System Dynamics at the Physiological and Tumour Level

Abstract

Cancers are complex dynamical systems dominated by non-linear processes. As a result, most critical system parameters exhibit significant temporal and spatial heterogeneity. This variability, while critical to the ability of cancers to adapt to a wide range of environmental perturbations including therapy, tends to be lost in molecular-level data which is typically an ‘average’ value for large numbers of heterogeneous tumour cells obtained at a single time point. The role of mathematical modelling in cancers at a tumour level is to identify the first principles that govern tumour growth, invasion, metastases, and response to therapy. Tumour biologists and oncologists often dismiss quantitative methods with the statement that cancer is ‘too complex’ for mathematical modelling. In fact, lessons from the history of physical sciences demonstrate that the opposite is true. While complex systems may be difficult to model, they are impossible to understand intuitively. Biologically realistic mathematical models are necessary to transform the reductionist approach of modern cancer biology into comprehensive models of the host-cancer interactions that govern the dynamics of tumour growth and therapy.