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