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Title: An avascular tumour growth model with random variation
Authors: Ang, Keng Cheng
Tan, Liang Soon
Issue Date: Dec-2003
Citation: 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.
Abstract: 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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