Modelling spatial heterogeneity in 3D tumour growth driven by phenotypic changes due to local oxygen concentration

Supervisor: Dr Cicely Macnamara

School: Mathematics and Statistics 


Tumour masses contain spatially heterogenous populations of cells, typically structured by their local environment along with their response to that environment. Cell phenotypes (broadly categorised as behaviours specific to the cell) govern this structuring. One driver of phenotype is cell response to local oxygen concentration i.e. cell behaviour changing based on a cell’s access to this vital nutrient. Hypoxia is the term given to describe tissue/cells with a low supply of oxygen. Hypoxic cells may respond aggressively, switching from healthy behaviours to more malignant ones. Indeed hypoxia is frequently indicated in the epithelial-to-mesenchymal (EMT) transition in which cells change from being proliferative, locally adhesive and with little motility to favouring motility, breaking adhesive bonds and invasion. EMT is a hallmark of cancer [1]. In this project we will use a previously developed c++ 3D off-lattice agent-based multi-scale model [2] which simulates the behaviour of, and spatio-temporal interactions between various tumour agents (namely cells and blood vessels) to investigate how tumour growth patterns and inherent spatial heterogeneity are driven by oxygen phenotypes of cells. Within the existing model mechanical interactions between agents occur through repulsion and adhesive forces and these are coupled to a finite element solver which solves a reaction-diffusion equation for chemical substances (e.g. oxygen) which diffuse throughout the 3D tissue domain from sources (e.g. blood vessels) and are consumed by agents (e.g. cells). Agent behaviour is governed both by the mechanical interactions and changes to their phenotype. In this project we will allow cells to sample across a discrete range of phenotypes representing a continuum between normoxic and hypoxic behaviour in order to investigate how cell phenotype is structured by the local environment and how in turn cell phenotype affects patterns of tumour growth. Thus allowing us to better understand the specific mechanisms that occur in the tumour microenvironment and underpin tumour development. This project seeks to apply an agent-based approach to compare to an earlier continuous PDE formalism of phenotypic heterogeneity in vascularised tumours [3]. The project would suit a student interested in mathematical and computational biology and/or cancer modelling.

[1] Hanahan & Weinberg doi: 10.1016/j.cell.2011.02.013

[2] Macnamara et al. doi:10.1016/j.jocs.2019.101067

[3] Villa et al. doi: 10.1137/19M1293971