Interfacial properties of a discrete model for cells cultures.

B. MOGLIA; GUISONI, N.; EZEQUIEL V ALBANO

KYOTO

Workshop; YITP Workshop: Interface fluctuations and the Kardar-Parisi-Zhang (KPZ) universality class; 2014

Yukawa Institute of Theoretical Physics, KYOTO.

We propose and study by means of Monte Carlo numerical simulations a minimal discretemodel for avascular tumor growth, which can also be applied for the description of cell culturesin vitro. The interface of the tumor is self-affine and its width can be characterized by thefollowing exponents: (i) the growth exponent  = 0.32(2) that governs the early time regime,(ii) the roughness exponent  = 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 thedirection parallel to the interface, e.g. xk / t1/z, where xk is the parallel correlation length. So,the interface belongs to the KPZ universality class in agreement with recent experiments of cellcultures in vitro. Furthermore, density profiles of the growing cells are rationalized in terms oftraveling waves that are solutions of the Fisher-Kolmogorov equation. In this way, we achievedexcellent agreement between the simulation results of the discrete model and the continuousdescription of the growth front of the culture/tumor.