JOURNAL OF AEROSOL MEDICINEVolume 19, Number 3, 2006© Mary Ann Liebert, Inc.Pp. 329–343

Characterization of Regional and Local Deposition ofInhaled Aerosol Drugs in the Respiratory System byComputational Fluid and Particle Dynamics Methods

ÁRPÁD FARKAS, M.Sc.,1 IMRE BALÁSHÁZY, Ph.D.,1,2 and KATALIN SZOCS, Ph.D.3

ABSTRACT

The present work describes the local deposition patterns of therapeutic aerosols in the oro-pharyngeal airways, healthy and diseased bronchi and alveoli using computational fluid andparticle dynamics techniques. A user-enhanced computational fluid dynamics commercial fi-nite-volume software package was used to compute airflow fields, deposition efficiencies,and deposition patterns of therapeutic aerosols along the airways. Adequate numericalmeshes, generated in different airway sections, enabled us to more precisely define trajecto-ries and local deposition patterns of inhaled particles than before. Deposition patterns showa high degree of heterogeneity of deposition along the airways, being more uniform for nano-particles compared to micro-particles in the whole respiratory system at all inspiratory flowrates. Extrathoracic and tracheobronchial deposition fractions of nanoparticles decrease withincreasing flow rates. However, vice versa happens to the micron-size particles, that is, thedeposition fraction is higher at high flow rates. Both airway constrictions and the presenceof tumors significantly increased the deposition efficiencies compared to the deposition ef-ficiencies in healthy airways by a factor ranging from 1.2 to 4.4. In alveoli, the deposition pat-terns are strongly influenced by particle size and direction of gravity. This study demon-strated that numerical modeling can be a powerful tool in the aerosol drug deliveryoptimization. Present results may be integrated in future aerosol drug therapy protocols.

Key words: aerosol drug delivery optimization, computational fluid and particle dynamicssimulations, local distribution of deposited particles, deposition enhancement factor

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INTRODUCTION

THE INHALATION of therapeutic aerosols is aneffective method of drug delivery, frequently

applied to the management of respiratory dis-eases. New advances in biotechnology and mol-

ecular biology generate scores of potent thera-peutic aerosols that could open doors in combat-ing diseases. More recently, it has been demon-strated that the lung may be an ideal site for drugsto pass into the systemic circulation. Thus, the in-halation of drugs can be a new way of treatment

1Health and Environmental Physics, Department, KFKI Atomic Energy Research Institute, Budapest, Hungary.2Respirisk Scientific Research Co. Ltd., Budapest, Hungary.3Technoorg-Linda Ltd., Budapest, Hungary.

of certain diseases, usually much more acceptableto patients than the injections used nowadays.(1,2)

Other advantages of the inhalation of therapeu-tic aerosols are that it offers a non-invasive de-livery method and a more favorable absorptionenvironment compared to oral delivery, associ-ated with low pH and high protease level. Therespiratory system offers an enormous surfacearea for absorption, and a highly permeable ep-ithelium. Thus, inhaled therapeutics delivered lo-cally to the lungs may be directly transported tothe systemic circulation across the epithelium.

The main challenges in the field of aerosol drugtherapy are related to the inhaler and particle de-sign in order to deliver the right medication tothe right place. For the optimization of drug tar-geting, knowledge of particle transport and de-position parameters within the respiratory sys-tem is needed. The fate of therapeutic aerosolswithin the airways depends on particle proper-ties, breathing parameters and lung geometry,(3)

all of which, except the latter, can be optimized.For this purpose, experimental and complex com-putational modeling techniques have been used.Recently, significant advances in experimentalmodeling of pulmonary drug delivery were re-ported by numerous authors.(4–9) However, com-putational modeling techniques are non-invasive,cost-effective, reproducible, and repeatable asmany times as is needed and in as many circum-stances as is necessary.

Mathematical modeling of aerosol depositionwithin the respiratory system can be performedeither with analytical or numerical methods, eachwith its particular advantages and limits. The so-called respiratory tract models can be either sim-ple compartment models or complex approxima-tions of the airway system constructed fromstraight and bent tubes and spherical alve-oli.(10–13) These deposition models can also be ap-plied for the description of deposition of toxicaerosols in the respiratory tract.(14–20) These ap-proaches apply analytical deposition formulasderived for straight or bent tubes and spheressupposing simple uniform, parabolic or rota-tional flow profiles or empirical deposition for-mulas fitted to measured data. In reality, the de-position pattern of particles in the human airwaysis strongly inhomogeneous,(21) which these mod-els cannot describe. From a physiological point ofview, deposition patterns in different airwaysmay play a key role in determination of the ef-fects of inhaled drugs on health.(22) Thus, the

quantification of the heterogeneity of depositionshould be an important direction of present andfuture optimization of aerosol drug delivery.

In the last 15 years, with the advent of ad-vanced computational fluid dynamics (CFD)models and algorithms, the numerical simulationof airflow and particle transport has become pos-sible in airways in a quite detailed manner.(23–30)

Some recent CFD based papers put special em-phasis on therapeutic aerosol transport and de-position.(31–34) However, even nowadays, thesemodels cannot describe the three-dimensional de-position patterns in the whole respiratory system,only in characteristic sections of the airway.(35–39)

Thus, they are not able to substitute for so-calledlung deposition models, which can characterizethe deposition of particles in the whole respira-tory system.

In this work, we propose computational fluidand particle dynamics models to solve some prac-tical tasks, which are related to the distributionof therapeutic aerosols in the airways. As it isknown, therapeutic aerosols should be deliveredto different regions of the lung, depending on thelocation of the disease to be treated. With the ef-ficient targeting of aerosolized therapeutics, theeffect to the desired region can be maximized andunwanted side effects can be minimized. In ad-dition, the cost-effectiveness of drug delivery canalso be improved. For the optimization of aerosoldrug delivery, knowledge of particle depositionin extrathoracic, central and peripheral airways isnecessary. Hence, the first aim of this study wasto represent and quantify the deposition of in-haled aerosol drugs along upper, bronchial andalveolar airways. It has also been evidenced thatinhaled aerosol deposition is different in diseasedlungs compared to healthy lungs. The other pur-pose of this work was to describe and quantifythese differences in constricted and tumorous air-ways.

METHODS

Airway geometry model

The first step of this work was the generationof airway geometry using the commercially avail-able UNIGRAPHICS software. The tracheo-bronchial airways were constructed on the basisof the exact mathematical description of humanairway bifurcations published by Hegedus et

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al.,(40) applying the morphological data selectedby the stochastic lung model of Koblinger andHofmann,(12) which is based on the Lovelace mea-surement data.(41) This model ensures smoothtransitions between the airway branches and re-alistic curved carinal ridges. The geometry of air-way generations 1–5, leading to the right upperlobe of the bronchial tree, was built up by asym-metric “morphologically realistic bifurcation” el-ements.

The oral model comparable to the human castof Cheng et al.(42) was also built up in the UNI-GRAPHICS environment. Unlike the originalreplica, present geometry has circular cross sec-tions with diameters equal to the hydraulic di-ameters measured from the cast. Other minormodifications (suggested by Kleinstreuer andZhang(37) were made at the level of soft palate,mouth inlet and at the glottis.

Our two-dimensional alveolus model devel-oped in GAMBIT (the pre-processor of FLUENTCFD code) consists of a semicircle with a diame-ter of 238 �m and 250 �m in deflated and inflatedstates respectively and a tube with diameter of250 �m. These data correspond to the airway gen-eration 27 in the stochastic lung depositionmodel. Equations of wall motion were derivedwith the assumption that the alveolus remainsself-similar during a contraction-expansion cycle.Figure 1 presents the upper, central and alveolarairways described above.

Numerical mesh generation

Computational fluid dynamics methods re-quire spatial discretization that is the generationof an appropriate mathematical grid. Thepresently used finite-volume method can handleeither structured or unstructured mesh types.(43)

After some investigation, unstructured meshesproved to be more appropriate for the simulationof air and particle transport within the airways.Hence, unstructured, boundary and velocity gra-dient adapted numerical meshes with tetrahedralelements were generated using GAMBIT. Severalmeshes were constructed, either with homoge-neous or inhomogeneous structures. Our sug-gested and proved observation was that a well-constructed inhomogeneous mesh could yieldmuch more precise flow and particle depositionresults than homogenous ones. We used a size-function technique to construct the inhomoge-neous mesh, which permitted us to create adenser grid in the vicinity of the airway surfaces,where air velocity gradients are higher. A finermesh allows a better description of flow and par-ticle behavior. At the same time, excessive cellnumbers can lead to unrealistic running times.Our goal was to optimally fit the mesh size tothese conditions, which resulted in meshes rang-ing from a few thousand cells in the case of two-dimensional alveolus to 0.6 and 2.2 million com-putational control volumes in the case of the

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FIG. 1. Numerical airway geometries. (a) 3D oropharyngeal. (b) 3D tracheobronchial. (c) 2D alveolar.

three-dimensional upper airways and tracheo-bronchial tree, respectively. Special care wastaken to apply a fine boundary mesh, which fullyresolves the viscosity-affected near-wall region ofthe upper airways, in which the flow may be tran-sitional or turbulent. The unstructured tetrahe-dral (triangular in 2D) meshes, used in our flowfield and particle trajectory simulations are pre-sented in Figure 2.

Flow field computations

For the description of airflow fields within the airways, the Navier-Stokes equations weresolved for incompressible fluid with constant vis-cosity by a segregated solver of the FLUENT CFDcode. The integral forms of the mass and mo-mentum conservation laws were discretized.Each discrete governing equation was linearizedimplicitly, and then a Gauss-Seidel point implicitlinear equation solver was used in conjunctionwith an algebraic multigrid (AMG) method. Forthe computation of cell face values, a second-or-der upwind scheme was applied. At the end ofevery iteration step, scaled residuals were com-puted for each conserved variable.

In the tracheobronchial region, steady inspira-tory laminar flow computations were carried out.The inlet velocity profile of the flow entering thetrachea was set to be the outlet profile of the up-per airways, while at the outlets a uniform pres-sure condition was imposed.

In the upper airways, turbulent steady inspi-ratory flow field computations were imple-mented. A low Reynolds number k-� turbulencemodel with enhanced wall treatment proved tobe appropriate for the modeling of the laminar toturbulent airflows within the oral pathway pre-sented in Figure 1. Uniform velocity inlet and“zero gauge pressure” outlet boundary condi-tions were assumed. The inlet values of the tur-bulent kinetic energy and specific dissipation ratewere computed assuming a turbulence intensityof 3%.

Both steady and unsteady laminar alveolarflow fields were examined assuming parabolicvelocity inlet and constant pressure outlet bound-ary conditions. For all computations a no-slip velocity boundary condition was applied at thewalls.

Particle selection and transport

In the model, aerosol particles were randomlyselected at the appropriate inlet cross sections bya Monte-Carlo random number generator in ac-cordance with the inlet air velocity profile. Thus,the inlet velocities of the air and of the particleswere equal at a given point. For this purpose anown code was used, which generates the particleinjection files. These files were than imported intothe FLUENT solver.

The computation of particle transport and sub-sequent deposition calculations were based on anEuler-Lagrange method. In this model, the fluidphase is treated as a continuum and the discretephase is based on the forces acting on the parti-cles. A comprehensive analysis of this particletransport model can be found in Gradon and Pod-gorski.(44) One-way coupling between the fluidand dispersed phases was assumed, which meansthat solid particles are transported by the air butthey do not influence the airflow field. This as-sumption allowed us to decouple the particle tra-jectory code from the flow simulations to reducecomputational time. The possible depositionmechanisms (i.e. inertial impaction, gravitationalsedimentation, and Brownian diffusion) are as-sumed to operate simultaneously. The Brownian

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FIG. 2. Generated unstructured tetrahedral computa-tional grids. (a) Homogeneous mesh (upper left panel),inhomogeneous mesh with finer structure where the airvelocity gradient is high (upper right panel). (b) Mesh inthe carinal region of the airway bifurcations; c) alveolarmesh.

force-computing model of FLUENT was not ap-propriate here, because it requires very small timesteps leading to unrealistic running times. In-stead, an own model valid for larger time stepswas implemented through a UDF (user definedfunction), which was attached to FLUENT. Localdeposition patterns within the geometry were de-termined by the intersection of the simulated par-ticle trajectories with the surrounding wall sur-faces.

In the turbulent airflow the particle trajectorieswere predicted using instantaneous flow veloci-ties by adding the fluctuating gas flow velocityto the mean fluid phase velocity. For this purposea stochastic method (random walk model) hasbeen implemented.

Quantification of deposition patterns in the airways

In order to quantify the local inhomogeneitiesof deposition, deposition enhancement factorshave been calculated based on the computed de-position patterns. As proposed by Balásházy etal.,(21) the particle deposition enhancement factoris defined as the ratio of local to average deposi-tion densities. Deposition densities are computedas the number of deposited particles in a surfacearea divided by the size of that surface area. Wescanned the whole surface of the geometry by apre-specified surface element. Because the depo-sition enhancement factors are very sensitive tothe area of the scanning surface element, we haveselected an about 2000 �m2 size scanning surfaceelement, which corresponds to 20–25 epithelialcells. In this way, we were able to study the bur-den of a cluster of neighboring cells.

The regional and total deposition of particles canbe characterized by deposition fractions or deposi-tion efficiencies in specific regions of the airways.The deposition fraction in a specific region is de-fined as the ratio of the number of deposited par-ticles in that region to the number of selected par-ticles at the inlet. The deposition efficiency (�) in aspecific region is defined as the ratio of the num-ber of deposited particles in that region to the num-ber of particles entering the region.

For post-processing purposes (e.g., depositionvisualization, enhancement factor computing andvisualization), some user supplied subroutineshave been written in c�� language. Their com-pilation was usually performed by the compilerof the FLUENT.

RESULTS AND DISCUSSION

Airflow behavior and therapeutic aerosoltransport and deposition were modeled by theapplication of the computational model describedabove. The results are separated into four differ-ent sections. In the first section, we present oursimulations on air velocity distributions in dif-ferent bronchial airway generations. In the sec-ond section, the characteristic deposition ofaerosol drug particles in the upper and bronchialairways is presented and quantified. In the thirdsection, we treat the differences of particle depo-sition in diseased bronchial airways compared tothe healthy one. In the fourth section, character-istic behaviors of alveolar deposition are pre-sented at both steady and unsteady airflows.

Airflow pattern simulations

Air is the carrier gas of therapeutic aerosols,thus its flow characteristics must be well under-stood. For the characterization of airflow fields,pressure and velocity values and their gradientswere determined in every cell center. Air veloc-ity and pressure values at points other than cellcenters were calculated using Taylor expansions.Figure 3 shows the computed air velocities in air-way generations 3–4 of the Weibel’s model(45) byvelocity isoline representation in the centralplane. An isoline represents the contour of equalvelocity points. In our representation, the incre-ment between adjacent lines is constant, so re-gions with closely spaced lines are regions of highvelocity gradients, whereas regions with widelyspaced lines represent a relatively flat velocityfield.

The calculations were performed at both in-spiration (upper panels) and expiration (bottompanels) at 18 (left panels) and 60 L/min (rightpanels) tracheal flow rates. Vector fields, repre-sented in planes perpendicular to the branches,are also demonstrated in Figure 3.

A pair of secondary vortices was found in thecross-sections of the daughter branches duringinhalation and four vortices in the cross-sectionsof the parent branches during the exhalation.These results agree with the experimental data ofIsabey and Chang,(46) which validate our meshand computational model. Figure 4 presents theresults of our flow field simulations in airwaygenerations 1–5 performed on airway segmentsbuilt up from five individual asymmetric bifur-

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cation units, namely the trachea, main bronchi,right upper and middle lobar bronchi, and seg-mental and sub-segmental bronchi of the rightupper lobe. The geometric parameters of the sys-tem (airway diameters, lengths, branching andgravity angles) were selected using a stochasticlung deposition model.(12) Figure 4 presents thevelocity fields of the computed air velocitiesalong the main planes of the five bifurcation unitsby velocity isoline representation. The calcula-tions were performed for inspiratory, laminar,steady flow rate of 18 L/min.

Comparing Figure 4 with the upper panel ofFigure 3 reveals some striking differences in flow

patterns. The flow field of the single bifurcationexhibits axial symmetry due to the parabolic,hence symmetric, inlet velocity profile and sym-metric branching structure. The flow in the morecomplex system of five asymmetric bifurcationunits is quite different. The separation region ap-pears immediately at the onset of the central zonerepresenting generations 1–2, 4–5.1, and partly3–4 of the bifurcations. However, in generations2–3 and 4–5.2 of the bifurcations, they are absent.Since different velocity gradients mean differentresidence times for the carried particles, it is ex-pected that the deposition patterns will be dif-ferent in various bifurcations. In order to deter-mine the exact deposition patterns, particletrajectory computations are needed.

Characterization of aerosol drug deposition in theupper and central airways

Based on the computed flow velocity fields, in-haled particle trajectories have been traced tak-ing into account the main deposition mechanismsof inertial impaction, gravitational settling andBrownian diffusion. Due to the relatively highflow rates in the upper and bronchial airways, forlarge particles (�1 �m), impaction is the most sig-nificant deposition mechanism. Brownian motionplays a major role in the case of ultra fine andnano size particles (�0.1 �m). In general, otherforces can be neglected using order of magnitudearguments.(47) The material of the particles is fardenser than the air, thus, the buoyancy force, the

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FIG. 3. Steady airflow simulations in airway genera-tions 3–4 of the Weibel model in a morphologically real-istic airway bifurcation geometry. Velocity isoline repre-sentation of the airflow in the main plane and vector fieldrepresentation in a plane perpendicular to the branchesat inspiration (upper panel) and expiration (bottom panel)at 10 and 60 L/min tracheal volumetric flow rates.

FIG. 4. Velocity isoline representation of the computedair velocities along the main planes of the five bifurcationunits of the geometry in Figure 1 at 18 L/min inspiratorylaminar steady flow rate.

virtual mass effect and the pressure forces arevery small. The Saffman lift force can also be ne-glected for the low-level shear fields existing inthe present flows.(48) We also took into accountthat the distribution of the randomly injectedspherical particles follows the inlet velocity pro-file, as well as that the mucus layer traps the par-ticles intersecting the wall.

Inspiratory local deposition patterns and re-lated deposition efficiencies of inhaled particlesare presented in Figure 5 in airway generations3–4 of the Weibel’s model with different particlediameters, covering the 1 nm to 10 �m respirableaerodynamic size range. The deposition patternbecomes more and more inhomogeneous with in-creasing particle size. The enhanced accumula-tion in the vicinity of the carinal ridges and onthe inner sides of the daughter airways is com-mon for any particle size between 1 nm and 10�m. The deposition efficiency (�) is smallest formedium sized particles. The dominant depositionmechanism depends on particle size. For ultra-fine particles the diffusion, for microsize particlesthe impaction is the dominant deposition mech-anism.(22)

Results of computations of deposition en-hancement factors on the same airway geometryare displayed in Figure 6. The upper panel of Fig-ure 6 indicates that the enhancement factor val-ues are quite high in the vicinity of the carinalridges. Besides, their values are higher for largerparticles than for ultrafine particles. This can be

due to the more inhomogeneous deposition char-acteristics of large particles. Inspection of theright bottom panel demonstrates that the maxi-mum enhancement factor values, local depositiondensities, and related aerosol drug doses, are twoto three orders of magnitude higher than the av-erage deposition densities. The peak of the curvecan be found at around 1–2 �m particle size,which is in accordance with the results reportedby Balásházy et al.(21) for this flow rate. However,we obtained higher values for the maximum en-hancement factors because of the applied smallerpatch size.

The deposition patterns in airway bifurcationsare strongly influenced by the inlet air velocityfield and distribution of particle release points.Thus, for a more precise analysis of the deposi-tion patterns it is recommended to build up morecomplex airway geometries. Figure 7 presents thedeposition pattern of 50,000 randomly selectedparticles in the geometry shown in Figure 1 (rightupper panel). The inhalation flow rate was 18l/min. The particle size is 1 nm in the left and 10�m in the right panel. The deposition pattern ismuch more uniform for nano-particles than for10 �m particles. The deposition efficiency at thislow flow rate is about 10 times higher in the caseof nano-particles, as it has been expected.

In order to characterize the aerosol drug be-havior in the oropharyngeal airways under dif-ferent breathing conditions, inhaled monodis-perse particles were tracked in the oral pathwaygeometry presented in the methods section. Fig-ure 8 shows the deposition efficiency values com-puted at 15, 30, and 60 L/min flow rates. Micron-size particle deposition results are compared tothe deposition measurements of Cheng et al.(42)

As can be seen, there is a good agreement be-tween the measured and computed values, whichvalidates our model. The related deposition frac-tions, extended with the 1 nm cases, are summa-rized in Figure 9. Since Cheng et al.(42) did notperform deposition measurements of nanoparti-cles, our deposition results in this size range werecompared to the simulations of Zhang and Kle-instreuer.(38) Again, a good matching between theresults of the two simulations was found. Dataare displayed for the upper airways, airway gen-erations 1–5 and the whole system, as well. Ascan be seen, the deposition fractions are the high-est at 1 nm particles. Particles of this size are fil-tered by the upper and central airways and havelittle chance to reach the acinus, although this

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FIG. 5. Deposition patterns of selected 50,000 particleswith different diameters in the whole respirable range inthe same geometry as in Figure 3 at 60 L/min trachealvolumetric flow rate and parabolic inlet flow profile. dp:particle diameter; �: deposition efficiency.

would be desirable in the case of systemic deliv-ery of therapeutic drugs. A possible explanationof this problem, suggested by Tsapis et al.,(49) canbe the delivery of larger (1–5 �m) particles to thelungs that dissolve into polymeric nanoparticlesafter deposition. Another observation regardingnanoparticle deposition is that deposition frac-tions decrease with the increase of flow rate. Thisis certainly due to the decrease of diffusive ca-pacity at higher flow rates. Furthermore, higherflow rates result in decreased residence times fornanoparticles to deposit. However, the oppositetendency, that is, the increase of deposition frac-tions following flow rate increase, can be ob-served at 1 and 10 �m size particles. The reasonof this reverse effect is that the impaction of mi-croparticles increases at higher inhalation flow

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FIG. 6. Deposition enhancement factors for 10 �m (upper left panel) and 1 nm (upper right panel) particles and de-position enhancement factor maximum versus particle size (lower right panel) based on the deposition patterns il-lustrated in Figure 5.

FIG. 7. Deposition patterns of 50,000 randomly se-lected particles in the airway generations 1–5 of 1 nm(left) and 10 �m (right) particle sizes. The 18 L/min in-spiratory laminar steady flow rate corresponds to rest-ing breathing conditions. The inlet velocity profile isparabolic.

rates. The deposition fractions are the lowest for1 �m particles. The deposition fractions of 1 �mparticles at 15 L/min flow rate are about the samein upper and central airway segments. However,at 60 L/min flow rate, the deposition fraction of1 �m particles is about three times higher in theoro-pharyngeal region than in the tracheo-bronchial region. This can be due to the differentgeometry, but the reason might also be the highrelative numerical error of the computation at thisparticle size. To decide which of these two hy-

pothesizes is correct, further numerical error re-duction would be necessary. This would requiremuch more computer capacity than is currentlyavailable.

Effect of bronchial airway constrictions andtumors on bronchial deposition

Aerosol drugs are usually applied not inhealthy but in diseased lungs. Some airway dis-orders, like chronic bronchitis, emphysema,asthma bronchiale, cystic fibrosis, bronchiectasiaor bronchiolitis obliterans may alter the airstreamsand related deposition. Intraluminar tumors mayalso have important effect on flow configurationand deposition patterns. This enhancement leadsto locally higher air velocities and a more inten-sive inertial deposition. However, the other de-position mechanisms (like gravitational settling ordiffusion) may be more important in some cir-cumstances. Accurate computer simulations canshow the effect of each parameter on the deposi-tion of particles within the diseased airways. Theeffect of airway constrictions and tumors on par-ticle deposition patterns is analyzed here in air-way generations 3–5. Characteristic depositionpatterns are presented in Figure 10 for 10 �m sizeparticles in the case of healthy airways (upper leftpanel), constricted airways (upper right panel),and tumorous airways (bottom panels) at a tra-cheal volumetric flow rate of 18 L/min. The de-

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FIG. 8. Comparison of simulated (empty symbols withlines) and measured (scatter plot with filled symbols)oropharyngeal deposition efficiencies.

FIG. 9. Upper and tracheobronchial airway deposition fractions of 1 nm, 1 �m, and 10 �m particles.

position efficiencies are also shown on Figure 10separately in each bifurcation unit and in thewhole system.

In case of constricted airways, a symmetric con-striction was simulated on both daughter air-ways, namely the airway diameter decreased lin-early to the half along its length. We simulatedtumorous airways by placing a 4-mm-diameterspherical indentation either on the inner side ofthe first daughter airway (bottom left panel) or inthe center of the carinal ridge (bottom rightpanel). The deposition pattern in healthy airwaysis similar to that reported by Comer et al.(28) Theapplied airway constriction strongly increases thedeposition efficiency. At the level of the wholesystem the deposition increased by a factor of 4.4while in the second bifurcations by a factor of17.8. In conclusion, large aerosol drug particleswill deposit more efficiently in the constricted air-ways (e.g., in the case of chronic obstructive pul-monary disease [COPD] patients). Similarly, both

tumor types enhance the deposition efficiency:the side-tumor with a factor of 1.7 and the cen-tral tumor with a factor of 1.9. The depositiondensity becomes quite high on the front side ofthe tumor surface.

Figure 11 presents the deposition patterns of 1�m particles calculated on the same system andwith the same conditions as in Figure 10. In thiscase, due to smaller impaction, the number of de-posited particles is significantly lower than in thecase of 10 �m particles. The deposition efficien-cies are 30-60 times smaller than they were in thecase of 10 �m particles. The modeled airway con-striction similarly increases deposition of largeparticles, with a factor of 4 compared to thehealthy system. The tumors increase depositionwith a factor of 1.2 (side tumor) and 2.6 (centraltumor) compared to the healthy system. The dif-ference between the deposition efficiencies in thecase of the two tumors is larger at small particles.It is also worth mentioning that the local deposi-

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FIG. 10. Deposition patterns of 50,000 randomly selected 10-�m-diameter particles in airway generations 3–5 (Weibelmodel, 1963) at stationer inspiratory laminar flow assuming a 18 L/min tracheal flow rate. Upper left panel: Healthyairways. Upper right panel: Constricted airways; Bottom left panel: 4-mm-diameter side tumor. Bottom right panel:4-mm-diameter central tumor.

tion density can be quite high at both types of tu-mors, before the indentation at side tumors andat the center of the indentation at central tumors.In reality the tumor can have shapes other thanspherical. However, the present model and re-sults might be useful during the implementationof aerosol drug therapies.

Simulation of alveolar deposition patterns

For pulmonary drug delivery, the degree of de-position and the distribution of deposition withinthe alveoli can also be important. Hopefully, inthe near future, more and more therapeutic mol-ecules will be delivered to the systemic circula-tion via acinus.(50)

In our study, the monodisperse spherical par-ticles were injected at the alveolar orifice. Spatialdistribution of the selected particles corre-sponded to the air velocity distribution at the ori-fice. The simulations presented in Figure 12 wereperformed for steady inspiratory flow and flowrates matching to sitting breathing conditions; thegravity orientation is also shown.

In the lower panels of Figure 12, the depositionpatterns in an alveolus with stationary wall arepresented. Although particles smaller than 0.1�m or larger than a few microns have little chanceto reach the acinus, they were included in oursimulations. Our scope was to see the general ten-dencies, that is, the effect of different orientationsand particle sizes in this region of the lungs. Theupper panels of Figure 12 demonstrate the dis-tribution of deposition along the axis of the tube(x coordinate). We set the channel width of thehistogram to 6.25 �m in order to approximate thesize of epithelial cells.(51) The strong dependenceof the local deposition patterns on particle size isdue to the different dominant deposition mecha-nisms. The deposition pattern of particles with di-ameter less than 0.1 �m was very similar. Henceonly the deposition of 0.1 �m particles is pre-sented. In the case of 0.1 �m particles, the den-sity of the particles is higher at the two ends ofthe alveolus along the x axis because of the lowdiffusion distance at these locations and of theshortage of effective gravitation and impactionforces (left panels in Fig. 12). In this case, the dom-

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FIG. 11. Deposition patterns of 1 �m size particles calculated with the same parameters as in Figure 10.

inant deposition mechanism is diffusion. In-creasing the particle size, the gravitational sedi-mentation and impaction may have more andmore effect on deposition. For medium size par-ticles, the deposition in the alveolus follow a dis-tribution as depicted in the middle panels of Fig-ure 12. The asymmetry of the distribution mightoriginate from the effect of impaction, gravity, orboth of them. In the assumption that impactionis the dominating deposition mechanism, theasymmetry of 10 �m particles deposition patternmust further intensify. However, the right panelsof Figure 12 reveal that the deposition pattern of10 �m particles is quite symmetric. The reasonmay be the gravity, which can be dominant at theexisting low particle velocities. To prove this, we

repeated the deposition simulations for 1 and 10�m particles with the same conditions as before,but without gravity. As a result, both the depo-sition efficiency of 1 and 10 �m particles fell to0%, because particles follow the air streamlines,which do not intersect the alveolar wall.

Since the gravity plays a major role in particledeposition in the pulmonary region, alveolar par-ticle deposition was investigated under differentgravitational orientations. The deposition effi-ciencies in the whole alveolus are represented foreight different orientations of the alveolus togravity as a function of particle size (Fig. 13). Themain outcome of the figure is that for small par-ticles (up to 0.1 �m) the deposition efficiencydoesn’t depend on the direction of gravity and its

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FIG. 12. Distributions of deposited 8,000 particles in an alveolus at stationary wall and steady inspiratory flow con-ditions for 0.1, 1, and 10 �m diameter particles. Geometric and flow parameters correspond to airway generation 27and sitting breathing conditions.

FIG. 13. Deposition efficiencies in an alveolus as a function of particle size at sitting breathing condition in the caseof eight different orientations of the alveolus to gravity. Left panel: steady inspiratory flow and stationary wall. Rightpanel: unsteady flow with inflating and deflating alveolus. Orientations: the angle between the gravity vector andthe normal vector of the orifice showing into the alveolus is A � 0°, B � 135°, C � 270°, D � 225°, E � 180°. F � 135°,G � 90°, H � 45°, measured in the (x,y) coordinate system settled in Figure 1.

value is roughly 50%. This is due to the dominanteffect of Brownian diffusion, which is responsi-ble for the statistical selection of particle deposi-tion. However, around and over 1 �m particlesize, the orientation of the alveolus to gravity hasa dominant role in the deposition and the effectof diffusion is negligible.

In order to increase the accuracy of these re-sults, we repeated the simulations describedabove for an alveolus with inflating and deflat-ing wall and unsteady airflow (right panel in Fig.13). Figure 13 reveals that the effect of gravity ondeposition appears between 0.1 and 1 �m, andbecomes dominant at 10 �m. Computations wereperformed down to 1 nm particle size becausenowadays and even in the near future also nano-size particles will be used for therapeutic pur-poses.(52–54)

CONCLUSION

This study demonstrated that CFD modelingcould be a powerful tool for the prediction of lo-cal deposition patterns and efficiencies in anycharacteristic region of the respiratory system.The method may play an important role inaerosol drug delivery optimization to deliverdrugs to the desired region of the respiratory tractwith the highest possible probability.

Most of the current numerical airway geome-try models were constructed from straight andbent tube elements. Our modeling efforts were fo-cused on the numerical construction of realisticshape geometry with smooth transitions amongthe airways and with curved airway carinas. Thegenerated computational mesh applies size func-tion techniques to allow a denser numerical gridin the vicinity of the surface than deeply insidethe airway lumen. Airflow, particle depositionpatterns, and deposition efficiencies have beensimulated in a large respirable particle size range(1 nm to 10 �m).

We found highly inhomogeneous depositionpatterns in the studied tracheobronchial airwaysegments. Heterogeneity of deposition patternswas analyzed by computing deposition enhance-ment factors. Maximum aerosol drug depositiondensities were two-three orders of magnitudehigher than the average values indicating highdrug doses in the hot spots. This is in agreementwith some earlier studies.(21,39) However, presenthigh mesh resolution enabled us to enhance the

accuracy of quantification of the deposition. Inaddition, the significant increase of the numberof simulated particle trajectories provided statis-tically more reliable data than ever before.

An oral pathway was used to analyze the ef-fect of oral airways to central airway deposition.In this manner, regional deposition computationsbecame possible. Our data showed that the up-per and bronchial airways filter the small andlarge particles, thus, the intermediate size parti-cles (0.1–1 �m) have the highest chance to reachthe acinus.

As therapeutic aerosols are delivered mostly todiseased lungs, deposition in airways with air-way constrictions and tumors were simulatedand compared to the healthy cases. Potential air-way constrictions or intraluminar tumors maysignificantly alter the flow and deposition char-acteristics.(32,55–57) Airway disorders led to the in-crease of deposition efficiency. This increase wasmore accentuated for airways with constrictions.To our knowledge, this paper is the first CFDstudy of nanoparticle deposition in diseasedlungs. The deposition distribution of nano parti-cles may play a significant role because mucocil-iary and phagocytic cleaning mechanisms are lesseffective for nano size particles(58,59); thus, theycan remain in the airways for a relatively longertime (about 1 day).

In addition, CFD simulations of alveolar drugdeposition patterns and efficiencies as a functionof particle size and orientation of gravity havealso been performed for the first time. The im-portance of optimized drug delivery to the alve-oli will increase with the spreading of medica-tions delivered to the systemic circulation via thelungs, which is expected in the near future.

Current simulations revealed that the deposi-tion of inhaled therapeutic aerosols is strongly inhomogeneous, depending on the airway geom-etry, breathing parameters, and particle charac-teristics. Thus, the optimal set-up of the change-able parameters will help us to deliver themedication to the right place. The methods andresults of this work may serve as useful infor-mation in this process.

The perspectives of the computational aerosoldrug delivery optimization can be based on theintegration of current respiratory tract models,like the stochastic lung deposition model and theCFD based local deposition pattern models. Inaddition, constructing the airway geometry fromindividual computer tomography or magnetic

LOCAL DEPOSITION OF AEROSOL DRUGS 341

resonance images can significantly enhance theaccuracy of the airway geometry models. Furtherimprovement in these directions is in progress.

ACKNOWLEDGMENTS

We wish to thank Gábor Barcsa for his help inpreparation of the manuscript. This research wassupported by the Hungarian NKFP-1/B-047/2004, NKFP-3/A-089/2004 Projects, and by theGVOP-3.1.1.-2004-05-0432/3.0 Hungarian-Euro-pean Union Project.

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Received on July 14, 2005 in final form, December 5, 2005

Reviewed by: Jeffry Schroeter, Ph.D.

Address reprint requests to:Árpád Farkas, M.Sc.

Health and Environmental Physics DepartmentKFKI Atomic Energy Research Institute

P.O. Box 49 H-1525 Budapest, Hungary

E-mail: farkasa@sunserv.kfki.hu

LOCAL DEPOSITION OF AEROSOL DRUGS 343

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