Theoretical Basis for the EDA Concept - Good Cascade Impactor Practices, AIM and EDA for Orally Inhaled Products - page 159

of the residuals about the individual regressions ( LPM / SPM vs. MMAD ), and by
definition reflects the precision of the fitted regression. RMSE is transformed by
dividing by the slope of the regression to express this statistic in terms of precision
of the estimated MMAD .
Both of these plots do the following:

1. They verify that setting the LPM / SPM boundary at the target MMAD provides
optimum precision.
2. They confirm that the precise selection of the boundary location with respect to
the MMAD value is not critical and can vary by an order of magnitude in the ratio
(from 0.3 to 3.0, as indicated by the placement of the solid vertical lines for ratio
in both plots), without serious degradation of precision.

7.7 Experimental Evidence for Ratio LPM / SPM as Measure

of Mean of the APSD

The most important aspects of applying abbreviated data acquisition and analysis
strategies for OIPs are the initial determination of the full-resolution APSD profile
for each product in a robust manner and subsequent confirmation that an AIM sys-
tem with a particular chosen boundary between LPM and SPM provides acceptable
predictive capability for MMAD .
Overall, Tougas et al. [ 11 ] showed in their investigations of OIP APSDs that
the LPM / SPM ratio appears to be capable of detecting small changes in MMAD of
the order of tenth(s) of microns. This finding is reflected in the magnitude of the
goodness-of-it statistic ( R 2 ) and [ RMSE /b], obtained for regressions of the
LPM / SPM ratio versus MMAD reported in Table 7.1 .
Tougas et al. observed that the relationship between MMAD and the LPM / SPM
ratio was approximately linear for every OIP type studied, illustrated by the magni-
tudes of the coefficient of determination and RMSE/b goodness-of-fit statistics [ 11 ].
They also noted that a small degree of systematic deviation from linearity was
observed in some cases and observed that such behavior is consistent with the
expectations for the ratio metric LPM / SPM . Thus, as values of MMAD approach the
lower bound (finest particles) of the size range of the CI, the LPM / SPM ratio trends
towards zero. Similarly, as values of MMAD approach the upper bound (coarsest
particles) of the size range, this ratio trends towards infinity.
The results in Table 7.1 reflect outcomes for the LPM / SPM boundary placement
that provided the best correlation between LPM/SPM ratio and MMAD (denoted as
the optimum boundary in this table). Figure 7.9 illustrates the nature and quality of
these regressions for two cases selected as examples (OIPs w9k001 and w9k901 ).
The 95% prediction bounds at the mean LPM / SPM ratio were projected onto the
x -axis (aerodynamic diameter in μm). Tougas et al . noted that the difference between
these projections of the upper and lower prediction intervals reflects the ability of
the LPM / SPM ratio to detect differences in MMAD and indicates that changes of a