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Respiratory Physiology & Neurobiology 163 (2008) 128–138

Contents lists available at ScienceDirect

Respiratory Physiology & Neurobiology

journa l homepage: www.e lsev ier .com/ locate / resphys io l

odeling airflow and particle transport/depositionn pulmonary airways�

lement Kleinstreuera,b,∗, Zhe Zhanga, Zheng Lia

Department of Mechanical & Aerospace Engineering, North Carolina State University, Raleigh, NC 27695-7910, USADepartment of Biomedical Engineering, North Carolina State University, Raleigh, NC 27695-7910, USA

r t i c l e i n f o

rticle history:Accepted 7 July 2008

eywords:ulmonary airways

a b s t r a c t

A review of research papers is presented, pertinent to computer modeling of airflow as well as nano- andmicron-size particle deposition in pulmonary airway replicas. The key modeling steps are outlined, includ-ing construction of suitable airway geometries, mathematical description of the air-particle transportphenomena and computer simulation of micron and nanoparticle depositions. Specifically, diffusion-

eposition enhancement factorracheobronchial airways

dominated nanomaterial deposits on airway surfaces much more uniformly than micron particles of thesame material. This may imply different toxicity effects. Due to impaction and secondary flows, micronparticles tend to accumulate around the carinal ridges and to form “hot spots”, i.e., locally high concen-trations which may lead to tumor developments. Inhaled particles in the size range of 20 nm ≤ dp ≤ 3 �mmay readily reach the deeper lung region. Concerning inhaled therapeutic particles, optimal parametersfor mechanical drug-aerosol targeting of predetermined lung areas can be computed, given representative

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pulmonary airways.

. Introduction and overview

Experimental and computational modeling of biomechanicsf the human respiratory system is quite challenging because ofhe complex airway geometries, three-phase flow phenomena,uid–structure interactions, and species mass transfer. Of basiconcern is the understanding and achievement of O2–CO2 gasxchange under normal and pathological conditions. Modelingpplications include: (i) dosimetry-and-health effects of inhaledoxic particulate matter, of interest to toxicologists, health-careroviders and regulators and (ii) optimal drug-aerosol targeting toredetermined sites to combat lung and systemic diseases. Clearly,he biomechanics phenomena occurring in a complete set of real-stic pulmonary airways cannot yet be simulated let alone for every

atient. However, based on CT-scans and MRI as well as benchmarkxperimental data sets, detailed computer simulations can be per-ormed at least for representative airway segments. In addition,global lung” models in terms of simple semi-empirical correla-

� The views and conclusions contained herein are those of the authors and shouldot be interpreted as necessarily representing the official policies or endorsements,ither expressed or implied, of the Air Force Office of Scientific Research.∗ Corresponding author at: Department of Mechanical & Aerospace Engineering

nd Department of Biomedical Engineering, Campus Box 7910, North Carolina Stateniversity, Raleigh, NC 27695-7910, USA. Tel.: +1 919 515 5261; fax: +1 919 515 7968.

E-mail address: ck@eos.ncsu.edu (C. Kleinstreuer).

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569-9048/$ – see front matter © 2008 Elsevier B.V. All rights reserved.oi:10.1016/j.resp.2008.07.002

© 2008 Elsevier B.V. All rights reserved.

ions have provided surprisingly accurate deposition efficienciesor a wide range of (spherical) particle diameters.

With the advent of petascale (1015 calculations/s) computing,uture simulation results will cover the most important biomechan-cs phenomena in actual human airways and provide solutions tohe patient-specific drug-aerosol targeting problem.

.1. Toxic particulate matter inhalation

Toxic material in vapor, liquid droplet and solid particle formss being inhaled, as it appears indoors or outdoors in all shapes andizes, typically ranging from nanometers (10−9 m) to micrometers10−6 m). Most severely affected by polluted air may be the childrennd the elderly. Given any set of ambient conditions in terms of pol-utant concentration, temperature and humidity, it is of interest toredict how much deposits where in the human respiratory tractnder realistic breathing conditions. Such results, usually obtainedia experimentally validated computer simulations, are of greatnterest to toxicologists, epidemiologists, health-care providers,nd regulators of air pollution standards. Toxic material dynamics isescribed in two size-dependent categories; because the transport

echanism for nanomaterial is diffusion dominant while micron

articles are impaction and possibly gravitation dominant. Hence,anoparticles, which include some vapors, are modeled with a massransfer equation and micron particles with Newton’s second lawf motion (Kleinstreuer, 2006).

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.1.1. Toxic nanomaterialNanotechnology and related manufacture of nano-scale materi-

ls are major growth industries (Roco, 2006). Clearly at the stages ofanomaterial production, handling and use, nanoparticles becomeirborne and inhaled (Service, 2003; Theodore and Kunz, 2005;mong others). Hence, the specter of serious health problems ariserom inhalation of such (toxic) metal, metal-oxide, carbon-basednd synthetic nanomaterials (Oberdörster et al., 2005; Kumar,006; among others). After nanoparticle inhalation, tissue absorp-ion and transport to extra-pulmonary organs, nanomaterial mayarget the central nervous system and immune system (Bang and

urr, 2002; Oberdörster et al., 2005). It is not just the level of tox-city of some nanomaterials which poses potential respiratory andther health risks; but, also their size, shape and surface distribu-ion which turns out to be even more toxic than inhaled micronarticles of the same material. Also, other toxins could bind withanoparticles and piggyback their way into the body. In summary,he enhanced toxicity of nanomaterial can be attributed to (i) thereater surface reactivity of nanoparticles due to high curvatures asell as the larger surface area relative to the nanoparticle mass; (ii)

he prolonged retention time and decreasing fraction of clearanceor ultrafine particles; (iii) an almost uniform coating of the air-ay surfaces by nanoparticles; (iv) larger deposition fractions (DF)f nanomaterial in deeper parts of the lung, including the alveolaregion.

So far, there are relatively few investigations of (spherical)anoparticle deposition in the human airways, primarily because ofhe difficulty of nanoparticle generation for experimental measure-

ents and accurate predictions with computational fluid-particleynamics (CFPD) simulations. In a series of papers, Cheng et al.1988, 1995, 1996, 1997a,b) and Smith et al. (2001) published their

easurements of mass transfer and deposition of nanoparticles3.6 nm < dp < 150 nm) in casts of human nasal, oral and upper tra-heobronchial (TB) airways; Cohen et al. (1990) reported theirxperimental work on nanoparticle deposition in an upper tra-heobronchial airway cast; (Kelly et al., 2004b) measured the nasaleposition efficiencies of nanoparticles with diameter between 5nd 150 nm; Daigle et al. (2003) and Kim and Jaques (2004) mea-ured total respiratory tract deposition fraction of nanoparticles8–100 nm) in healthy adults. Examples of numerical simulationsor nanoparticle deposition include Asgharian and Anjilvel (1994),alashazy and Hofmann (1993, 1995), Yu et al. (1996, 1998), Moskalnd Gradon (2002), Hofmann et al. (2003), Kelly et al. (2004b),hang and Kleinstreuer (2004), Shi et al. (2006), Zamankhan et al.2006), and Longest and Xi (2007b).

Almost all theoretical as well as experimental studies describ-ng the diffusional deposition in the tracheobronchial airwaysssumed uniform or parabolic inlet velocity profiles and particleistributions. However, the actual velocity profiles and particleistributions are quite different from those axisymmetric pro-les and distributions due to flow development, secondary flows,nd non-uniform particle transport in the upstream airway sec-ion (Kleinstreuer and Zhang, 2003a). In addition, many publishedumerical simulations were lacking detailed model validations.ecently, the Euler–Euler approach has been validated as an accu-ate and effective modeling technique for spherical nanoparticleeposition in idealized airway segments (Shi et al., 2004; Zhangnd Kleinstreuer, 2004; Zhang et al., 2005). So far, little infor-ation is available about modeling of nanoparticle (<100 nm)

eposition in the alveolar region. In fact, major nanoparticle depo-

ition may occur in the pulmonary region (e.g., about 20–35%f 40–100 nm particles, see Kim and Jaques, 2004). The low sur-ace tension produced by a surfactant film in the deeper parts ofhe lung, including the alveolar region, may aid the transfer ofanoparticles through the liquid wall layer (Geiser et al., 2000)

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& Neurobiology 163 (2008) 128–138 129

o that the toxicity effect of deposited particles in these regionss enhanced. Furthermore, the coupling of fluid flow and alveolarall movement during expansion/contraction (i.e., fluid–structure

nteractions) and its effects on particle transport/deposition havearely been analyzed (Tsuda et al., 1994; Haber et al., 2003; Dar-uenne and Prisk, 2003; Haber and Tsuda, 2006). Reliable studiesf transport and deposition of non-spherical nanoparticles are eveness available. Non-spherical particle motion, say, of carbon nan-tubes, is much more complicated than that of spherical particlesecause these particles undergo simultaneous translation, rotationnd re-orientation when traveling in shear flow (Brenner and Con-iff, 1972; Bernstein and Shapiro, 1994). Due to the complicatedotion of non-spherical particles, most of the existing models for

on-spherical particles, such as fiber deposition in human airways,ocus on deposition of fibers with diameters in the micro-size rangen single airway bifurcation models assuming simple shear flowr simple fiber transport (e.g., Cai and Yu, 1988; Asgharian andnjilvel, 1995; Zhang et al., 1996; Balashazy et al., 2005).

.1.2. Toxic micron particlesWhile the potential health hazards of nanomaterials has only

een very recently acknowledged, inhaled micron-particle deposi-ions for dosimetry-and-health-risk assessments have been studiedor decades (Heyder, 2004). Clearly, the experimental and com-utational contributions reviewed deal with spherical micronarticles that are completely neutral concerning toxic or therapeu-ic effects.

For example, Schlesinger et al. (1982), Gurman et al. (1984),nd Kim and Garcia (1991) showed that cyclic inhalation gener-tes higher particle deposition efficiencies than steady inhalationt the mean Reynolds number of the inlet flow waveform. Specifi-ally, Gurman et al. (1984) have estimated a 15% increase in inertialmpaction with cyclic flows. Kim and Garcia (1991) calculated thathe deposition efficiency (DE) should increase by about 23% withine-wave type flows regardless of the cyclic frequency. Cheng and

ang (1976) measured the deposition of 0.58–2.05 �m aerosolslong the airway walls of a second generation under condition ofonstant and cyclic inspiratory flows for a single mean inspira-ory flow rate. Overall deposition was found to be greater underyclic flow. The maximum increase was 26% above that observedhen constant flow at the mean Reynolds number was assumed.

chlesinger et al. (1982) and Gurman et al. (1984) measured theeposition of 3 and 8 �m monodispersed aerosols in replicate castsf the human tracheobronchial tree under conditions of constantnd cyclic “inspiratory flows”. Their results also showed that theeposition efficiencies within hollowed airway casts under cyclicow were greater than those under constant flow assuming theean flow rate. For a high flow rate (60 L/min), the deposition

fficiencies (DEs) increase by about 100% for 8 �m particle andp to 600% for 3 �m particles. However, this marked increase inE may be attributed to turbulence effects under cyclic flow con-itions in their experiments. Kim and Garcia (1991) measuredhe deposition of micron-sized particles in a single bifurcation

odel approximately representing generations G3–G4 for cyclicow at mean Reynolds numbers of 679–5547 and Stokes numbersf 0.028–0.25. Their results showed that the DE with cyclic flowas also higher than that obtained with constant flow. More in

itro experimental studies of micron-particle deposition in tracheo-ronchial airways focused on steady inhalation in glass or metalasts of the TB tree from one to several bifurcations (see Ferron,

977; Kim and Iglesias, 1989; Oldham et al., 1997, 2000; Kim andisher, 1999; Zhang and Finlay, 2005; among others), or realis-ic airway replica based on cadavers representing trachea (G0) toenerations G3, G4 or G5 (see Schlesinnger and Lippmann, 1972;chlesinger et al., 1977; Zhou and Cheng, 2005; among others).

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he deposition efficiencies at each generation were usually mea-ured in these studies for different combinations of particle size andnspiratory flow rate. However, detailed air/particle transport phe-omena as well as local deposition patterns and surface densitiesf deposited particle in bifurcating airways are difficult to obtainxperimentally.

Clearly, computational fluid dynamics (CFD) simulation is anffective way to gain such information. Examples of such con-ributions focusing on tracheobronchial trees, include Comer etl. (2001), Zhang et al. (2002a,2005), Nowak et al. (2003), vanrtbruggen et al. (2005), Li et al. (2007a), and Longest and Xi2007a). So far, most of these studies concentrated on one toeveral bifurcations of the TB tree. Some of these studies lackedufficient model validations (e.g., Nowak et al., 2003). Consider-ng the large amount of branches in the lower airways (say, 215

or the 16th generation in Weibel’s lung model), the direct simu-ation of particles in the entire tracheononchial airways (say, from0 to G16) is still impossible. However, petascale computing mayllow for rather accurate patient-specific lung modeling in the nearuture.

.2. Mechanical drug-aerosol targeting

Inhalation of drug aerosols, typically in the effective diameterange of 3–10 �m, is a standard procedure for treating respira-ory ailments, especially chronic obstructive pulmonary diseasesCOPD) and asthma. The nasal and oral pathways are now also beingsed as portals to deliver medicine for pain management and toombat systemic diseases, respectively, where oral inhalation ofnsulin for diabetes patients is one modern example. However, toe successful and cost-effective, drug-aerosol delivery has to be tar-eted. Obviously, maximum deposition of suitable therapeutic solidarticles (or droplets or vapor) at predetermined sites, which areelated to specific diseases, minimizes potential side-effects in casef aggressive drugs and reduces health-care cost with the increasedfficacy. “Targeting” is here understood as a mechanical goal toring drug aerosols from their release points (i.e., the inhaler exit)o a desired landing area in the respiratory system for maximum

edical effectiveness. In order to achieve that goal, future inhalerevices have to operate based on a targeting methodology featur-

ng optimal: (i) particle characteristics, (ii) inhalation waveform,iii) particle-release positions, and (iv) concentration range. This

echanistic approach differs from drug targeting via special designf molecular, carrier and controlled-release properties which causeelective distribution characteristics and pharmacokinetic behavioreading to improved therapy.

Several aspects of drug-aerosol delivery have been recentlyeviewed in the books edited by Gradon and Marijnissen (2003)s well as Hickey (2004). The book by Finlay (2001) and the volumedited by Bissgard et al. (2002) also discuss pertinent elementsf drug delivery to the lungs. Experimentally validated computerimulations of micron-particle transport and deposition, employ-ng pressurized metered dose inhalers (pMDIs) and a new delivery

ethodology for optimal drug-aerosol targeting, are discussed byleinstreuer et al. (2007a).

. Geometric models of the oral and pulmonary airways

Accurate and realistic airway models are the necessary pre-ursor for experimental or computational airflow and particle

ransport/deposition analyses. Once a comprehensive, flexible andxperimentally validated computer simulation model has beeneveloped, local and segmentally averaged concentrations of toxicarticles as well as operational parameters for optimal drug-aerosolargeting can be determined. Ultimately, such tasks can be accom-

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& Neurobiology 163 (2008) 128–138

lished for individual patients, eliminating the present problem ofnter-subject variability.

In any case, the nasal plus oral airways are labeled the extratho-acic region which forms with the tracheobronchial and alveolaregions the respiratory system. From a functional viewpoint, theespiratory tract is divided into the conducting zone (i.e., Genera-ions 0–16) and the respiratory zone (Generations 17–23) where the2–CO2 gas exchange takes place. An alternative geometric divisionould include the extrathoratic, upper bronchial, lower bronchial,

nd alveolar region (see Fig. 1). There are two basic approaches forenerating geometric lung models, i.e., either via algorithms whichpecify inhaled-volume-based rules for the relationships betweenarent and daughter airways (e.g., Kitaoka et al., 1999 and Tawhait al., 2000) or lung replicas digitally reconstructed from CT-scan orRI data (e.g., van Ertbruggen et al., 2005). Using the first approach,

ebockhorst et al. (2007) also included in their computer modelung-airway morphogenesis, due to development in children orriggered by lung diseases.

Finlay (2001) in his Chapter 5 summarized human lung geo-etric and breathing data, while Hickey and Thompson (2004)

ocused more on the structure and function of the human air-ays. For experimental studies and computational analyses the

espiratory tract has been traditionally segmentized into the nasalavities, oral airway (i.e., mouth to trachea), the tracheobronchialree (typically Generations 0–3 or 6) and part of the alveolar regionanging from single alveolar cells to alveolated ducts. Historically,

eibel (1963) was the first to provide idealized geometric data, i.e.,ube diameter and length, of symmetrically bifurcating lung air-ays, known world-wide as the Weibel Type A model. In contrast,orsfield et al. (1971) and Raabe et al. (1976) published geom-try information on asymmetric airways obtained from humanung resin casts, while Hammersley and Olson (1992) focused onmall airway bifurcations. Phalen et al. (1985) published measure-ents of the right upper lobe airways taken from 20 replica casts

f people aged 11 days to 21 years. Morphometric data of theuman pulmonary acinus, i.e., all the daughter generations of aingle terminal bronchiole, was collected by Haefeli-Bleuer and

eibel (1988). Modern imaging techniques allow for an even moreetailed mapping of the human respiratory tract. For example, Leyt al. (2002) obtained from CT-scan data a semi-automatically gen-rated tracheobronchial tree, while Tawhai et al. (2004) as wells Cebral and Summers (2004) used CT-scans to construct cen-ral airways. Others, mainly focusing on the human upper airwaysor meshing and subsequently computer simulations, constructedigid 3D configurations which somewhat represent actual airwayssee Kleinstreuer and Zhang, 2003a; Matida et al., 2004; Farkas etl., 2006; Jin et al., 2007; Xi and Longest, 2007; among others).ynamic effects of finer geometric aspects of the upper respi-

atory tract were also investigated, such as local area changesuring inhalation (Ehtezazi et al., 2004; Zhang and Finlay, 2005),artilaginous rings in the trachea (Zhang and Finlay, 2005), andifferent static glottis openings (Brouns et al., 2007). Rather faith-ul replicas of the upper respiratory tract for experimental studiesere employed by Cheng et al. (1999) and Grgic et al. (2004),

mong others. Transient geometric changes have to be consideredn the throat while speaking, swallowing or switching breath-ng modes and in the alveolar region during inhalation/exhalationEhtezazi et al., 2004; Haber and Tsuda, 2006). Transport phe-omena and certain airway diseases may also be coupled toemporary changes in local airway geometry and hence should

e considered as well. Examples include mucus-layer flow (Kimt al., 1987) and clearance (Grotberg, 2001) as well as patientsith asthma, COPD, cystic fibroses, tumors, etc., as reviewed byeyer et al. (2003), Brown and Bennett (2004), and Yang et al.

2006).

C. Kleinstreuer et al. / Respiratory Physiology & Neurobiology 163 (2008) 128–138 131

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. Computational aspects of airflow and particle transportimulations

As alluded to in Section 1.1, “lung aerosol dynamics” investi-ations were historically mainly concerned with toxic particulateatter deposition and subsequently with the implications of

osimetry-and-health effects. Especially maturing CFD techniquesllowed for non-invasive, high-resolution, cost-effective and safeimulations of airflow pattern, particle transport and particle depo-ition as well as particle mass transfer into the lung tissue. Majorimplifications made include somewhat idealized rigid airwaysith smooth (sticky) surfaces, spherical non-interacting fine orltrafine particles, and constant inhalation flow rates.

Clearly, the geometry of an actual respiratory system is veryomplex, augmented by changing wall boundaries, rough surfaces,nd moving mucus layers. Nevertheless, the goal is patient-specificodeling, and the generic step-by-step procedure for generating

irway geometry data is as follows:

CT-scan images of a subject’s respiratory tract (i.e., DiCom files),enhanced with a contrasting agent, are obtained from a radiol-ogist or surgeon. It should be noted that the determination ofairway or vessel wall thicknesses is still rather difficult. Magneticresonance imaging (MRI) is good for distinguishing different tis-sues; thus, may help to estimate variable wall thickness. The timebetween contrast agent intake and scanning is crucial because thechemical should only change the apparent blood density beforemigrating into the tissue and by then greatly diminishing con-trasts between blood and tissue.

The DiCom files are loaded into geometry-file-conversion soft-ware, such as Mimics/Geomagic (Materialise, Belgium) orSimpleware (Simpleware Ltd., Exeter, UK). It enables the modelerto edit the images, isolate the structures of interest, and generate3D geometry models.

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e of actual airways (from Kleinstreuer et al., 2008).

The CAD-like geometry files are then exported in suitable for-mats, typically to CFD software, for numerical fluid flow and solidstructure analysis (see, for example, Wolters et al., 2005, Li andKleinstreuer, 2005, and Shi et al., 2006, among many others).Alternatively, the 3D finite element computer model can beexported as an STL-file (stereolithography) to a rapid prototyp-ing machine to build a physical model for laboratory studies (e.g.,Kratzberg et al., 2005).

The condition of deposition is usually fulfilled when a particles one radius away from the wall, i.e., it touches an airway sur-ace. The assumption of dilute micron-particle suspensions allowsor separate computations of the airflow (Eulerian approacholving the Navier–Stokes equations) and the particle dynamicsLagrangian approach solving Newton’s second law of motion).he same holds for the analysis of submicron particles; however,n that case an Euler–Euler approach is recommended, i.e., theanoparticle (or vapor) phase is described with the mass trans-

er equation containing an appropriate diffusion term (Crowe etl., 1998; Kleinstreuer, 2003; Zhang et al., 2005). For dense sus-ension flows, e.g., nasal droplet sprays, both phases are couplednd hence fluid–particle interactions have to be modeled, typi-ally via a “momentum source term” (Kleinstreuer, 2003; Shi andleinstreuer, 2007). Most naturally occurring and man-made par-

icles, including most drug aerosols, are non-spherical and henceequire special mathematical description for accurate trajectorynd deposition simulations (see, for example, Shenoy and Klein-treuer, 2008). Droplets as well as thermal and humidity effectsn the respiratory environment require also special considera-

ions (Zhang and Kleinstreuer, 2003b; Zhang et al., 2006). Thessumption of quasi-steady inhalation is justifiable for micron-article deposition modeling, when an equivalent inlet Reynoldsumber is selected. Specifically, Zhang et al. (2002a) showed thatuch an equivalent dimensionless group is the arithmetic mean of

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he maximum and mean Reynolds numbers of the given inhala-ion waveform. For elevated inhalation flow rates, i.e., Qin > 12 L/minuring exercise, transition to turbulent airflow after the larynx (seeig. 1) may occur with relaminarization further downstream. It washown that the low Reynolds number k–ω turbulence model of

ilcox (1998) adequately describes these changing flow regimesKleinstreuer and Zhang, 2003a; Varghese and Frankel, 2003; Zhangnd Kleinstreuer, 2003a; Ryval et al., 2004).

The rapidly growing interest in using the mouth/nose as por-als for the delivery of medicine caused a shift in the applicationnd interpretation of computational/experimental inhalation stud-es, i.e., “toxic particle deposition” results appeared as “therapeuticrug-aerosol targeting” outcome. One early example is the determi-ation of a critical tumor radius for which drug-aerosol depositionas at a maximum for all inlet Reynolds and Stokes number com-inations (Kleinstreuer and Zhang, 2003b).

.1. Inhaled air flow fields

The understanding of airflow structures in the human airwaysnderlies the basis for analyzing particle transport and deposition.teady and transient inspired air flows in the human nasal/oralnd bronchial airways have been reviewed by Pedley (1977) androtberg (1994, 2001). Detailed investigations, both experimen-

ally and theoretically, were recently provided by Lieber and Zhao1998), Fujioka et al. (2001), Caro et al. (2002), Gemci et al. (2002),hang and Kleinstreuer (2002, 2004), Kleinstreuer and Zhang2003a), Liu et al. (2003), Nowak et al. (2003), Horschler et al. (2003,

006), Johnstone et al. (2004), van Ertbruggen et al. (2005), Shi et al.2006), Adler and Brucker (2007), and Grosse et al. (2007), amongthers. Effects of geometric airway changes are most pronounceduring inhalation. So far, experimental and computational analysesocused mainly on isolated sections of the human airways and only

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ig. 2. Velocity profiles in the bifurcation airway model at steady inhalation with Qin = 30xial velocity contours and secondary velocity vectors at different cross sections (see Zha

& Neurobiology 163 (2008) 128–138

or laminar airflows. However, at moderate to high breathing rateshe air flow from the larynx to generation G3 is transitional-to-urbulent which may complicate flow structures as well as aerosolransport and deposition (Kleinstreuer and Zhang, 2003a; Zhangnd Kleinstreuer, 2004). Usually, the turbulent intensity in the oralirway rises rapidly after the constriction caused by the soft palate,nd then decreases until the disturbance is activated again by thehroat (glottis) (Zhang and Kleinstreuer, 2003a; Lin et al., 2007).urbulence levels, in terms of kinetic energy k, seem to increaseuickly through the strong varying diameter-zone after the glottis,nd then decay approaching an asymptotic level of approximately.2–0.3 (k/�in

2) at six-diameter station from the throat (Corcorannd Chigier, 2000). The flow instabilities may be induced again athe bifurcation region due to the great geometric transition fromhe parent tube to two daughter tubes, while the strongest tur-ulence fluctuations occur just around the flow dividers due tohe contraction of top and bottom surfaces in the carinal ridgesZhang and Kleinstreuer, 2004). Then, turbulence decays rapidly inhe straight segments of the bifurcating tubes. Generally, turbu-ence which occurs after the throat can propagate to at least a fewenerations even at a low local Reynolds number (say, Re = 700)ecause of the enhancement of flow instabilities just upstream ofhe flow divider (Olson et al., 1973; Zhang and Kleinstreuer, 2004).

Typical inspiratory airflow patterns in bifurcating airways arehown in Fig. 2. The essential flow characteristics includes: (i)he air stream splits at the flow dividers and new boundary lay-rs are generated at the inner walls of daughter tubes; (ii) theelocity patterns vary with the development of upstream flows

nd the generation of the new boundary layers near the inneralls at the dividers; (iii) the skewed profile with a maximum

xial velocity near the inner wall may be observed just after theow divider so that different tubes may experience different airow rates; (iv) strong secondary vortices appear inside the branch

L/min. The left panel exhibits mid-plane speed contours. The right panel shows theng and Kleinstreuer, 2004).

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ubes. The upstream flow fields (i.e., flow history), and realistic air-ay geometry features (e.g., asymmetric bifurcations, non-planarranches, cartilaginous rings and local obstructions) will influencehe specific airflow characteristics, including patterns of skewedxial velocity profiles, axial velocity magnitude, as well as loca-ions and intensities of secondary vortices (see Zhang et al., 2002d;Nowak et al., 2003; Yang et al., 2006; Li et al., 2007b; Lin et al.,007).

.2. Particle deposition

.2.1. Micron vs. nano-size particlesIn general, both transport and deposition of inhaled particu-

ate matter are definitely size-dependent. Typically, nanomaterialispersion is due to diffusion and convection, while micronarticles are transported via convection and/or sedimenta-ion. Specifically, micron-particle deposition in the lung occurs

ainly by impaction, including secondary airflow convectingarticles to the airway walls, as well as diffusional or gravita-ional effects. Clearly, inertial impaction (IP) is proportional tohe air flow rate (Q) and the (aerodynamic) particle diameter

dp) squared, as expressed with the impaction parameter, i.e.,

P = Qd2p (1)

Concerning particle deposition mechanisms, diffusional andravitational phenomena are measurable at very low flow rates,.e., typically in the lower lung regions, where diffusion is domi-ant for ultrafine particles in areas of high concentration gradientsnd gravity effects significant for relatively large/heavy particlesHeyder, 2004). Key in diffusional transport of spherical nanoma-erial due to the Brownian motion effect is the diffusion coefficientiven by the Stokes–Einstein equation:

nano = kBTCslip

3��dp(2)

here kB is the Boltzmann constant (1.38 × 10−23 J K−1), T is theemperature, � is the fluid viscosity, and Cslip is the Cunninghamlip correction factor (Clift et al., 1978).

For particle deposition studies the Stokes number (St) is gener-lly being used in the form

t = �pd2pU

18�D(3)

hich can be also interpreted as the ratio of particle relaxation andow characteristic times. In Eq. (3), �p is the particle density. Thus,he Stokes number, being mainly a function of particle-diameterquared as well as the characteristic air velocity U and length scale, is a measure of the influence of the inertial effects during aarticle’s trajectory. However, in the (human) respiratory systemhe local airway geometries are rather complex or exhibit sud-en changes, while the airflow velocities are rapidly changing asell. Thus, Stokes numbers as well as Reynolds numbers have to beefined locally to capture more accurately the underlying physics

DFparticle

DEparticle

f micron-particle deposition.

.2.2. Micron-particle depositionAssuming non-interacting spherical micron particles, a

agrangian frame of reference can be employed and in light

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& Neurobiology 163 (2008) 128–138 133

f the large particle-to-air density ratio, dilute particle suspen-ions and negligible particle rotation, drag is the dominant forceith additional forces relevant near the airway walls. Thus,ewton’s second law of motion can be written for laminar and

urbulent micron-particle transport as:

ddt

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i+ Fi,lubrication + Fi,interact (4)

here uPi

and mp are the velocity and mass of the particle, respec-

ively, FD is the drag force, Fgravityi

is gravity, and the underlinedorce terms (lubrication and interaction forces) are activated nearhe airway wall (Longest et al., 2004). For high aerosol loadings,particle-particle interaction (or collision) force has to be added.hen non-isothermal effects have to be considered, including par-

icle growth (i.e., hygroscopicity), modeling details are given byhang and Kleinstreuer (2003b) and Broday and Georgopoulos2001), among others.

The regional deposition of micron particles in human airwaysan be quantified in terms of the deposition fraction or depositionfficiency in a specific region (e.g. oral airway, first, second and thirdifurcation, etc.). They are defined as:

number of deposited particles in a specific regionumber of particles entering the mouth and/or nose

(5)

umber of deposited particles in a specifc regionnumber of particles entering this region

(6)

The regional deposition efficiency is mainly used to develop theeposition equation for algebraic (total) lung modeling.

The local deposition patterns of micron particles can be quanti-ed in terms of a deposition enhancement factor (DEF). The particleeposition enhancement factor is defined as the ratio of local toverage deposition densities, where deposition densities are com-uted as the number of deposited particles in a surface area dividedy the size of that surface area (Balashazy et al., 1999, 2003; Zhangt al., 2005). Clearly, if the overall and maximum DEF-values inne airway region are close to one, the distribution of depositedarticles tends to be uniform. In contrast, the presence of high DEF-alues indicates non-uniform deposition patterns, including “hotpots”. Some “hot spots” of toxic particulate matter are related tohe induction of certain lung diseases, e.g., cancer.

Focusing mainly on the oral and bronchial airways, micron-article transport and deposition has been extensively investigatedy Stahlhofen et al. (1989), Katz and Martonen (1996), Li et al.1998), Balashazy et al. (1999, 2003), Cheng et al. (1999), Katz etl. (1999), Kim and Fisher (1999), Corcoran and Chigier (2000),tapleton et al. (2000), Gemci et al. (2002), Zhang et al. (2002a,b,c,005), Kleinstreuer and Zhang (2003a, 2003b), Grgic et al. (2004),eyder (2004), Matida et al. (2004), van Ertbruggen et al. (2005),hang and Finlay (2005), Zhou and Cheng (2005), Longest et al.2006), Kleinstreuer et al. (2007b), and Xi and Longest (2007),mong others. Recently, micron-particle transport and deposi-ion in the human nasal airways have gained attention due to thedvancements in new nasal drug delivery technologies and com-uter simulations (Cheng, 2003; Kelly et al., 2004a; Su and Cheng,005; Inthavong et al., 2006; Shi et al., 2007). However, very lit-le information is available regarding transport and deposition ofaporizing droplet in the human nasal airways (Shi et al., 2007).

As shown in Fig. 3, micron-particle deposition during inhala-ion is mainly due to impaction, secondary flow convection, and

urbulent dispersion (Li et al., 2007a). Thus, they largely deposit attagnation points for axial particle motion, such as the tongue por-ion in the oral cavity, the outer bend of the pharynx/larynx, andhe regions just upstream of the glottis and the straight trachealube. As expected, for micron particles the high DEF-values appear

134 C. Kleinstreuer et al. / Respiratory Physiology & Neurobiology 163 (2008) 128–138

F(

mswlfl

tifpahfuR

FiQ

edX

3

pe(E(2a

wn

t

D

wwba(a

D

tt1d

ig. 3. Micron-particle deposition pattern in an oral-tracheobronchial airway modelQin = 30 L/min, dp = 5 �m) (see Li et al., 2007c).

ainly around the carinal ridges due to inertial impaction, but thepecific distribution of DEFs at each carina is different and variesith the inhalation flow rate as well. Some micron particles also

and outside the vicinities of the cranial ridges due to secondaryows and turbulent dispersion.

The local particle deposition patterns can be further quantita-ively described by 3D surface distributions of DEF results. As shownn Fig. 4 (Zhang et al., 2005), the maximum DEF-value is about 1400or dp = 10 �m. This implies that the deposition patterns of micronarticles in the upper airways are highly non-uniform, and hence

small surface area where the maximum DEF occurs, may receiveundred times higher dosages when compared to the average value

or the whole airway. Such a site of massive particle deposition issually located around the carinal ridges in the bronchial airways.ecent CFPD studies have also shown that more realistic models,

tecte

ig. 4. 3D distributions of deposition enhancement factor (DEF) of micron particlesn a bifurcation airway model representing G0–G3 under steady inhalation with

in = 30 L/min and dp = 10 �m (see Zhang et al., 2005).

.g., asymmetric and non-planar geometries, may result in someifferent local deposition rates (Nowak et al., 2003; Li et al., 2007a,c;i and Longest, 2007).

.3. Nanomaterial transport and deposition

The appropriate modeling approach for ultrafine particle trans-ort is the mass transfer equation with the Stokes–Einsteinquation for the Brownian motion type nanoparticle diffusivityDnano) (see Eq. (2)); although, a few researchers adopted theuler–Lagrange approach when simulating nanoparticle transportHofmann et al., 2003; Zamankhan et al., 2006; Longest and Xi,007b). Thus, the proper convection–diffusion equation for laminarnd turbulent transport reads:

∂Y

∂t+ ∂

∂xj

(ujY

)= ∂

∂xj

[(Dnano + �T

�Y

)∂Y

∂xj

](7)

here Y is the mass fraction and �Y is the turbulence Schmidtumber for Y.

The regional deposition fraction can be determined accordingo Fick’s law (Zhang and Kleinstreuer, 2004), i.e.,

Fregion =n∑

i=1

−Ai(D̃ + (�T/�Y ))(∂Y/∂n)∣∣i

QinYin(8)

here Ai is the area of the local wall cell (i), and n is the number ofall cells in one certain airway region, e.g., oral airway, first airwayifurcation, etc. The local deposition patterns of nanoparticles cangain be quantified in terms of a deposition enhancement factorBalashazy et al., 1999, 2003; Zhang et al., 2005), which is defineds the ratio of local to average deposition densities, i.e.,

EF =(D̃ + (�T/�Y ))(∂Y/∂n)

∣∣i∑n

i=1

[Ai(D̃ + (�T/�Y ))(∂Y/∂n)

∣∣i

]/∑n

i=1Ai

(9)

Assuming that the airway wall is a perfect sink for aerosols uponouch, the boundary condition at the wall is Yw = 0. This assump-ion is reasonable for fast aerosol-wall reaction kinetics (Fan et al.,996) and also suitable for estimating conservatively the maximumeposition of particles or toxic vapors in airways.

A typical nanoparticle deposition pattern is shown in Fig. 5 in

erms of DEF-distributions in a bifurcation airway model (Zhangt al., 2005). Again, the enhanced deposition mainly occurs at thearinal ridges and the inside walls around the carinal ridges dueo the complicated air flows and large particle concentration gradi-nts in these regions. As the particle size increases, wall depositions

C. Kleinstreuer et al. / Respiratory Physiology

Fig. 5. 3D distributions of deposition enhancement factor (DEF) of nanoparticlesin a bifurcation airway model representing G0–G3 under steady inhalation withQin = 30 L/min and dp = 10 nm (see Zhang et al., 2005).

Ffa

dfwtn2DmactamtstgHptccia2

hZttlrstftrdt(paa

4

msamatattmlmrptr

raoaps

A

RFGgtbCa

R

ig. 6. Experimentally validated computer simulation results of particle depositionractions in human upper airways as a function of particle size (see Shi et al., 2007nd Zhang et al., 2005).

ecrease and the air–particle mixtures become much more uni-orm, featuring flat similar particle distribution profiles and henceall gradients, which reduce the differences in local wall deposi-

ion rates (Zhang and Kleinstreuer, 2004). Geometric effects mayot significant for nanoparticle deposition (see Xi and Longest,008). Although the enhanced deposition sites (i.e., those with highEF-values) in the bifurcating airways are similar for nano- andicro-size particles, the maximum DEF-values for nanoparticles

re two to three orders of magnitude smaller than for microparti-les. Specifically, the DEFmax for microparticles is of the order of 102

o 103, while DEFmax for nanoparticles is of the order of 1 (Zhang etl., 2005). A more uniform distribution of deposited nanoparticlesay relate to a different toxicity effect when compared to fine par-

icles made of the same materials. Specifically, not only the largerurface areas relative to the particle mass but also, more impor-antly, the larger surface areas with a near-uniform deposition canenerate a higher probability of interaction with cell membranes.ence, it may result in a greater capacity to absorb and trans-ort toxic substances into tissue, blood and the whole body, andhe enhanced possibility of systematic diseases, such as cardiovas-ular diseases (see Hoet et al., 2004, Oberdörster et al., 2005). In

ontrast, the extremely high local DEF-values for micron particlesndicates the possibility of local pathological changes in bronchialirways, such as the formation of lung tumors (Balashazy et al.,003).

A

A

& Neurobiology 163 (2008) 128–138 135

A summary graph of regional particle deposition fraction inuman upper airways is given in Fig. 6 (see Shi et al., 2007 andhang et al., 2005, for details). It shows that inhaled particles inhe diameter range of 0.01 to about 1 �m are difficult to be cap-ured by the upper respiratory tract, i.e., they may reach the deeperung region if not exhaled (Heyder, 2004). Both inspiratory flowate and particle size play a significant role in the particle depo-ition process. Specifically, with an increasing particle diameterhe DFs decrease for nanoparticles because of the decrease in dif-usive capacity while they may increase for micron particles dueo increasing impaction. Similarly, the higher the inhalation flowate, the lower the deposition of nanoparticles and the higher theeposition of micron particles (Zhang et al., 2005). Furthermore,he location of bifurcation airways and airway geometry featurese.g., asymmetry, non-planar, obstruction) may influence inhaledarticle deposition as well, as numerically confirmed by Zhang etl. (2002d), Nowak et al. (2003), Farkas and Balashazy (2007), Li etl. (2007c), and Luo et al. (2007).

. Conclusions and future work

A review of research papers is presented, pertinent to computerodeling of airflow as well as nano- and micron-size particle depo-

ition in mainly pulmonary airway replicas. The key modeling stepsre outlined, including construction of suitable airway geometries,athematical description of the air–particle transport phenomena

nd computer simulation of micron and nano-particle deposi-ions. Specifically, diffusion-dominated nanomaterial deposits onirway surfaces much more uniformly than micron particles ofhe same material. This may imply different toxicity effects. Dueo impaction and secondary flows, micron particles tend to accu-

ulate around the carinal ridges and to form “hot spots”, i.e.,ocally high concentrations which may lead to tumor develop-

ents. Inhaled particles in the size range of 20 nm ≤ dp ≤ 3 �m mayeadily reach the deeper lung region. Concerning inhaled thera-eutic particles, optimal parameters for mechanical drug-aerosolargeting of predetermined lung areas can be computed, given rep-esentative pulmonary airways.

Future computational work will center around simulationealism and accuracy in order to understand and predict dosimetry-nd-health-risk effects in case of inhaled toxins and optimalperational conditions of smart inhaler systems in case of drug-erosol targeting. New hardware and software developments in theetascale computing environment will allow for patient-specificolutions to these problems.

cknowledgements

This effort was sponsored by the Air Force Office of Scientificesearch, Air Force Material Command, USAF, under grant numberA9550-07-1-0461 (Dr. Walt Kozumbo, Program Manager). The U.S.overnment is authorized to reproduce and distribute reprints forovernmental purposes notwithstanding any copyright notationhereon. The use of both CFX software from ANSYS Inc. (Canons-urg, PA) and IBM Linux Cluster at the High Performance Computingenter at North Carolina State University (Raleigh, NC) are gratefullycknowledged as well.

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