The development of a primary solid tumour (e.g., a carcinoma) begins with a single normal
cell becoming transformed as a result of mutations in certain key genes (e.g. P53), this leads to uncontrolled proliferation. An individual tumour cell has the potential, over successive divisions, to develop into a cluster (or nodule) of tumour cells consisting of approximately 106 cells. This avascular tumour cannot grow any further, owing to its dependence on diffusion as the only means of receiving nutrients and removing waste products. For any further development to occur the tumour must initiate angiogenesis. Angiogenesis, the formation of blood vessels from a preexisting
vasculature, is a process whereby capillary sprouts are formed in response to externally
supplied chemical stimuli. The sprouts then grow and develop, driven initially by endothelial cell
migration, and organise themselves into a dendritic structure. Subsequent cell proliferation near the sprout-tip permits further extension of the capillary and ultimately completes the process.
After the tumour has become vascularised via the angiogenic network of vessels, it now has the
potential to grow further and invade the surrounding tissue. There is now also the possibility of tumour cells finding their way into the circulation and being deposited in distant sites in the body, resulting in metastasis.
In this talk we present two applications of the hybrid discrete/continuum mathematical modelling
technique which focus on the processes of (i) angiogenesis and (ii) invasion. Each of the
mathematical models consist of systems of partial differential equations describing the reaction and diffusion of different chemicals, the extra-cellular matrix (ECM) coupled with either endothelial cells or tumour cells. The hybrid model allows one to easily link the macro-scale to the micro-scale (individual cell) and therefore enables us to model migration at the level of discrete cells whilst still allowing the chemicals (e.g. TAF, MDE, ECM, oxygen) to remain continuous. Hence it is possible to include micro-scale processes both at the cellular level (such as proliferation, branching, anatomosis, cell/cell adhesion) and at the sub-cellular level (such as cell mutation properties). (i) The angiogenesis model describes the formation of a capillary sprout network in response to chemical stimuli (tumour angiogenic factors, TAF) supplied by a solid tumour and interactions with the extracellular matrix. We examine the impact of tumour geometry (i.e. different TAF sources) on these structures - particularly network connectedness (anastomosis density) and discuss implications for drug delivery to the tumour.
(ii) In the invasion model, we focus on four key variables implicated in the invasion process,
namely, tumour cells, host tissue (ECM), matrix-degradative enzymes (MDE) associated with
the tumour cells and oxygen supplied by the angiogenic network. We consider a heterogeneous
tumour population made up of several different phenotypes. This in turn allows us to discuss
the impact of the microenvironment on both tumour morphology and genetic makeup.
Audio (MP3 File, Podcast Ready)
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