R

where Vt ■ -t ■ ■ cos i¡//R has been designated the deposition parameter.

From equation (1), VT includes a term for the particle size and gravitational acceleration. Landahl's expression adds terms describing the geometry of the tube and the residence time of the particle to allow a probability of deposition to be derived. As an example of the manner in which this expression is applied, assuming a deposition parameter of one and a probability of deposition of 55% for 2-\im particles, l-|im and 0.5-|im particles would be expected to deposit with 29% and 10% efficiency, respectively. The probabilities of particle deposition, by the U.S. Atomic Energy Commission and American Conference of Governmental and Industrial Hygienists, have been used to designate the fraction of an aerosol that is respirable, as shown in Table 4. This considers deposition in all of the airways of the lungs. Thorough descriptions of theoretical and experimental studies of lung deposition have been collated and may be found in the literature (20).

Particulate diffusion does not play a significant role in the deposition of pharmaceutical aerosols. However, it is worth noting the mechanism by which diffusion of particles occurs in the lungs. The principle of Brownian motion is responsible for particle deposition under the influence of impaction with gas molecules in the airways. The amplitude of particle displacement, A, is given by the following equation:

where R is the universal gas constant, Tis absolute temperature (Kelvin), Nis Avogadro's number, C is the slip correction factor, t is time, rj is the air viscosity, and d is the particle diameter.

Table 4 Respirable Fractions as Designated by the American Conference of Governmental and Industrial Hygienist (ACGIH) and the U.S. Atomic Energy Commission (USAEC)

Aerodynamic diameter (|xm)

Respirable fraction® (%)

Respirable fraction0 (%)

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