Mark Chaplain (Applied Mathematics, University of Dundee UK)
Abstract:Cancer growth is a complicated phenomenon involving many inter-related processes across a wide range of spatial and temporal scales, and as such presents the mathematical modeller with a correspondingly complex set of problems to solve. This talk will present multi-scale mathematical models for the growth and spread of cancer and will focus on three main scales of interest: the sub-cellular, cellular and macroscopic. The sub-cellular scale refers to activities that take place within the cell or at the cell membrane, e.g. DNA synthesis, gene expression, cell cycle mechanisms, absorption of vital nutrients, activation or inactivation of receptors, transduction of chemical signals. The cellular scale refers to the main activities of the cells, e.g. statistical description of the progression and activation state of the cells, interactions among tumour cells and the other types of cells present in the body (such as endothelial cells, macrophages, lymphocytes), proliferative and destructive interactions, aggregation and disaggregation properties. The macroscopic scale refers to those phenomena which are typical of continuum systems, e.g. cell migration, diffusion and transport of nutrients and chemical factors, mechanical responses, interactions between different tissues, tissue remodelling. The models themselves will range from systems of partial differential equations, to individual force-based models and hybrid discrete-continuum models.