The Development of a Mathematical Approximation Technique to Determine the Mass Median Aerodynamic Diameter (MMAD) and Geometric Standard Deviation (GSD) of Drug Particles in an Inhalation Aerosol Sprat

The aerodynamic diameter of an airborne particle is the key property in determining its respiratory deposition. Two particles may differ in their shape, size, and/or density and still be aerodynamically indistinguishable because they have similar behavior in a moving airstream. A cascade impactor has been used to measure the range of aerodynamic diameters for drug particles in an aerosol spray product. The two terms associated with aerodynamic particle sizing are Mass Median Aerodynamic Diameter (MMAD) and the Geometric Standard Deviation (GSD). Both terms are determined from the visual fit of a straight line to data manually plotted on log-probability paper. The plotting of this data is a time consuming activity and the fit of the line to the data can be very subjective.Although this technique is an excellent candidate for computerization, it cannot be done directly since the probability axis is an integral function not easily adaptable to the computer packages generally used in the laboratory. A mathematical approximation has been developed that in effect “linearizes” the probability axis. The mathematical relationship (a fifth degree polynomial expression) when incorporated into a general computer program allows for the direct computation of the two aerodynamic terms. Since the subjectiveness of manually plotting the data and fitting the line are removed, the results obtained are potentially more accurate. Also, the results are obtained more quickly with significantly less effort. This paper explores the development of the mathematical relationship and provides a comparison of values obtained by both the manual and computer methods.