Multiphase modeling of tumor growth and extracellular matrix interaction: Mathematical tools and applications

In a multiphase modeling framework tumors are described as a mixture of tumor and host cells within a porous structure constituted by a remodeling extracellular matrix (ECM), which is wet by a physiological extracellular fluid. The main focus of the model presented in this article is the description of the mechanical interactions of the growing tumor with the host tissue, their influence on tumor growth, and the attachment/detachment mechanisms between cells and ECM. Starting from some recent experimental evidences, the model proposes to address the interaction forces involving the extracellular matrix via some concepts deriving from viscoplasticity. Then it is applied to describe the growth of tumor cords and the formation of fibrosis.