Current Approaches to APSD Measurements of OIPs Based on Inertial Impaction - Good Cascade Impactor Practices, AIM and EDA for Orally Inhaled Products - page 38

this analysis the Fast Screening Impactor (FSI, MSP Corp., St Paul, MN, USA), as
this abbreviated system is based on the NGI preseparator [ 46 ] and is therefore not
simply a full-resolution NGI comprising fewer stages.
Roberts and Mitchell first calculated how the lognormally distributed aerosol
described above would distribute in all stages of a full-resolution ACI or NGI,
accounting for the actual stage efficiency curves. They then calculated where in the
appropriate abbreviated apparatus the mass actually distributes, according to the
stage efficiency curves for this reduced system. Next, they compared these values to
the relevant values of mass from summed stages of the full-resolution parent CI.
Finally, to complete the validation, they compared the mass on the summed stages
from the parent CI and the mass on the abbreviated impactor stages to the actual
mass in the size range present in the input aerosol.
Equation (2.12) was evaluated numerically using Simpson's rule to calculate the
fraction of the input aerosol that goes to a given stage of either a full-resolution or
an abbreviated CI configuration. Note that numerical integration was not necessary
for calculating the inlet aerosol mass in a given size range, because an analytical
expression could be derived by setting the E i ( x ) functions in (2.13) equal to step
functions at the impactor d 50 sizes:

D D

D

50 , N − 1 50 , N

ln ln

(2.16)

1
2

D

f = erf − erf

( ) ( )

N

2 ln 2ln s g

s

g

The error function (erf) given by the expression from Matthews and Walker [ 47 ]
was used:

(2.17)

x

2

∫

erf () x = exp ( − hdh

2

)

p

0

For the incoming aerosol that is in the size range larger than the d 50 size for the
first stage, the value of d 50, N −1 is set to infinity, and it is known that erf( ) = 1.

As in the investigation of the full-resolution CIs, a series of model aerosols were
evaluated, having MMAD values in the range 1.0-5.0

∞

m and GSD values selected
between 1.2 and 2.0. There was always less mass found on the first stage of the
abbreviated ACI than on the corresponding sum of the stages on the full-resolution
CI (see the two examples shown in Figs. 2.12 and 2.13 ). This bias was

μ

5% for the
broadest (GSD = 2.0) APSDs comprising the largest particles (MMAD = 5.0

≤

m).
However, it increased to as much as 11% for narrow (GSD = 1.2) and finer
(MMAD = 1.0

μ

m) aerosols. In the context of Figs. 2.12 and 2.13 , it should be noted
that a ratio of mass on “AIM” to “summed stage” of unity would represent an abbre-
viated system without bias arising from the nonideal nature of the stage collection
efficiency curves.
Similar trends were also detected with the NGI system analysis (Figs. 2.14 and
2.15 ). However, the bias associated with the abbreviated NGI was

μ

≤ 2.5% regardless