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Modelling the deposition of inhaled powdered drug aerosols
Pergamon
MODELLING
J. AerosolSci., Vol.25, No. 1, pp. 175-186,1994
Copyright © 1994ElsevierScienceLtd Printedin GreatBritain.All fightsreserved 0021-8502/94$6.00+0.00
THE DEPOSITION OF INHALED DRUG AEROSOLS
POWDERED
ANDREW R. CLARK *t a n d MIKE EGAN ~ t Genentech Inc., 460 Point San Bruno Boulevard, South San Francisco, CA 94080, U.S.A. AEA Technology, Consultancy Services, SRD, Risley, Cheshire WA3 6AT, U.K. (Received 25 January 1993; and in final form 14 June 1993)
Abstract--A computer modelling study of inhaled aerosol transport and deposition, under flow conditions relevant to the use of pharmaceutical dry powder inhalers, has been carried out. Extrathoracic deposition was estimated using a semi-empirical expression developed by Rudolf et al. (1990, J. Aerosol Sci. 21, 403) representing the filtering efficiency of the oropharynx. Lung deposition was investigated using the model of Egan and Nixon (1985, Radiat. Prot. Dosim. 11, 5). Calculations have been performed for several breathing patterns, with peak flow rates ranging from 7.5 to 1201 min- 1. The range of particle diameters included in the simulations covers the typical range of sizes found in powder inhalation aerosols, extending from 0.5 to 30 #m.
1. I N T R O D U C T I O N The performance of powder inhalers for delivering drugs either via or to the respiratory tract is traditionally judged on the basis of deposition patterns derived for application in the field of industrial hygiene. However, the breathing conditions that apply to deposition during occupational exposure are not generally relevant to powdered drug delivery systems, for which special breathing conditions are invariably recommended (Pedersen, 1986). It is therefore unlikely that deposition functions applicable to the field of industrial hygiene, or any test apparatus that has been calibrated against such data, will represent a valid basis for the prediction of the fate of inhaled powdered drugs. For example, the prescribed method for using a Dry Powder Inhaler (DPI) involves inhaling through the device at high flow rate followed by a period of breath holding (Auty et al., 1987). Aerosol intake is recommended to follow a maximum exhalation, and inhalation is intended to continue until vital capacity is achieved. For asymptomatic subjects, this might entail an inspired volume of more than 4 1 over several seconds, with a sustainable maximum flow rate in excess of 601 min- 1. By contrast, normal breathing at rest or under conditions of light exercise, the condition usually used for the assessment of occupational exposure, involves tidal volumes of around 1 1, breathed in a regular pattern. with an inhalation time of approximately 2 s and no breath holding pause. A computer modelling study of inhaled aerosol transport and deposition under flow conditions relevant to the use of DPIs has therefore been undertaken. The analysis described in this paper is a theoretical assessment of the transport and deposition of powder drug aerosols of varying aerodynamic particle diameters in the lungs of healthy human adults. A computer model for simulating the behavior of inhaled aerosol, which has been successfully validated against experimental data for a wide variety of inhalation conditions and particles sizes (Egan and Nixon, 1985) has been used to evaluate the deposition pattern of powdered drug within the lungs as a function of particle size and flow rate. Extra-thoracic deposition was determined using an empirical expression representing the filtering efficiency of the oropharynx. Calculations have been performed for several breathing patterns, with peak flow rates ranging from 7.5 to 120 l min -~. The range of aerodynamic particle diameters included in the simulations covers the typical size distribution associated with * Formerly at Fisons Pharmaceuticals, Loughborough, Leicestershire, U.K. t Present address. 175
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A.R. CLARKand M. EGAN
aerosols generated from DPIs, extending from 0.5 to 30 #m. Since powdered drug aerosol particles are generally irregular in shape and are of a size range were hygroscopic and electrostatic effects would be expected to be small (Clark, 1987; Hashish, 1988) the effects of particle shape, hygroscopicity and electrostatic charge were neglected.
2. THEORETICAL MODEL Extra-thoracic deposition The complex nature of the flow patterns associated with aerosol transport through the mouth and oropharynx and into the trachea preclude the evaluation of deposition using simple physical models based on idealized flow patterns. Instead, it is normal practice, for the purpose of computer simulation, to base the calculation of extra-thoracic deposition efficiency on semi-empirical models. A recent summary of available data on deposition efficiency of the oral cavity and oropharynx of adult male subjects has been provided by Rudolf et al. (1990). A model based on these data has been adopted in the recent work of the International Commission for Radiological Protection Task Group on human respiratory tract models for radiological protection (James et al., 1991). A model based on Rudolf's analysis is used in the present study. In general, it is considered that the bulk of the deposition in the oral passageway occurs in the larynx. Deposition efficiency is assumed to depend on the aerodynamic particle diameter, d,e (/~m), the flow rate through the mouth, Q (cm 3 s- 1), and the tidal volume, Vt (cm3), according to the formula: q(ET),,= 1-[-1.1 x lO-4(d~.Q°'6V;-°'z)L4+ 1 ] - '
(1)
Equation (1) indicates that oropharyngeal deposition efficiency is not merely a function of particles Stokes numbers. The form of the equation is heavily influenced by the effects of changes in laryngeal geometry with both inhaled volume and inhaled flow rate. The equation nevertheless represents an 'empirical' best fit to the available experimental data for particles greater than 0.2/~m. The experimental data on extra-thoracic deposition of inhaled aerosols also indicate substantial inter-subject variability (Rudolf et al., 1990). Upper and lower 95% confidence limits on the validity of equation (1) to any given individual adult male have been established by considering the variability in the available data. In practice, the corresponding bounding curves are evaluated by allowing the numerical coefficient in equation (1) to vary from 3.3 x 10-5 (lower 95% limit) to 3.6 x 10 -4 (upper 95% limit). The implications of these wide confidence limits will be discussed further. It should be noted here that the validity of using Rudolf's model in the present study relies upon two extrapolations. The first is that mouthpiece design does not have a significant effect on deposition efficiency, and the second is that equation (1) can be used at flow rates as high as 120 1min-1. Both of these points will be discussed further below. However, the range of data analyzed by Rudolf corresponds to situations in which filtering efficiency is very close to 100%. It is therefore unlikely that the overall uncertainty in deposition associated with extrapolation to higher flow rates will be particularly important, provided that the efficiency remains a monotonic function.
Deposition in the lungs The theoretical model used to simulate aerosol transport and deposition in the thoracic airways was that of Egan and Nixon (1985, 1987, 1988). The model was originally developed by Pack et al. (1977) to describe pulmonary gas transport and was modified to describe the behavior of inhaled aerosols by Egan and Nixon (1985). Details of the model are described elsewhere; however, a brief description is given below.
Deposition of powdereddrug aerosol
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The basis of the computational model is a modified partial differential gas transport equation representing aerosol transport and deposition:
where Aa is the cross-sectional area for aerosol transport, summed over all airways a distance x from the origin of the trachea; A T represents the total cross-sectional area which, in the lung periphery, includes the additional volume associated with alveoli; c is the aerosol concentration; u is the mean convective flow velocity; D is the effective axial diffusion coefficient; and L is the deposition rate per unit length. All variables are function of time, t, and distance, x. Equation (2) is solved numerically for c(x, t), adopting relevant initial boundary conditions. Anatomical data are used to define the geometry (Aa, AT) of the transport component of the model and to yield individual airway dimensions for evaluating the deposition term, L. The data used in the present study correspond to the ICRP Task Group's anatomical model (James et al., 1991) for an adult male of height 1.78 m. The alveolated region of the model is scaled according to the degree of inflation of the lungs which, in this study, is assumed to range over a breath from residual volume to vital capacity. The aerosol flow velocity at any depth in the lung airways, u(x, t), is then determined from rate of change in lung volume distal to that point assuming the volume fluctuations act upon an incompressible fluid. The diffusional component of the transport model reflects the impact of bulk mixing between incoming tidal air and residual air, caused by the complex airflow patterns in the lung. Such mixing has been investigated experimentally (Scherer et al., 1975) and the reported values form the basis for the axial diffusion coefficients, D(x, t), used in the present model. The importance of mixing between tidal and residual air varies according to whether consecutive breaths or single inhalations are considered. The mixing process therefore contributes to the variation in the pattern of deposition experienced between occupational exposure and aerosol drug delivery. Deposition is evaluated as being due to the combined effects of inertial impaction, sedimentation and Brownian diffusion. However, for the range of particle sizes considered here, only the first two mechanisms have any significant effect. Modelling for the contributions of L(x, t) from the various sources is essentially the same as has been reported elsewhere (Egan et al., 1989). It is pertinent to note, however, that, whereas gravitational settling is evaluated on the basis of a theoretical model, calculations of inertial deposition efficiency are based on experimental data obtained using human lung casts (Gurman et al., 1984). The model described above is particularly appropriate to studies where predictions of aerosol deposition are required under conditions where the experimental data base is sparse. Confidence is lent to the calculations because the model incorporates explicitly each of the important physical factors governing aerosol transport in the lung. Validation of the model (Nixon and Egan, 1987; Egan et al., 1989) under a wide range of inhalation conditions and particle sizes has also been performed, demonstrating the effectiveness of this simulation approach. However, it must be remembered that the application of the model to the flow profiles investigated in the current study does involve extrapolation beyond this 'validated' range. From the viewpoint of making reliable predictions however, it is significant to note that good agreement between experimental results and corresponding model calculations does not depend on the "tuning" of the model parameters. The primary limitation of the model is that all the factors relating to aerosol transport and deposition are constrained to depend solely upon a single spatial dimension, the axial distance along the airways from the trachea. The one-dimensional simplification only affects the modelling of those mechanisms that depend for their action on the occurrence of secondary flows. Thus, as described above, both the calculation of deposition due to impaction and bulk mixing of tidal and residual air volumes are simulated on an empirical basis.
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The use of the diffusion coefficient of Scherer et al. (1975) at high flow rates, 60-1201rain -1, represents a significant extrapolation. However, for single breaths of aerosol, comprising large inhaled volumes followed by breath hold (the conditions considered here), the effects of mixing between tidal and reserve air volumes on overall patterns of deposition are in fact very weak. The use of effective diffusion coefficients based on the experimental work of Scherer et al. (1975) is therefore unlikely to have a significant impact upon the conclusions drawn from this study. Impaction deposition is simulated through the evaluation of airway-dependent filtering efficiency, using the Stokes number, Stk, as a basis for determining an empirical correlation with available data. The deposition term for impaction efficiency takes the form: r h = a S t k b,
(3)
where a and b are empirical constants (Egan et al., 1989). The Stokes number, in turn, is determined on the basis of anatomical data and airflow velocities calculated for a given lung depth. The range of validity of equation (3), as used within the model, is constrained by coverage of the experimental data from which the empirical constants are determined. Aerosol deposition data have been obtained from lung casts (Gurman et al., 1984) over a range of particle sizes and air flows. These data cover the Stokes number range 0.003-0.2. For the situations reported here only those data for the highest flow rates (60 and 1201 min- 1) and largest particle sizes fall outside this Stokes number range. Nevertheless, extrapolation of the empirical formula to higher Stokes numbers is not considered likely to give rise to large errors. 3. S I M U L A T I O N S The object of this study was to obtain predictions of regional deposition of inhaled aerosols under conditions representative of those obtained during the use of DPIs. Two sets of simulations were performed. First, a series of "base case" calculations for various peak flow rates and a range of particle sizes were performed, simulating aerosol transport and deposition on the basis of simplified inhalation patterns. Secondly, sensitivity studies were performed to assess the importance of the different simplifying assumptions for predictions obtained under specific inhalation conditions.
Physiological data Pneumotachograph traces of the time variation in airflow rate through the mouth of normal subjects breathing through a Spinhaler R were obtained. A Mercury Instruments FL300 flow head was coupled to the air inlet of a 'sealed' Spinhaler ~ and a Furness Controls FC012 micromanometer was used to monitor the flow profiles. Each subject was instructed to inhale through the device from residual volume (i.e. following a maximum expiration) up to vital capacity, with the aim of achieving a sustained constant flow rate. Five different flows were used, ranging from 7.5 to 1201min -1. The digital output from the flow monitoring equipment was used as the positive feedback mechanism to enable the volunteers to maintain the target flow rate. The simulations reported here are based on the flow profiles for one of four volunteers, the profile for each volunteer being essentially similar. The flow profiles used as a basis for the computer simulations are shown in Fig. 1. The primary parameters describing the flow profiles are the sustained maximum flow rate and the total inhaled volume. A feature of all of the flow profiles was that they exhibit a trend towards larger inhaled volumes at higher flow rates. Another general trend for all subjects was that a finite time was required to both reach and decline from the peak sustainable flow. In most cases the subjects achieved a reasonably constant sustained peak flow, although there were the inevitable minor fluctuations.
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Base calculations Each of the simulations was based on a simplified representation of the breathing pattern achieved by the normal subjects. For the purposes of the simulation the subject was assumed to breathe through the mouth from a residual volume of 1.741. The sustained maximum flow rate was based on the target value. Inspiratory flow was assumed to rise linearly from zero to the m a x i m u m sustained flow over a period of one second and to return to zero over the same period. The total inhaled volume was the same as that recorded in Fig. 1. Following inhalation, breath holding for 10 s was assumed. Expiration was then assumed to follow at a constant flow rate over a period of 4 s. The volume expired was set at 60% of that inhaled, reflecting a return to functional residual capacity. A schematic illustration of the simplified breathing pattern is shown in Fig. 2. Calculations of transport and deposition were performed for a range of monodisperse aerosols, with aerodynamic diameters from 0.5 to 30 #m. In the base case calculations, the aerosol was assumed to be delivered at a constant concentration throughout the breath.
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Aerosol deposition as a fraction of the total amount inhaled was evaluated as a function of particle size and flow rate for extra-thoracic airways and each branching generation of the lung model. Extra-thoracic deposition was evaluated using equation (1). Tracheobronchial and alveolar deposition, generations 1-16 of the model and generations 16 and beyond, respectively, were aggregated to yield total thoracic deposition.
Sensitivity studies As described above the base calculation set involved a number of approximations and assumptions. In order to evaluate the potential significance of these a number of additional simulations were performed. Each sensitivity study corresponded to a maximum sustained flow rate of 60 1min- t.
The effect of simplified representation of flow rate. An additional calculation was performed utilizing the actual 601 min-~ flow profile presented in Fig. 1. The effect of breath hold. Recommended methods for using DPIs involve a breath holding pause after inhalation (Pedersen, 1986). This pause was included in the base calculation. However, an indication of the significance of the breath hold was thought to be valuable. A simulation was therefore carried out where exhalation was assumed to directly follow the inspiratory phase. The effect of aerosol concentration. Drug delivery from DPI may not necessarily be uniform during the inhaled breath. Indeed it is logical to assume from DPI design that drug delivery will be of a bolus nature. The potential importance of bolus delivery was investigated by carrying out a simulation where all of the aerosol was delivered over the first 25% of the inhalation cycle.
4. RESULTS
Base calculations Figure 3 illustrates the extra-thoracic deposition efficiency calculated as a function of particle size and flow rate on the basis of equation (1). As might be expected there is a trend towards higher deposition for larger particle diameters and higher flow rates, reflecting the importance of inertial impaction on the larynx and at the back of the throat. 100
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Deposition of powdered drug aerosol
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For aerodynamic diameters as large as 30/~m, deposition is virtually 100% for higher flow rates and is approximately 90% for the lowest flow rate simulated in the present study (7.5 lmin-1). However, at particle sizes between 3 and 20/~m, there is a marked difference between the extra-thoracic filtering efficiency at different flow rates. Moving deeper into the lung, Figs 4 and 5 show the predicted deposition, also as a function of particle diameter with flow rate as a parameter, for the tracheobronchial and pulmonary airways, respectively. Deposition fractions in these figures include the effects of extra-thoracic filtering. The results correspond to the "base case" calculations assuming a constant aerosol concentration and a 10 s breath hold. Given the high rate of extra-thoracic filtering at large particle diameters, it is perhaps not surprising that the deposition in the bronchial airways falls to very low values for each of the simulated flow rates. The maximum bronchial deposit, at all particle diameters, is predicted to occur at the lowest inhaled flow rate, reflecting both the importance of gravitational settling within the bronchi and the low rate of removal in the oropharynx. Thus, although impaction in the bronchial airways becomes progressively more important
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A.R. CLARKand M. EGAN
at higher flow rates, its effect tends to be counteracted by a corresponding increase in extrathoracic removal. Peak deposition in the bronchial airways as a whole varies from around 55% at the lowest inhaled flow rate to 30% for a peak inhaled flow of 1201min -1. The particle diameter at which the maximum deposition occurs varies from 10/~m at low flow to 6/~m for the highest flow rate. However, close examination of the detailed deposition profiles (by airway generation) also reveals that the airway generation in which peak deposition occurs also changes with inhaled flow rate. At high flow rates deposition peaks in the upper bronchi whereas at lower flow rates the deposition is more even. The overall deposition in the alveolated, pulmonary, airways clearly depends upon the removal that has already taken place in the oropharynx and conducting airways. Thus, at high flow rates, deposition in the deep lung is virtually zero for particle diameters greater that 10 #m, impaction having already accounted for all aerosol entering the respiratory tract. In general, there is a trend towards increased deposition in the deep lung with lower flow rates. The effect is most marked for particle diameters larger than 3/zm and for the higher flow rates, where filtering by the mouth and bronchial airways is determined primarily by impaction. There are much smaller differences for smaller particle sizes. Respiratory tract deposition as a whole can be calculated by summing the deposition for the three lung regions. It will be seen that for particle diameters greater than 3/~m total deposition is approximately 100%o. Below 3 #m deposition decreases in a linear manner with particle diameter reaching a value of between 60 and 70% at a diameter of 0.5/~m depending upon inhaled flow rate.
Sensitivity studies The effect of simplified representation of flow rate. Figure 6 presents a comparison between the computed tracheobronchial and pulmonary deposition calculated using the experimental profile shown in Fig. 1 and the simplified profile illustrated in Fig. 2. The same extra thoracic filtering has been assumed for both cases. The results for two simulations are very similar, indicating that the simplified profile adopted for the purposes of the study provides an adequate representation of the actual flow profile. The slightly higher bronchial deposition obtained using the simplified function is due to a higher effective flow rate over the first 2 s of inhalation.
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Deposition of powdered drug aerosol
183
The effect of breath hold. It has already been mentioned that the recommended procedure for inhaling from a powdered drug generator entails a deep inhalation followed by a breath holding pause. Figure 7 illustrates the impact of the breath holding pause following a 601 min-1 inspiration. It can be seen that the breath holding pause only affects particles with diameters 3 #m and less. In effect, virtually 100% of the aerosol inhaled during a deep breath at a peak flow rate of 601 min- 1 is deposited during the inspiratory phase. The mean residence time, combined with the settling velocity, of the large-sized particles that are not deposited by impaction is such that deposition by gravitational settling in the deep lung will have occurred before the breath hold begins. However, for smaller particles, particularly those with diameters in the region of 0.5-1 #m, the intrinsic mobility of the aerosol is so low that the breath hold can have a significant impact on overall deposition. The effect of aerosol concentration. The "base case" calculations were all undertaken on the assumption that aerosol delivery was adequately represented by a constant concentration throughout the inspiratory phase. By contrast, it is likely that aerosol delivery from a powder inhaler will be of a bolus nature. Figure 8 presents a comparison between simulations performed assuming a constant
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aerosol concentration during inspiration and simulations assuming that aerosol delivery takes place in the first 25% of the inhalation. Deposition in the bronchial airways is slightly smaller in the case of bolus delivery. This result probably reflects the fact that proportionally more aerosol is delivered at lower inhalation flows whereas with the constant aerosol concentration a significant amount is delivered during the peak flow phase. For particles greater than approximately 3 #m there is very little difference between the two results. Below this size the average residence time for the bolus aerosol results in higher deposition fractions. 5. DISCUSSION The primary objective of this study has been to assess the potential importance of inhalation flow pattern on deposition of inhaled powdered drug aerosol. The various modelling results described above provide a wide ranging summary of predicted deposition of monodisperse aerosols in the lung under the typical flow patterns experienced with powder inhalers. In particular, the results show the effects of varying inspiratory flow rate and aerosol particle size on predicted deposition within the regions of the respiratory tract. It can be seen that the data presented predict higher deposition fractions than that previously reported for normal tidal breathing situations (James et al., 1991). This increased deposition fraction is attributable to the much longer residence times associated with the breathing patterns normally used with powder inhalers and confirms that data based on the standard breathing patterns investigated by the industrial hygiene community cannot be used as a reliable base for the calculation of deposition fractions when considering powder inhaler devices. Sensitivity studies indicate that the simplified representations of the inhaled flow profiles do not have an important influence on the overall predictions of deposition pattern. Similarly, breath hold after a deep inhalation from residual lung volume does not seem to have a significant impact on overall deposition, except for particles with intrinsically low mobility (i.e. less than 2/~m). This also indicates that the assumed airflow pattern during expiration will be insignificant in terms of overall deposition pattern, since virtually all mass deposition takes place during the inspiratory phase. The assumed aerosol delivery profile during the breath can have a small effect upon the predicted deposition. In particular, if most of the aerosol is delivered before maximum flow is achieved, the impaction in the upper airways will be slightly less and a more even deposition pattern results. However, in assessing the importance of the potential significance of this and the other assumptions underlying the simulations, due account needs to be taken of possible sources of uncertainty in the basic modelling approach. One of the major sources of uncertainty in the calculations is likely to be that associated with the determination of extra-thoracic filtering. For particles larger than 3/~m aerodynamic diameter, the extra-thoracic and thoracic deposition are complementary, together giving rise to nearly 100% deposition. Any variation in extra-thoracic deposition is therefore likely to be compensated for by a corresponding change in deposition within the lungs. The range of inter-subject variability in normal adult males has already been discussed above. The curves presented in Fig. 9 show the profiles for the mean and 95% confidence limits calculated using the confidence limits given by Rudolf et al. (1990). The effect of variations in extra-thoracic deposition upon tracheobronchial deposition can clearly be seen. Although the pulmonary region is only slightly affected the tracheobronchial deposition varies quite dramatically. Peak tracheobronchial deposition ranges from 60 to 65% at the upper 95% level to around 15% at the lower 95% level. However, this does not negate the foregoing conclusions since in any individual the trends identified would be correct. It is also constructive to compare the computational predictions with the available data on the deposition profiles from DPI's. However, although there are numerous papers detailing the deposition profiles obtained from DPIs (Newman et al., 1988, 1989; Vidgren et al., 1988, 1990), this comparison is confounded by the lack of concomitant deposition and
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aerosol size data. The existing sizing data are either limited to detailing 'respirable fraction' or are limited to documenting the efficacy of the radiolabeling process. The somewhat limited comparisons generally possible support the models predictions. For example, the high total deposition and low exhaled fraction predicted by the convolution of the model calculations and available sizing data (Newman et al., 1988, 1989) is supported by the low exhaled fractions obtained in the papers cited above. Also the increase in thoracic deposition with increasing flow rate is that expected from a delivery system where increased powder dispersion at high flow rates (Newman et al., 1989, 1991) outstrips the increased probability of oral deposition. However, in general, it was found that the convolution calculations overestimated thoracic deposition by a factor of 1.5-2. It is as yet unclear as to the reason for this overestimation. As stated above, total deposition is approximately 100%, both experimentally and theoretically, and therefore the determinant of both the experimental and theoretical values relies upon oral deposition and the use of Rudolf's equation (Rudolf et al., 1990). Further, since Rudolf's equation is an empirical analysis based upon widely-varying inspiratory conditions in healthy human subjects, it is difficult to understand why it should be in error in these particular circumstances. However, as alluded to above, it may be that mouthpiece design significantly affects deposition or that the extrapolation of equation (1) to high flow rates has resulted in considerable error. It would seem unlikely that the latter is case, for both the reasons discussed above and since in a number of the above deposition studies the flow rates were well within the range analyzed by Rudolf. Moreover, it may also be possible that the sizing techniques used in the above studies were incapable of sufficient resolution for accurate convolution calculations. Either way, the resolution of this enigma will have to wait for further data and the application of high resolution aerosol sizing techniques coupled to further deposition profile measurements.
REFERENCES Auty, R. M., Brown,K., Neale, M. and Snashall, P. D. (1987)Respiratorytract depositionof sodium cromoglycate is highly dependent upon techniqueof inhalation using the Spinhaler. Br. d. Dis. Chest. 81, 371-380. Clark, A. R. (1987)A theoreticalanalysisof aerosol growth in the respiratorytract. Proceedings of the First Annual Conference of the Aerosol Society, pp. 65-68. Egan, M. J. and Nixon,W. (1985)A model of aerosol deposition in the lung for use in inhalation dose assessments. Radiat. Prot. Dosim. 11, 5-17. Egan, M. J. and Nixon, W. (1987)Mathematical modellingof fine particledeposition in the respiratorysystem.In Deposition and Clearance of Aerosols in the Human Respiratory Tract (Edited by Hofman, W.), Facultas Universitatsverlag, pp. 34-40, Vienna.
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Egan, M. J. and Nixon, W. (1988) A modelling study of regional deposition of inspired aerosols with reference to dosimetric assessment. Ann. Occup. Hyg. 32, 909-918. Egan, M. J., Nixon, W., Robinson, N. I., James, A. C. and Phalen, R. F. (1989) Inhaled aerosol transport and deposition calculations for the ICRP Task Group. J. Aerosol Sci. 20, 1305-1308. Gurman, J. L., Lippman, M. and Schlesinger, R. B. (1984) Particle deposition in replicate casts of human upper tracheo-bronchial tree under constant and cyclic inspiratory flow. 1. Experimental. Aerosol Sci. Technol. 3, 245-252. Hashish, A. H. (1988) The influence of electrostatic charge on deposition of theraputic aerosols. Ph.D. Thesis, University of Southampton. James, A. C., Stahlhofen, W., Rudolf, G., Egan, M. J., Nixon, W., Gehr, P. and Briant, J. K. (1991) The Respiratory Tract Deposition Model Proposed by the ICRP Task Group. Radiat. Prot. Dosim. 38, 159-165. Newman, S. P., Moren, F., Trofast, E., Talaee, N. and Clarke, S. W. (1989) Deposition and clinical efficacy of terbutaline sulphate from Turbuhaler, a new multi-dose powder inhaler. Eur. Respir. J. 2, 247. Newman, S, P., Moren, F., Trofast, E., Talaee, N. and Clarke, S. W. (1991) Terbutaline sulphate Turbuhaler: effect of inhaled flow rate on drug deposition and efficacy. Int. J. Pharm. 74, 209-213. Newman, S. P., Moren, F., Trofast, E., Woodman, G. and Clarke, S. W. (1988) Deposition patterns in man from Turbuhaler: a preliminary report. Proceedings of Int. Workshop on a New Inhaler (Edited by Newman, S. P., Moren, F. and Crompton, G. K.). Medicom, London. Nixon, W. and Egan, M. J. (1987) Modelling study of regional deposition of inhaled aerosols with special reference to effects of ventilation asymmetry. J. Aerosol Sci. 18, 563-579. Pack, A., Hooper, M. B., Nixon, W. and Taylor, J. C. (1977) A computational model of pulmonary gas transport incorporating effective diffusion. Respir. Physiol. 29, 101-124. Pedersen, S. (1986) How to use the Rotahaler. Arch Dis. Childhood, 61, 11-14. Rudolf, G., Kobrich, R. and Stahlhofen, W. (1990) Modelling and algebraic formulation of regional aerosol deposition in man. J. Aerosol Sci. 21, $403-$406. Scherer, P. W., Shendalman, L. H., Greene, N. M. and Bouhuys, L. A. (1975) A Measurement of axial diffusivities in a model of the bronchial airways. J. Appl. Physiol. 38, 719-723. Vidgren, M., Karkkainen, A., Karjalainen, P., Paronen, P. and Nuutinen, J. (1988) Effect of powder inhaler design on drug deposition in the respiratory tract. Int. J. Pharm. 42, 211-216. Vidgren, M., Paronen, P., Vidgren, P., Valino, P. and Nuutinen, J. (1990) Radiotracer evaluation of the deposition of drug particles inhaled from a new powder inhaler. Int. J. Pharm. 64, 1-6.
MODELLING
J. AerosolSci., Vol.25, No. 1, pp. 175-186,1994
Copyright © 1994ElsevierScienceLtd Printedin GreatBritain.All fightsreserved 0021-8502/94$6.00+0.00
THE DEPOSITION OF INHALED DRUG AEROSOLS
POWDERED
ANDREW R. CLARK *t a n d MIKE EGAN ~ t Genentech Inc., 460 Point San Bruno Boulevard, South San Francisco, CA 94080, U.S.A. AEA Technology, Consultancy Services, SRD, Risley, Cheshire WA3 6AT, U.K. (Received 25 January 1993; and in final form 14 June 1993)
Abstract--A computer modelling study of inhaled aerosol transport and deposition, under flow conditions relevant to the use of pharmaceutical dry powder inhalers, has been carried out. Extrathoracic deposition was estimated using a semi-empirical expression developed by Rudolf et al. (1990, J. Aerosol Sci. 21, 403) representing the filtering efficiency of the oropharynx. Lung deposition was investigated using the model of Egan and Nixon (1985, Radiat. Prot. Dosim. 11, 5). Calculations have been performed for several breathing patterns, with peak flow rates ranging from 7.5 to 1201 min- 1. The range of particle diameters included in the simulations covers the typical range of sizes found in powder inhalation aerosols, extending from 0.5 to 30 #m.
1. I N T R O D U C T I O N The performance of powder inhalers for delivering drugs either via or to the respiratory tract is traditionally judged on the basis of deposition patterns derived for application in the field of industrial hygiene. However, the breathing conditions that apply to deposition during occupational exposure are not generally relevant to powdered drug delivery systems, for which special breathing conditions are invariably recommended (Pedersen, 1986). It is therefore unlikely that deposition functions applicable to the field of industrial hygiene, or any test apparatus that has been calibrated against such data, will represent a valid basis for the prediction of the fate of inhaled powdered drugs. For example, the prescribed method for using a Dry Powder Inhaler (DPI) involves inhaling through the device at high flow rate followed by a period of breath holding (Auty et al., 1987). Aerosol intake is recommended to follow a maximum exhalation, and inhalation is intended to continue until vital capacity is achieved. For asymptomatic subjects, this might entail an inspired volume of more than 4 1 over several seconds, with a sustainable maximum flow rate in excess of 601 min- 1. By contrast, normal breathing at rest or under conditions of light exercise, the condition usually used for the assessment of occupational exposure, involves tidal volumes of around 1 1, breathed in a regular pattern. with an inhalation time of approximately 2 s and no breath holding pause. A computer modelling study of inhaled aerosol transport and deposition under flow conditions relevant to the use of DPIs has therefore been undertaken. The analysis described in this paper is a theoretical assessment of the transport and deposition of powder drug aerosols of varying aerodynamic particle diameters in the lungs of healthy human adults. A computer model for simulating the behavior of inhaled aerosol, which has been successfully validated against experimental data for a wide variety of inhalation conditions and particles sizes (Egan and Nixon, 1985) has been used to evaluate the deposition pattern of powdered drug within the lungs as a function of particle size and flow rate. Extra-thoracic deposition was determined using an empirical expression representing the filtering efficiency of the oropharynx. Calculations have been performed for several breathing patterns, with peak flow rates ranging from 7.5 to 120 l min -~. The range of aerodynamic particle diameters included in the simulations covers the typical size distribution associated with * Formerly at Fisons Pharmaceuticals, Loughborough, Leicestershire, U.K. t Present address. 175
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A.R. CLARKand M. EGAN
aerosols generated from DPIs, extending from 0.5 to 30 #m. Since powdered drug aerosol particles are generally irregular in shape and are of a size range were hygroscopic and electrostatic effects would be expected to be small (Clark, 1987; Hashish, 1988) the effects of particle shape, hygroscopicity and electrostatic charge were neglected.
2. THEORETICAL MODEL Extra-thoracic deposition The complex nature of the flow patterns associated with aerosol transport through the mouth and oropharynx and into the trachea preclude the evaluation of deposition using simple physical models based on idealized flow patterns. Instead, it is normal practice, for the purpose of computer simulation, to base the calculation of extra-thoracic deposition efficiency on semi-empirical models. A recent summary of available data on deposition efficiency of the oral cavity and oropharynx of adult male subjects has been provided by Rudolf et al. (1990). A model based on these data has been adopted in the recent work of the International Commission for Radiological Protection Task Group on human respiratory tract models for radiological protection (James et al., 1991). A model based on Rudolf's analysis is used in the present study. In general, it is considered that the bulk of the deposition in the oral passageway occurs in the larynx. Deposition efficiency is assumed to depend on the aerodynamic particle diameter, d,e (/~m), the flow rate through the mouth, Q (cm 3 s- 1), and the tidal volume, Vt (cm3), according to the formula: q(ET),,= 1-[-1.1 x lO-4(d~.Q°'6V;-°'z)L4+ 1 ] - '
(1)
Equation (1) indicates that oropharyngeal deposition efficiency is not merely a function of particles Stokes numbers. The form of the equation is heavily influenced by the effects of changes in laryngeal geometry with both inhaled volume and inhaled flow rate. The equation nevertheless represents an 'empirical' best fit to the available experimental data for particles greater than 0.2/~m. The experimental data on extra-thoracic deposition of inhaled aerosols also indicate substantial inter-subject variability (Rudolf et al., 1990). Upper and lower 95% confidence limits on the validity of equation (1) to any given individual adult male have been established by considering the variability in the available data. In practice, the corresponding bounding curves are evaluated by allowing the numerical coefficient in equation (1) to vary from 3.3 x 10-5 (lower 95% limit) to 3.6 x 10 -4 (upper 95% limit). The implications of these wide confidence limits will be discussed further. It should be noted here that the validity of using Rudolf's model in the present study relies upon two extrapolations. The first is that mouthpiece design does not have a significant effect on deposition efficiency, and the second is that equation (1) can be used at flow rates as high as 120 1min-1. Both of these points will be discussed further below. However, the range of data analyzed by Rudolf corresponds to situations in which filtering efficiency is very close to 100%. It is therefore unlikely that the overall uncertainty in deposition associated with extrapolation to higher flow rates will be particularly important, provided that the efficiency remains a monotonic function.
Deposition in the lungs The theoretical model used to simulate aerosol transport and deposition in the thoracic airways was that of Egan and Nixon (1985, 1987, 1988). The model was originally developed by Pack et al. (1977) to describe pulmonary gas transport and was modified to describe the behavior of inhaled aerosols by Egan and Nixon (1985). Details of the model are described elsewhere; however, a brief description is given below.
Deposition of powdereddrug aerosol
177
The basis of the computational model is a modified partial differential gas transport equation representing aerosol transport and deposition:
where Aa is the cross-sectional area for aerosol transport, summed over all airways a distance x from the origin of the trachea; A T represents the total cross-sectional area which, in the lung periphery, includes the additional volume associated with alveoli; c is the aerosol concentration; u is the mean convective flow velocity; D is the effective axial diffusion coefficient; and L is the deposition rate per unit length. All variables are function of time, t, and distance, x. Equation (2) is solved numerically for c(x, t), adopting relevant initial boundary conditions. Anatomical data are used to define the geometry (Aa, AT) of the transport component of the model and to yield individual airway dimensions for evaluating the deposition term, L. The data used in the present study correspond to the ICRP Task Group's anatomical model (James et al., 1991) for an adult male of height 1.78 m. The alveolated region of the model is scaled according to the degree of inflation of the lungs which, in this study, is assumed to range over a breath from residual volume to vital capacity. The aerosol flow velocity at any depth in the lung airways, u(x, t), is then determined from rate of change in lung volume distal to that point assuming the volume fluctuations act upon an incompressible fluid. The diffusional component of the transport model reflects the impact of bulk mixing between incoming tidal air and residual air, caused by the complex airflow patterns in the lung. Such mixing has been investigated experimentally (Scherer et al., 1975) and the reported values form the basis for the axial diffusion coefficients, D(x, t), used in the present model. The importance of mixing between tidal and residual air varies according to whether consecutive breaths or single inhalations are considered. The mixing process therefore contributes to the variation in the pattern of deposition experienced between occupational exposure and aerosol drug delivery. Deposition is evaluated as being due to the combined effects of inertial impaction, sedimentation and Brownian diffusion. However, for the range of particle sizes considered here, only the first two mechanisms have any significant effect. Modelling for the contributions of L(x, t) from the various sources is essentially the same as has been reported elsewhere (Egan et al., 1989). It is pertinent to note, however, that, whereas gravitational settling is evaluated on the basis of a theoretical model, calculations of inertial deposition efficiency are based on experimental data obtained using human lung casts (Gurman et al., 1984). The model described above is particularly appropriate to studies where predictions of aerosol deposition are required under conditions where the experimental data base is sparse. Confidence is lent to the calculations because the model incorporates explicitly each of the important physical factors governing aerosol transport in the lung. Validation of the model (Nixon and Egan, 1987; Egan et al., 1989) under a wide range of inhalation conditions and particle sizes has also been performed, demonstrating the effectiveness of this simulation approach. However, it must be remembered that the application of the model to the flow profiles investigated in the current study does involve extrapolation beyond this 'validated' range. From the viewpoint of making reliable predictions however, it is significant to note that good agreement between experimental results and corresponding model calculations does not depend on the "tuning" of the model parameters. The primary limitation of the model is that all the factors relating to aerosol transport and deposition are constrained to depend solely upon a single spatial dimension, the axial distance along the airways from the trachea. The one-dimensional simplification only affects the modelling of those mechanisms that depend for their action on the occurrence of secondary flows. Thus, as described above, both the calculation of deposition due to impaction and bulk mixing of tidal and residual air volumes are simulated on an empirical basis.
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The use of the diffusion coefficient of Scherer et al. (1975) at high flow rates, 60-1201rain -1, represents a significant extrapolation. However, for single breaths of aerosol, comprising large inhaled volumes followed by breath hold (the conditions considered here), the effects of mixing between tidal and reserve air volumes on overall patterns of deposition are in fact very weak. The use of effective diffusion coefficients based on the experimental work of Scherer et al. (1975) is therefore unlikely to have a significant impact upon the conclusions drawn from this study. Impaction deposition is simulated through the evaluation of airway-dependent filtering efficiency, using the Stokes number, Stk, as a basis for determining an empirical correlation with available data. The deposition term for impaction efficiency takes the form: r h = a S t k b,
(3)
where a and b are empirical constants (Egan et al., 1989). The Stokes number, in turn, is determined on the basis of anatomical data and airflow velocities calculated for a given lung depth. The range of validity of equation (3), as used within the model, is constrained by coverage of the experimental data from which the empirical constants are determined. Aerosol deposition data have been obtained from lung casts (Gurman et al., 1984) over a range of particle sizes and air flows. These data cover the Stokes number range 0.003-0.2. For the situations reported here only those data for the highest flow rates (60 and 1201 min- 1) and largest particle sizes fall outside this Stokes number range. Nevertheless, extrapolation of the empirical formula to higher Stokes numbers is not considered likely to give rise to large errors. 3. S I M U L A T I O N S The object of this study was to obtain predictions of regional deposition of inhaled aerosols under conditions representative of those obtained during the use of DPIs. Two sets of simulations were performed. First, a series of "base case" calculations for various peak flow rates and a range of particle sizes were performed, simulating aerosol transport and deposition on the basis of simplified inhalation patterns. Secondly, sensitivity studies were performed to assess the importance of the different simplifying assumptions for predictions obtained under specific inhalation conditions.
Physiological data Pneumotachograph traces of the time variation in airflow rate through the mouth of normal subjects breathing through a Spinhaler R were obtained. A Mercury Instruments FL300 flow head was coupled to the air inlet of a 'sealed' Spinhaler ~ and a Furness Controls FC012 micromanometer was used to monitor the flow profiles. Each subject was instructed to inhale through the device from residual volume (i.e. following a maximum expiration) up to vital capacity, with the aim of achieving a sustained constant flow rate. Five different flows were used, ranging from 7.5 to 1201min -1. The digital output from the flow monitoring equipment was used as the positive feedback mechanism to enable the volunteers to maintain the target flow rate. The simulations reported here are based on the flow profiles for one of four volunteers, the profile for each volunteer being essentially similar. The flow profiles used as a basis for the computer simulations are shown in Fig. 1. The primary parameters describing the flow profiles are the sustained maximum flow rate and the total inhaled volume. A feature of all of the flow profiles was that they exhibit a trend towards larger inhaled volumes at higher flow rates. Another general trend for all subjects was that a finite time was required to both reach and decline from the peak sustainable flow. In most cases the subjects achieved a reasonably constant sustained peak flow, although there were the inevitable minor fluctuations.
Deposition of powdered drug aerosol 140
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Base calculations Each of the simulations was based on a simplified representation of the breathing pattern achieved by the normal subjects. For the purposes of the simulation the subject was assumed to breathe through the mouth from a residual volume of 1.741. The sustained maximum flow rate was based on the target value. Inspiratory flow was assumed to rise linearly from zero to the m a x i m u m sustained flow over a period of one second and to return to zero over the same period. The total inhaled volume was the same as that recorded in Fig. 1. Following inhalation, breath holding for 10 s was assumed. Expiration was then assumed to follow at a constant flow rate over a period of 4 s. The volume expired was set at 60% of that inhaled, reflecting a return to functional residual capacity. A schematic illustration of the simplified breathing pattern is shown in Fig. 2. Calculations of transport and deposition were performed for a range of monodisperse aerosols, with aerodynamic diameters from 0.5 to 30 #m. In the base case calculations, the aerosol was assumed to be delivered at a constant concentration throughout the breath.
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180
A.R. CLARKand M. EGAN
Aerosol deposition as a fraction of the total amount inhaled was evaluated as a function of particle size and flow rate for extra-thoracic airways and each branching generation of the lung model. Extra-thoracic deposition was evaluated using equation (1). Tracheobronchial and alveolar deposition, generations 1-16 of the model and generations 16 and beyond, respectively, were aggregated to yield total thoracic deposition.
Sensitivity studies As described above the base calculation set involved a number of approximations and assumptions. In order to evaluate the potential significance of these a number of additional simulations were performed. Each sensitivity study corresponded to a maximum sustained flow rate of 60 1min- t.
The effect of simplified representation of flow rate. An additional calculation was performed utilizing the actual 601 min-~ flow profile presented in Fig. 1. The effect of breath hold. Recommended methods for using DPIs involve a breath holding pause after inhalation (Pedersen, 1986). This pause was included in the base calculation. However, an indication of the significance of the breath hold was thought to be valuable. A simulation was therefore carried out where exhalation was assumed to directly follow the inspiratory phase. The effect of aerosol concentration. Drug delivery from DPI may not necessarily be uniform during the inhaled breath. Indeed it is logical to assume from DPI design that drug delivery will be of a bolus nature. The potential importance of bolus delivery was investigated by carrying out a simulation where all of the aerosol was delivered over the first 25% of the inhalation cycle.
4. RESULTS
Base calculations Figure 3 illustrates the extra-thoracic deposition efficiency calculated as a function of particle size and flow rate on the basis of equation (1). As might be expected there is a trend towards higher deposition for larger particle diameters and higher flow rates, reflecting the importance of inertial impaction on the larynx and at the back of the throat. 100
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Deposition of powdered drug aerosol
181
For aerodynamic diameters as large as 30/~m, deposition is virtually 100% for higher flow rates and is approximately 90% for the lowest flow rate simulated in the present study (7.5 lmin-1). However, at particle sizes between 3 and 20/~m, there is a marked difference between the extra-thoracic filtering efficiency at different flow rates. Moving deeper into the lung, Figs 4 and 5 show the predicted deposition, also as a function of particle diameter with flow rate as a parameter, for the tracheobronchial and pulmonary airways, respectively. Deposition fractions in these figures include the effects of extra-thoracic filtering. The results correspond to the "base case" calculations assuming a constant aerosol concentration and a 10 s breath hold. Given the high rate of extra-thoracic filtering at large particle diameters, it is perhaps not surprising that the deposition in the bronchial airways falls to very low values for each of the simulated flow rates. The maximum bronchial deposit, at all particle diameters, is predicted to occur at the lowest inhaled flow rate, reflecting both the importance of gravitational settling within the bronchi and the low rate of removal in the oropharynx. Thus, although impaction in the bronchial airways becomes progressively more important
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182
A.R. CLARKand M. EGAN
at higher flow rates, its effect tends to be counteracted by a corresponding increase in extrathoracic removal. Peak deposition in the bronchial airways as a whole varies from around 55% at the lowest inhaled flow rate to 30% for a peak inhaled flow of 1201min -1. The particle diameter at which the maximum deposition occurs varies from 10/~m at low flow to 6/~m for the highest flow rate. However, close examination of the detailed deposition profiles (by airway generation) also reveals that the airway generation in which peak deposition occurs also changes with inhaled flow rate. At high flow rates deposition peaks in the upper bronchi whereas at lower flow rates the deposition is more even. The overall deposition in the alveolated, pulmonary, airways clearly depends upon the removal that has already taken place in the oropharynx and conducting airways. Thus, at high flow rates, deposition in the deep lung is virtually zero for particle diameters greater that 10 #m, impaction having already accounted for all aerosol entering the respiratory tract. In general, there is a trend towards increased deposition in the deep lung with lower flow rates. The effect is most marked for particle diameters larger than 3/zm and for the higher flow rates, where filtering by the mouth and bronchial airways is determined primarily by impaction. There are much smaller differences for smaller particle sizes. Respiratory tract deposition as a whole can be calculated by summing the deposition for the three lung regions. It will be seen that for particle diameters greater than 3/~m total deposition is approximately 100%o. Below 3 #m deposition decreases in a linear manner with particle diameter reaching a value of between 60 and 70% at a diameter of 0.5/~m depending upon inhaled flow rate.
Sensitivity studies The effect of simplified representation of flow rate. Figure 6 presents a comparison between the computed tracheobronchial and pulmonary deposition calculated using the experimental profile shown in Fig. 1 and the simplified profile illustrated in Fig. 2. The same extra thoracic filtering has been assumed for both cases. The results for two simulations are very similar, indicating that the simplified profile adopted for the purposes of the study provides an adequate representation of the actual flow profile. The slightly higher bronchial deposition obtained using the simplified function is due to a higher effective flow rate over the first 2 s of inhalation.
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Deposition of powdered drug aerosol
183
The effect of breath hold. It has already been mentioned that the recommended procedure for inhaling from a powdered drug generator entails a deep inhalation followed by a breath holding pause. Figure 7 illustrates the impact of the breath holding pause following a 601 min-1 inspiration. It can be seen that the breath holding pause only affects particles with diameters 3 #m and less. In effect, virtually 100% of the aerosol inhaled during a deep breath at a peak flow rate of 601 min- 1 is deposited during the inspiratory phase. The mean residence time, combined with the settling velocity, of the large-sized particles that are not deposited by impaction is such that deposition by gravitational settling in the deep lung will have occurred before the breath hold begins. However, for smaller particles, particularly those with diameters in the region of 0.5-1 #m, the intrinsic mobility of the aerosol is so low that the breath hold can have a significant impact on overall deposition. The effect of aerosol concentration. The "base case" calculations were all undertaken on the assumption that aerosol delivery was adequately represented by a constant concentration throughout the inspiratory phase. By contrast, it is likely that aerosol delivery from a powder inhaler will be of a bolus nature. Figure 8 presents a comparison between simulations performed assuming a constant
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184
A.R. CLARKand M. EGAN
aerosol concentration during inspiration and simulations assuming that aerosol delivery takes place in the first 25% of the inhalation. Deposition in the bronchial airways is slightly smaller in the case of bolus delivery. This result probably reflects the fact that proportionally more aerosol is delivered at lower inhalation flows whereas with the constant aerosol concentration a significant amount is delivered during the peak flow phase. For particles greater than approximately 3 #m there is very little difference between the two results. Below this size the average residence time for the bolus aerosol results in higher deposition fractions. 5. DISCUSSION The primary objective of this study has been to assess the potential importance of inhalation flow pattern on deposition of inhaled powdered drug aerosol. The various modelling results described above provide a wide ranging summary of predicted deposition of monodisperse aerosols in the lung under the typical flow patterns experienced with powder inhalers. In particular, the results show the effects of varying inspiratory flow rate and aerosol particle size on predicted deposition within the regions of the respiratory tract. It can be seen that the data presented predict higher deposition fractions than that previously reported for normal tidal breathing situations (James et al., 1991). This increased deposition fraction is attributable to the much longer residence times associated with the breathing patterns normally used with powder inhalers and confirms that data based on the standard breathing patterns investigated by the industrial hygiene community cannot be used as a reliable base for the calculation of deposition fractions when considering powder inhaler devices. Sensitivity studies indicate that the simplified representations of the inhaled flow profiles do not have an important influence on the overall predictions of deposition pattern. Similarly, breath hold after a deep inhalation from residual lung volume does not seem to have a significant impact on overall deposition, except for particles with intrinsically low mobility (i.e. less than 2/~m). This also indicates that the assumed airflow pattern during expiration will be insignificant in terms of overall deposition pattern, since virtually all mass deposition takes place during the inspiratory phase. The assumed aerosol delivery profile during the breath can have a small effect upon the predicted deposition. In particular, if most of the aerosol is delivered before maximum flow is achieved, the impaction in the upper airways will be slightly less and a more even deposition pattern results. However, in assessing the importance of the potential significance of this and the other assumptions underlying the simulations, due account needs to be taken of possible sources of uncertainty in the basic modelling approach. One of the major sources of uncertainty in the calculations is likely to be that associated with the determination of extra-thoracic filtering. For particles larger than 3/~m aerodynamic diameter, the extra-thoracic and thoracic deposition are complementary, together giving rise to nearly 100% deposition. Any variation in extra-thoracic deposition is therefore likely to be compensated for by a corresponding change in deposition within the lungs. The range of inter-subject variability in normal adult males has already been discussed above. The curves presented in Fig. 9 show the profiles for the mean and 95% confidence limits calculated using the confidence limits given by Rudolf et al. (1990). The effect of variations in extra-thoracic deposition upon tracheobronchial deposition can clearly be seen. Although the pulmonary region is only slightly affected the tracheobronchial deposition varies quite dramatically. Peak tracheobronchial deposition ranges from 60 to 65% at the upper 95% level to around 15% at the lower 95% level. However, this does not negate the foregoing conclusions since in any individual the trends identified would be correct. It is also constructive to compare the computational predictions with the available data on the deposition profiles from DPI's. However, although there are numerous papers detailing the deposition profiles obtained from DPIs (Newman et al., 1988, 1989; Vidgren et al., 1988, 1990), this comparison is confounded by the lack of concomitant deposition and
Deposition of powdereddrug aerosol
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100
Aerodynamicdiameter ( ~ m ) Fig. 9. Illustration of the effectsof inter-subject variability on regional deposition.
aerosol size data. The existing sizing data are either limited to detailing 'respirable fraction' or are limited to documenting the efficacy of the radiolabeling process. The somewhat limited comparisons generally possible support the models predictions. For example, the high total deposition and low exhaled fraction predicted by the convolution of the model calculations and available sizing data (Newman et al., 1988, 1989) is supported by the low exhaled fractions obtained in the papers cited above. Also the increase in thoracic deposition with increasing flow rate is that expected from a delivery system where increased powder dispersion at high flow rates (Newman et al., 1989, 1991) outstrips the increased probability of oral deposition. However, in general, it was found that the convolution calculations overestimated thoracic deposition by a factor of 1.5-2. It is as yet unclear as to the reason for this overestimation. As stated above, total deposition is approximately 100%, both experimentally and theoretically, and therefore the determinant of both the experimental and theoretical values relies upon oral deposition and the use of Rudolf's equation (Rudolf et al., 1990). Further, since Rudolf's equation is an empirical analysis based upon widely-varying inspiratory conditions in healthy human subjects, it is difficult to understand why it should be in error in these particular circumstances. However, as alluded to above, it may be that mouthpiece design significantly affects deposition or that the extrapolation of equation (1) to high flow rates has resulted in considerable error. It would seem unlikely that the latter is case, for both the reasons discussed above and since in a number of the above deposition studies the flow rates were well within the range analyzed by Rudolf. Moreover, it may also be possible that the sizing techniques used in the above studies were incapable of sufficient resolution for accurate convolution calculations. Either way, the resolution of this enigma will have to wait for further data and the application of high resolution aerosol sizing techniques coupled to further deposition profile measurements.
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