ORIGINALARBEIT

Theoretical models for dynamic shape factors and lungdeposition of small particle aggregates originating from

combustion processes

Robert Sturm ∗

Brunnleitenweg 41, 5061 Elsbethen, Salzburg, Austria

Received 24 November 2009; accepted 17 April 2010

Abstract

A theoretical model was developed which allows the gen-eration of irregularly shaped aggregate particles due tothe stepwise joining of spherical components with variablediameters. The mathematical approach is mainly thoughtto act as a supporting tool for the simulation of the trans-port and deposition behaviour of combustion aerosolsin the atmosphere and the human respiratory tract. Incombination with aggregate construction essential par-ticle parameters (dynamic shape factor χ, aerodynamicdiameter dae) are computed using the model. As a mainresult of aggregate generation, an increasing particle size,expressed by an increasing number of spherical compo-nents, leads to an enhancement of χ and dae, wherebyvalues of the first parameter range from 2 to 70. Depo-sition of small aggregates (sizes between 2 and 200 nm)in the human respiratory tract is commonly marked byhigh rates of bronchial particle accumulation (40-60%)and declined rates of extrathoracic (20-30%) and alveolaraccumulation (2-15%). Concerning aggregate depositionby airway generation, increased cluster size causes a sig-nificant decrease of particle accumulation in the proximalairways, whilst accumulation in the intermediate to dis-tal airways is dramatically enhanced. The model wasvalidated using experimental deposition data of tobacco

Theoretische Modelle der dynamischenFormfaktoren und Lungendeposition vonkleinen, aus Verbrennungsprozessenstammenden Partikelaggregaten

Zusammenfassung

Ein theoretisches Modell wurde entwickelt, welchesdie Generierung unregelmäßig gestalteter Aggregat-teilchen infolge des stufenweisen Aneinanderfügens vonsphärischen Komponenten mit variablem Durchmessergestattet. Die mathematische Näherung ist hauptsäch-lich dazu gedacht, als unterstützendes Werkzeug für dieSimulation des Transport- und Depositionsverhaltens vonVerbrennungsaerosolen in der Atmosphäre und im mensch-lichen Respirationstrakt zu dienen. In Verbindung mit derKonstruktion der Aggregatteilchen steht die Berechnungessentieller Partikelparameter (dynamischer Formfak-tor χ, aerodynamischer Durchmesser dae). Als einwesentliches Resultat der Aggregatkonstruktion ist dieErhöhung von χ und dae mit steigender Teilchengröße –ausgedrückt durch eine steigende Anzahl an sphärischenKomponenten – anzusehen, wobei ersterer Parameterzwischen 2 und 70 variiert. Die Deposition kleiner Aggre-gate (Größen zwischen 2 und 200 nm) im menschlichen

∗ Brunnleitenweg 41, A-5061 Elsbethen, Salzburg, Austria. Tel.: +43 662 633321.E-mail: Robert.Sturm@sbg.ac.at.

Z. Med. Phys. 20 (2010) 226–234doi:10.1016/j.zemedi.2010.04.001

http://www.elsevier.de/zemedi

R. Sturm / Z. Med. Phys. 20 (2010) 226–234 227

smoke. An excellent correspondence between experimentaland theoretical results was found.

Keywords: Combustion aerosols, aggregates,particle shape, lung deposition

Respirationstrakt ist durch hohe bronchiale Teilchenakku-mulationsraten (40-60%) und verringerte extrathorakale(20-30%) und alveolare Akkumulationsraten (2-15%)gekennzeichnet. Hinsichtlich der Ablagerung von Aggre-gatteilchen in einzelnen Luftwegsgenerationen bewirkteine Erhöhung der Clustergröße verringerte Depositionin den proximalen Luftwegen, während die Deposition inden mittleren bis distalen Luftwegen deutlich ansteigt. ZurValidierung des Modells wurden experimentelle Daten zurLungendeposition von Tabakrauch herangezogen. Dabeikonnte eine exzellente Übereinstimmung zwischen experi-mentellen und theoretischen Resultaten festgestellt werden.

Schlüsselwörter: Verbrennungsaerosole, Aggregate,Teilchengeometrie, Lungendeposition

Introduction

Aerosol particles may be regarded as serious health haz-ards, but may also have remarkable effects on the climaticcycle, atmospheric transparency, and environmental deposi-tion of acidic or toxic substances. Besides this hygienic andenvironmental significance, aerosol particles have also foundnumerous industrial applications. Independent of the site,where an aerosol is formed, properties of aerosol particlesare mainly affected by the particle shape and size. There-fore, many methods of aerosol concentration measurementare based on the determination of particle diameter classes[1–4].

Aerosol particles derived from combustion or thermaldecomposition processes, summarily termed smokes andsoots, are commonly characterised by a highly irregular shape,regardless of origin and chemical composition. Such irregu-larly shaped particulate material is frequently composed ofhigh numbers of individual primary particles that form a so-called aggregate [5]. In the past, the primary components ofan aggregate were remarkably simplified in so far, as theywere defined as small spheres without showing any shapeeffects or geometric imperfections [5–9]. Recently conductedmeasurements of atmospheric aerosols have provided clearevidence that soot aggregates are practically always detectedin the ambient air volume [10] and thus perform a considerableinfluence on human state of health. Due to the circumstancethat soot aggregate geometry may be categorised as highlychaotic, mathematical approaches using fractal geometry havebeen developed to describe aggregate shape with sufficientaccuracy [11]. According to our current knowledge highest

Theoretical models of aggregate geometry and relatedbehaviour of such particle complexes in the continuum regimeand slip flow regime already date back to the 1970 s [6–9]and 1980 s [5,14]. Kasper [5] divided aggregates accordingto their shape into two main categories: First, clusters whichcan be treated like a porous sphere and, second, chains whichcorrespond in their behaviour to prolate bodies. In more cur-rently conducted mathematical approaches to the shape ofaggregates Kasper’s classification was subjected to a furtherrefinement. Regarding irregularly shaped aerosol particlesconsisting of small, equally sized spheres clusters withoutvoids were distinguished from compact aggregates with inter-nal voids as well as loose aggregates with internal voids[10,15,16]. Each of these three categories is characterisedby individual diameters, volumes, and dynamic shape factors(Table 1). As demonstrated by microscopic studies on soot par-ticles deposited in the lungs and captured in the bronchial andalveolar parenchyma of laboratory animals [17,18], clustergeometry may be most appropriately approximated by looseand compact aggregates of spherules with internal voids.

The work presented here has two main objectives: First,a mathematical model is introduced for the generation ofclusters containing non-equally sized spherules and the com-putation of related size parameters and dynamic shape factors.Second, deposition of these theoretically generated particlesin a stochastic lung architecture is simulated. Results derivedfrom the deposition calculations are compared with respectivedata obtained from experimental studies.

Methods

amounts of soot particles are emitted by diesel engines andhave sizes between several tens to hundreds of nanometers. Inmedical respects these very special aggregates have excitedpublic interest because of their proven contribution to theburden of pulmonary and cardiovascular diseases [12,13].

Modelling aggregate geometry and related dynamic

shape factors

Concerning the theoretical generation of aggregates con-sisting of a pre-defined number of spherules with various

228 R. Sturm / Z. Med. Phys. 20 (2010) 226–234

Table 1Shapes of aggregates and related diameters, volumes, and dynamicshape factors [10]. Variables: dme. . .mass equivalent diameter,dve. . .volume equivalent diameter, dm. . .electrical mobility diam-eter, δ. . .fraction of internal void spaces, ρp. . .particle density,ρm. . .material density, χ. . .dynamic shape factor, χ’. . .dynamicshape factor based on dme.

sin

· de

diameters a model based on the following assumptions wasdeveloped: First, positions of single spherical components ofthe aggregate are determined by the distances between theircentres (x1. . .xn) and the two angles α and γ , describing the

angles between the connecting lines x1. . .xn from the X-axisand from the XY-plane (Fig. 1). Second, single spherules toucheach neighbour at a common point, so that each connectingline x consists of the two radiuses of the adjacent compo-nents. Third, if a location of a spherical component is already

occupied by a previous spherule, a new location is computedaccording to the random number concept. Forth, each spheri-

des =√

(sin α1 · x1)2 + (sin α2 · x2)2 − 2

dnes =

√(sin α

dn−1es

· dn−1es )

2 + (sin αn · xn)2 − 2 sin αdn−1es

cal component may share several points of contact with otherspherules, thereby guaranteeing the generation of both chainsand compact aggregates (Table 1).

Based on the paradigms noted above the diameter of thesphere enveloping the whole aggregate, des, which is highly

Figure 1. Main distance and angular parameters used for the theoret-ical construction of aggregates that consist of variably sized sphericalcomponents.

essential for an accurate estimation of the aggregate’s dynamicshape factor, may be evaluated by application of rather simpletrigonometric considerations (Fig. 1). Assuming an aggregatesolely containing three spherical components, des is derivedfrom the equation

α1 · x1 · sin α2 · x2 · cos[γ1 + (180◦ − γ2)] + r1 + r3, (1)

where x1 and x2 denote the connecting lines between the cen-tres of spherule 1 and 2 as well as spherule 2 and 3, α1, α2, γ1,and γ2 the angular deviations of the connecting lines alreadyexplained above, and r1 and r3 the radiuses of spherule 1 and3. In the general case of an aggregate consisting of n spher-ical components, the diameter of the enveloping sphere, dn

es,is computed according to the formula

n−1s · sin αn · xn · cos[γ

dn−1es

+ (180◦ − γn)] + r1 + rn. (2)

In Eq. (2) dn−1es represents the enveloping sphere diameter

of the same aggregate, but with n-1 spherical components,whilst αdes(n-1) and γdes(n-1) are the specific angles describ-ing the position and orientation of dn−1

es in space (Fig. 1). As

in Eq. (1) r1 denotes the radius of the first spherical com-ponent, whereas rn has to be associated with the radius ofthe last spherical component. The two angles αdes(n-1) andγdes(n-1), representing essential parts of Eq. (2), are calculated

s. 20 (2010) 226–234 229

0 − αn−1))

s(αdn−2es

+ (180 − αn−1))

⎤⎦ (3)

−s(γ

⎤

R. Sturm / Z. Med. Phy

according to:

αdn−1es

= αdn−2es

+ arcsin

⎡⎣ xn−1 · sin(α

dn−2es

+ (18

(dn−2es )

2 + x2n−1 − 2dn−2

es · xn−1 · co

γdn−1es

= γdn−2es

− arcsin

⎡⎣ xn−1 · sin(γn−1 + (180

(dn−2es )

2 + x2n−1 − 2dn−2

es · xn−1 · co

By taking into account Eqs. (1) to (4), arbitrary values ofdes, α, and γ are most easily obtained by application of aforward-modelling algorithm, according to which the aggre-gate of interest is built due to the addition of single sphericalcomponents. An example of such an algorithm, within whichthe number of spherules defining an aggregate is continuouslyincreased, is illustrated in Figure 2.

Estimation of the dynamic shape factor, χ, is based on thesimple equation [5]

χ = des

dve

, (5)

where des again denotes the diameter of the sphere envelopingthe aggregate, whilst dve represents the diameter of a spherewith identical volume as the aggregate of interest (‘volumeequivalent diameter’). Thus, dve is calculated according to

dve = 3

√√√√ n∑i=1

d3i , (6)

with n representing the number of spherical components of theaggregate and di being the diameter of spherical componenti. The aerodynamic diameter, dae, is finally obtained from thefollowing equation [5,10,19,20]:

dae = dve ·√

1

χ· ρp

ρ0· CC(dve)

CC(dae). (7)

ρp and ρ0 correspond to the density of the aggregate andto unit density (1 g/cm3), respectively, whereas CC(dve) andCC(dae) are the so-called Cunningham slip correction factors.In general, particle slip correction is calculated according to

CC(d) = 1 + 2λ

d·[a + b · exp

(c

2λ/d

)], (8)

where λ corresponds to the mean free molecular path length inair (0.066 �m at 20 ◦C), whilst a, b, and c are empirical coeffi-cients that can be obtained from comprehensive reviews [21].Eq. (7) may be applied to both the continuum regime andthe free-molecular regime. In the continuum regime, which

γdn−2es

))

n−1 + (180 − γdn−2es

))⎦ (4)

is commonly assumed for the calculation with large parti-cles (d > 0.5 �m), the Cunningham slip correction factors areapproximately 1, so that they may be omitted from Eq. (7).

Modelling the deposition of aggregates in the humanrespiratory tract

Computations of aggregate deposition in the human res-piratory tract based on the aerodynamic diameter conceptintroduced in Eqs. (5) to (8) were carried out using a fre-quently validated stochastic particle transport and depositionmodel [19,20]. Within this mathematical approach trajectoriesof single aggregates through the tracheobronchial tree are ran-domly selected, whereby at each airway bifurcation the furtherprogress of a particle is computed separately. Therefore, thedecision of a particle entering one of the two daughter airwaysof a bifurcation among other depends on the distribution ofinhaled air volume between the two daughter tubes (the higherthe air volume flowing through a tube, the higher the proba-bility of the particle for entering this airway). The structureof the lung is systematically generated by the random selec-tion of essential geometric parameters (airway diameter andlength, bifurcation and gravitation angle) from related airwaygeneration-specific probability density functions [21], whichare founded on morphometric data sets of the human lung[22,23].

Simulation of aggregate deposition is performed by apply-ing empirical formulae for the three main deposition forces(Brownian diffusion, inertial impaction, and gravitationalsettling [24,25]). Deposition probability due to Browniandiffusion, which exhibits highest efficiency for particles<100 nm, mainly depends on airway geometry (radius,length), the velocity of the air stream passing an airway, andthe diffusion coefficient [25,26]. Mathematically, this rela-tionship is expressed by an empirically derived exponentialfunction. Deposition of aggregates caused by sedimentationis also represented by an exponential function, underlining theinfluence of airway geometry, the orientation of the airwayswithin the gravitational force field as well as properties of theparticle and the transport fluid (Eq. (3) in [26]). Deposition

by inertial impaction, which is most prominent for particles>1 �m, mainly depends on the branching angle of an airwaybifurcation passed by the air stream and the Stokes numberincluding particle and transport fluid characteristics (Eq. (4)-

230 R. Sturm / Z. Med. Phys. 20 (2010) 226–234

Figure 2. Flow chart illustrating the main steps of aggregate generation. In a first step main geometric parameters (diameters d, angles α androglarted

γ) are selected using a random-number concept. Subsequently, the pspheres. This is avoided by a repeated random selection of the anguenveloping diameter, densities, and dynamic shape factor are compu

(5) in [26]). The combined effect of these forces on an inhaledparticle is expressed by mathematical equations, within whichthe fraction of each deposition mechanism mainly depends on

particle size.

In order to obtain statistical parameters of particle deposi-tion in the human respiratory tract, deposition scenarios arecalculated for a high number (usually 10,000) of particles that

ram asks for any duplicates of α and γ resulting in a total overlap ofparameters. After complete construction of the aggregate, maximal.

walk randomly through the airway structure. These computa-tions are additionally optimised by application of the statisticalweight method [20,26], where each particle may perform mul-

tiple deposition events. Thus, deposition of a particle in a givenairway is simulated by decreasing its statistical weight insteadof terminating its path at the site of impact on the airway wall.Hence, the particle continues its trajectory with reduced sta-

R. Sturm / Z. Med. Phys. 20 (2010) 226–234 231

Figure 3. Linear dependence of the dynamic shape factor χ on the

enveloping sphere diameter des. In the inserted diagram the χ- des

relationship of 10-sphere aggregates is demonstrated in detail usinglinear scales.

tistical weight. Finally, the contribution of a single depositionevent to deposition in a given airway is determined by theproduct of the actual statistical weight of the particle and therespective deposition probability [20]. Particle deposition isexpressed as a function of various regions of the respiratorytract (extrathoracic, bronchial, alveolar) and as a function ofdifferent airway generations.

Modelling results

Geometric properties and dynamic shape factors oftheoretically constructed aggregates

Aggregates were generated according to the algorithm pre-sented above, assuming a cluster composition of differentnumbers of spherical components (10, 50, 100, and 1,000)and single spherules ranging from 0.1 to 1 nm in size. Asillustrated in Figures 3 and 4a, the range of des is subject toa remarkable enhancement with increasing number of spher-ical components. Whilst aggregates containing 10 spherulesare commonly characterised by an enveloping sphere diame-ter ranging from about 2 to 6 nm, clusters consisting of 1,000spherules exhibit a variation of des between 20 and 640 nm.Since the variation of dve is much lower, the dynamic shapefactor χ is marked by a linear dependence on des (Fig. 3).Therefore, χ continuously increases with growing diameterof the enveloping sphere. For an aggregate containing 10spherules χ ranges from 1 to 3.5, whereas the dynamic shape

factors of the 1,000 spherule clusters vary between 3 and 70(Fig. 4b). Hence a loosely arranged cluster of 10 sphericalcomponents may show a similar aerodynamic behaviour as acompact aggregate consisting of 1,000 spherical components.

Figure 4. Dependence (mean ± standard deviation) of des (a) andχ (b) on the number of spherical components of the theoreticallyconstructed aggregates.

Deposition behaviour of aggregates with variable sizein the human respiratory tract

Deposition of theoretically constructed aggregates in thehuman respiratory tract was simulated by using the meanvalues of χ exhibited in Fig 4b and assuming two differentbreathing conditions: 1) sitting breathing and 2) light-workbreathing [24]. Particle density, representing a main param-eter of Eq. (7), was set to a value of 1.0 g/cm3. Concerningaggregate deposition in the extrathoracic, bronchial, and alve-olar region of the human respiratory tract, increased clustersize, expressed by an increased number of spherical compo-nents, entails several effects (Fig. 5): First, total deposition issubject to a continuous decline. Whilst 10 spherule clustersare almost completely deposited in the airways and alve-oli, 1,000 spherule clusters exhibit a total deposition rangingfrom 60 to 70%. Second, deposition in the extrathoracic andbronchial region also decreases continuously. Extrathoracicdeposition is reduced from 20–30% (10 spherule cluster) toabout 10% (1,000 spherule cluster), whereas bronchial depo-sition is dropped from 55 to 65% to values smaller than 40%.Third, alveolar deposition is characterised by a considerableincrease from 1–2% in the case of small aggregates to val-

ues greater than 10% in the case of large aggregates. Bymodifying the breathing conditions from sitting to light-workinhalation general tendencies noted above remain unchanged,but bronchial and alveolar deposition occur on a slightly

232 R. Sturm / Z. Med. Phys. 20 (2010) 226–234

Figure 5. Deposition of variably sized aggregates in the extratho-racic, bronchial, and alveo-lar region of the human respiratory tract:

Figure 6. Deposition of variably sized aggregates in single airway

and females) using environmental tobacco smoke particles(CMD = 200 nm, σg = 1.8; [27]) were simulated. Lung mor-phology and inhalation parameters were fitted to the data of therespective experimental protocols. Additionally an enhanced

Figure 7. Results of inhalation experiments (10 subjects) using

a) sitting breathing, b) light-work breathing [24]. Mean values (Fig.4) were used for deposition calculations.

higher level, whereas extrathoracic deposition is generallydecreased.

Regarding the deposition of aggregates in single airwaygenerations of the tracheobronchial tree the same modellingassumptions as for the simulation of regional cluster depo-sition were applied. Here, increase of cluster size is mainlycombined with two phenomena (Fig. 6): First, cluster depo-sition in the upper bronchial airway generations 1 to 10is subject to a remarkable decrease. Whilst deposition ofsmall aggregates in the uppermost bronchi takes place onthe order of several percent, deposition of large aggregatesat the same sites is marked by values much smaller than 1%.Second, cluster deposition in the intermediate to peripheralairway generations 11 to 23 shows a significant increase. Forinstance, in airway generation 16 deposition of large aggre-gates is three to four times higher than deposition of smallaggregates. Comparison of single deposition curves in Fig. 6shows that deposition of larger aggregates is continuouslydisplaced towards the more distal parts of the human respira-tory tract. A modification of the breathing conditions fromsitting to light-work inhalation has an effect on the depo-

sition curves in so far, as proximal deposition is generallydeclined, whilst at the same time distal deposition is enhanced(Fig. 6).

generations of the human respiratory tract: a) sitting breathing, b)light-work breathing [24]. Mean values (Fig. 4) were used for depo-sition calculations.

Comparison of experimental data with theoreticalresults

For an appropriate validation of the aggregate parti-cle model inhalation experiments with 10 subjects (males

environmental tobacco smoke particles (CMD = 200 nm, σg = 1.8)compared with corresponding data derived from model calculations(mean values ± standard deviations).

s. 2

R. Sturm / Z. Med. Phy

amount of particles with compact shapes, resulting in declinedvalues of the dynamic shape factor, was assumed. Accordingto the experimental results total deposition of tobacco parti-cles amounts to (58 ± 16)% in the case of breathing throughthe nose and to (49 ± 12)% in the case of breathing throughthe mouth (Fig. 7). Theoretical data obtained under identicalbreathing conditions only deviate slightly from the experi-mental output; whilst total deposition for nose breathing takesa value of (60 ± 18)%, total deposition for mouth breathingamounts to (51 ± 15)%. Differences between experiment andmodel are in the order of a few percent.

Discussion and Conclusions

In this study a computer program for the construction ofirregularly shaped aggregate particles and the calculation ofshape parameters relevant for both their transport and depo-sition behaviour was presented. The model is based on theassumption that aggregates originating from combustion pro-cesses consist of a high number of smaller components. This isconfirmed by microscopic studies [17,18]. The shape of thesecomponents was assumed to be spherical which significantlysimplifies the efficient calculation of related particle shapeparameters. The dynamic shape factor χ was found to increasewith growing number of aggregate components (Fig. 4) andthus with growing particle size. This phenomenon was alreadyreported in earlier contributions [5–9,28], where respectivedynamic shape factors were estimated for anisometric parti-cles with fibrous or disk-like geometry. As outlined by Kasper[5], combustion aerosols commonly show a wide range ofdynamic shape factors, whereby a dependence of this param-eter on the formation mechanism and age of the aerosol isobserved. Whilst for sodium oxide and Pu-U-oxide mixturesχ takes values between 2 and 3 [29–31], loosely coagulatedexploding wire clusters may attain shape factors of up to 15[32]. In the present study dynamic shape factors of aggregateparticles with up to 100 spherical components have values thatare very similar to those described in the literature, whereasaggregates containing 1,000 spherules show estimations forχ which clearly exceed those reported hitherto. According tothe model high values for χ are mainly computed for thoseaggregates which tend towards an ideal chain-like structure(Table 1). In this case Eq. (5) for the calculation of χ is char-acterised by a significantly decreased accuracy and should bereplaced by a respective formula which is exclusively validfor chain aggregates [5,10].

Lung deposition computations were conducted with aggre-gate particles containing various numbers of nanospheres (10,50, 100, 1,000) and thus reaching diameters between 2 and200 nm. There was produced clear evidence that larger aggre-

gates have a higher ability to penetrate towards peripheralparts of the respiratory tract than small clusters (Fig. 5). Thisessential observation is largely confirmed by similar modelcalculations using ideal spherical particles of the same orderof magnitude [19,20]. According to the physical properties of

0 (2010) 226–234 233

nanometer particles in a flow regime Brownian motion rep-resents the main deposition force of this particle class. Withrising particle size this deposition mechanism is successivelyjoined by two further mechanisms, i.e. inertial impactionand gravitational settling [19,24,25,33]. Aggregates solelyaffected by Brownian motion are already deposited in theextrathoracic region and uppermost airways of the tracheo-bronchial tree, whereas clusters affected by a bundle ofdeposition forces may reach deeper lung compartments. High-est deposition of these particles takes place in that part of thelung, where the sum of deposition forces attains its maximum(Fig. 6). However, the role of inertial impaction and gravi-tational settling regarding the deposition of nano-aggregatescannot be quantified appropriately and therefore has to be rel-ativised. Increasing particle size within the nano-scale has themain effect that radial diffusion is declined with respect toaxial particle transport, resulting in higher penetration dis-tances with enhancing aggregate dimensions.

As demonstrated by this study aggregate deposition in therespiratory tract may be additionally influenced by the modeof breathing: higher breathing frequencies and inhalation vol-umes cause a measurable displacement of cluster depositiontowards more peripheral lung regions and vice versa. Thisphenomenon may be traced back to the physical fact that anyincrease of flow velocity is associated with an enhancementof the axial particle transport at the cost of the radial parti-cle transport caused by Brownian motion [25]. Hence, underworking conditions alveolar deposition of nano-scale aggre-gates and the associated risk of pulmonary and cardiovasculardiseases may be dramatically increased [12,13].

Validation of the model introduced here was carried out byusing data of environmental tobacco smoke inhalation exper-iments [27]. Lung deposition of smoke particles derived fromthe experiments could successfully be simulated by the modeldue to the application of appropriate dynamic shape fac-tors. Previous simulations using spherical particles resulted indeposition values that were much smaller than the theoreticalvalues, and several physical reasons (e.g. particle coagulationdue to electric forces) were discussed to overcome this deficit[27]. However, the authors assumed a particle growth in theairways to explain the difference between experimental andtheoretical results, but according to the current knowledgeand conclusions drawn from this study the effective particlediameter, expressed by dae, is remarkably smaller than thegeometric diameter. This results in the increase of theoreticaldeposition values and a partly perfect correspondence betweenexperiment and theory (Fig. 7).

From the theoretical descriptions and computational resultspresented here it can be concluded that aggregate particlesmay be characterised by dynamic shape factors and related

aerodynamic diameters which clearly deviate from respectiveparameters calculated for fibers or disks with similar volumeequivalent diameter. Therefore, aggregate particles exhibita pulmonary transport and deposition behaviour that maydeviate significantly from the behaviour of regularly shaped

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234 R. Sturm / Z. Med.

anisometric particles. Clusters of nano-scale size are filteredin the upper regions of the human respiratory tract to a highextent, but may reach also the compartments of gas exchange,where they can act as triggers of severe lung burdens.

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