Mathematical model of a heterogeneous pulmonary acinus structure

Abstract

The pulmonary acinus is a gas exchange unit distal to the terminal bronchioles. A model of its structure is important for the computational investigation of mechanical phenomena at the acinus level. We propose a mathematical model of a heterogeneous acinus structure composed of alveoli of irregular sizes, shapes, and locations. The alveoli coalesce into an intricately branched ductal tree, which meets the space-filling requirement of the acinus structure. Our model uses Voronoi tessellation to generate an assemblage of the alveolar or ductal airspace, and Delaunay tessellation and simulated annealing for the ductal tree structure. The modeling condition is based on average acinar and alveolar volume characteristics from published experimental information. By applying this modeling technique to the acinus of healthy mature rats, we demonstrate that the proposed acinus structure model reproduces the available experimental information. In the model, the shape and size of alveoli and the length, generation, tortuosity, and branching angle of the ductal paths are distributed in several ranges. This approach provides a platform for investigating the heterogeneous nature of the acinus structure and its relationship with mechanical phenomena at the acinus level.

Keywords: Biological microstructure; Computational geometry; Gas exchange; Pulmonary biomechanics; Pulmonary physiology; Rat acinus; Structure modeling.