Journal of Applied Physiology, Vol 58, Issue 2 582-591, Copyright © 1985 by American Physiological Society
A model for determining alveolar and small airway dimensions from aerosol recovery data
F. S. Rosenthal
A mathematical model is presented that allows the determination of alveolar
and small airway dimensions from a series of aerosol recovery measurements
performed at different inspiration volumes. The model assumes 1) a
symmetric dichotomous lung, 2) representation of airway and alveoli as
ensembles of straight tubes, and 3) Gaussian dispersion of the aerosol
bolus. Calculations with this model using dimensions given by Weibel show
general agreement with experimental data on six human subjects obtained by
Palmes et al. (J. Appl. Physiol. 34: 356-360, 1973). Close agreement is
found by varying two parameters describing alveolar size and airway size to
obtain the best fit. The resulting estimates of size are almost independent
of the choice of the dispersion coefficient; however, the estimate of
alveolar size is quite dependent on the form of settling assumed during
breath holding. The values of alveolar diameter in the six subjects,
determined under the assumption of stirred settling, ranged from 0.13 to
0.33 mm, whereas under the assumption of still settling the range was
0.24-0.65 mm. Small airway (generations 18-24) dimensions ranged from 0.41
to 0.66 mm under the still-settling assumption and 0.39 to 0.63 mm under
the stirred-settling assumption. With the assumption of an intermediate
(partially stirred) form of settling, the alveolar diameter in the six
subjects is 0.28 +/- 0.02 mm, in close agreement with morphometric
measurements by other investigators. A partially stirred form of settling
is also consistent with model predictions of recovery vs. breath-holding
time and with cardiogenic gas mixing in the lung.
