ABSTRACT

This chapter analyzes the metastatic invasion of tissue by cancer cells with a system of delay partial differential equations. One of the first steps of invasion is the remodelling of the surrounding tissue or extra cellular matrix (ECM) and a major part of this process is the over-expression of proteolytic enzymes, such as the urokinase-type plasminogen activator (uPA) and matrix metalloproteinases, by the cancer cells to break down ECM proteins. The chapter undertakes an analysis of a mathematical model of cancer cell invasion of tissue, or ECM, which focuses on the role of the urokinase plasminogen activation system. The model consists of a system of five reaction–diffusion–taxis partial differential equations describing the interactions between cancer cells, uPA, uPA inhibitors, plasmin, and the host tissue.