Deterministic Convection-Diffusion Approach for Modeling Cell Motion and Spatial Organization: Experimentation on Avascular Tumor Growth

To investigate cell spatial organization in complex biological dynamics, an individual-based model that represents cell motion in a deterministic way is proposed and then experimented on avascular tumor growth case. Cell motion remains a fundamental process in many complex biological dynamics such as morphogenesis or cell aggregation. Mathematical models are often used to represent cellular motility and spatial dynamics. However, the variability and the interactions between individuals, which are crucial to build accurate predictive models, are difficult to represent using differential equations. We propose, in this paper, an individual-based approach that allows describing cell motion at deterministic way with diffusion and convection processes. Such approach is built using Smoothed Particle Hydrodynamics (SPH) method and allows representing spatially each cell and its basic biological primitives. The relevance of this approach is illustrated on avascular tumor growth to study the effects of microenvironment (nutrients) and cell individual motion in tumor development. The results shown that the model can qualitatively predict a number of cellular behaviors that have been observed in experiments.