Evaluation of probability density functions to approximate particle size distributions of representative pharmaceutical aerosols

The purpose of this work was to evaluate the application of probability density functions (PDFs) and curve-fitting methods to approximate particle size distributions emitted from four pharmaceutical aerosol systems characterized using standard methods. The aerosols were produced by a nebulizer, pressurized metered dose inhaler (pMDI), dry powder inhaler (DPI) and nasal spray. PDFs selected for analysis were (i)log-normal, (ii) upper-limit, (iii) Nukiyama-Tanasawa (iv) Rosin-Rammler and (v) modified Rosin-Rammler. Two curve-fitting methods were used to estimate the adjustable parameters of the PDFs: linear least-squares fit of the cumulative distribution function (Method A) and non-linear least-squares fit of the probability density function (Method B). Large truncation of the pMDI and DPI particle size distributions obtained by cascade impaction resulted in poor fits of the PDFs. The nebulizer and nasal spray were not affected by truncation and were well represented by the Rosin-Rammler and log-normal PDFs, respectively (Method B only). Probability distribution functions (Method B) were fitted without bias from linear coordinate transformation and produced significantly better fits than Method A for each aerosol system (p < 0.05). Considerable caution must be used when estimating representative parameters from cumulative or probability distributions. (C) 2000 Elsevier Science Ltd. All rights reserved.