Biomedical Engineering Reference
In-Depth Information
of the products. The intervals that represent the total variability were just under 4σ
units in width, σ representing the estimated standard deviation (SD) and μ
representing the estimated mean in MMAD for that product. This interval was spe-
cifically defined as
m
+
(. )[ (. )]
196
s
-
m
-
1 96
s
=
392
.
s
(8.3)
in which 1.96 σ is the width of an interval that would contain, approximately, 95%
of the individual MMAD values. This figure of merit is a comparison of the vari-
ability associated with estimating the average MMAD to the total variability in the
individual MMAD measurements. In all cases, the variation in estimating the aver-
age MMAD through the LPM / SPM ratio was consistently severalfold smaller than
the variability expected from individual measurements, indicating the consistent
ability to adequately detect difference in MMAD within the normal observed vari-
ability of the product.
In contrast, the grouped stages consistently exhibited poorer performance.
Groups 1 and 3 were consistently unable to detect difference in MMAD within this
range, and groups 2 and 4 exhibited inconsistent performance with respect to being
able to detect differences. Even in those cases where one of these metrics might be
judged adequate to detect changes in MMAD , its performance was inferior to the
corresponding LPM / SPM metric.
The results in Table 8.5 and Fig. 8.12 confirm that for the eight products exam-
ined, the LPM / SPM ratio consistently out-performed all stage groupings with
respect to a measurement related to the central tendency of the APSD (as reflected
in the values of MMAD ). Note that the CI stage d 50 in this table refers to the cut-
point size of the stage separating LPM from SPM . The two MSA figures of merit
also confirmed the early observations concerning groups 1 and 3, i.e., that these
stage groupings contain virtually no information related to the central position of
the APSD.
The values obtained for the discrimination index indicate that the LPM / SPM
ratio is consistently able to detect differences in MMAD of the order of tenths of
microns. While groups 2 and 4 exhibited some ability to detect changes in MMAD ,
the performance was both inconsistent and always inferior to the LPM / SPM ratio
for the same product.
Another graphical approach to comparing performance is to plot MMAD pre-
dicted by the metric through the regression model versus the actual MMAD as deter-
mined through the full-resolution CI results. The comparison was limited to
comparing the ratio metric to only the group 2 and group 4 results since the other
two groupings consistently appear unable to offer any information about the MMAD .
The results of this analysis are depicted in Figs. 8.13 , 8.14 , 8.15 , 8.16 , 8.17 , 8.18 ,
8.19 , and 8.20 and again clearly demonstrate the consistent superiority of the ratio
metric over stage groups with respect to measuring changes in the MMAD , i.e., any
shift in the average particle size of the emitted aerosol from any OIP.
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