Combination of The Cellular Potts Model and Lattice Gas Cellular Automata For Simulating The Avascular Cancer Growth

摘要

The advantage of Cellular Potts Model (CPM) is due to its ability forintroducing cell-cell interaction based on the well known statistical modeli.e. the Potts model. On the other hand, Lattice gas Cellular Automata (LGCA)can simulate movement of cell in a simple and correct physical way. Thesecharacters of CPM and LGCA have been combined in a reaction-diffusion frame tosimulate the dynamic of avascular cancer growth on a more physical basis.Thecellular automaton is evolved on a square lattice on which in the diffusionstep tumor cells (C) and necrotic cells (N) propagate in two dimensions and inthe reaction step every cell can proliferate, be quiescent or die due to theapoptosis and the necrosis depending on its environment. The transitionprobabilities in the reaction step have been calculated by the Glauberalgorithm and depend on the KCC, KNC, and KNN (cancer-cancer, necrotic-cancer,and necrotic-necrotic couplings respectively). It is shown the main feature ofthe cancer growth depends on the choice of magnitude of couplings and theadvantage of this method compared to other methods is due to the fact that itneeds only three parameters KCC, KNC and KNN which are based on the well knownphysical ground i.e. the Potts model.