Diameter-based analysis of the branching geometry of four mammalian bronchial trees

A diameter-based classification technique, which we have previously used to analyse human bronchial geometry (Phillips et al., Respir. Physiol. 98: 193-217, 1994) is applied also to the partial measurements of the dimensions of dog, rat and hamster conducting airways, made by Raabe et al. (Tracheobronchial Geometry: Human, Dog, Rat, Hamster, 1976). The local branching patterns are characterised by means of three parameters, which reflect the asymmetry and the degree of expansion at each bifurcation, and the ratio of the length of each branch to its diameter. The mean values of these parameters as functions of diameter, calculated from the raw morphometric data, are shown for the four species. A statistical reconstruction technique is then used to estimate from the incomplete measurements of Raabe and coworkers some geometrical properties of the whole system of conducting airways, which are likely to influence transport processes in the lung. These include the distribution of the total airway volume between branches of different diameters, the mean and variance of the total lengths of different pathways through the bronchial tree, and a simple model for the variation of flow velocity with airway diameter. Our results show significant differences between the branching structures of all four species. In particular, the human differs from the others in branching much more symmetrically, and in that branches of a given diameter are typically much longer than in the other species; together, these observations imply that the human bronchial tree is geometrically very different from those of the other species.