JOURNAL OF AEROSOL MEDICINEVolume 18, Number 4, 2005© Mary Ann Liebert, Inc.Pp. 439–451

Analysis of Cascade Impactor Mass Distributions

CRAIG DUNBAR, Ph.D.,1 and JOLYON MITCHELL, Ph.D.2

ABSTRACT

The purpose of this paper is to review the approaches for analyzing cascade impactor (CI)mass distributions produced by pulmonary drug products and the considerations necessaryfor selecting the appropriate analysis procedure. There are several methods available for an-alyzing CI data, yielding a hierarchy of information in terms of nominal, ordinal and con-tinuous variables. Mass distributions analyzed as a nominal function of the stages and aux-iliary components is the simplest approach for examining the whole mass emitted by theinhaler. However, the relationship between the mass distribution and aerodynamic diameteris not described by such data. This relationship is a critical attribute of pulmonary drug prod-ucts due to the association between aerodynamic diameter and the mass of particulates de-posited to the respiratory tract. Therefore, the nominal mass distribution can only be utilizedto make decisions on the discrete masses collected in the CI. Mass distributions analyzed asan ordinal function of aerodynamic diameter can be obtained by introducing the stage sizerange, which generally vary in magnitude from one stage to another for a given type of CI,and differ between CIs of different designs. Furthermore, the mass collected by specific sizeranges within the CI are often incorrectly used to estimate in vivo deposition at various re-gions of the respiratory tract. A CI-generated mass distribution can be directly related to aero-dynamic diameter by expressing the mass collected by each size-fractionating stage in termsof either mass frequency or cumulative mass fraction less than the aerodynamic size appro-priate to each stage. Analysis of the aerodynamic diameter as a continuous variable allowscomparison of mass distributions obtained from different products, obtained by different CIdesigns, as well as providing input to in vivo particle deposition models. The lack of infor-mation about the mass fraction emitted by the inhaler that is not size-analyzed by the CI maybe perceived as a disadvantage from the standpoint of comparing the total mass per actua-tion emitted from the inhaler mouthpiece. However, this is a limitation of the CI measure-ment technique rather than the data analysis procedure. Data reduction techniques can en-able the large quantity of information conveyed in a mass-size distribution to be summarizedin terms of representative parameters, but care needs to be exercised if utilizing model sizedistribution function fitting routines to avoid introducing error by the fitting procedure.

Key words: cascade impaction, particle size distribution, aerodynamic diameter

439

1Alkermes, Inc., Cambridge, Massachusetts.2Trudell Medical International, London, Ontario, Canada.

5967_07_p439-451 12/6/05 1:25 PM Page 439

INTRODUCTION

THE MASS DISTRIBUTION scaled as a function ofaerodynamic diameter is a critical attribute of

pulmonary drug products due to its relationshipwith the mass of aerosol particulates deposited inthe respiratory tract.(1) Multi-stage cascade im-pactors (CIs), illustrated in Figure 1, measure themass distribution of the inhaler-produced aerosolin terms of aerodynamic diameter, a size para-meter that takes into account the effects of both

particle density and shape on particle motion.(2)

CIs are widely utilized during the development,quality control (batch release and stability), andin vitro bioequivalence studies of pulmonarydrug products.(3–5) There are several means of an-alyzing CI data, yielding a hierarchy of informa-tion, in terms of nominal, ordinal and continuousvariables. The purpose of this paper is to reviewthese approaches and examine the considerationsnecessary for selecting the appropriate dataanalysis method.

DUNBAR AND MITCHELL440

FIG. 1. Schematic of CI components.

5967_07_p439-451 12/6/05 1:25 PM Page 440

CI stage collection characteristics

Multi-stage CIs size-fractionate the incomingaerosol onto a series of stages arranged such thatsuccessively finer particles are removed as theaerosol passes through the instrument. The col-lection efficiency of an ideal impactor stage in-creases in a step-wise manner between limits of0–100%, as shown in Figure 2.(6) In this example,the ideal impactor stage would operate such that100% of the incoming particles with an aerody-namic diameter larger than the median collectionefficiency (E50), known as the effective cut-off di-ameter (ECD), are collected by the stage, with theremaining particles penetrating through to thenext stage of the CI. However, real CI stages havenon-ideal particle collection characteristics, dueto secondary forces influencing particle motionthrough the stage, notably gravitational sedi-mentation, boundary layer thickening at lowflow Reynolds numbers, and cross flow betweenadjacent nozzles in multi-nozzle stages.(7,8) Theseeffects result in a monotonic, sigmoidal-shapedcollection efficiency curve as a function of aero-dynamic diameter. Figure 2 illustrates such a col-lection efficiency curve that was obtained fromcalibration of stage 3 of the next generation phar-maceutical impactor (NGI) at 60 LPM.(9) Thisparticular curve exhibits symmetry about theECD, which occurs at an aerodynamic diameterof 2.85 �m. To a first approximation, the com-plete collection efficiency curve can be repre-sented by the ECD on the basis that the non-idealcollection effects cancel, so that particles equal insize or larger than the ECD are assumed to befully collected, whereas smaller particles pene-trate the stage. Inversion methods have been de-veloped in an attempt to improve the accuracyof the CI measurement by taking into account thecomplete functional form of each stage collectionefficiency curve.(10–12) However, these proce-dures are complex, incorporating assumptionsthat can introduce additional uncertainty in the data, and are therefore seldom used in practice.(11)

Stage collection efficiency curves for multi-stage CIs used in the assessment of inhaler per-formance have been reported for the Andersencascade impactor (ACI), next generation phar-maceutical impactor (NGI), and the multistageliquid impinger (MSLI), and are summarized inFigure 3. Calibrations were undertaken withmonodisperse aerosols of known aerodynamic

diameter. The calibrations for the MSLI and NGIare well described.(9,13) However, the source ofthe calibration for the ACI supplied by the man-ufacturer is less well defined, but the data arewidely accepted as being representative for thisimpactor.(14) Independent studies have indicatedthat there are only minor deviations from themanufacturer-specified curves.(15,16) The size-axes of CI collection efficiency curves are typi-cally represented on a logarithmic scale forgraphical clarity, rather than implying a func-tional relationship between the collection charac-teristics and aerodynamic diameter.

When reducing the collection efficiency curveof a multi-stage CI to its ECD value, a further as-sumption is made that there is negligible overlapbetween collection efficiency curves of adjacentstages. This is not entirely true with current CIdesigns, although in many instances stage over-lap occurs only at the extremes of the collectionefficiency curve (15% � E � 85%), so that biasfrom this effect can be neglected. The NGI wasdesigned to minimize stage overlap while main-taining resolution in the aerodynamic diameterrange of 0.5–5.0 �m.(17)

The size range associated with a given stage ina multi-stage CI is defined as the size-separationbetween the ECD of that stage (stage [i]) and thecorresponding ECD of the one immediately pre-ceding it (stage [i-1]). The size width for stage (i)(�ECDi) is calculated as the difference betweenthe upper and lower boundary sizes of therange:

�ECDi � ECDi�1 � ECDi (1)

CASCADE IMPACTOR MASS DISTRIBUTIONS 441

FIG. 2. Collection efficiency curves for an ideal singlestage of a CI (dashed line) compared with actual calibra-tion data for that stage (solid line). ECD, effective cut-offdiameter; E50, median collection efficiency.

5967_07_p439-451 12/6/05 1:25 PM Page 441

The mid-point size for that stage can be used toestimate a representative aerodynamic diameter(da,i) of the particles collected by calculating thearithmetic mean of the upper and lower bound-ary ECD values:

DUNBAR AND MITCHELL442

da,i � (2)

Values of ECD, range, width, and da are sum-marized in Table 1 for the ACI, NGI and MSLI.The NGI filter or micro-orifice collector (MOC)is assumed to collect all the particles presentedto it, so that in practice, its ECD (nominally 0.3�m at 30 LPM) can be treated as if it werezero.(17)

ANALYSIS

Mass distributions as a nominal function of CI stages and auxiliary components

The simplest approach to analyzing the massdistribution obtained by a multistage CI is to pre-sent the mass collected as a nominal function ofthe stages and auxiliary components. The valuesof mass are related to the discrete stages and aux-iliary components by name only and without or-der. This analysis can be illustrated by calculat-ing the mass fractions obtained in an ACI with amodel aerosol having a uni-modal, log-normalparticle size distribution. The mass fraction (Fm)is the mass collected on a stage (mi), or auxiliarycomponent, divided by the mass emitted fromthe inhaler mouthpiece (ME):

Fm � (3)

The mass fraction (Fm) collected on stage i of theACI for a model log-normal particle size distrib-ution is calculated as follows:

(Fm)i � �(zi) � �(zi�1) (4)

where �(zi) is the normal probability integral forstage i, given by:

�(zi) � ��i

��exp � � �dz (5)

zi � (6)

and MMAD is the mass median aerodynamic di-ameter and �g is the geometric standard devia-tion. �(zi) can be solved using Excel 2002 (Mi-crosoft, Seattle, WA), as follows:

�(zi) � NORMSDIST ( (LN (ECDi) � LN (MMAD)) / LN(�g) ) (7)

ln(ECDi) � ln(MMAD)���

ln(�g)

zi2

�2

1����

mi�ME

ECDi-1 � ECDi��2

FIG. 3. Collection efficiency curves of the ACI at 28.3 LPM(14) (a), NGI at 30 LPM(9) (b) and MSLI at 60LPM(13) (c).

5967_07_p439-451 12/6/05 1:25 PM Page 442

Mass fractions collected in an ACI for a log-nor-mal particle size distribution were calculatedfor MMAD � 5.0 �m and �g � 2.0, and areshown in Figure 4, arranged in two equallyvalid ways: (a) in the order in which the aerosolpasses through the CI system, and (b) rank-or-dered in terms of decreasing magnitude of massfraction. Figure 4 illustrates that the mass frac-tions neither have order nor association withaerodynamic diameter.

The advantage, and therefore popularity, ofundertaking this type of mass distribution analy-sis is in its simplicity, as well as the ability to rep-resent the profile of the entire dose emitted fromthe inhaler mouthpiece, including the dose col-lected in the auxiliary components (e.g., the in-

duction port). Regulatory authorities, recogniz-ing the need to have knowledge of the disposi-tion of the entire emitted medication, have there-fore adopted the practice of assessing the qualityof pulmonary drug products either by this route,or by the similar approach in which the absolutemass, rather than mass fraction, is assessed.(4)

However, these procedures do not provide ameasure of the mass distribution relative to theaerodynamic diameter, which is the critical at-tribute of the formulation that determines re-gional deposition in the respiratory tract.(1) Forexample, changes to the mass collected on dif-ferent stages within the CI will not reflect differ-ences in the mass-weighted aerodynamic size distribution, without reference to a particle size-

CASCADE IMPACTOR MASS DISTRIBUTIONS 443

TABLE 1. COLLECTION CHARACTERISTICS OF THE ACI, NGI, AND MSLI

ACI NGI MSLI(28.3 LPM)(14) (30 LPM)(9) (60 LPM)(13)

Component ECD Range Width da ECD Range Width da ECD Range Width dastage (�m) (�m) (�m) (�m) (�m) (�m) (�m) (�m) (�m) (�m) (�m) (�m) (�m)

IP — — — — — — — — — — — —Stage 0 9.0 �9.0 — — NA NA NA NA NA NA NA NAStage 1 5.8 5.8–9.0 3.2 07.4 11.6 �11.6 — — 13.0 �13.0 — —Stage 2 4.7 4.7–5.8 1.1 05.3 06.4 06.4–11.7 5.3 9.1 06.8 06.8–13.0 5.2 9.9Stage 3 3.3 3.3–4.7 1.4 04.0 04.0 4.0–6.4 2.4 5.2 03.1 3.1–6.8 3.7 5.0Stage 4 2.1 2.1–3.3 1.2 02.7 02.3 2.3–4.0 1.7 3.1 01.7 1.7–3.1 1.4 2.4Stage 5 1.1 1.1–2.1 1.0 01.6 01.4 1.4–2.3 0.9 1.8 NA NA NA NAStage 6 0.7 0.7–1.1 0.4 00.9 00.8 0.8–1.4 0.6 1.1 NA NA NA NAStage 7 0.4 0.4–0.7 0.3 00.6 00.5 0.5–0.8 0.3 0.7 NA NA NA NAFilter/MOC 0.0 0.0–0.4 0.4 00.2 00.0 0.0–0.5 0.2 0.4 00.0 0.0–1.7 1.7 0.9

ACI, Andersen cascade impactor; NGI, next generation impactor; MSLI, multi-stage liquid impinger; ECD, effec-tive cut-off diameter; da, aerodynamic diameter; IP, induction port; NA, not applicable; MOC, micro-orifice collector.

FIG. 4. Mass distribution of a model aerosol (MMAD � 5.0 �m; �g � 2.0) as it would be collected in the ACI (28.3LPM), presented as a nominal function of stages and auxiliary components in order of component location in the CIsystem (a) and rank-ordered (b).

5967_07_p439-451 12/6/05 1:25 PM Page 443

related parameter, typically the ECDs of the CIstages. Furthermore, the mass collected on a stagehas no association with the mass collected on theother CI stages and components, such that com-parisons between nominal mass distributions mustbe performed discretely (i.e., stage-by-stage).

Mass distributions as an ordinal function of stage size range

Stage collection characteristics can be intro-duced into the analysis of CI-generated data byassociating either the absolute mass or mass frac-tion with the stage size range, as shown in Fig-ure 5, for the previously described model aerosolcollected by the ACI (MMAD � 5 �m, �g � 2.0).The mass fractions of the stages now have orderand a discrete association with the aerodynamicdiameter scale via the stage size range defined bythe ECDs (Table 1). Stages and auxiliary compo-nents that do not have well defined collectioncharacteristics, such as the induction port andstage 0 of the ACI, whose upper bound size is un-specified, cannot be directly included in this typeof analysis. Data from these components aretherefore shown separately in Figure 5, with noformal association being made with the stage sizerange scale.

An apparent advantage of introducing thestage size range into CI data analysis is the abil-ity to compare mass distributions from groupingsof CI stages of the same CI design, since the in-dependent variable (stage size range) has both ascale and order. This type of comparison is illus-trated by Figure 6 for the previously describedmodel aerosol, in which the mass fractions col-

lected on stages 1–2, stages 3–4, stages 5–6, andstage 7-filter of an ACI, have been arbitrarily com-bined for each pair of components. However, thisprocess has resulted in a difference between themass fraction-stage size range profiles comparedwith data where stage grouping has not takenplace. Such comparisons of distributions based on mass-stage size range indicate that differentaerosols were measured, despite the fact that theaerosol under consideration is the same. This be-havior is caused by the dependency of the singleand grouped stage data on the non-uniform stagewidths associated with this design of CI (Table1). A similar situation exists if data comparisonsof this sort are made between different designs ofCI having different stage width profiles (Table 1).Thus, Figure 7 shows distributions based on massfraction-stage size range as they would appear ifcollected by an ACI and NGI. This type of be-havior will also occur if CI-based data are com-pared on this basis with measurements made byanother particle sizing technique, such as time-of-flight aerodynamic particle size analysis. Su-perficial inspection of both Figures 6 and 7 mightresult in an erroneous conclusion being drawnthat the aerosols presented were not identical.

The mass collected within a stage size rangehas been associated with regional deposition inthe human respiratory tract, as illustrated by Fig-ure 8. This approach effectively treats the CI as ifit were a simulator of the human respiratory tract,which is an oversimplification of the comparison

DUNBAR AND MITCHELL444

FIG. 5. Mass distribution obtained by ACI as an ordinalfunction of stage size range (MMAD � 5.0 �m; �g � 2.0).

FIG. 6. Mass distributions obtained by single stages(hatched) and grouped stages (bold-faced) of the ACI asan ordinal function of stage size range (MMAD � 5.0 �m;�g � 2.0).

5967_07_p439-451 12/6/05 1:25 PM Page 444

between the two systems. For example, thesteady-state volumetric flow rate required to op-erate CIs do not represent the inspiratory flowrate or profile achieved by patient popula-tions.(18–21) The lack of validity of this approachcan be illustrated from a theoretical standpoint

by the use of a bolus lung deposition model toestimate the regional lung deposition associatedwith the mass fractions collected on ACI stagesand components. This model calculates the ex-trathoracic deposition using the model of the In-ternational Commission on Radiological Pro-tection (ICRP), with the remaining fraction of the aerosol bolus assumed to deposit in thelungs.(22,23) Aerosol polydispersity is captured bysumming the regional lung deposition calculatedfor the discrete CI stage size intervals.(23) This ap-proach has provided comparable estimates of themean in vivo lung deposition of aerosols withMMADs of 3 and 5 �m produced from a passivedry powder delivery system.(22) Figure 9 showsthat half of the dose collected on stage 1 of theACI would be predicted to deposit in the lungsof a healthy male subject breathing with an in-haled volume (V) of 2 L and peak inspiratory flowrate (PIFR) of 28.3 LPM (MMAD � 5 �m and�g � 2.0). However, the over-simplified modeldepicted by Figure 8 assigns the mass collectedon stage 1 exclusively to the oral cavity.

Fundamentally, the disparity between deposi-tion in the respiratory tract and CI is attributable

CASCADE IMPACTOR MASS DISTRIBUTIONS 445

FIG. 7. Mass distributions obtained by the ACI(hatched) and NGI (bold-faced) as an ordinal function ofstage size range (MMAD � 5.0 �m; �g � 2.0).

FIG. 8. Presentation of regional lung deposition relative to ACI stage size range (28.3 LPM; courtesy of Westech In-strument Services, Upper Stondon, UK).

5967_07_p439-451 12/6/05 1:25 PM Page 445

to the more size-selective nature of individual CIstages compared with the processes that governregional lung deposition. CIs are designed to sep-arate particles primarily by inertial impaction ata constant volumetric flow rate for the purposeof measuring the aerodynamic particle size dis-tribution. The lungs separate particles by thecombined processes of inertial impaction, sedi-mentation and diffusion within an envelope ofcontinuously varying flow rate, in order to filterand condition inhaled air in preparation for gasexchange. The differences between the particlesize separating function of a CI and that of therespiratory tract are illustrated in Figure 10 byoverlaying the collection efficiency curves of theACI, chosen as a representative multi-stage CI,with the corresponding empirical/theoreticalparticle collection efficiency curves associatedwith the morphological regions within the respi-ratory tract.(14,23) The lack of similarity betweenthe two sets of curves implies that the CI cannotbe used directly as an in vitro surrogate to mimicdeposition in the respiratory tract. Rather, the CIshould be used to measure the mass-weightedaerodynamic diameter distribution, which can inturn be used as an input to estimate in vivo de-position using appropriate mathematical modelsthat reflect the processes governing deposition, as

well as the flow dynamics of the respiratory tract,for example, ICRP.(23) Respiratory tract depo-sition models and in vitro–in vivo correlations(IVIVCs) are being developed for pulmonarydrug products.(22,24–26) However, in the absenceof a suitable lung deposition model or IVIVC,pulmonary inhaler product performance is mostappropriately assured by monitoring changes inthe mass-weighted aerodynamic diameter distri-bution.

Mass distributions as a continuous function ofaerodynamic diameter

The dependency of the mass distribution pro-files on the non-uniform stage widths can be elim-inated by calculating the mass frequency (alsotermed probability or differential mass) as a con-tinuous function of the aerodynamic diameter(2):

Mass frequency (da,i) � (8)

where �ECDi is the stage width defined in Equa-tion 1, mi and ME are the mass on stage (i) andthe total mass emitted from the inhaler mouth-piece, respectively, and da,i is the aerodynamic di-ameter associated with stage (i). To illustrate thistype of data presentation, the mass frequencies ofthe previously described model aerosol(MMAD � 5 �m and �g � 2.0) collected by ACIand NGI are illustrated in Figure 11. The area ofeach block associated with a given stage, asshown in Figure 11, is equal to the mass fractioncollected within the size range of that stage, and

1��ECDi

mi�ME

DUNBAR AND MITCHELL446

FIG. 9. ACI mass distribution of a model aerosol(MMAD � 5.0 �m; �g � 2.0) and the corresponding re-gional lung deposition estimated using the ICRP boluslung deposition model (PIFR � 28.3 LPM; V � 2 L;healthy male).

FIG. 10. Collection efficiencies of the ACI (Q � 28.3LPM) and morphological regions of the lung (PIFR � 28.3LPM; V � 2 L; healthy male).

5967_07_p439-451 12/6/05 1:25 PM Page 446

the relationship between mass frequency andaerodynamic diameter is a continuous represen-tation of the distribution of the aerosol emittedfrom the inhaler mouthpiece. The continuousforms of these mass-weighted aerodynamic sizedistributions for each type of CI are identical, andit is therefore evident that the same aerosol hasbeen measured.

This analysis provides a continuous relation-ship between the distribution of mass relative tothe aerodynamic diameter, which is the criticalattribute of the formulation most closely associ-ated with regional deposition in the respiratorytract. Continuous mass distributions can be uti-lized to make decisions on the whole distributionrelative to the aerodynamic diameter, because themass collected on a given stage is now associatedwith the mass collected on each of the otherstages. Also, this type of analysis provides a di-rect means to transition from one type of CI toanother (e.g., from the ACI to the NGI) when considering CI-measured data for a given in-haler/formulation. Furthermore, comparison canbe made between distributions obtained at dif-ferent operating flow rates for which calibratedECDs are available. By contrast, the nominal massdistributions can only be utilized to make deci-sions on the discrete masses collected by the in-dividual CI stages for a given CI at a specific op-erating flow rate.

An alternative presentation of the mass fre-quency aerodynamic diameter distribution can beobtained by calculating the area under the curve,to produce the cumulative mass fraction undersize:

Cumulative mass fraction � ECDi �

�Stage i�11

j�Filtermj (9)

The cumulative mass fraction for the modelaerosol (MMAD � 5 �m and �g � 2.0) as it wouldbe measured by both ACI and NGI is illustratedin Figure 12.

Presentations of CI data scaled either in termsof mass frequency or cumulative mass fractionare calculated relative to the mass emitted fromthe inhaler mouthpiece, and therefore the sizedand non-sized fractions collected in the samplingsystem are still related via the emitted dose fromthe inhaler mouthpiece. For example, an increasein the mass of drug emitted from the inhalermouthpiece that is collected in the induction portwill produce a corresponding decrease in themass fraction that is assigned to the CI. Figure 13illustrates how this process results in a corre-sponding change in the profile of the cumulativemass fraction undersize, with a consequent shiftin MMAD for a given model aerosol. The profilerepresented by the open circles provides infor-mation about the magnitude of the non-sizedcomponent of the inhaler-produced aerosol andrepresents the complete aerosol emitted by the in-haler. The profile represented by the solid circlesis based on only that portion of the aerosol capa-ble of penetrating as far as the size-fractionatingstages of the CI.

Despite the rigor of the approach shown in Fig-ure 13, the fact that the whole distribution of the

1�ME

CASCADE IMPACTOR MASS DISTRIBUTIONS 447

FIG. 11. Mass distributions obtained by ACI(hatched/open circle) and NGI (bold-faced closed circle)as a continuous function of aerodynamic diameter(MMAD � 5.0 �m; �g � 2.0).

FIG. 12. Cumulative mass distribution as a continuousfunction of aerodynamic diameter obtained by ACI(hatched/open circle) and NGI (bold-faced closed circle;MMAD � 5.0 �m; �g � 2.0).

5967_07_p439-451 12/6/05 1:25 PM Page 447

emitted mass from the inhaler is not representedcan be perceived as an important restriction to theuse of data expressed in terms of aerodynamic di-ameter. For example, with many products, theportion available for particle size analysis in theCI can be less than half of the total mass emittedfrom the inhaler mouthpiece.(27) It is commonpractice to normalize the mass fraction relative tothe mass collected in the CI to avoid includingdata from the non size-fractionating componentsof the CI system.(28,29) However, the analysis ofpressurized metered dose inhalers (pMDI) by thisapproach renders inhaler alone data superficiallysimilar to equivalent measurements obtainedwith a spacer or valved holding chamber in place,despite the emission of the ballistic componentinto the CI system only when the add-on deviceis not present. The effectiveness of the spacer orholding chamber cannot therefore be properlydemonstrated, as the bulk of the coarser ballisticparticulate that is present when a pMDI is usedalone, is collected by the add-on device that is ex-ternal to the CI. It therefore follows that in vitrospacer or holding chamber performance in termsof modifying the pMDI-produced aerosol sizedistribution, can only be properly demonstratedwhen the CI-data are referenced to the mass emit-ted at the inhaler mouthpiece.

Fundamentally, the lack of information aboutthe inhaler-emitted aerosol that is not size-ana-lyzed is a limitation of the CI measurement tech-nique (i.e., the lack of size-fractionating com-ponents to analyze the coarsest particles), ratherthan of the data analysis procedure itself. Thesize range appropriate to the use of CIs does notfully encompass the broad range of particle

sizes that is typically produced by pulmonarydrug products.(30) Alternative techniques, suchas time-of-flight aerodynamic particle sizeanalysis, may therefore be appropriate if moreinformation is required about the mass fractionof the aerosol that is not size-analyzed by CI,notwithstanding the limitations of these meth-ods.(31,32)

CI data reduction

It is often desirable to be able to reduce thelarge amount of information contained in a CI-measured mass-weighted size distribution to afew representative parameters. Data reductioncan be as simple as determining descriptive sta-tistics that represent particular locations on thesize distribution. This information is most con-veniently obtained from the cumulative massfraction undersize. Examples of descriptive sta-tistics are:

d0.1: diameter at the 10th percentile of the cumu-lative mass fraction undersize

d0.5: diameter at the 50th percentile of the cumu-lative mass fraction undersize, which by de-finition is identical to the mass median aero-dynamic diameter (MMAD)

d0.9: diameter at the 90th percentile of the cumu-lative mass fraction undersize

When characterizing inhaler-produced aerosols,it is more common to report a measure of thespread of the distribution as well as the MMADvalue.(28,29) However, an underlying assumptionis made that the size distribution is both uni-

DUNBAR AND MITCHELL448

FIG. 13. Cumulative mass fraction undersize of the dose emitted from the inhaler mouthpiece (open circle) and ofthe dose collected in the ACI (closed circle).

5967_07_p439-451 12/6/05 1:25 PM Page 448

modal and log-normal in shape when calculatingthe geometric standard deviation (�g):

g � � (10)

This assumption may not be valid with many in-haler-produced aerosols, especially those fromliquid atomization processes, or where carrierparticles are present, such as in certain dry pow-der inhaler–produced aerosols.(33) If the size dis-tribution is uni-modal but not log normal inshape, an alternative approach is to calculate arelative span factor (RSF) based on arbitrarilychosen limits that encompass most of the particlesize distribution:

RSF � (11)

However, visual inspection of the size distribu-tion data is necessary to confirm that the data arenot multi-modal, in which case it may be moreappropriate to determine the aerodynamic diam-eter for each mode.

The fine particle fraction (FPF), defined as thefraction of the mass-weighted size distributioncontained in particles smaller than a specifiedaerodynamic diameter, typically 5 �m, is a de-scriptive statistic that can be directly obtainedfrom the cumulative mass fraction undersize.(28)

Calculation of extra-fine particle fraction, basedon particles finer than 1.1 �m in aerodynamic di-ameter has also been advocated with the adventof solution-based hydro-fluoroalkane formula-tions delivered by pMDI, such as Qvar™ (IVAXCorp., Miami, FL), since a large portion of theaerosol from these products is contained in par-ticles finer than this limit.(34,35)

Application of an empirical or mathematicalexpression to describe the distribution is a morecomplex, but potentially more accurate ap-proach than interpolation. These expressionstake the form of probability density functions(PDFs) that are linked in terms of an indepen-dent variable (aerodynamic diameter) with twodependent adjustable parameters, e.g., meanand deviation about the mean. PDFs have beendeveloped to describe a variety of atomizationsystems, popular examples being the log-nor-mal and Rosin-Rammler distributions.(2,36) Theutility of PDFs to characterize mass distribu-tions produced by pulmonary drug products ishowever limited by failure to meet the PDF fit-

d0.9 � d0.1��d0.5

d0.84�d0.16

ting criteria, for instance, central tendency of themass distribution and greater than 90% of themass emitted by the inhaler being collected inthe CI.(33) The scope to apply this technique toanalyze CI-generated data from most currentlymarketed inhalers appears to be very re-stricted.(33) However, even where this approachis possible, data manipulation involves eitherlinear or non-linear interpolation procedures,which inevitably result in a loss of accuracy thatis linked to the goodness-of-fit of the raw datato the regression model distribution. In the caseof pMDI-generated aerosols, this problem hasbeen addressed by proposing that the ballisticfraction captured by the induction port be sep-arated from the non-ballistic fraction that is col-lected by the CI, on the basis that the latter isoften well described in terms of a log-normalfunctional relationship.(37)

CONCLUSION

Mass distributions may be presented as anominal function of the size-fractionating stagesand auxiliary non-sizing components, withoutrelation either to aerodynamic diameter or or-der in the CI system. This approach is useful forrepresenting the profile of the entire dose emit-ted from the inhaler. Stage collection character-istics can be introduced by associating masswith the ordinal size range for each stage. How-ever, such data cannot be analyzed as a contin-uous distribution of the aerodynamic diameter,because these ranges generally vary from onestage to another within a given CI, and betweendifferent CI designs. A CI-generated mass dis-tribution can be related to aerodynamic diame-ter by expressing the mass collected by eachsize-fractionating stage in terms of either massfrequency or cumulative mass fraction. Thiscontinuous relationship is a critical attribute ofpulmonary drug products due to the associationbetween aerodynamic diameter and the mass ofparticulates deposited to the respiratory tract.Data reduction techniques can enable the largequantity of information conveyed in a mass-sizedistribution to be summarized in terms of rep-resentative parameters, but care needs to be ex-ercised if utilizing model size distribution func-tion fitting routines to avoid introducing errorby the fitting procedure.

CASCADE IMPACTOR MASS DISTRIBUTIONS 449

5967_07_p439-451 12/6/05 1:25 PM Page 449

ACKNOWLEDGMENTS

We would like to acknowledge the stimulatingdiscussions on CI mass distribution analysis withthe Product Quality Research Institute (PQRI)Particle Size Distribution Profile ComparisonsWorking Group.

REFERENCES

1. Heyder, J., J. Gebhart, G. Rudolf, et al. 1986. Deposi-tion of particles in the human respiratory tract in thesize range 0.005–15 �m. J. Aerosol Sci. 17:811–825.

2. Hinds, W.C. 1998. Aerosol Technology: Properties,Behavior and Measurement of Airborne Particles.John Wiley and Sons, Inc., New York.

3. Food and Drug Administration. 2003. Bioavailabilityand bioequivalence studies for nasal aerosols andnasal sprays for local action—draft guidance for in-dustry. Center for Drug Evaluation and Research, U.S.Food and Drug Administration.

4. Food and Drug Administration. 1998. Metered doseinhaler (MDI) and dry powder inhaler (DPI) drugproducts: chemistry, manufacturing and controlsdocumentation—draft guidance for industry. Centerfor Drug Evaluation and Research, U.S. Food andDrug Administration.

5. Mitchell, J.P., and N.M. Nagel. 2004. Cascade im-pactors for the size characterization of aerosols frommedical inhalers: their uses and limitations. J. AerosolMed. 16:341–377.

6. Marple, V.A., and K.L. Rubow. 1986. Theory and de-sign guidelines. In J. Lodge and T. Chan, eds. CascadeImpactor Sampling and Design. AIHA, Akron, OH,79–101.

7. Marple, V.A., B.Y.H. Liu, and K.T. Whitby. 1974. Onthe flow fields of inertial impactors. J. Fluids Eng.394–400.

8. Radar, D.J., and V.A. Marple. 1985. Effect of ultra-Stokesian drag and particle interception on impactioncharacteristics. Aerosol Sci. Technol. 4:141–156.

9. Marple, V.A., B.A. Olson, K. Santhanakrishnan, et al. 2003. Next generation pharmaceutical impactor (a new impactor for pharmaceutical inhaler testing).Part II: Archival calibration. J. Aerosol Med. 16:301–324.

10. Picknett, R.G. 1972. A new method of determiningaerosol size distributions from multi-stage samplerdata. J. Aerosol Sci. 3:185–198.

11. Cooper, D.W. 1993. Methods of size distribution dataanalysis and presentation. In K. Willeke and P. Baron,eds. Aerosol Measurement: Principles, Techniquesand Applications. Van Norstrand Reinhold, NewYork, 146–176.

12. O’Shaughnessy, P.T., and O.G. Raabe. 2003. A com-parison of cascade impactor data reduction methods.Aerosol Sci. Technol. 37:187–200.

13. Asking, L., and B. Olsson. 1997. Calibration at differ-ent flow rates of a multistage liquid impinger. AerosolSci. Technol. 27:39–49.

14. Thermo-Electron. 1985. Operating Manual for An-dersen 1 ACFM Non-Viable Ambient Particle SizingSamplers. Thermo-Electron, Franklin, MA.

15. Mitchell, J.P., P.A. Costa, and S. Waters. 1988. An as-sessment of an Andersen mark-II cascade impactor. J.Aerosol Sci. 19:213–221.

16. Vaughan, N.P. 1989. The Andersen impactor: calibra-tion, wall losses and numerical simulation. J. AerosolSci. 20:67–90.

17. Marple, V.A., D.L. Roberts, F.J. Romay, et al. 2003.Next generation pharmaceutical impactor (a new im-pactor for pharmaceutical inhaler testing). Part I: De-sign. J. Aerosol Med. 16:283–299.

18. Stocks, J., and P.H. Quanjer. 1995. Reference valuesfor residual volume, functional residual capacity andtotal lung capacity. Eur. Respir. J. 8:492–506.

19. Clark, A.R., and R. Bailey. 1996. Inspiratory flow pro-files in disease and their effects on the delivery char-acteristics of dry powder inhalers. In P. Byron, R.Dalby, and S. Farr, eds. RDD V. Interpharm Press,Buffalo Grove, IL, 221–230.

20. Finlay, W.H., and M.G. Gehmlich. 2000. Inertial siz-ing of aerosol inhaled from two dry powder inhalerswith realistic breath patterns versus constant flowrates. Int. J. Pharm. 210:83–95.

21. Miller, N.C., M.J. Maniaci, S. Dwivedi, et al. 2000.Aerodynamic sizing with simulated profiles: totaldose capture and measurement. In R.N. Dalby, P.R.Byron, S.J. Farr, et al., eds. RDD VII. Serentec Press,Raleigh, NC, 191–196.

22. Dunbar, C.A., G. Scheuch, K. Sommerer, et al. 2002.In vitro and in vivo dose delivery characteristics oflarge porous particles for inhalation. Int. J. Pharm.245:179–189.

23. Annals of the International Commision on Radiolog-ical Protection. 1994. Human Respiratory Tract Modelfor Radiological Protection. Pergamon Press (ElsevierScience), Tarrytown, NY.

24. Clark, A.R., and M. Egan. 1994. Modelling the depo-sition of inhaled powdered drug aerosols. J. AerosolSci. 25:175–186.

25. Weda, M., P. Zanen, A.H. de Boer, et al. 2004. An in-vestigation into the predictive value of cascade im-pactor results for side effects of inhaled salbutamol.Int. J. Pharm. 287:79–87.

26. Farr, S.J., S.J. Warren, P. Lloyd, et al. 2000. Compari-son of in vitro and in vivo efficiencies of a novel unit-dose liquid aerosol generator and a pressurized me-tered dose inhaler. Int. J. Pharm. 198:63–70.

27. Steckel, H., and B.W. Müller. 1997. In vitro evaluationof dry powder inhalers I: drug deposition of com-monly used devices. Int. J. Pharm. 154:19–29.

28. European Pharmacopeia. 1997. Preparations for in-halation: aerodynamic assessment of fine particles.European Pharmacopoeia Convention, 143–150.

29. United States Pharmacopeia �601�. 1999. Aerosols,metered-dose inhalers and dry powder inhalers

DUNBAR AND MITCHELL450

5967_07_p439-451 12/6/05 1:25 PM Page 450

�601�. United States Pharmacopeial Convention,Rockville, MD, 4933–4949.

30. Prime, D., P.K.P. Burnell, B. Johal, et al. 2000. Char-acterizing the full particle size distribution (PSD) fordoses emitted from dry powder inhalers (DPIs). In P.Byron, R. Dalby, S. Farr, et al., eds. RDD VII. SerentecPress, Raleigh, NC, 397–400.

31. Mitchell, J.P., M.W. Nagel, K.J. Wiersema, et al. 2003.Aerodynamic particle size analysis of aerosols frompressurized metered dose inhalers: comparison ofAndersen 8-stage cascade impactor, next genera-tion pharmaceutical impactor, and Model 3321 aero-dynamic particle sizer aerosol spectrometer. AAPSPharm. Sci. Tech. 4:1–9.

32. Mitchell, J.P., and M.W. Nagel. 2004. Particle sizeanalysis of aerosols from medicinal inhalers. KONA-Powder and Particle 22:32–65.

33. Dunbar, C.A., and A.J. Hickey. 2000. Evaluation ofprobability density functions to estimate particle sizedistributions of pharmaceutical aerosols. J. Aerosol Sci.31:813–831.

34. Leach, C. 1996. Enhanced drug delivery through re-formulating MDIs with HFA propellants—drug de-position and its effect on preclinical programs. In R.Dalby, P. Byron, and S. Farr, eds. RDD V. InterpharmPress, Buffalo Grove, IL, 133–144.

35. Canadian Standards Association. 2002. Spacers andholding chambers for use with metered-dose inhalers.CAN/CSA/Z264.1-02.

36. Lefebvre, A.H. 1989. Atomization and Sprays. Hemi-sphere Publishing, New York.

37. Thiel, C.G. 2002. Cascade impactor data and the log-normal distribution: non-linear regression for a bet-ter fit. J. Aerosol Med. 15:369–378.

Received on November 24, 2004in final form, May 19, 2005

Reviewed by:Myrna B. Dolovich, P.Eng

Chong S, Kim, Ph.D.

Address reprint requests to:Craig Dunbar, Ph.D.

Alkermes, Inc.88 Sidney St.

Cambridge, MA 02139

E-mail: craig.dunbar@alkermes.com

CASCADE IMPACTOR MASS DISTRIBUTIONS 451

5967_07_p439-451 12/6/05 1:25 PM Page 451

This article has been cited by:

1. D. L. Roberts, J. P. Mitchell. 2013. The Effect of Nonideal Cascade Impactor Stage Collection Efficiency Curves on theInterpretation of the Size of Inhaler-Generated Aerosols. AAPS PharmSciTech . [CrossRef]

2. Gabriela Apiou-Sbirlea, Steve Newman, John Fleming, Ruediger Siekmeier, Stephan Ehrmann, Gerhard Scheuch, GuentherHochhaus, Anthony Hickey. 2013. Bioequivalence of inhaled drugs: fundamentals, challenges and perspectives. TherapeuticDelivery 4:3, 343-367. [CrossRef]

3. Hlack Mohammed, Daryl L. Roberts, Mark Copley, Mark Hammond, Steven C. Nichols, Jolyon P. Mitchell. 2012. Effect ofSampling Volume on Dry Powder Inhaler (DPI)-Emitted Aerosol Aerodynamic Particle Size Distributions (APSDs) Measuredby the Next-Generation Pharmaceutical Impactor (NGI) and the Andersen Eight-Stage Cascade Impactor (ACI). AAPSPharmSciTech 13:3, 875-882. [CrossRef]

4. Trevor Riley, David Christopher, Jan Arp, Andrea Casazza, Agnes Colombani, Andrew Cooper, Monisha Dey, Janet Maas, JolyonMitchell, Maria Reiners, Nastaran Sigari, Terrence Tougas, Svetlana Lyapustina. 2012. Challenges with Developing In VitroDissolution Tests for Orally Inhaled Products (OIPs). AAPS PharmSciTech 13:3, 978-989. [CrossRef]

5. Jolyon Mitchell, Mark Copley, Yvonne Sizer, Theresa Russell, Derek Solomon. 2012. Adapting the Abbreviated ImpactorMeasurement (AIM) Concept to Make Appropriate Inhaler Aerosol Measurements to Compare with Clinical Data: A ScopingStudy with the “Alberta” Idealized Throat (AIT) Inlet. Journal of Aerosol Medicine and Pulmonary Drug Delivery 25:4, 188-197.[Abstract] [Full Text HTML] [Full Text PDF] [Full Text PDF with Links]

6. Carole Evans, David Cipolla, Tim Chesworth, Eva Agurell, Richard Ahrens, Dale Conner, Sanjeeva Dissanayake, Myrna Dolovich,William Doub, Anders Fuglsang, Afredo García Arieta, Michael Golden, Robert Hermann, Günther Hochhaus, Susan Holmes,Paul Lafferty, Svetlana Lyapustina, Parameswaran Nair, Dennis O'Connor, David Parkins, Ilse Peterson, Colin Reisner, DennisSandell, Gur Jai Pal Singh, Marjolein Weda, Patricia Watson. 2012. Equivalence Considerations for Orally Inhaled Products forLocal Action—ISAM/IPAC-RS European Workshop Report. Journal of Aerosol Medicine and Pulmonary Drug Delivery 25:3,117-139. [Abstract] [Full Text HTML] [Full Text PDF] [Full Text PDF with Links]

7. Nazrul Islam, Matthew J. Cleary. 2012. Developing an efficient and reliable dry powder inhaler for pulmonary drug delivery – Areview for multidisciplinary researchers. Medical Engineering & Physics 34:4, 409-427. [CrossRef]

8. Lester I. Harrison, Christopher C. Novak, Michael J. Needham, Paul Ratner. 2011. Comparative Pulmonary Function andPharmacokinetics of Fluticasone Propionate and Salmeterol Xinafoate Delivered by Two Dry Powder Inhalers to Patients withAsthma. Journal of Aerosol Medicine and Pulmonary Drug Delivery 24:5, 245-252. [Abstract] [Full Text HTML] [Full Text PDF][Full Text PDF with Links]

9. Terrence P. Tougas, Dave Christopher, Jolyon Mitchell, Svetlana Lyapustina, Michiel Oort, Richard Bauer, Volker Glaab. 2011.Product Lifecycle Approach to Cascade Impaction Measurements. AAPS PharmSciTech 12:1, 312-322. [CrossRef]

10. Peter T Daley Yates, Dave A Parkins. 2011. Letter to the Editor, British Journal of Clinical Pharmacology. British Journal ofClinical Pharmacology no-no. [CrossRef]

11. Terrence P. Tougas, David Christopher, Jolyon P. Mitchell, Helen Strickland, Bruce Wyka, Mike Oort, Svetlana Lyapustina.2009. Improved Quality Control Metrics for Cascade Impaction Measurements of Orally Inhaled Drug Products (OIPs). AAPSPharmSciTech 10:4, 1276-1285. [CrossRef]

12. Daryl L. Roberts. 2009. Theory of Multi-Nozzle Impactor Stages and the Interpretation of Stage Mensuration Data. AerosolScience and Technology 43:11, 1119-1129. [CrossRef]

13. Maren Kuhli, Maximilian Weiss, Hartwig Steckel. 2009. A sampling and dilution system for droplet aerosols from medicalnebulisers developed for use with an optical particle counter. Journal of Aerosol Science 40:6, 523-533. [CrossRef]

14. Mario Solomita, Gerald C. Smaldone. 2009. Reconciliation of Cascade Impaction during Wet Nebulization. Journal of AerosolMedicine and Pulmonary Drug Delivery 22:1, 11-18. [Abstract] [Full Text PDF] [Full Text PDF with Links]

15. J. P. Mitchell, M. W. Nagel, V. Avvakoumova, H. MacKay, R. Ali. 2009. The Abbreviated Impactor Measurement (AIM) Concept:Part 1—Influence of Particle Bounce and Re-Entrainment—Evaluation with a “Dry” Pressurized Metered Dose Inhaler (pMDI)-Based Formulation. AAPS PharmSciTech 10:1, 243-251. [CrossRef]

16. Susan Hoe, Paul M. Young, Hak-Kim Chan, Daniela Traini. 2009. Introduction of the Electrical Next Generation Impactor(eNGI) and Investigation of its Capabilities for the Study of Pressurized Metered Dose Inhalers. Pharmaceutical Research 26:2,431-437. [CrossRef]

17. D.J. Musk, P.J. Hergenrother. 2008. Chelated iron sources are inhibitors of Pseudomonas aeruginosa biofilms and distributeefficiently in an in vitro model of drug delivery to the human lung. Journal of Applied Microbiology 105:2, 380-388. [CrossRef]

18. Matthew Bonam, David Christopher, David Cipolla, Brent Donovan, David Goodwin, Susan Holmes, Svetlana Lyapustina,Jolyon Mitchell, Steve Nichols, Gunilla Pettersson, Chris Quale, Nagaraja Rao, Dilraj Singh, Terrence Tougas, Mike Oort,Bernd Walther, Bruce Wyka. 2008. Minimizing Variability of Cascade Impaction Measurements in Inhalers and Nebulizers. AAPSPharmSciTech 9:2, 404-413. [CrossRef]

19. Stephen B. Shrewsbury, Thomas A. Armer, Stephen P. Newman, Gary Pitcairn. 2008. Breath-synchronized plume-control inhalerfor pulmonary delivery of fluticasone propionate. International Journal of Pharmaceutics 356:1-2, 137-143. [CrossRef]

20. Stephen P. Newman, Hak-Kim Chan. 2008. In Vitro/In Vivo Comparisons in Pulmonary Drug Delivery. Journal of AerosolMedicine and Pulmonary Drug Delivery 21:1, 77-84. [Abstract] [Full Text PDF] [Full Text PDF with Links]

21. Stephen P. Newman, Hak-Kim Chan. 2008. In Vitro / In Vivo Comparisons in Pulmonary Drug Delivery. Journal of AerosolMedicine, ahead of print080207080519480-8. [CrossRef]

22. Jolyon Mitchell, Steve Newman, Hak-Kim Chan. 2007. In vitro and in vivo aspects of cascade impactor tests and inhalerperformance: A review. AAPS PharmSciTech 8:4, 237-248. [CrossRef]

23. J.C. Waldrep, A. Berlinski, R. Dhand. 2007. Comparative Analysis of Methods to Measure Aerosols Generated by a VibratingMesh Nebulizer. Journal of Aerosol Medicine 20:3, 310-319. [Abstract] [Full Text PDF] [Full Text PDF with Links]

24. David Christopher, Wallace P. Adams, Douglas S. Lee, Beth Morgan, Ziqing Pan, Gur Jai Pal Singh, Yi Tsong, SvetlanaLyapustina. 2007. Product Quality Research Institute evaluation of cascade impactor profiles of pharmaceutical aerosols: Part 2—Evaluation of a method for determining equivalence. AAPS PharmSciTech 8:1, E39-E48. [CrossRef]

25. M YAO, G MAINELIS. 2006. Effect of physical and biological parameters on enumeration of bioaerosols by portable microbialimpactors. Journal of Aerosol Science 37:11, 1467-1483. [CrossRef]

26. C. Majoral, A. Pape, P. Diot, L. Vecellio. 2006. Comparison of Various Methods for Processing Cascade Impactor Data. AerosolScience & Technology 40:9, 672-682. [CrossRef]