Modelling Cell Migration in Cancer Spread as a Response to Multi-Cue Heterogeneous Environments: A Kinetic Approach

Understanding the microscopic mechanisms that influence cancer cell migration is a problem of utmost interest in cancer research, as these processes are responsible for the progression and dissemination of the tumour cells into the body. Cells perform directed motion in response to external stimuli, which they detect by sensing the environment. Precisely, cells have to sort and combine these different, and potentially competitive, stimuli, which can have both a biochemical and biophysical nature and characterise the multi-cue environment where cells move. In this chapter, we review a possible approach for the description and study of this problem, which is based on the classical kinetic equations implementing velocity-jump processes. We derive the kinetic models from the microscopic stochastic processes underlying the tactic mechanisms driving cell migration and we present three different cases of study, aimed at showing cell behaviour in response to different superposing stimuli.