Biomedical Engineering Reference
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100
80
60
40
20
0
0.6 0.8
1
2
4
6
10
d 10
d 90
MMAD
Aerodynamic Diameter ( m m)
Fig. 4.13 Cumulative mass-weighted APSD, showing relationships between span-related metrics
d 10, d 90 and MMAD
where d 10 and d 90 are the 10th and 90th percentiles of the cumulative mass-
weighted APSD, respectively.
Assuming the APSD is unimodal, the moment of central tendency, MMAD,
is identical to the size that corresponds to the 50th mass percentile, whether or
not the distribution is lognormal , so that a relative span factor (RSF), based on
the relationship
[
]
dd
MMAD
90
10
(4.8)
RSF
=
can be a useful way to report the spread of the APSD (Fig. 4.13 ).
4.4.2.2
Estimation of the MMAD
Seldom will the APSD provide an exact value of the MMAD that can be obtained
directly from the plotted data because of alignment of one of the stage d 50 sizes with
the 50th mass percentile of the distribution. Under most circumstances, it is therefore
necessary to estimate this value. The method described in the pharmacopeias relies on
the underlying assumption of lognormality, which is frequently not the case with OIP-
generated aerosols. In 2010, the CI Working Group of IPAC-RS published a Stimulus
to Revision article, in which they provided evidence from an extensive database of
OIP APSDs that two multipoint curve-fitting methods [Chapman-Richards (CR) and
Mercer-Morgan-Flodin (MMF) Models], as well as the linear two-point interpolation
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