Traveling wave behavior in a two-phase flow model of tumor growth

Tumor growth which undergoes complex bio-mechanical processes has been a significant focus for mathematical modeling, with particular interest in its dynamic behavior. In this paper, we consider a two-phase flow model for describing the dynamics of tumor growth. The model accounts for aggregate cell movement and mechanical interactions between tumor cells as well as cell proliferation. In suitable limits, by using the dynamical systems theory approach, tumor growth in this mechanical model is shown to occur in the form of traveling waves that can propagate either forward or backward, depending on the values of the parameters. Our results, in particular, the wave profiles of tumor cell density are more realistic and explain those obtained in a recently developed simple, experiment-based, model for studying non-spatial dynamics of tumor cells.