A moving mesh study for diffusion induced effects in avascular tumour growth

Studying the dynamical evolution of complex systems as biological ones from the continuum point of view, requires monitoring several parameters involved, whose modelling leads to system of non linear coupled partial differential equations. The interaction of the urokinase plasminogen activator system with a model for cancer cell in the avascular phase is faced with the moving mesh partial differential equation numerical technique, monitoring the dynamical evolution of the system as a function of the diffusion properties of cancer cells and of cell proliferation factor, over a one-dimensional biological domain. The computations are consistent with previous results, confirming that cancer proliferation in the very early stage of invasion occurs through highly irregular spatio-temporal pattern, which depends essentially on cancer motility characteristics, but non-obvious effects are observed which depend on the model proliferation parameters.