Prediction of traveling front behavior in a lattice-gas cellular automaton model for tumor invasion

Abstract

a b s t r a c tCancer invasion is the process of cells detaching from a primary tumor and infiltrating the healthy tissue. Cancer invasion has been recognized as a complex system, since a tumor's invasive behavior emerges from the combined effect of tumor cell proliferation, tumor cell migration and cell-microenvironment interactions. Cellular automata (CA) provide simple models of self-organizing complex systems in which collective behavior can emerge out of an ensemble of many interacting ''simple'' components. Here, we introduce a latticegas cellular automaton (LGCA) model of tumor cell proliferation, necrosis and tumor cell migration. The impact of the tumor environment on tumor cells has been investigated in a previous study. Our analysis aims at predicting the velocity of the traveling invasion front, which depends upon fluctuations that arise from the motion of the discrete cells at the front. We find an excellent agreement between the velocities measured in simulations of the LGCA and an analytical estimate derived in the cut-off mean-field approximation via the discrete Lattice Boltzmann equation and its linearization. In particular, we predict the front velocity to scale with the square root of the product of probabilities for mitosis and the migration coefficient. Finally, we calculate the width of the traveling front which is found to be proportional to the front velocity.

A parallel implementation of an off-lattice individual-based model of multicellular populations

“…By imposing that the physical representation of cells is restricted to a fixed geometric lattice and updating their location in terms of rules or the minimisation of a heuristic potential function, lattice-based models such as cellular automata [7,8] and the cellular Potts model (CPM) [9,10,11] offer a simple description of the dynamics of cells within the population. This typically makes computation less expensive.…”

Mathematical Ecology of Cancer

“…Recent mathematical modelling has focused on various aspects of tumor invasion. Models are of the form of advection-reaction-diffusion equations and transport equations [55] on the one hand and individual based models (cellular automata [29], Potts model etc., [56]) on the other. The choice of model is largely guided by the available data.…”

Investigation of the Migration/Proliferation Dichotomy and its Impact on Avascular Glioma Invasion

“…It has already been shown (see [14] for example) that the macroscopic mean-field description generally fails to evaluate the exact behavior of the invasive front as observed in the LGCA model. This is mainly due to the fact that correlations built by the local fluctuating dynamics at the tip of the front are neglected in the macroscopic description (see also the discussion below for critical perspectives).…”

“…However, this estimate loses accuracy for large values of the mitotic rate and overestimates the LGCA front speed when one uses a "naive" mean-field approximation [14] as our RDE system (4.18), in which correlations built by the local fluctuating dynamics at the tip of the front are neglected. An alternative mean-field approach has been proposed by Hatzikirou and coworkers, in which a simple RDE model of tumor growth is derived as a cut-off mean-field approximation of a LGCA model [14]. Such a cut-off reaction-diffusion approach enables to phenomenologically include the effect of the foremost single cell fluctuations and would allow, in our current model, for an accurate evaluation of the traveling wave speed.…”