# Philip Maini

Philip Maini abstract

**Philip K Maini**, Mathematical Institute, Oxford University
Case Studies in Modelling Collective Cell Motion

This talk will review three biological problems in which cell movement plays an important role: (i) acid-mediated cancer cell invasion, (ii) cranial neural crest cell invasion, (iii) intestinal crypt dynamics. Each example will illustrate a particular modelling technique, ranging from (i) coupled systems of partial differential equations, to (ii) a simple hybrid agent-based model, to (iii) an individual discrete-based model. It will be shown that, at least for simple cases, all these models have the same mathematical form for the cell density, namely a nonlinear partial differential equation where the specific form of nonlinearity in the diffusion term is determined by the hypothesised behaviour of cells at the discrete level.