Mathematical modelling of cancer cell invasion of tissue: The role of the urokinase plasminogen activation system

The growth of solid tumours proceeds through two distinct phases: the avascular and the vascular phase. It is during the latter stage that the insidious process of cancer invasion of peritumoral tissue can and does take place. Vascular tumours grow rapidly allowing the cancer cells to establish a new colony in distant organs, a process that is known as metastasis. The progression from a single, primary tumour to multiple tumours in distant sites throughout the body is known as the metastatic cascade. This is a multistep process that first involves the over-expression by the cancer cells of proteolytic enzyme activity, such as the urokinase-type plasminogen activator (uPA) and matrix metalloproteinases (MMPs). uPA itself initiates the activation of an enzymatic cascade that primarily involves the activation of plasminogen and subsequently its matrix degrading protein plasmin. Degradation of the matrix then enables the cancer cells to migrate through the tissue and subsequently to spread to secondary sites in the body. In this paper we consider a mathematical model of cancer cell invasion of tissue (extracellular matrix) which focuses on the role of the plasminogen activation system. The model consists of a system of reaction-diffusion-taxis partial differential equations describing the interactions between cancer cells, urokinase plasminogen activator (uPA), uPA inhibitors, plasmin and the host tissue. The focus of the modelling is on the spatio-temporal dynamics of the uPA system and how this influences the migratory properties of the cancer cells through random motility, chemotaxis and haptotaxis. The results obtained from numerical computations carried out on the model equations produce rich, dynamic heterogeneous spatio-temporal solutions and demonstrate the ability of rather simple models to produce complicated dynamics, all of which are associated with tumour heterogeneity and cancer cell progression and invasion.