A model of the lung structure and its validation

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Abstract
As a framework to describe the structure of the lung, a theory is presented under the assumptions that all alveoli are initially equal and space filling, are ventilated as uniformly as possible, and obey the laws of elasticity. A combination of the tetrakaidecahedron (14-hedron) and the order-2 14-hedron formed by 14 14-hedra surrounding a central one that is perforated for ventilation meets the requirements. Alveolar ductal tree is formed by these order-2 polyhedra. Equilibrium and elasticity require the alveolar mouths to be curved and convex toward the alveolar wall. Perforation of additional walls causes a variety of alveolar shapes. The predicted shapes of the alveoli, the shapes of alveolar mouths, the lengths of sacs and ducts, the statistics of the dihedral angles, stars, corners, lines, dots, and vertices compare well with available morphometric data. The vascular and bronchial trees are joined at the alveolar level: each arteriole supplies 0.75 and each venule drains 0.72 order-2 polyhedra.