A model for determining alveolar and small airway dimensions from aerosol recovery data

Abstract

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.