Document qaVoNXa99y0Z5Bv0Y4aJ71945

ASULSTOS IN Till; HUMAN RESPIRATORY TRACT 33 MINOR DIAMETER (MICRONS) FIGURE 2 Fraction of inhaled panicles deposited in the lower (alveolated) region of the respiratory tract, vs equa torial diameter of the panicle, for various values of p. lung was taken as 2000 cm*. The total and alveolar deposition curves for p values of 1, 4, 16, and 64 are shown in Figures 1 and 2. The abscissa repre sents the equatorial diameter of the ellipsoidal particles, in microns. These results art perhaps most easily understood by considering the effect of increasing p on the panicle mobility. It is easily shown, using equations (1) and. (2), that 3Cln(fl Lim B 20np`P (8) Thus as p is increased indefinitely, B tends to 2ero. This accounts for the reduoed deposition of the elongated ellipsoids in the particle size range 0.02 (i to approximately 0.2 p, because diffusion is the predominant mechanism for deposition in this region, and the diffusion coefficient of a particle is proportional to its mobility. Thus the exponential factor in Eq. (3) will tend to zero as p increases indefinitely. :iml consequently /),' will nlsii tciul to zero. In the panicle-size region above 0.2 /> scdiiucutnlion and impaction are more importam mechanisms than diffusion. The exponential factor in the sedi mentation equation (Eq. 4) is proportional to the sedimentation velocity of the panicle, which in turn is proportional to piJ. This product becomes proportional to In P as P increases indefinitely. Consequently increasing P increases the sedimenta tion velocity, and increases the rale of deposition due to sedimentation. A similar argument for im paction shows that the slopping distance becomes proportional to In p as p increases indefinitely, and consequently the factor approaches unity. Now the equations for impaction and sedimentation both contain the factor ppB\ consequently an in crease in p at fixed p can be simulated as far as these two mechanisms are concerned by an appro priate increase in p at fixed p. In other words, the deposition behaviour of ellipsoids of a given density and of a given equatorial diameter is equal to that of spheres of equal diamater, but having a greater density such that (p?B) is equal for both classes of particles. This is true only in the particle size region where diffusion is insignificant. Landahl*-* and Beeckmans4, * had shown that as the density of spherical panicles is increased, the total and alveolar deposition curves are shifted towards the left, and the same can be seen in the results pre sented here as p is increased. Finally, it is peninent to ask if interception might not play a role in deposition for very elongated particles. Interception might be expected to be of significance when the polar diameter of the particle approaches the dimensions of the smaller airways. The respiratory tract model used in this study is due to Weibel,* who calculated a value of 0.041 cm for the diameter of the alveolar sacs, at a functional residual capacity of 4.8 liters. In the present study, the functional residuat capacity was 2 liters, and the tidal volume was 1 liter. Consequently the mean lung volume during the breathing cycle was 2.5 liters, and the corresponding alveolar diameter was 0.041 x (2 5/4.6) cm, or 349 /*. The longest par ticle for which calculations are reported here had a P value of 64 and an equatorial diameter of 3ji. Consequently its length was 192 p. Moreover, as can be seen from the figures, this type of particle is virtually completely deposited in the upper respiratory tract, and consequently inter ception in the lower respiratory tract, if it were to occur, would not be of significance. U I/I-- { I I l I t I i I > 8000 1528 PRODUCED BY FORD