## Mass Median Diameter Microns

Figure 1 Task Group on Lung Dynamics model for lung deposition. The shaded area represents the range of effects when the sg varies between 1.2 and 4.5 at a tidal volume of 1450 mL. (With permission of Health Physics.)

Figure 1 Task Group on Lung Dynamics model for lung deposition. The shaded area represents the range of effects when the sg varies between 1.2 and 4.5 at a tidal volume of 1450 mL. (With permission of Health Physics.)

dose. Thus, the largest particles capable of penetrating into the deep lung offer the greatest therapeutic advantage, and the target size range of 1-5 mm is generally accepted as the formulator's guide to optimized lung deposition [16,17]. To some extent, this range has been dictated by the technology available for aerosol generation [10,18]. However, if it were possible to generate submicrometer pharmaceutical aerosols easily, the time period required for delivery of a therapeutic dose would generally be prohibitively long.

It is rarely the case that the sizes of all particles in an aerosol are the same, or monodisperse [19]. An aerosol consists of particles of numerous sizes, and each one of these will deposit in different regions in the lung. The range of particle sizes is known as the distribution. Figure 2 shows a typical distribution. The skew to the left of this distribution is indicative of log normality [20,21]. This expression refers to the fraction of particles of a particular size that, when plotted against logarithms of the particle sizes, exhibit a normal, bell-shaped, or Gaussian, distribution. A narrow distribution indicates an aerosol whose particles have similar sizes. The most common expression of particle sizes divides the distribution in half (50% above and 50% below that size and is known as the median size) according to statistical convention. A broad distribution may have the same median particle size as the narrow one, but there will be a considerable range of particle sizes.

1 2 3 4 5 6 7 Particle Diameter

Figure 2 Representative log-normal particle size distribution. The values in parentheses are based on a count median diameter of 1.0 mm and a sg of 2.0. (With permission of Health Physics.)

### 1 2 3 4 5 6 7 Particle Diameter

Figure 2 Representative log-normal particle size distribution. The values in parentheses are based on a count median diameter of 1.0 mm and a sg of 2.0. (With permission of Health Physics.)

Assuming a median diameter in the respirable range, then a larger proportion of a narrowly distributed aerosol will be respirable than for a broad distribution. It would seem that a broad distribution is not desirable to achieve the goal of targeting the lower airways. The conventional measure of the log-normal distribution of particle size is the geometric standard deviation [22,23]. Given the median diameter and geometric standard deviation of aerosol particles, the size distribution can be constructed.

As with all dosage forms, it is the amount of drug reaching the site of action that dictates the therapeutic effect. The importance of this observation to a formulator can be emphasized by two examples: [1] When expressing the particle size of an aerosol, it might seem appropriate to count the number of particles of each size and to plot the distribution as shown in Fig. 2. In a hypothetical aerosol sample consisting of one 10-mm particle and 1000 1-pm particles, the number of particles of a particular size leads to the belief that the vast majority (> 99.9%) of the aerosol is respirable. Unfortunately, from a therapeutic standpoint, one 10-mm particle carries the same mass as 1000 1-^m particles. Thus, only 50% of the mass of the aerosol (mass of 1-^m particles divided by the mass of 1- and 10mm particles combined) would reach the lung. [2] A solution aerosol droplet of an appropriate size will not carry the same amount of drug as a solid particle because part of its composition is solvent. Both of these examples are important formulation considerations when considering the dose.

Gonda [24] described the influence of polydispersity on deposition of aerosol particles in the lung assuming a variety of distributions (sg = 1, 2, and 3.5). Figure 3 shows that a small median diameter results in the highest deposition in the pulmonary region. The narrow distribution (sg = 1) results in maximum deposition in the pulmonary region when the median diameter is 2 mm. As the distribution is increased and as the aerosol becomes more polydisperse, the maximum at 2 mm disappears into a general trend toward increased deposition in the pulmonary region as the median diameter is reduced. One interpretation of this observation is that, as referred to earlier, aerosols formulated to achieve a small median diameter and a narrow distribution will be most effective in penetrating the lower airways. It is also true that the narrow distribution is more sensitive to a change in the median diameter, with a 10-fold variation in the range 1-10 mm. A highly polydisperse aerosol is less sensitive to changes in median diameter but does not achieve maximum pulmonary deposition. These are important considerations because an aerosol may be subject to changes in median diameter resulting from manufacture storage or generation.

Other characteristics of particles that influence their deposition are density, charge, shape, solubility, and hygroscopicity. These play a secondary role to particle size. The density of the particle contributes to its mass and, thus, inertia [20,23]. Increasing density will result in increased, or more rapid, deposition of particles. Charge has a number of effects. First, particles may aggregate as

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