyzed by comparing the results obtained for the standardbranching angle of 35◦ with those for a branching angle of 60◦.For the 60◦ branching angle, the deposition efficiency is about20% higher over the whole range of the examined fiber lengths(10–200 µm), as one would expect in an impaction-dominatedsystem.

Three-dimensional deposition patterns of 25 µm long and4 µm thick randomly oriented glass fibers are presented inFigure 4 in three different projections in the physiologically re-alistic bifurcation geometry model of airway generations 4–5.The deposition sites are identified by dots, which refer to thefiber’s center of mass, and their total number is a measure ofthe deposition efficiency. The figure illustrates the depositiondistributions caused by only inertial impaction (left panel) andonly interception (right panel) deposition mechanisms, based on2000 trajectory simulations. A common feature of these simu-lations is the formation of enhanced deposition sites (hot spots),particularly in the vicinity of the carinal ridge. In case of im-paction, the hot spots at the carinal region extend downstreamon the inner side of the daughter airways due to the inertia ofthe particles. Inspection of the two panels of Figure 4 revealsthat the deposition efficiency for impaction is much higher thanthat for interception at the selected conditions of geometry, flowand particle size (76.6% vs. only 2.2%). The right panel of Fig-ure 4 also illustrates the effect of reverse flows in the vicinityof the carinal ridge, as there is no deposition exactly at thatsite. The reverse flow at curved carina and its effect on deposi-tion patterns of spherical particles in central airway bifurcationsduring inhalation were analyzed in Balashazy et al. (1996) andFarkas et al. (1999). These results suggest that in Figure 4 in-

FIG. 3. Effect of flow rate on the deposition efficiency of ran-domly oriented fibers as a function of fiber length for three dif-ferent inspiratory tracheal flow rates: 10 L/min (upper panel),60 L/min (middle panel), 120 L/min (bottom panel).

terception is not strong enough to overcome the reverse flows.In contrast, inertial forces are stronger than the reverse flows,resulting in dense “hot spots” at the carinal ridge and down-stream on the inner sides of the daughter airways (left panel ofFigure 4).

The effect of flow rate on the deposition patterns of randomlyoriented 200 µm long and 4 µm wide glass fibers during inhala-tion in the physiologically realistic airway bifurcation model ispresented in Figure 5 for the simultaneous actions of all three


FIG. 4. Deposition patterns of randomly oriented rigid fibers in the central human airways due to impaction (left panels) andinterception (right panels) at 60 L/min inspiratory tracheal flow rate, based on 2000 trajectory simulations.

FIG. 5. Deposition patterns of randomly oriented rigid fibers in central human airways at two different tracheal flow rates, Q =10 L/min (left panels) and Q = 60 L/min (right panels), based on 5000 trajectory simulations.


deposition mechanisms. For the 10 L/min inspiratory flowrate (left panels), deposition is much more diffuse than at the60 L/min flow rate (right panels). Although there is some en-hancement at the carinal ridge even at the low flow rate, theextension and density of the hot spot are much greater at themore intense breathing condition. This is also reflected in themagnitude of the related deposition efficiencies, which is about5 times higher at 60 L/min than at the 10 L/min flow rate.

To test the validity of our calculations, the present resultsare compared in Figure 6 with other previously published ex-perimental (upper panel) and theoretical (bottom panel) studies.For limiting cases, the computed parallel and the perpendicularorientations are also displayed. Thus, the random or any otherorientations may result in a deposition efficiency, which falls be-tween these two values at any Stokes number. The comparisons

FIG. 6. Comparison of simulated deposition efficiencies withexperimental data (upper panel) and with other published theo-retical data (lower panel) as a function of the Stokes number forrandom, parallel, and perpendicular orientations of rigid fibers(branching angle is 35◦).

are for fibrous particles. The upper panel presents the measuredglass fiber deposition data of Myojo (1990, 1997) and Myojoand Takaya (2001) in model bifurcations of airway generations4–5.

Measured and predicted deposition efficiencies are plottedversus the fibers’ Stokes numbers. Here, Stokes numbers arecomputed based on the Stokes diameters, which can be approxi-mated by the inertial impaction equivalent diameters (Asgharianet al., 1988). Myojo (1990, 1997) and Myojo and Takaya (2001)measured the deposition efficiency of rigid glass fibers only atrelatively small Stokes numbers. When extrapolating their mea-sured data to larger Stokes numbers, they are in good agree-ment with our computed results. The measurements of Myojo(1990, 1997) and Myojo and Takaya (2001) indicate that bothdeposition densities and efficiencies increase by increasing fiberlength, fiber diameter, or flow rate. Our calculations show simi-lar tendencies. In addition, their reported locations of enhanceddeposition areas agree with our simulated results.

The bottom panel of Figure 6 presents the computed depo-sition efficiencies as a function of Stokes number, assumingparabolic inlet flows, in comparison with the theoretical data ofCai and Yu (1988) and Zhang et al. (1996) for fibers. Our resultsare in good agreement with all the other theoretical predictions,except for the Cai and Yu (1988) data, which are consistentlysmaller at higher Stokes numbers, although they also applied theequivalent diameter concept. This difference can be attributedto differences in airway geometry and consequently in airflowfield, since Cai and Yu (1988) approximated the bifurcation ge-ometry with a curved tube and simple rotational flow profile,for which deposition efficiencies are significantly smaller thanin a real three-dimensional bifurcation with complex flow field,particularly at high Stokes numbers.

In conclusion, these comparisons demonstrate that the equiv-alent diameter concept, if including interception, produces rea-sonable results for the parameter ranges employed in the presentstudy.

DISCUSSION AND CONCLUSIONSOn the basis of the experimental and epidemiological studies,

glass wool and other man-made mineral fibers were formerlyanticipated to be carcinogenic for humans (Doll, 1987). De-spite the large average diameter of the manmade mineral fibers,they have a non-zero inhalable fraction. This fraction, in caseof instillation, was capable of producing proliferative bronchiallesions in rats (Kerenyi et al., 1995). In the present work, de-position efficiencies and local deposition patterns of large rigidfibrous particles were numerically simulated in a physiologi-cally realistic bifurcation model of the large human airways bythe equivalent diameter concept, considering also the intercep-tion mechanism. Inhalation parameters varied in this study werefiber length, orientation relative to the main air streamlines, in-spiratory flow rate, and branching angle. The parallel and theperpendicular orientations can be regarded as limiting cases re-garding orientations. Deposition increased with rising flow rate,


length of fiber, and branching angle, and was highest for parallelorientation of the fibers. Our predictions of deposition efficien-cies and also deposition patterns show fair agreement with thepresently available experimental evidence on fibers and equiva-lent spherical particles.

One of the goals of the research presented here was to inves-tigate the relative contributions of individual deposition mecha-nisms to total deposition. The strong dependence of the deposi-tion efficiencies on the Stokes number highlights the dominantrole of inertial impaction for the deposition of large fibers inlarge airway bifurcations. Even at resting breathing conditions,a slight hot spot is formed at the carinal ridge. Interception maybe dominant for thin fibers and mainly in the more distal airways.

In the present analysis, only large fibers were studied, first be-cause man-made fibers are big and usually only a small fractionof them are inhalable, and second to ensure statistically reliableresults for the individual deposition mechanisms. The 4 µm di-ameter size was selected to characteristize the small inhalablefraction of the man-made mineral fibers, which, despite of theirlarge diameters, may reach the large bronchial airways and thusmay induce cancers there.

The clearance of initially deposited fibers in the bronchial air-ways is much more complex than that of the spherical particles.Sharp and rigid fibers, like glass or asbestos, may penetrate intoor pierce the airway epithelium, thereby hampering clearanceof mucus transport. The stuck fiber then can cause permanentirritation of the lung tissue affected, which may eventually leadto the formation of lung tumors. Our simulations suggest thatfibers are accumulated at and in the vicinity of carinal ridges,where deposition is highest and mucociliary clearance is slow-est, which is consistent with the experimental results of Kerenyiat al. (1995). Indeed, these sites have previously been identi-fied as the preferential sites of tumor occurrence (Schlesinger &Lippmann, 1978).

The smaller pathogenicity of man-made mineral fibers ascompared to asbestos is due to their decreased ability to producerespirable dust, as diameters are too high for to reach the lungsupon inspiration. In the case of glass wool, the carcinogenicityis further reduced because of its biosolubility.

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Simulation of Fiber Deposition in Bronchial Airways

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