A GENERAL-THEORY OF THE MACROTRANSPORT OF NONDEPOSITING PARTICLES IN THE LUNG BY CONVECTIVE DISPERSION

A theoretical model of (gas or) aerosol-particle dispersion phenomena in the conducting airways and acini of a symmetrically-bifurcating lung network is proposed. Founded upon the methods of macrotransport analysis for spatially periodic systems (Brenner and Edwards, Macro-transport Processes, Butterworth-Heinemann, Boston, 1993), the model characterizes the transport of nondepositing aerosol particles (or gas molecules) into and out of the lung (following a single inhalation/exhalation breath cycle) as occurring within a spatially periodic expanding/contracting branched network of one-dimensional capillaries (whose transport properties depend, inter alia, upon their specific cross-sectional geometrical and physicochemical characteristics). The model is shown to generalize and (in this and a subsequent article) improve upon former network models of lung dispersion. General formulas are derived for the mean velocity U*BAR with which an aerosol bolus transports through the network (at constant gas flow rate), as well as for the dispersion D*BAR about this mean. Various physical bases of the model in regards to dispersion phenomena in the lung are discussed, as is the experimental accessibility of the effective transport coefficients U*BAR and D*BAR. Explicit expressions for U*BAR and D*BAR are derived in various limits. These are compared with numerical results based upon the symmetrical Weible Model A of the human lung in the special cases of (i) Taylor dispersion within the airways, for which comparison is made with former network models; and (ii) axial streaming within the airways, for which comparison is made with experimental data. In the latter case, encouraging agreement is found between theory and experiments when the degree of axial streaming in the conducting airways is chosen to be similar as that observed in the branched-tube-network experiments of Scherer et al.