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Recent experimental results suggest that during proliferation, tumour cells express growth factors that modify their growth dynamics. In this paper we extend the standard model of avascular tumour growth to study the effect that two types of growth factors (localised or nondiffusible and diffusible) can have on the tumour's development. In both cases we assume that the growth factor is produced in inactive form and becomes activated when it binds to a tumour cell. We show how the inclusion into the model of such GFs endows the tumour with history dependence, in that its evolution depends not only on its structure at a given instant but also on its structure at earlier times. We also present numerical simulations to illustrate the various ways in which the two types of growth factors affect the tumours' growth dynamics. The physical implications of the results are discussed briefly and several experiments are suggested which could be performed to validate the model hypotheses and results.

Original publication




Journal article


Mathematical Models and Methods in Applied Sciences

Publication Date





541 - 568