How do cell crowding and starvation affect avascular tumor growth of the EMT6/Ro tumor?

Here we re-examine experimental in vitro data for the EMT6/Ro tumor volume and viable rim thickness. This shows that the growth speed is constant in time, and independent of nutrient concentration at large concentrations, but that the viable rim thickness increases in this high concentration regime. We then present a simple mechanistic reaction-diffusion equation that includes crowding and starvation effects, and show that the model qualitatively captures the experimental observations. Moreover, the model predicts that the cancer cell concentration is characterised by a wave pulse (soliton), and the pulse shape is explored through zero th order perturbation analysis corresponding to large wave speeds. It is shown that this zeroth order term is dominant for the experimental condition, further indicating that the non-linear reaction governs the pulse characteristic shape. Finally, at low nutrient concentrations we find that the front is a pulled-front, that is, the growth speed is determined by the cell multiplication at the wave front edge in accordance with earlier modelling approaches.