PLS regression analysis method was used to develop a model to predict the FFC value from the PSD statistics for each material
type. A single model to describe all material types could not predict the FFC value as well as a model built for a single
material type. Therefore, separate models were built for active blends, active granulations, excipients, and APIs. This is
not surprising considering the shape of the PSD curves and their response to shear stresses can be quite different across
material types; for example, single component systems are typically uni-modal, but granulations are typically polymodal.
The authors developed a four-parameter model using the most commonly reported PSD statistics for each material type to predict
the FFC value from the PSD statistics, as shown below.
FFC = exp(b
1 ln D10 + b
2 ln D50 + b
3 ln D90 + b
4 ln D[4,3])
A plot of the measured versus predicted FFC value for each material type is shown in Figure 1. Visual inspection of these
plots suggests that the predictions for the API and excipient FFC values are superior to the active blends and active granulations.
2 values in Table I describe the quality of the fit of linear regressions through the data in Figure 1 and, therefore, confirm
this observation. The R
2 values for the API and excipient models were 0.93 and 0.79, respectively, suggesting good model fits. The R
2 values for the active blends and active granulations were all <0.32, suggesting that the models were not able to describe
the flow performance of these materials using particle-size data with the same level of confidence. These results suggests
that PSD statistics alone in the PLS models are more appropriate for predicting the flow performance of single component APIs
or excipients. The models, however, may be useful for investigating potential differences in flow performance for like-composition
formulations that have been subjected to different manufacturing process conditions.
Figure 1 (FIGURES ARE COURTESY OF THE AUTHORS.)
Tree-based classification model.
A tree-based classification approach was used to categorize flow performance of the powders based on the relevant PSD statistics.
The literature has reported similar rules of thumb for estimating flow behavior from particle size. For example, Staniforth
reports that particles larger than 250 μm are usually free flowing; particles smaller than 100 μm become cohesive; and particles
less than 10 μm are extremely cohesive (2). This statistical method selects the particle size parameters that are most significant
in describing or categorizing the flow performance. The tree-based model was generated from the data using four parameters
of the PSD: D10, D50, D90, and D[4,3].
The classification tree results in Figure 2 show that, for both models, only two distribution statistics were significant
when predicting the flow category: the D10 and 50. These results further support the hypothesis formed in the PLS discussion
that models that use PSD statistics to predict powder flow do not require (or cannot be any better predicted by) a multitude
of parameters. These models are probably the most useful for forming "rules of thumb" when using PSD data to predict powder-flow
performance. When higher resolution flow characterization is required, the PLS model described above or measuring the flow
performance of the powder is preferred.
Testing the models.
To investigate the predictive power of the PLS model, the authors evaluated the PSD and powder-flow performance of additional
powder samples to test the predictions. Data from these materials were not used for the development of these models. In most
cases, the models predicted the FFC value within the same flow category (excellent, good, marginal, poor) as the measured
value (see Figure 3). Case 2 was an exception. In this case, the active blend contained an unusually high proportion of fines
(D10=4 μm) because of a 25% loading of an API with a median diameter of 10 μm. Even with this discrepancy, however, a simplified
set of PSD statistics (i.e., D10, D50, D90, D[4,3]) was found to suitably predict an estimated FFC on average to plus or minus
one FFC unit for these newly characterized materials.