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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.

Type

Journal article

Journal

Bull Math Biol

Publication Date

07/1999

Volume

61

Pages

601 - 623

Keywords

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