フエーズフイールド法を用いた肺微細構造のモデリング

摘要

We have developed a novel technique for modeling the realistic lung microstructure using phase-field method. In the phase-field method for the lung microstructure, the state (air and tissue) of a system is measured with an order parameter and the time-evolutions of the order parameters in the system, a tissue initially including seeds of the air, are obtained by solving the time-dependent bistable reaction-diffusion equations modified from the Allen-Cahn equation. The field of the order parameters is reconstructed as the 3D lung microstructure model by using the binalized slice images with a certain threshold of the order parameter between the two states (air and tissue) on the binalization. We found that irrespective of the number of the initial seeds, the results demonstrate isotropic evolution of alveolar regions (air) from the initial seeds, and the alveolar regions came closer with evolution, but were never merged because of the presence of alveolar wall (tissue). A further evolution of alveolar regions develops into spatially compartmentalized pore structure, which appeared to be similar to a natural lung. Variations in the number of, and the shape of the initial seeds, and the threshold of the order parameter for binalization result in various patterns of the ductal porous structure (i. e., alveolar duct or alveolar sac), satisfying the experimentally-obtained mean alveolar volume and mean alveolar wall thickness. Furthermore, the radial distribution function calculated from the centroids of alveoli were saturated to one without any significant peaks when the inter-alveolar distance exceeds a certain value, indicating that the alveoli in our model are disorderly distributed and repel each other with a certain distance. In conclusion, those results demonstrate that the method developed here is the promising method for parametric control and anatomically realistic production of lung microstructure model.