Analysis of lattice-gas cellular automaton models for tumor growth by means of fractal scaling

Mathematical modeling of tumor development has become a real hype within the last decade. The abundance of mathematical models has created a great need for the validation of their biological relevance. Recently, in order to characterize the tumor growth dynamics, Brú et al. have determined some statistical properties of both in vitro and in vivo solid tumor-surfaces by using fractal scaling analysis. Surprisingly, for all tumor surfaces, the statistical observables converged to a unique set of critical exponents which indicates some common features of tumor growth dynamics (linear growth rate, growth activity limited to the outer rim of the tumor mass and diffusion of newborn tumor cells on the surface from lower to higher curvature regions, typical of Molecular Beam Epitaxy (MBE) Universality). Here, we develop and analyze a lattice-gas cellular automaton (LGCA) model of solid tumor growth. Random walk dynamics are assumed for tumor cell migration and a density-dependent birth process describes the cell mitotic dynamics. Fractal scaling analysis shows that for any parameter variation the model interface dynamic follows Edward - Wilkinson (EW) Universality, which differs from experimental findings. However, the model recovers some features, i.e. linear growth rate for tumor size and proliferative activity restricted to the outer layer, observed in experiments.