A three-dimensional (3D) model of the human airway tree is proposed using a deterministic algorithm that can generate a branching duct system in an organ. The algorithm is based on two principles: 1) the amount of fluid delivery through a branch is proportional to the volume of the region it supplies; and 2) the terminal branches are arranged homogeneously within the organ. These principles define the basic process of branching: generation of the dimensions and directionality of two daughter branches is governed by the properties of the parent branch and the region the parent supplies. The algorithm is composed of nine basic rules and four complementary rules. When the contour of an organ and the position of the trunk are specified, branches are successively generated by the algorithm. Applied to the human lung, the algorithm generates an airway tree that consists of approximately 54,000 branches. Its morphometric characteristics are in good agreement with those reported in the literature. The algorithm and the 3D airway model are useful for studying the structure-function relationship in the lung.

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A three-dimensional (3-D) model of the human pulmonary acinus, a gas exchange unit, is constructed with a labyrinthine algorithm generating branching ducts that fill a given space completely. Branching down to the third respiratory bronchioles is generated with the proposed algorithm. A subacinus, a region supplied by the last respiratory bronchiole, is approximated to be a set of cubic cells with a side dimension of 0.5 mm. The labyrinthine algorithm is used to determine a pathway through all cells only once, except at branching points with the smallest path lengths. In choosing each step of a pathway, random variables are used. Resulting labyrinths have equal mean path lengths and equal surface areas of inner walls. An alveolus can be generated by attaching alveolar septa, 0.25 mm long and 0.1 mm wide, to the inner walls. Total alveolar surface area and numbers of alveolar ducts, alveolar sacs, and alveoli in our 3-D acinar model are in good accordance with those reported in the literature.

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