Theoretical Basis for the EDA Concept - Good Cascade Impactor Practices, AIM and EDA for Orally Inhaled Products - page 150

Fig. 7.2 Comparison of a continuous APSD (frequency distribution) with a corresponding mass-
weighted histogram obtained from an 8-stage ACI operated at 28.3 L/min

estimating the APSD is directly related to the number of impactor stages. For practical
reasons (i.e., to minimize errors due to overlapping stage collection efficiency
curves with respect to the aerodynamic diameter axis), the resolution between the
important size range for OIP aerosols from 0.5 to 5.0 μm aerodynamic diameter is
limited to five measurements of API mass [ 18 ].
This outcome arises because the CI-generated APSD is not a continuous fre-
quency distribution, as shown by the blue line in Fig. 7.2 , but is a series of discrete
values of API mass that are connected by the appropriate stage cut sizes ( d 50 ) values
for the CI at the flow rate ( Q ) at which it is being operated (black histogram in
Fig. 7.2 ). The width (size range, Δ d 50, i ) for each value of API mass is determined by
the relationship between adjacent stage d 50 sizes, whose values for the CIs listed in
the pharmacopeial compendia are given in Chap. 2 . This relationship for stage “ i ” is
described by the equation

D= -
-

d ( d d )

(7.1)

50 , i 50 , i 1 50 , i

in which “ i − 1” represents the immediately preceding stage in the CI.
The assumption is normally made that the collection efficiency E stage, i of a given
stage is a step function at its d 50 size. In reality, E stage, i is a smooth function of aero-
dynamic diameter, transitioning from its minimum to maximum values about the
aerodynamic size at which the stage is 50% efficient (solid line in Fig. 7.3 ). This
relationship is often assumed to be symmetrical, in that the mass of particles larger
than d 50, i , but which penetrate the stage in question, is exactly compensated by the
mass associated with particles which are finer than this size, but which are collected
thereon [ 19 ]. Thus, d 50 ,i can still be defined as a single-valued constant for operation