2D Phase-Field Analyses of Axonal Extension of Nerve Cell

In this study, we aimed to develop a computer-aided simulation technique to predict the axonal extension in the neuronal network evolution processes for design new scaffolds to activate the nerve cell and promote the nerve regeneration. We developed a mathematical model of axonal extension by using phase-field method and evaluated the validity of the mathematical model by comparison with the experiments. In the previous experimental studies, the peripheral nerve scaffold has been introduced to guide the axonal extension. Damaged part of nerve was replaced by the artificial tube as the scaffold to induce the axonal growth through the artificial tube and regenerate the nerve network. However, the scaffold made of biodegradable materials has a problem that it is degraded and absorbed before the nerve regenerate, and then the nerve cannot regenerate. Therefore, there is a need for the design and development of a scaffold for nerve regeneration to promote nerve regeneration. For that purpose, it is necessary to understand the difference between the axonal extensions by the surrounding environment, such as the shape or materials of the scaffold for nerve regeneration. In particular, the numerical technique to analyze the remodeling process of the nerve in the scaffold is strongly required to be established because the in-vivo experimental observation technology at the micro scale, bioethical issues in the animal experiment and requires time and money are also remained as unresolved problems. In this study, we developed a new simulation code which employed the phase-field method to predict the two-dimensional dendritic and axonal growth processes of nerve cells on cultivation scaffolds. We curried out the phase-field analyses to make clear how the parameters of Kobayashi–Warren–Carter (KWC) phase-field model affected on the morphologic growths of dendrite and axon. Simultaneously, we had observed the axonal extension process by using the PC-12D cells with nerve growth factor (NGF) on two-dimensional cultivation dish. Based on these axonal extension observation results, we approximated the morphological changes and establish the phenomenological model for phase-field analysis. Finally, we confirmed the validity of our newly developed phase-field simulation scheme in two dimensions by comparison with the experiments.