A diameter-based reconstruction of the branching pattern of the human bronchial tree. Part II. Mathematical formulation.

In this paper we present the mathematical details of the diameter-based reconstruction technique used in the companion paper (Phillips et al., 1994 - referred to below as Part I) to analyse the morphometric data of Raabe et al. (1976) on the human bronchial tree. In the first section we outline the technique as applied to the incomplete set of measurements in order to estimate properties of the bronchial tree as a whole; in the second section we consider what form these properties would take if the bronchial tree were geometrically self-similar, as has often been assumed to be approximately the case.