Diameter, length and branching ratios in the bronchial tree

This paper is concerned with morphology and pattern of branching in the bronchial tree and their interrelationships. Branching ratio (Rb), diameter ratio (Rd), and length ratio (R1) are the factors by which the number of branches, mean diameter and mean length increase in successive orders of branching. An analysis based on the concept of minimum work suggests that ideally Rd = R1/3 b, whilst geometric considerations suggest that R1 = R1/3 b. Thus Rd = R1. These theoretical results are compared with those obtained from measuring one human and six dog bronchial tree casts. Values obtained from the human lung are in close agreement with the predicted values, whilst in the dog lungs the agreement, though less good, is still close. Rb is determined antenatally, the reason for its particular value being unknown. Diameter and length of branches may be modelled postnatally by growth in a manner which ensures that Rd = R1 - R1/3 b.