A Hybrid Mathematical Model of Solid Tumour Growth: Bridging the Genotype to Phenotype Chasm

Cancer is a complex, multiscale process, in which genetic mutations occurring at a subcellular level manifest themselves as functional changes at the cellular and tissue scale. Existing models of solid tumour growth tend to focus on a single spatial scale. Bigger challenges for the future lie in developing models that combine phenomena that act on different scales and developing models of genuine clinical relevance. Much of the vast amount of data being collected concerning cancer is at the molecular scale using micro‐array based methods. Whilst some insight can be obtained by examining the similarity or variation in micro‐arrays from different cell lines, this gives little indication of the multitude of processes that might be triggered by such differences. Here we shall present a new technique that hopes to bridge the chasm between gene expression and cell phenotype by using a mathematical model that treats the genotype to phenotype mapping as a complex neural network. We shall consider this in the context of cancer and present a hybrid model of tumour invasion. This model considers the tumour as a collection of many interacting individual cancer cells and the environment through which the cells grow and migrate as a system of reaction diffusion equations. We will discuss the importance of the microenviroment, not only on tumour morphology but also on evolution of the tumour population. In this talk we discuss a hybrid discrete/continuum mathematical model which describes the invasion of host tissue by tumour cells and examines how changes in this tissue microenvironment may influence mutations at the gene scale and subsequently effect the cell at the phenotype scale (e.g. cell‐cell adhesion, proliferation). This in turn allows us to examine the effects of such micro‐scale changes upon the overall tumour morphology.