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An avascular tumour growth model with random variation
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Ang, K. C., & Tan, L. S. (2003, December). An avascular tumour growth model with random variation. Paper presented at the 8th Asian Technology Conference in Mathematics, Hsin-Chu, Taiwan.
A mathematical model is developed to describe the processes of avascular tumour growth. The
tumour is treated on a macroscopic perspective, in which the spatio-temporal dynamics of
cell concentrations are modelled based on reaction-diffusion dynamics and mass conservation
law. Novel features of the model include the dependence of the cell proliferation rate on the
growth inhibiting factors secreted by necrotic cells and the incorporation of random variation
to the mitotic rate and nutrient supply. It is assumed that these random components play an
important role in the tumour’s asymmetric growth. With the aid of computational technology,
numerical techniques are used to investigate the growth patterns of the proliferating, quiescent
and necrotic cell densities in response to changes in various model parameters. The biological
and clinical implications of these results are discussed.
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