Cascade Impactor Data and the Lognormal Distribution: Nonlinear Regression for a Better Fit

Abstract

At present, cascade impactors are the instruments of choice for measuring the particle size distribution of aerosol present in the complex discharge from pharmaceutical inhalers. The distribution of drug captured in the cascade impactor may be most usefully represented by the lognormal distribution. Only two parameters must be extracted from the analysis of cascade impactor data in order to describe the distribution. These two parameters are the mass median aerodynamic diameter (MMAD) and the geometric standard deviation (GSD). A cumulative version of the lognormal curve or more frequently, a linearized version of the cumulative curve called a "log probability plot," is used as a surrogate for the lognormal curve. The probability plot has great appeal since a lognormal distribution yields a straight line on log probability paper. One may easily determine the apparent MMAD and GSD from this linear plot. However, when one plots a lognormal curve, using the MMAD and GSD derived from a log probability plot, over a histogram constructed from cascade impactor data, an obvious mismatch is frequently seen. In order to derive parameters that more truly reflect the impactor data, a computer program, which uses nonlinear regression to derive an MMAD and GSD for the lognormal curve, has been written. It is presented here.