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Tumor growth has long been a target of investigation within the context ofmathematical and computer modelling. The objective of this study is to proposeand analyze a two-dimensional probabilistic cellular automata model to describeavascular solid tumor growth, taking into account both the competition betweencancer cells and normal cells for nutrients and/or space and a time-dependentproliferation of cancer cells. Gompertzian growth, characteristic of sometumors, is described and some of the features of the time-spatial pattern ofsolid tumors, such as compact morphology with irregular borders, are captured.The parameter space is studied in order to analyze the occurrence of necrosisand the response to therapy. Our findings suggest that transitions existbetween necrotic and non-necrotic phases (no-therapy cases), and between thestates of cure and non-cure (therapy cases). To analyze cure, the control andorder parameters are, respectively, the highest probability of cancer cellproliferation and the probability of the therapeutic effect on cancer cells.With respect to patterns, it is possible to observe the inner necrotic core andthe effect of the therapy destroying the tumor from its outer borders inwards.

A cellular automata model for avascular solid tumor growth under the effect of therapy