So, working on the basis that dry dispersion is suitable for our model sample, and that the above assessment is realistic in terms of identifying the CQAs for the method, one of the steps needed to scope the MODR is to determine how air pressure influences the results of the analysis. The experiment that delivers the necessary data is commonly referred to as a pressure titration.
Figure 4 shows results from two pressure titrations. These were carried out using the Mastersizer 3000, which has a number of modular dry dispersion units that allow the intensity of dry dispersion to be matched to the sample. The upper of the two plots was measured using a dry dispersion unit fitted with the system’s standard venturi disperser, while the lower plot was generated using a venturi designed to provide high dispersion energies.
The aim with dry dispersion is to completely break up any agglomerates present, without causing damage to the primary particles. The results show that with each venturi increasing pressure decreases particle size. This raises the question of how to determine whether a given pressure is breaking up agglomeratesas required, or is causing damage to primary particles. A comparison with a reference liquid dispersion measurement helps to answer this question since liquid dispersion very rarely results in particle damage.
Results from liquid measurements are shown in blue in Figure 4. These indicate that the standard venturi disperser delivers complete dispersion at a compressed air pressure of around 3 bar, whereas using the high energy venturi disperser an air pressure of around 1 bar is required.
These data suggest that it would be possible to use either of the venturi tested. However, by plotting particle size as a function of air pressure for each venturi (Figure 5) it can be seen that the standard venturi is the better option. This plot shows that the MODR is larger with the standard venturi than with the high energy disperser.
These results show that with the high energy disperser any variation in air pressure will have a significant effect on particle size, compromising the ability of the method to meet the ATP. Using the standard venturi, on the other hand, the particle size results are reasonably consistent across the pressure range 3 to 4 bar. This venturi will therefore deliver an inherently more robust measurement. The MODR associated with its use can be determined, in terms of suitable air pressure, on the basis of these data.
The data shown in Figure 5 enable the selection of a dispersion pressure which would be expected to deliver robust results. To ensure that a proposed method meets the ATP, it is essential to verify that any variability in the way the method is applied does not shift the precision of the results outside the intended limits. This requires the method to be validated, following the guidance outlined in ICH Q2.
Two concepts are central to confirming that a particle sizing method is fit for purpose: repeatability and reproducibility. Assessing repeatability involves duplicate measurements of the same sample. It therefore tests the precision of the instrument, and the consistency of the sampling and dispersion process. Reproducibility is a broader concept that also encompasses multiple operators or even multiple analytical system installations.
Both the USP  and EP  recommend acceptance criteria for reproducibility testing. A Coefficient of Variability (COV) of less that 10% is suggested as acceptable for the median (Dv50) particle size or any similar value which is close to the center of the particle size distribution. This figure rises to 15% on values towards the edge of the distribution, such as Dv10 and Dv90, the particle size below which 10 and 90% of the population lies on the basis of volume. These limits are doubled for samples containing particles smaller than 10 microns because of the difficulties associated with dispersing such fine powders.
In our example then, where the acceptance criteria for the results are based on pharmacopoeial guidance, robust definition of the MODR requires that any source of variability does not take data reproducibility outside these limits. For example, the precision of air pressure control during dispersion is a function of the analyzer. If air pressure, a CQA, is controlled to within +/-0.1 bar, it is necessary to conduct experiments to determine the level of variability that this introduces in terms of the repeatability and reproducibility of the measured data. All potential sources of variability must be investigated in this way.