Interfacial properties in a discrete model for tumor growth

BELÉN MOGLIA ; NARA GUISONI; EZEQUIEL V. ALBANO

PHYSICAL REVIEW E - STATISTICAL PHYSICS, PLASMAS, FLUIDS AND RELATED INTERDISCIPLINARY TOPICS

APS - American Physical Society

Año: 2013 vol. 87 p. 327131 - 3271310

1063-651X

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 beta = 0.32(2) that governs the early time regime, (ii) the roughness exponent alpha = 0.49(2) related to the fluctuations in the stationary regime, and (iii) the dynamic exponent z = alpha/beta ~ 1.49(2), which measures the propagation of correlations in the direction parallel to the interface, e.g., ξ ~ t ^(1/z) , where ξ is the parallel correlation length. Therefore, the interface belongs to the Kardar-Parisi-Zhang 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 or tumor.