  The advantage of Cellular Potts Model (CPM) is due to its ability for
introducing cell-cell interaction based on the well known statistical model
i.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. These
characters of CPM and LGCA have been combined in a reaction-diffusion frame to
simulate the dynamic of avascular cancer growth on a more physical basis.The
cellular automaton is evolved on a square lattice on which in the diffusion
step tumor cells (C) and necrotic cells (N) propagate in two dimensions and in
the reaction step every cell can proliferate, be quiescent or die due to the
apoptosis and the necrosis depending on its environment. The transition
probabilities in the reaction step have been calculated by the Glauber
algorithm and depend on the KCC, KNC, and KNN (cancer-cancer, necrotic-cancer,
and necrotic-necrotic couplings respectively). It is shown the main feature of
the cancer growth depends on the choice of magnitude of couplings and the
advantage of this method compared to other methods is due to the fact that it
needs only three parameters KCC, KNC and KNN which are based on the well known
physical ground i.e. the Potts model.
