The initial stage of solid tumour growth is limited by the ability of externally-supplied nutrients to diffuse into the tumour. As the tumour grows the amount of nutrient reaching its centre falls until there is insufficient nutrient there to sustain viable cells. This cell death leads to the formation of a central necrotic core whose size increases as the tumour continues to grow. Thus a well-developed avascular tumour comprises an outer rim of nutrient-rich, proliferating cells and a central core of nutrient-starved necrotic cells, with an intermediate layer of viable, but non-proliferating cells sandwiched between them. A mathematical description of this stage of solid tumour growth lends itself to formulations involving free boundaries. These may be used to mark, for example, the outer boundary of the tumour or the interface between the outer, nutrient-rich portion of the tumour where cells proliferate rapidly and the intermediate region that contains non-proliferating hypoxic cells. In this talk existing models of solid tumour growth that involve free boundaries will be reviewed. Directions for future work will also be mentioned.

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1998-1999 Mathematics in Biology