Mathematical modeling of pulmonary acinus structure: Verification of acinar shape effects on pathway structure using...

The pulmonary acinus is the gas exchange unit in the lung and has a very complex microstructure. The structure model is essential to understand the relationship between structural heterogeneity and mechanical phenomena at the acinus level with computational approaches. We propose an acinus structure model represented by a cluster of truncated octahedra in conical, double-conical, inverted conical, or chestnut-like conical confinement to accommodate recent experimental information of rodent acinar shapes. The basis of the model is the combined use of Voronoi and Delaunay tessellations and the optimization of the ductal tree assuming the number of alveoli and the mean path length as quantities related to gas exchange. Before applying the Voronoi tessellation, controlling the seed coordinates enables us to model acinus with arbitrary shapes. Depending on the acinar shape, the distribution of path length varies. The lengths are more widely spread for the cone acinus, with a bias toward higher values, while most of the lengths for the inverted cone acinus primarily take a similar value. Longer pathways have smaller tortuosity and more generations, and duct length per generation is almost constant irrespective of generation, which agrees well with available experimental data. The pathway structure of cone and chestnut-like cone acini is similar to the surface acini's features reported in experiments. According to space-filling requirements in the lung, other conical acini may also be acceptable. The mathematical acinus structure model with various conical shapes can be a platform for computational studies on regional differences in lung functions along the lung surface, underlying respiratory physiology and pathophysiology.