/
`
`attralqgl-
`
`w
`
`* 2st
`
`‘U 8‘
`
`J. Pharm. Pharmacol. 19817337693696
`Received March 12, 1981
`
`0022—3573/8 l/ l 10692—05 $02.50/0
`© 1981 J. Pharm. Phannacol.
`
`A semi-empirical model of aerosol deposition in the
`human respiratory tract for mouth mhalation
`
`IGOR GONDA
`
`Department of Pharmacy, University of Aston in Birmingham. Costa Green, Birmingham B4 7ET, U. K.
`
`sition of aerosols following inhalation via mouth has
`A mathematical model for regional de
`been developed. The model is in the orm of algebraic equations which make it particularly
`efficient for computation of deposition of polydis
`rse aerosols. The parameters of the model
`were derived from avera e experimental data or ‘head‘ and tracheobronchial deposition
`which were supplemente
`by results of previous theoretical calculations and mass balance
`considerations. An example is presented to illustrate an application of the model to a problem
`in formulation of inhalation aerosols. To make the calculations more reliable for particular
`patho-physiological groups of
`atients, some modifications of the parameters used in the
`model are necessary. The mo el may be suitable, e.g. for testing the changes in regional
`deposition which would be likely to result from modification of particle size and related
`formulation properties of inhalation aerosols.
`
`Therapeutic aerosols are examples of systems typi-
`cally exhibiting a fairly high degree of polydispersity
`(Mercer et al 1968a,b; Hallworth & Andrews 1976;
`Hallworth & Hamilton 1976; Davies et al 1978;
`Ruffin et al 1978; Groom et al 1980). The aim of this
`work has been to combine experimental and, where
`appropriate,
`theoretical results for deposition of
`monodisperse aerosols in the human respiratory
`tract into a set of algebraic equations which could be
`used for predictions of deposition of polydisperse
`aerosols with the minimum amount of computing
`involved.
`
`METHODS
`
`The starting point was the semi~empirical model
`proposed by the TASK group (Task Group on Lung
`Dynamics, 1966. 1967) for nasal inhalation. Mercer’s
`method (Mercer 1975) for conversion of data for the
`nasal route into values for deposition during mouth
`inhalation was followed with some modifications.
`
`Unless stated otherwise. the assumptions of Mercer
`were made. In particular, it was assumed, as did the
`authors of experimental deposition data (Lippmann
`1977; Stahlhofen et al 1980). that deposition ‘above‘
`the trachea takes place only during inspiration. In
`contrast to the TASK group approach, in which a
`number of equations had to be solved for deposition
`at
`each individual value of
`the
`aerodynamic
`diameter, curve-fitting of theoretical and experimen-
`tal data was used. This diminishes the potential for
`deposition calculations under physiological condi-
`tions different from those used for the curve-fitting:
`however. a substantial saving in calculations is
`
`gained when the model is applied to polydisperse
`aerosols.
`
`The mathematical model developed consists of
`algebraic equations relating deposition in various
`parts of the respiratory tract directly to the aero-
`dynamic diameter D, defined as ‘the diameter of a
`unit sphere with the same settling velocity as the
`particle in question' (Task Group on Lung Dynamics
`1966). Because the deposition equations for different
`ranges of D have been derived from various sources,
`the slopes of the deposition functions change discon-
`tinuously at certain values of D whilst
`the actual
`deposition values form continuous sequences. It is
`important
`to bear in mind the above mentioned
`discontinuity when an integration routine is selected
`for application of the model.
`The depositions in tracheobronchial and pul-
`monary regions for nasal inhalation, TBN and PN
`(Table 1 in the Task group publication 1966) were
`converted to the corresponding quantities for mouth
`inhalation,TBMand PM,usingtheformula*
`
`TBM or PM = (TBN or PN)(1—N)’1(1-M)
`
`(1)
`
`N is the fraction of the inhaled dose deposited in the
`nasopharynx during nasal breathing, and M is the
`fraction deposited above the trachea (i.e.
`in the
`
`‘ The formula presented by Mercer (1975) on p. 675 of
`his paper for 'deposition in the designated compartments
`relative to the number of particles entering the trachea‘. has
`a printing error. The correct ex ression has the form ofeqn
`1 above without the last term a - M).
`
`Liquidia's Exhibit 1054
`Page 1
`
`Liquidia's Exhibit 1054
`Page 1
`
`

`

`AEROSOL DEPOSITION FOR MOUTH INHALATION
`
`693
`
`‘head') during mouth breathing. For N we employed
`the empirical equation of Pattle (1961)
`
`N = —0.62 + 0-475 log (DEF)
`
`(2)
`
`The average inspiratory flow rate, F. was calculated
`from
`
`F=2xTfo
`
`(3)
`
`The TASK group used respiratory frequency
`f = 15 minrl; the corresponding F values for their
`tidal volumes TV = 0-75. 1-45 and 2-15 dm3 are
`
`F = 22-5, 43-5 and 64-5 dm3 min—l. Lippmann
`(1977) found that his experimental data for M could
`be described by a function similar to equation 2. The
`following equations were obtained from Lippmann’s
`eye-fit to his results for non-smokers:
`
`For(0S M <0-1): M = M1 =
`-O-2674 + 01337 log (D2 F)
`
`For (0-1 S M s 1-0): M = M2 =
`—-1-983 + 0758 log (D2 F)
`
`(4)
`
`(5)
`
`Combination of equations 1—5 facilitated the calcula-
`tion of TBM and PM for aerodynamic diameters
`from D = 0-01 pm up to the size where TASK
`group’s values for TBN or PN became zero. The
`non-linear least mean square program of Metzler
`(1969). NONLIN, was used to fit the curves of TBM
`and PM vs. D. The rational functions describing
`these curves are given below. There is a ‘kink‘ in the
`PM curve forTV = 0-75 dm3 at D = 0-06 pm which
`consistently caused a deterioration in the goodness
`of the fit. It was therefore decided for this particular
`tidal volume to approximate PM in the range
`0-01 pm < DS 0-06 um by a straight
`line. This
`simplification has no effect on calculations for typical
`pharmaceutical aerosols because usually only a
`negligible amount of drug is contained in the fraction
`below D = 0-06 pm. The difference between the
`‘actual‘ and fitted fractional deposition values was at
`most 002; the fitted curves showed no oscillations at
`intermediate values of D.
`
`At this stage. experimental results for tracheo-
`bronchial deposition were introduced thus: Lipp-
`mann (1977) found that when the tracheobronchial
`deposition was expressed as the deposition fraction.
`TBT. of those particles which enter the trachea. i.e.:
`
`TBT = TBM(1 — M)-lorTBN(1 — N)-I
`
`(6)
`
`the
`function of
`linear
`then TBT was again a
`logarithm of the ‘impaction parameter' DZF. From
`Lippmann's eye-fit for non-smokers. the slope of the
`line was calculated as 0-68. Stahlhofen et al (1980)
`found that their data showed a similar slope but.
`generally.
`they found somewhat
`lower values for
`
`TBT. Lippmann’s data began at approximately
`TBT = 0-1. Therefore.
`the TASK model detailed
`above had to be used from D = 0-01 pm up to the
`size D = DTI at which TBT became approximately
`0-1. A nearest higher value ofTBT derived from the
`TASK data was then substituted into the equation:
`
`(7)
`I = TBT — 0-68 log (D2 F)
`The intercept
`I for each tidal volume was thus
`calculated. The curves describing TBM above the
`size DTl therefore have the form
`
`(8)
`TBM = [I + 0-68 log (DZF)] - [1-0 - M]
`A further cut-off diameter had to be introduced at
`
`the point D = DT2 when all particles entering the
`trachea deposited in the tracheobronchial region,
`i.e. when
`
`I + 0-68 log (D2 F) = 1-0
`For diameters greater than DT2, therefore.
`
`TBM = 1-0 — M
`
`(9)
`
`(10)
`
`A natural constraint on any deposition model is
`that
`the sum of
`fractions of
`the inhaled dose
`
`deposited in all compartments must not exceed
`unity. In the present model. this was accomplished
`first by putting the pulmonary deposition equal to
`
`(11)
`PM =1-0 — M -,TBM
`from D = DP2 where the sum of the unadjusted PM
`plus (M + TBM) became greater than 1-0. From the
`point D = DP3 where either the sum (M + TBM)
`alone exceeded unity (DP3 = DT2 forTV = 1-45 &
`2~15 dm3), or, before that. PM derived from the
`TASK model
`reached zero
`(DP3 = DP2
`for
`TV = 0-75 dm3), PM was put as PM = 0. These last
`impositions upon the model at
`large values of
`aerodynamic diameters caused only minor modifica-
`tions in the predicted values of TBM and PM.
`However, they did introduce a guarantee of correct
`mass balance necessary for any applications of the
`model. Both the TASK group (1966) and Mercer
`(1975) corrected the total deposition by a small term
`TV/(TV + 005) where 0-05 dm3 represented the
`volume of
`the nasopharynx which, supposedly,
`would not contain any aerosol. This minor. and
`somewhat arbitrary. correction was felt
`to un-
`necessarily complicate the present model. and it was
`therefore omitted.
`
`RESULTS AND DISCUSSION
`
`the equations derived as
`form of
`The general
`described above are now presented. The actual
`parameter values are in Table I. To reduce the
`amount of computation. equations 4. 5 and 8 have
`
`
`
`Liquidia's Exhibit 1054
`Page 2
`
`Liquidia's Exhibit 1054
`Page 2
`
`

`

`694
`
`1. GONDA
`
`Table 1. Parameters for equations 12—22 in the text for the
`.
`three tidal volumes used in the model.
`
`The results generated from equations 12-22 are
`,
`shown graphically in Fig. 1A—C.
`
`Head de
`
`Parameters
`ition:
`A1
`pos
`A2
`Tracheobronchial deposition;
`Bl
`B2
`B}
`B4
`BS
`B6
`B7
`38
`Pulmonary deposition:
`Cl
`C:
`C3
`C:
`C5
`C6
`C7
`C8
`Cut-off diameters (um)
`DMl
`DM:
`DM3
`DT1
`DTZ
`DPI
`DP2
`DP3
`
`Tidal volume (dml)
`
`0-75
`
`[-45
`
`2-15
`
`-0-0866
`-0-958
`—1-5758
`6-3568
`‘0-50348
`1-1422
`207-057
`«+9717
`34805
`—l)-5135
`
`-0-0255
`—0-0483
`-0-6ll-3
`—0-7410
`-0-51409
`~2-3058
`11-4455
`8-7217
`1-5257
`—0-22301
`-0- 13754
`10496
`494-469
`277-727
`—7l-8424 —136-993
`9-2269
`34-8649
`~0-4154
`—0-2914
`
`—4-8067
`~1-9446
`10-2572
`3-9034
`[-0164
`—0-347$7
`1-5052
`[-0399
`— 10-6135
`8-1507
`54-3737
`00025967
`0-275705 —25-8617
`0-04063
`5-0927
`
`—3-1810
`10-8935
`077-126
`[-3357
`—4-2879
`63-5294
`-36-2478
`7-5831
`
`2-108
`4-990
`19-568
`3-011)
`13-400
`0-06
`10-730
`10-730
`
`1-516
`3-587
`14-073
`2-500
`10983
`0-01
`6-300
`10983
`
`1246
`2-946
`11-559
`2-000
`8-9in
`0-01
`3-100
`8-900
`
`been expanded. with the appropriate values of F for
`each tidal volume substituted from equation 3.
`
`‘Head‘ deposition:
`
`M = 0, for 0-01 pm S D < DMl
`
`(12)
`
`M = A1 + 02674 log D, for DMl S D < DMZ
`(13)
`
`M = A2 + 1-516 log D, for DMZ s D s DM3
`(14)
`
`M = 1.0, for D > DM3
`Tracheobronchial deposition:
`
`(15)
`
`TBM=(1-0+BIXD+B2><D2+
`B3XD3)/(B4+BSXD+B6XD:+B7XD3)
`for 0-01 pm S D S DT1
`(16)
`
`TBM = (BS + 1-36 log D) (1-0 — M)
`for DT1 < D S DT2
`
`(17)
`
`
`
`TBM = 1-0 — M. for D > DTZ
`Pulmonary deposition:
`for 0-01 pm S D S
`PM = 0-4902 + 1-58 x D,
`0-06 um. TV = 0-75 dm-‘ only
`
`(18)
`
`(19)
`
`PM =
`
`(1-0+C1xD+C2xD2+C3xDJ)
`(C4+C5XD+C6XD3+C7XD5+C8XD‘)
`for DP1 < D < DPZ (20)
`PM = 1-0 — TBM — M. for DPZ s D s DP3
`(:1)
`
`PM = 0-0. for D < DP3
`
`(22
`
`A
`
`1'0!
`
`I,
`08i-
`1
`‘_
`i
`,
`.
`
`Fractibnal
`
`deposition
`
`
`
`2
`001002 0050102 05 I
`Aerodynamic diameter(um)
`
`5
`
`10 20
`
`FIG. 1A. B. C. Regional deposition of monodisperse
`aerosols following mouth inhalation in the ‘head‘ (-————).
`tracheobronchial
`(—--) and pulmonary (——-) compart-
`ments vs aerodynamic diameter. Tidal volume 075 dm5
`(A). 1-45 dm3 (B). 2-15 dm3 (C).
`
`
`
`Liquidia's Exhibit 1054
`Page 3
`
`Liquidia's Exhibit 1054
`Page 3
`
`

`

`AEROSOL DEPOSITION FOR MOUTH INHALATION
`
`695
`
`Application of equations 12—22 can be illustrated
`by the following examples: we shall compare the
`regional deposition of two aerosols with log-normal
`distribution. LN, with the same degree of poly-
`dispersity characterized by the geometric standard
`deviation og = 3 but differing in the drug mass
`median aerodynamic diameter (Byron et al 1977)
`MMD. This parameter for the first aerosol is chosen
`to be 4 mm. i.e. near the maxima of tracheobronchial
`and pulmonary depositions. MMD for the second
`aerosol is put equal to 10 um. Thus. the comparison
`of the regional deposition of these two aerosols could
`be a simplified analogy of the effects of an increase in
`MMD due to coagulation of suspended drug par-
`ticles in pressurized aerosols. poor regeneration of
`the primary particle size distribution,
`incomplete
`evaporation of the propellant before the entry of the
`aerosol into mouth, or rapid condensation of water
`and formation of equilibrated aqueous droplets from
`the powder aerosol containing a water-soluble drug
`(Groom & Gonda 1980; Groom et al 1980). The
`fractions, Y. of the dose depositing in the three
`respiratory regions can be calculated from the
`product LN times the compartmental deposition
`probability R (given by either M. TBM or PM in
`eqn 17—22) integrated with respect to the aerody-
`namic diameter:
`
`Y = f LN(MMD,og,D) . R(D)dD
`-c
`LN has the form:
`
`(33)
`
`LN = (V23 D 1n og)‘I exp [—0-5(ln D —-
`(24)
`ln MMplz/(in og)3]
`The differences between the regional depositions of
`the two aerosols are contrasted in Table 2. It is
`apparent that the aerosol with MMD = 10 pm is
`likely to be captured in the ‘head‘ region to a much
`greater extent
`than an aerosol which would be
`presented to the respiratory tract with the intended
`MMD = 4 pm preserved. The increase in ‘head‘
`deposition is largely mirrored by a reduction in
`pulmonary deposition. On the other hand,
`the
`tracheobronchial deposition seems quite insensitive
`to this effect. The exhaled fraction is not included in
`Table 2; the present model makes no allowance for a
`prolonged breath-holding manoeuvre (Byron et al
`1977; Newman et al 1979) which would reduce the
`exhalation of small particles (Palmes et al 1967.
`1971).
`Figs 1—3 represent regional depositions of mono-
`disperse aerosols. Comparison of the data in these
`figures with results for the polydisperse aerosols in
`Table 2 reveals that
`the width of aerosol size
`distribution may have a marked effect on the
`
`
`
`Table 2. Values predicted by the model equations 12-2-1 for
`deposition of
`two aerosols with the same
`eometric
`standard deviations but different mass median iameters.
`M. TB and P stand for
`‘head'.
`tracheobronchial and
`pulmonary compartments. respectively.
`Tidal
`0-75
`1-45
`volume(dm-‘)
`“—
`Regmn
`M TB
`P
`MMAD = 4 gm
`0g = 3
`MMAD = 10 um
`ng = 3
`
`M TB
`
`P
`
`2-15
`
`M TB
`
`1’
`
`0-16 0-19 0-31
`
`0-35 0-17 0-39
`
`0-41 017 0-26
`
`0-54 0-“) 0-18
`
`(164 0-14 0-15
`
`0-70 0-13 0-13
`
`deposition. For example. a ‘nearly’ monodisperse
`aerosol with MMD = 10 um would not be expected
`to deposit in the pulmonary region at all. except at
`very low tidal volumes. However, a polydisperse
`aerosol with the same MMD, but a distribution width
`characterized by og 2 3. should have appreciable
`pulmonary deposition (Table 2). A more detailed
`analysis of this phenomenon is presented by Gonda
`( 1981).
`Another important feature which emerges from
`Table 2 is the influence of the magnitude of the tidal
`volume on deposition. particularly on the aerosol
`with MMD = 10 um. Physiological variables, ana-
`tomical differences and breathing patterns undoubt-
`edly affect the extent of deposition in various parts of
`the respiratory tract (Muir & Davies 1967; Palmes et
`a1 1967, 1971: Lippmann 6‘; Altshuler 1976; Davies et
`al 1977; Heyder et al 1978). Inter-subject variations
`in deposition which can be classified broadly accord-
`ing to patho-physiological groups are well documen-
`ted (Lippmann et al 1971; Thomson & Pavia 1974;
`Love & Muir 1976; Fazio et al 1978: Short et al 1979;
`Chan & Lippmann 1980'). It must be emphasized,
`therefore. that the current version of the model will
`
`not generate reliable quantitative predictions for
`regional deposition in subjects with serious morphol-
`ogical changes of airways or abnormal breathing
`patterns. Chan & Lippmann (1980)
`suggested
`recently a method which accounts for variation in
`tracheobronchial deposition between healthy non-
`smokers, cigarette smokers and patients with chronic
`obstructive lung disease. Their method could be
`incorporated into equation 17. Some modification of
`the parameters used in the equations for pulmonary
`deposition would then be required as well. Further
`work is necessary to establish if a model of the type
`presented here has the capacity and flexibility to
`cater for different groups of subjects. particularly
`those affected by disorders of the respiratory tract.
`The model is. perhaps. sufficient already to detect
`the changing trends in regional deposition likely to
`result from modifications of particle size and related
`characteristics of aerosol formulation.
`
`Liquidia's Exhibit 1054
`Page 4
`
`Liquidia's Exhibit 1054
`Page 4
`
`

`

`696
`
`I. GONDA
`
`The parameters describing the fitted curves were
`derived from average results for deposition behav-
`iour of subjects from the general population. It is
`envisaged therefore that the model may be useful
`particularly when modification of physicochemical
`and size characteristics of mass produced aerosols is
`considered with the view to optimizing the average
`deposition of therapeutic agents in the desired areas
`of the respiratory tract. For example, we suggested
`(Gonda & Byron 1978) that one of the reasons for
`poor bioavailability of inhalation aerosols lies in
`their potential to increase in size by condensation
`growth immediately after inspiration. The model
`provides the means to test the likely magnitude of
`this effect. and also a method for investigating
`whether changes in the particle size distribution,
`formulation, or both. would lead to substantial
`modifications of
`the fractions deposited in the
`traditionally recognised 'head’, tracheobronchial or
`pulmonary regions of the respiratory tract.
`The underlying philosophy has been to provide
`estimates of average deposition values for certain
`populations of subjects. rather than to attempt to
`develop models with adjustable parameters to suit
`individuals. This latter approach has been taken by
`Davies (Davies et al 1977; Davies 1980); of course.
`such a method requires that some experimental tests
`are performed on the patient. Perhaps. Davies’s
`model could be applied to aerosol
`treatment
`in
`hospitals.
`
`Acknowledgements
`The author wishes to thank Drs L. J. Aarons and P.
`
`R. Byron for making the NONLIN program avail-
`able, and the technical staff at Aston University for
`their services. Discussions with Ms C. V. Groom
`
`concerning this work are gratefully acknowledged.
`Drs Stahlhofen. Gebhard and Heyder were kind to
`provide a preprint of their publication.
`
`REFERENCES
`
`Byron P. R. Davis S. S. Bubb. M D. Cooper P. (1977)
`Pest. Sci. 8: 521-526
`Chan. T. L.. Lippmann. M. (1980) Am Ind. Hyg. Assoc. J.
`41: 399—409
`Davies. C. N. (1980) J. Aerosol Sci. 11: 213—224
`Davies. C. N. Lever M. J.. Rothenberg. S. J. (1977)1n
`Walton W H. McGovern. B. (eds) Inhaled Particles
`IV. Part1. lstedn.. Oxford Pergamon Press p 151
`.Davies. P. J.. Muxworthy. E. M. Pickett. J. M.. Smith G
`A. (1978)J. Pharm. Pharmacol. 30(Suppl.:) 40PM
`Fazio. F. Miniati. M. Greening. A. P. Clay.
`(1978) Bull. Eur. Physiol-Pathol. Resp. 14: 187PM
`
`..M
`
`I. (1980) J. Pharm. Pharmacol.
`
`U. G.
`
`(1976) J. Pharm.
`
`Gonda I. (1981) International Symposium on Deposition
`and Clearance of Aerosols in the Human Respiratory
`Tract (organised by GAF & IGAeM). Bad Gleichen-
`berg, Austria Mayy22/23 1981
`Gonda. 1.. Byron. P. R. (1978) Drug Dev. 1nd. Pharm. 4:
`243—259
`Groom. C. V.. Gonda.
`32(Suppl.): 1P
`Groom. C. V.. Gonda. 1.. Fildes. F. J. T. (1980) 2nd Int.
`Conf. Pharm. Tech. (organised by APGI) Paris. June
`1980. pp 124-131
`Hallworth. G. W.. Andrews.
`Pharmacol. 28: 898—907
`.Hallworth. G. W.. Hamilton. R. R.
`890—897
`Hevder. J.. Gebhart. J.. Roth. C.. Stahlhofen. W.. Stuck.
`B.. Tarroni. G.. DeZaiacomo, T.. Formignani. M..
`Melandri. C. Prodi, V. (1978)J. Aerosol Sci 9. 147455
`Li pmann. M.
`(1977) in: Lee D. H. K. Falk. H. L.
`urphy. S. D. Geiger. S. R.
`(eds) Handbook of
`Physiolyogy. Section
`Reactions
`to Environmental
`Agents
`ethesda. Maryland. Am. Physiol Soc. andThe
`Williams& Wilkins Co. (distr)ch. 14. p. 213
`Ligpmann M. Altshuler. B (1976)1n Aharonson. E. F..
`en<David. A. Klingberg. M. A. (eds) Air Pollution
`and The Lung. New York J. Wiley&Sons. p25
`Ligvpmpmann, M. Albert, R. E. Peterson H. T. .Jr(l97l)in:
`alton. W. H. (ed.) Inhaled Partlcles 111 vol. 1. Woking
`(England). Unwin Bros. Ltd p 105
`Love. R. G. Muir. D C. F. (1976) Am. Rev. Resp. Dis.
`114: 891-897
`Mercer T. T. (1975) Health Phys. 29: 673—680
`Mercer T. T. Goddard. R. F. Flores. R. L. (1968a) Ann
`Allergy 26:18—27
`Mercer. T. T. Tillery. M. I. Chow. H. Y. (1968b) Am.
`Ind. Hyg. Assoc. J. 29: 66—78
`Metzler. C. M (1969) A Lsers Manual for NONLIN.
`Technical Report 7292/69/7292/005 Kalamazoo (Michi-
`gan): Upjohn Co
`Muir. D7C. F.Davies C. N. (1967) Ann Occup.1-1yg. 10:
`161—1 4
`Newman. S. P.. Bateman. J. R. M.. Pavia. 0.. Clarke. 5.
`W.
`(1979)
`in: Baran. D. (ed.) Recent Advances in
`Aerosol Therapy. Brussels (Belgium): Internal. Soc. for
`Aerosols in Med. (IGAeM) p 117
`Palmes. E. D.. Altshuler. 8.. Nelson. N. (1967) in: Davies.
`C. N. (ed.) Inhaled Particles and Vapours II. Oxford:
`Pergamon Press. p. 339
`Palmes. E. D.. Goldring. R. M.. Wang. C.. Altshuler. B.
`(1971) in: Walton. W. H. (ed.) Inhaled Particles III. vol.
`1. Old Woking (England): Unwin Bros. Ltd. p 123
`Pattle. R. E.
`(1961)
`in: Davies. C. N.
`(ed.)
`Inhaled
`Particles and Vapours. Oxford: Pergamon Press. p 302
`Ruffin. R. E.. Kenworthy. M. C.. Newhouse. M. T. (1978)
`Clin. Pharmacol. Ther. 23: 338—345
`Short. M. D.. Dowsett. P. J.. Heaf. P. J. D.. Pavia. D..
`Thomson. M. L. (1979) J. Nucl. Med. 20: 194-200
`Stahlhofen. W.. Gebhart. J.. Heyder. J. (1980) Am. Ind.
`Hyg. Assoc. J. 41: 385-398
`Task Group on Lung Dynamics (1966) Health Phys. 12:
`173—207
`
`(1976)
`
`Ibid. 28:
`
`
`
`Task Group on Lung Dynamics (1967) Ibid. 13: 1251
`Thomson. M. L.. Pavia. D. (1974) Arch. Environ. Health
`29: 214—219
`
`Liquidia's Exhibit 1054
`Page 5
`
`Liquidia's Exhibit 1054
`Page 5
`
`