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In this paper a mathematical model is developed to describe the migration of labelled particles within a multicell spheroid. In the model, spatial variations in cell proliferation and death create an internal velocity field which leads to redistribution of the labelled and unlabelled cells. By applying a range of numerical and analytical techniques to the model equations, it is possible to show that, whilst the speed with which the labelled cells migrate through the tumour is independent of the type of cells that are labelled, their limiting distribution depends crucially on whether inert polystyrene microspheres or live tumour cells are labelled. These predictions are shown to be in good qualitative agreement with independent experimental results.

Original publication




Journal article


Bull Math Biol

Publication Date





601 - 623


Cell Death, Cell Movement, Cell Proliferation, Mathematics, Microspheres, Models, Biological, Polystyrenes, Spheroids, Cellular, Tumor Cells, Cultured