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.

Solid tumours grow through two distinct phases: the avascular and the vascular phase. During the avascular growth phase, the size of the solid tumour is restricted largely by a diffusion-limited nutrient supply and the solid tumour remains localised and grows to a maximum of a few millimetres in diameter. However, during the vascular growth stage the process of cancer invasion of peritumoral tissue can and does take place. A crucial component of tissue invasion is 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 relatively simple mathematical model of cancer cell invasion of tissue (extracellular matrix) which focuses on the role of a generic matrix degrading enzyme such as uPA. The model consists of a system of reaction-diffusion-taxis partial differential equations describing the interactions between cancer cells, the matrix degrading enzyme and the host tissue. The results obtained from numerical computations carried out on the model equations produce dynamic, heterogeneous spatio-temporal solutions and demonstrate the ability of a rather simple model to produce complicated dynamics, all of which are associated with tumour heterogeneity and cancer cell progression and invasion.

The ability of cancer cells to break out of tissue compartments and invade locally gives solid tumours a defining deadly characteristic. One of the first steps of invasion is the remodelling of the surrounding tissue or extracellular 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 (MMPs), by the cancer cells to break down ECM proteins. Degradation of the matrix enables the cancer cells to migrate through the tissue and subsequently to spread to secondary sites in the body, a process known as metastasis. In this paper we undertake 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. Cancer cells react chemotactically and haptotactically to the spatio-temporal effects of the uPA system. The results obtained from computational simulations carried out on the model equations produce dynamic heterogeneous spatio-temporal solutions and using linear stability analysis we show that this is caused by a taxis-driven instability of a spatially homogeneous steady-state. Finally we consider the biological implications of the model results, draw parallels with clinical samples and laboratory based models of cancer cell invasion using three-dimensional invasion assay, and go on to discuss future development of the model.

In the present study, the nanoindentation creep behaviour of untreated and ultraviolet (UV) treated polydimethylsiloxane (PDMS) samples was investigated, accompanied with adhesion analysis and Fourier transform infrared spectroscopy (FTIR) characterisation. Different hold times, in the range of 5-2000 s (at 10 mN of applied load), were incorporated into each nanoindentation measurement. The increase in hold time results in an increase in change in depth of the indenter in both samples. The error in hardness/modulus due to creep can be neglected for hold times of y400 s or more for untreated PDMS and y200 s or more for UV treated PDMS. The FTIR obtained data revealed surface deterioration, while the bulk nanomechanical properties were almost identical. A decrease in adhesive energy in the case of UV treated PDMS was observed, indicating that adhesive forces play a significant role at the nanometre scale in the indentation tests (real contact area determination during nanoindentation measurements).

Tumor survival, growth and dissemination are associated with the formation of both new blood vessels (angiogenesis) and new lymph vessels (lymphangiogenesis). A mathematical model of tumor lymphangiogenesis was recently developed by the authors, based on experimental results established in the last five years. The model consists of a coupled system of eight parabolic equations. In this paper we prove existence and uniqueness of a solution for this system, for all t>0.