A cellular automaton model for the growth dynamics of neural stem cell spheroid

Purpose: Cell transplantation for the diseased central nervous system requires a substantial amount of neural stem cells (NSCs) to be generated in vitro. High expansion rates of NSCs in culture are thus crucial for the clinical application. When the size of a neurosphere cultured in vitro reaches a certain critical value, a necrotic core appears inside the neurosphere because of the lack of oxygen or other nutrients transport from medium to the cells in the neurosphere. Large necrotic core will greatly reduce the expansion of NSCs. Therefore, it is important to simulate the dynamic process of the growth of neurospheres and analyze the critical size of the neurosphere at which the necrotic core appears. Methods: A cellular automaton approach was proposed in this article to model the growth of NSCs in sphere state. The appearance and enlargement of the necrotic core in a neurosphere is calculated by coupling the CA (cellular automaton) model with the nutrient diffusion analysis. Results: The calculation results indicated that the culture conditions, including seeding density, concentration of nutrients in medium and the mass transfer coefficient between a neurosphere and medium, have influence on the appearance of the necrotic core. The necrotic core mainly depends on the inner diffusion. Necrotic core appeared when the size of neurosphere was large enough even the outside mass transfer was in a good condition. Additionally, the appearance of necrotic core resulted from the shortage of oxygen was earlier than that caused by the limitation of glucose. And the growth of necrotic core was very fast after its appearance, and the whole neurosphere may become necrotic. Conclusion: The established automaton model could simulate NSCs growth in vitro.