An agent-based modelling framework for tumour growth incorporating mechanical and evolutionary aspects of cell dynamics

We develop an agent-based modelling framework for tumour growth that in-corporates both mechanical and evolutionary aspects of the spatio-temporal dynamics of cancer cells. In this framework, cells are regarded as viscoelastic spheres that interact with other neighbouring cells through mechanical forces. The phenotypic state of each cell is described by the level of expression of an hypoxia-inducible factor that regulates the cellular response to available oxygen. The rules that govern proliferation and death of cells in different phenotypic states are then defined by integrating mechanical constraints and evolutionary principles. Computational simulations of the model are carried out under a variety of scenarios corresponding to different intra-tumoural distributions of oxygen. The results obtained, which indicate excellent agreement between simulation outputs and the results of formal analysis of phenotypic selection, recapitulate the emergence of stable phenotypic heterogeneity among cancer cells driven by inhomogeneities in the intra-tumoural distribution of oxygen. This article is intended to present a proof of concept for the ideas underlying the proposed modelling framework, with the aim to apply the related modelling methods to elucidate specific aspects of cancer progression in the future.