Figure 15.

Automaton cells were created using Voronoi tessellation (a) based on the centers of the spheres (b) which were created with RSA process. Reproduced with permission from ref 173. Copyright 2011 Yang Jiao, Salvatore Torquato. In this model, each automaton cell could be either ECM of a specify density, invasive, proliferative, quiescent, or necrotic cell. The microenvironment heterogeneity could easily be considered by varying the distributions of the ECM densities. An invasive cell would degrade the surrounding ECM and migrated from one automaton cell to another if the associated ECM in that cell has a “zero” density (i.e., fully degraded). The detailed rules of this CA model are illustrated in Figure 16. Using this model, the authors successfully captured the cancer cell invasion process by considering various tumor–host interactions (e.g., the mechanical interactions between tumor cells and microenvironment (ECM), degradation of ECM by the tumor cells, and oxygen/nutrient gradient driven cell motions).