Computational Model of Population Dynamics Based on the Cell Cycle and Local Interactions

Our study bridges cellular (mesoscopic) level interactions and global population (macroscopic) dynamics of carcinoma. The morphological differences and transitions between well and smooth defined benign tumors and tentacular malignat tumors suggest a theoretical analysis of tumor invasion based on the development of mathematical models exhibiting bifurcations of spatial patterns in the density of tumor cells. Our computational model views the most representative and clinically relevant features of oncogenesis as a fight between two distinct sub-systems: the immune system of the host and the neoplastic system. We implemented the neoplastic sub-system using a three-stage cell cycle: active, dormant, and necrosis. The second considered sub-system consists of cytotoxic active (effector) cells - EC, with a very broad phenotype ranging from NK cells to CTL cells, macrophages, etc. Based on extensive numerical simulations, we correlated the fractal dimensions for carcinoma, which could be obtained from tumor imaging, with the malignat stage. Our computational model was able to also simulate the effects of surgical, chemotherapeutical, and radiotherapeutical treatments.