Statistical modelling of cell movement

Many important biological processes, such as wound healing, tissue development and cancer cell invasion, are based on the collective movement of cells. One of the main mechanisms for directed cell movement is chemotaxis, where cells follow chemical gradients (chemoattractants) present in their environment. These gradients might arise from the presence of a local source of chemoattractant or due to local depletion of the chemical in the environment (Tweedy et al. 2016). An example of the former scenario is the migration of breast tumour cells that respond to the epidermal growth factor released by macrophages. In an attempt to acquire a deeper understanding of the mechanisms behind cell movement many population based models have been formulated using partial differential equations, with very few of them attempting to fit these models to actual data. In this paper, we propose a model that describes the movement of any individual cell being driven by an external resource gradient using SDEs of the form: