Interfacial properties of a discrete model for cells cultures

BELÉN MOGLIA; NARA GUISONI; EZEQUIEL V. ALBANO

Kyoto

Workshop; Interface fluctuations and KPZ universality class - unifying mathematical, theoretical, and experimental approaches; 2014

We propose and study by means of Monte Carlo numerical simulations a minimal discrete model for avascular tumor growth, which can also be applied for the description of cell cultures in vitro. The interface of the tumor is self-affine and its width can be characterized by the following exponents: (i) the growth exponent β = 0.32(2) that governs the early time regime, (ii) the roughness exponent α = 0.49(2) related to the fluctuations in the stationary regime, and (iii) the dynamic exponent z = 1.49(2), which measures the propagation of correlations in the direction parallel to the interface, e.g. x ∝ t1/z , where x is the parallel correlation length. So, the interface belongs to the KPZ universality class in agreement with recent experiments of cell cultures in vitro. Furthermore, density profiles of the growing cells are rationalized in terms of traveling waves that are solutions of the Fisher-Kolmogorov equation. In this way, we achieved excellent agreement between the simulation results of the discrete model and the continuous description of the growth front of the culture/tumor.