Cascade impactor data and the lognormal distribution: nonlinear regression for a better fit

Area of Science:

• Pharmaceutical technology
• Aerosol science
• Particle characterization

Background:

• Cascade impactors are standard for measuring aerosol particle size distribution from pharmaceutical inhalers.
• Lognormal distribution, defined by mass median aerodynamic diameter (MMAD) and geometric standard deviation (GSD), is often used to represent this data.
• Traditional log probability plots for determining MMAD and GSD can lead to inaccuracies when fitting the lognormal curve to impactor data.

Purpose of the Study:

• To address the limitations of traditional log probability plots in accurately characterizing particle size distribution from cascade impactor data.
• To present a computer program that utilizes nonlinear regression for more precise determination of MMAD and GSD.
• To improve the fitting of lognormal distribution models to cascade impactor measurements.

Main Methods:

• Development of a computer program employing nonlinear regression techniques.
• Analysis of cascade impactor data to extract distribution parameters.
• Comparison of nonlinear regression results with traditional log probability plot methods.

Main Results:

• The nonlinear regression approach provides MMAD and GSD values that better represent the actual cascade impactor data.
• A frequent mismatch is observed when plotting lognormal curves derived from log probability plots over empirical data histograms.
• The developed program offers a more accurate method for parameter estimation.

Conclusions:

• Nonlinear regression is a superior method for deriving MMAD and GSD from cascade impactor data compared to traditional log probability plots.
• The presented computer program enhances the accuracy of particle size distribution analysis for pharmaceutical aerosols.
• Improved parameter estimation leads to a more faithful representation of drug delivery characteristics from inhalers.