Connecting mesoscale and macroscale models of cellular migration

Continuum, partial differential equation (PDE) descriptions of cell movement are often employed in modelling studies because of their analytical tractability, and the wealth of numerical methods available for their solution. Derived from, for example, conservation of mass approaches these models describe how cell density changes with time due to random movements of cells, different types of taxes/kineses and cell proliferation/death. In the main, these processes are represented in the model equations in a phenomenological manner, providing gross descriptions not necessarily derived from the underlying cell behaviour. Moreover, choice of a specific particular functional form is generally based on calibration arguments rather than any physical connection with the underlying individual-level properties of the cell processes.

However, with recent advances in experimental technologies, we can now characterise these systems on finer spatial and temporal scales, being able to visualize events taking place on single-cell and intracellular levels. This means we can formulate hypotheses on different scales, asking how population-level phenomena arise from the combined effects of several cell-scale behaviours. In this talk I will consider effects such as cell shape and volume, discussing how such phenomena may be modelled at the mesoscale, and how population-level macroscale models may be derived from these descriptions.