Mathematical and computational models are of great help to study and predict phenomena associated with cancer growth and development. These models may lead to introduce new therapies or improve current treatments by discovering facts that may not be easily discovered in clinical experiments. Here, a new two-dimensional (2D) stochastic agent-based model is presented for the spatiotemporal study of avascular tumor growth based on the effect of the immune system. The simple decision-making rules of updating the states of each agent depend not only on its intrinsic properties but also on its environment. Tumor cells can interact with both normal and immune cells in their Moore neighborhood. The effect of hypoxia has been checked off by considering non-mutant proliferative tumor cells beside mutant ones. The recruitment of immune cells after facing a mass of tumor is also considered. Results of the simulations are presented before and after the appearance of immune cells in the studied tissue. The growth fraction and necrotic fraction are used as output parameters along with a 2D graphical growth presentation. Finally, the effect of input parameters on the output parameters generated by the model is discussed. The model is then validated by an in vivo study published in medical articles. The results show a multi-spherical tumor growth before the immune system strongly involved in competition with tumor cells. Besides, considering the immune system in the model shows more compatibility with biological facts. The effect of the microenvironment on the proliferation of cancer and immune cells is also studied.

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Hypoxia and the pH level of the tumor microenvironment have a great impact on the treatment of tumors. Here, the tumor growth is controlled by regulating the oxygen concentration and the acidity of the tumor microenvironment by introducing a two-dimensional multiscale cellular automata model of avascular tumor growth. The spatiotemporal evolution of tumor growth and metabolic variations is modeled based on biological assumptions, physical structure, states of cells, and transition rules. Each cell is allocated to one of the following states: proliferating cancer, nonproliferating cancer, necrotic, and normal cells. According to the response of the microenvironmental conditions, each cell consumes/produces metabolic factors and updates its state based on some stochastic rules. The input parameters are compatible with cancer biology using experimental data. The effect of neighborhoods during mitosis and simulating spatial heterogeneity is studied by considering multicellular layer structure of tumor. A simple Darwinist mutation is considered by introducing a critical parameter ( Nmm ) that affects division probability of the proliferative tumor cells based on the microenvironmental conditions and cancer hallmarks. The results show that Nmm regulation has a significant influence on the dynamics of tumor growth, the growth fraction, necrotic fraction, and the concentration levels of the metabolic factors. The model not only is able to simulate the in vivo tumor growth quantitatively and qualitatively but also can simulate the concentration of metabolic factors, oxygen, and acidity graphically. The results show the spatial heterogeneity effects on the proliferation of cancer cells and the rest of the system. By increasing Nmm , tumor shrinkage and significant increasing in the oxygen concentration and the pH value of the tumor microenvironment are observed. The results demonstrate the model’s ability, providing an essential tool for simulating different tumor evolution scenarios of a patient and reliable prediction of spatiotemporal progression of tumors for utilizing in personalized therapy.

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