Phase-field modeling for axonal extension of nerve cells

In this study, we applied a modified Kobayashi-Warren-Carter (KWC) phase-field model to the neurite growth process. To confirm the applicability of this model, we observed axonal extension of PC-12D cells cultured with nerve growth factor (NGF). Based on our observations, we defined three stages of nerve cell axonal extension: neurite generation, neurite contraction, and axon extension. We further determined the parameters in the phase-field equations to express the three extension stages. Finally, our results show that the modified KWC phase-field model reasonably expresses the morphologies of nerve cells and predicts the three stages of nerve cell axonal extension. Although, we employed the binary alloy solidification model as a sample model in the present phase-field simulations, this work will be extensible to relatively more realistic models for nerve cell growth.