Modelling phenotypic and spatial heterogeneity in solid tumours
In cancer, treatment failure and disease recurrence have been associated with tumour heterogeneity, where cells with different traits (i.e., phenotypes) coexist. Mathematical modelling is an effective tool to understand how the tumour micro-environment drives intra-tumour heterogeneity and to identify effective treatment strategies. In this talk, I will focus on the role that oxygen levels play in the dynamics of a population of tumour cells structured according to their stem cell propensity. I will introduce a mathematical model that describes the growth of cancer cells in a slice of tissue which is oxygenated from the boundary by a vessel. The model consists of a system of coupled non-local partial differential equations that links the phenotypic evolution of tumour cells to the local oxygen levels. By leveraging numerical bifurcation analysis and dynamic simulations, I will explore how heterogeneity emerges and evolves during tumour development. The results presented give insight on the critical role that oxygen levels play in shaping tumour composition and determining its ability to invade. If time permits, I will also discuss extensions that account for treatment with radiotherapy.