Oxygen induced effects on avascular tumour growth: a preliminary simulation using an adaptive grid algorithm

Cancer cells oxygenation from surrounding healthy tissue influences tumour growth in the avascular phase. The effects induced by oxygen on cancer cells dynamics during their interaction with the urokinase plasminogen activator system, are simulated mimicking hypoxic conditions in the early stage of human tumour proliferation, using oxygen supply parameters determined from in vivo experiments. The system of six coupled partial differential equations, arising from the problem modelling, is solved over a one-dimensional domain implementing a moving mesh numerical technique, using the finite element method. Our preliminary computations show that oxygen concentration at hypoxic conditions cause cancer cells to build inhomogeneous proliferation pattern, similarly to what happens in absence of oxygen.