profile analysis of cascade impactor data: an alternative view andrew r clark, ph.d. orally inhaled...

Profile Analysis of Cascade Impactor Data:

An Alternative View

Andrew R Clark, Ph.D.

Orally Inhaled and Nasal Drug Products Subcommittee of the Advisory Committee for Pharmaceutical Science

April 26, 2000

Comparing impactor distributions - Why and how

• Batch release

– Is the current batch equivalent to those used in pivotal trials ?

• Bioequivalence

– Is a “new” product equivalent to the innovator ?

• Marker or label validation

– Does the marker or label match well enough to represent the active drug ?

Simple statistical “distance” or a measure with physical significance ?

Physical significance of distribution differences

0

0.2

0.4

0.6

0.8

1

0.1 1 10

Al. DepositionTB depositionF

ract

ion

Dep

osit

ion

Aerodynamic diameter (um)

0

20

40

60

80

100

0.1 1 10

Test MMAD 3 um, GSD 3Reference MMAD 3 um, GSD 2

Cum

ulat

ive

% u

nder

size

% Undersize difference

12 at both 9.0 and 1.2 m

Deposition Probability 0.9, 0.8 at 9.0 mand 0.4, 0.0 at 1.2 mfor TB and Al respectively

W0

W5

f(wi)

Pd.f(wi)

A model for investigations of F2 and Changes in size distribution for a log-normal model

1

10

.1 1 5 10 20 30 50 70 80 90 95 99 99.9

Reference MMAD 3 um, GSD 2Test MMAD 1 um, GSD 2Test MMAD 3 um, GSD 3

Aer

odyn

amic

dia

met

er (

um

)

Cumulative undersize (%)

Median diameter

Change inmedian diameter

Change inGSD

GSD = d50

/d16

F2 variation as a function of MMAD and GSD relative to a reference distribution for the ACI

0

20

40

60

80

100

1 1.5 2 2.5 3

F2

GSD

Reference ( MMAD = 2.0, GSD = 2 )

0

20

40

60

80

100

1 1.5 2 2.5 3

F2

MMAD (um)

Reference ( MMAD = 2.0, GSD = 2 )

f n W Wref tests

s n

2

2

0

0 5

50 100 1 1

log.

How F2 measures changes in size distribution

Response of F2 for the ACI to changes in MMAD and GSD relative to a 2 m MMAD, GSD = 2 reference aerosol

1.2

1.6

2

2.4

2.8 1.4

1.61.8

22.2

2.43

0102030405060708090

100

f2

GSD

MMAD (um)

90-100

80-90

70-80

60-70

50-60

40-50

30-40

20-30

10-20

0-10

f n W Wref tests

s n

2

2

0

0 5

50 100 1 1

log.

F250 Contours for relative change in MMAD and GSD

F25o contours for the ACI for reference aerosols ranging of 1 to 8 m MMAD with GSD of 2.

(Aerosols with MMAD and GSDs lying within the contours would be judged to be similar, i.e. F2 = > 50 .)

0.5

1

1.5

2

2.5

3

0.6 0.8 1 1.2 1.4

1 um

2 um

4 um

6 um

8 um

GS

D t

est /

GS

D r

efer

ence

MMAD test

/ MMAD reference

For 1 um referencedmax - dmin ~ 0.7 m

For 4 um referencedmax - dmin ~ 2.5 m

F250 Contours for relative change in MMAD and GSD

0.5

1

1.5

2

2.5

3

0.6 0.8 1 1.2 1.4

F250 contours for the MLI for reference aerosols ranging of 1 to 8 um MMAD with GSD of 2.

(Aerosols with MMAD and GSDs lying within the contours would be judged to be similar, i.e. F2 = > 50 .)

1 um

2 um

4 um

8 um

GSD

aero

sol /

GSD

refe

renc

e

MMADaerosol

/ MMAD reference

For 1 um referencedmax - dmin ~ 0.5 m

For 4 um referencedmax - dmin ~ 2.5 m

How 2 measures changes in size distribution

Response of 2 for the ACI to changes in MMAD and GSD relative to a 3 m MMAD, GSD = 2 reference aerosol

2.2

2.6

3

3.4

3.8

1.4

1.6

1.8

22.2

2.43

-80-70-60-50-40-30-20-10

0

Ch

i-sq

uar

ed

MMAD (um)

GSD

-10-0

-20--10

-30--20

-40--30

-50--40

-60--50

-70--60

-80--70

ns

s reftest

reftest

dd

dd

0

2

2

2

Theoretical total lung and alveolar deposition for an inhaled aerosol (GSD of 2) with and without a 5 second breath hold

Alveolar deposition with 5s breatholdAlveolar deposition without breatholdTotal lung deposition with 5s breatholdTotal lung deposition without breathold

0

0.2

0.4

0.6

0.8

1

0 2 4 6 8 10 12

Deposi

tion

[ %

] of

inhale

d

MMAD [um]

F2 = 50 dp ~ 4 %

F2 = 50 dp ~ 150 %

Martonen T B (1993) Mathematical model for the selective deposition of inhaled pharmaceuticals.J Pharm. Sci., Vol 82, (12)

1.41.6

1.82

2.22.4

3

-30

-25

-20

-15

-10

-5

0

Ch

ang

e in

to

tal

lun

g d

epo

siti

on

GSD

MMAD ( um )

-5-0

-10--5

-15--10

-20--15

-25--20

-30--25

Change in deposition as a function of MMAD and GSD relative to a reference aerosol with an MMAD of 2 m and a GSD of 2(Note. All deposition changes have been shown as negative to facilitate comparison with Figure 3.)

 How changes in size distribution affect deposited dose

Comparison of F250 and 10% deposition contours

Comparison of F250 contours for the MLI with “10% change in lung deposition”

contours derived from a lung deposition model

0.5

1

1.5

2

2.5

3

0.6 0.8 1 1.2 1.4

10% change in deposition contours for 4 um MMAD

10% change in deposition contours for 8 um MMAD

f2 contour for 4 um MMAD

f2 contour for 8 um MMAD

GS

Dte

st / G

SD

ref

MMADtest

/ MMADref

Note. f2 similarity, but greater than 10% change in deposition

An alternative :Theoretical Deposition Fraction & weighted distributions

Location Cut-off dia. Mid-point Depositionweights*

% on stage Weighteddistribution

Pd Wtstage

Throat 20 40.0 0.01 0.0 0.0Stage 0 9.0 14.5 0.16 1.5 0.2Stage 1 5.8 7.40 0.56 4.7 2.6Stage 2 4.7 5.35 0.76 4.7 3.6Stage 3 3.3 3.90 0.88 12.6 11.1Stage 4 2.1 2.70 0.95 23.7 22.5Stage 5 1.2 1.65 0.99 29.7 29.4Stage 6 0.7 0.95 1.00 16.6 16.6Stage 7 0.4 0.55 1.00 5.5 5.5Filter 0.20 1.00 1.0 1.0

Normalize andapply

“distance” statistic ?

Throat

Filterstagedep WtPTDF .

Deposition weights (Pd) determined from lung deposition model

Weighted distribution = Wtstage * Pd

Weighted distributions and TDF for pMDI data

Mean TDF for the interlaboratory comparison carried out by the EuropeanPharmacoepial Commission

Laboratory MLI ACI

Mean TDF(g)

SD Mean TDF(g)

SD

1 63.9 2.5 64.9 4.92 57.5 4.5 57.4 2.63 60.9 4.9 56.2 3.04 64.4 3.2 45.0 11.35 54.7 3.5 50.3 2.8

Grand mean 60.3 5.1 54.8 8.8

NB. Weighting factors calculated at 28 l /min throughout.

weightloss throat stage 0 stage 1 stage 2 stage 3 stage 4 stage 5 stage 6 stage 7 filtermg/dose µg/dose µg/dose µg/dose µg/dose µg/dose µg/dose µg/dose µg/dose µg/dose µg/dose

Grand mean 90.32 73.58 91.29 72.51 74.36 74.51 34.26 62.69 13.10 2.19 0.91Lab 4 84.57 62.70 0.52 0.00 0.72 5.05 19.15 16.56 1.55 0.00 1.41

Stein S W & Olson B A (1997) Variability in size distribution measurements obtained using multiple

Andersen Mk II Cascade impactors Pharm Res., 14(12), 1718-1725

Weighting technique applied to label validation data

TDF used to assess label match for a patient driven dry powder inhaler

Flow rate (l/min) TDF (% of nominal)Drug Radiolabel

60 17.8 22.9120 19.2 22.6

NB. Even though n = 8, statistical comparisons of TDF were not possible because only means were reported.

Newman S P, Hollingworth A H & Clark A R (1994) Effect of different modes of inhalation on drug

delivery from a dry powder inhaler. Int. J . Pharm., 102, 127-132

Issues with Weighting and TDF approach

• Advantages– Flexibility

• Choose weighting factors for drug / product application

– Can apply simple statistics to values to Wt. or %– Has physical relevance

• Disadvantages– How to choosing weighting factors

• Deposition models• Receptor distribution

– Whole lung versus deposition pattern (TB/AL ratio ?)– Not a primary measure

• Combination Weights plus “distance” statistic ?