A New Mathematical Model for Controlling Tumor Growth Based on Microenvironment Acidity and Oxygen Concentration

Abstract

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.

Melatonin: Regulation of Prion Protein Phase Separation in Cancer Multidrug Resistance

“…As adaptation to hypoxia, changes in gene expression affecting cellular and physiological functions often result in increased cancer aggressiveness and treatment resistance [ 650 , 651 , 652 ]. A recent study using in silico modeling and the simulation of in vivo cancer cell growth found that increasing oxygen concentration and pH value in the TME could result in significant shrinkage of tumor growth size [ 653 ]. Melatonin is an effective oncostatic agent capable of modulating important elements in TME that drive immunosuppression, cell proliferation, metastasis, and resistance to apoptosis [ 654 ].…”

Searching for the Metabolic Signature of Cancer: A Review from Warburg’s Time to Now

“…It is difficult to experimentally access all the states precisely, especially those existing on shorter time scales, which is why the use of computational models is a real asset. Several models have explored possible states of tumor metabolism and the environment [ 79 , 80 , 81 , 82 , 83 , 84 ]. A recent model [ 85 ], addressed the issue using statistical approaches by attempting to characterize metabolic attractors and their transition zones.…”

Analytical Models of Intra- and Extratumoral Cell Interactions at Avascular Stage of Growth in the Presence of Targeted Chemotherapy

“…As an example, Ansarizadeh et al [ 8 ] suggest a complex model, which describes the interaction among normal, immune and tumor cells in a tumor with a chemotherapeutic drug, using a set of coupled PDEs. Moreover, there are approaches such as that in [ 9 ], designed by Pourhasanzade et al, which even look into the microenvironmental factors, as well as at separate types of nutrients and various cell groups of a tumor. These types of models appear to be more detailed and sophisticated PDE sets.…”

“…As can be seen from Table 1 , different models have been developed for the prediction of tumor growth, considering the effects of different factors employing a range of assumptions. For example, many studies consider a single type of generic tumor cells [ 3 , 4 , 5 , 8 , 10 , 11 , 12 , 13 , 14 , 15 ], while others consider separate proliferating, quiescent and necrotic cells within the tumor [ 6 , 7 , 9 , 16 , 17 , 18 ]. The benefit of considering these separate types of cells is a full understanding of intra-tumoral interactions, which prove to be more realistic than a generalized approach.…”