An Avascular Tumour Model With Spatio-Random Supply of Nutrients

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 a spatio-random supply of nutrients to govern cell growth and death. It is assumed that the random component in the nutrient supply 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.