UC Irvine

In this paper we develop a general mixture model that incorporates a non-constant water fraction. A novel energy for the system is devised that allows for different water levels to be considered in the host and viable cell regions. For the first time the energy provides a way to flux the water out of the necrotic core and produce stable tumor spheroids with liquid centers. The model is also capable of producing invasive tumors with a detailed morphology.

Parameter studies are performed to characterize the model. The parameters that can influence the size of the stable tumor and the growth rate are identified and the parameter regimes that can destabilize the tumor are explored. We demonstrate that this model is able to capture a wide range of tumor behavior. In particular, water fraction parameters for the host and viable cell regions allows us to consider the effects of different water fraction levels in the host and viable cell regions.

Finally, the non-constant water fraction model is extended to describe hierarchical structures that incorporate cancer stem cells. This model is capable of producing a detailed invasive morphology that has hierarchical and heterogeneous cell distributions and develops necrotic cores. The model is also capable of forming stable tumors with heterogeneous cell distributions. A parameter study on the positive and negative feedback rates for the stem cell differentiation rate shows how the morphology of the tumor is dependent on the sensitivity to these parameters and possible avenues for therapy are seen.