Abstract
We propose probabilistic cellular automata on a square lattice for simulating the dynamic of cancer growth in a reaction-diffusion frame. In the reaction step each cancerous cell can proliferate, be quiescent, or die due to apoptosis or necrosis phenomenon. The three-state Potts model is used for calculating the probabilities in the reaction step. We consider the effect of nutrient in the tumor growth in order to improve the precision of the model. We use a simple and suitable method for the diffusion step to simplify movement of cells and nutrient in the model. In the diffusion step the lattice is partitioned by 3×3 blocks. In each block we count the number of different types of cells and redistribute them in the block. In the next time step, each block will be shifted one row down and one column to the right and the operation will be continued. The redistribution step for nutrient molecules is same as cells. It is shown tumor growths asymmetrically toward nutrient source. It has been shown such a simple model could simulate tumor growth with good accuracy, which is based on the well known physical ground i.e. the three-state Potts model.
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Ghaemi, M., Naderi, O., Zabihinpour, Z. (2010). A Novel Method for Simulating Cancer Growth . In: Bandini, S., Manzoni, S., Umeo, H., Vizzari, G. (eds) Cellular Automata. ACRI 2010. Lecture Notes in Computer Science, vol 6350. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15979-4_15
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DOI: https://doi.org/10.1007/978-3-642-15979-4_15
Publisher Name: Springer, Berlin, Heidelberg
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