From discrete to continuum models of a multi-cellular system
Phillip Murray (University of Dundee)
Thursday 9th November, 2017 14:00-15:00 311B Mathematics and Statistics Building
(Lunch with the speaker will be at One A The Square, leaving from the school front foyer at 12.45.)
The scale on which a given biological problem is defined depends on a range of factors (e.g. availability of experimental data and computational tools, preferences of the modeller etc.). Historically, multi-cellular systems were described using continuum models. Amongst the advantages of this approach is the availability of existing mathematical tools that allow one to analyse models and gain qualitative insights. More recently, discrete cell-based models have been used to study multicellular systems. Amongst their advantages are that they are conceptually easy to communicate and can naturally accommodate features such as heterogeneity and stochasticity. As these (typically N-body) problems are solved using brute force approaches, it can be difficult to gain qualitative insight from the computed solutions.
In this talk I will describe how to take the continuum limit of a particular family of discrete cell-based models. By performing a travelling wave analysis on the resultant equations, I will describe interesting features of the underlying simulations and show how they can be qualitatively related to the model parameters.