BioMaths Colloquium - 24/02/2017

BioMaths Colloquium Series - 2016/17

24 February 2017 - 3pm Maths Seminar Room

(room 224 Talbot Building 2nd floor)

From discrete to continuum models of a multi-cellular system

Dr Philip Murray

(Department of Mathematics,University of Dundee, UK) 

Our BioMaths Colloquium Series for the winter term continues with a seminar by Dr Philip Murray from the Department of Mathematics at the University of Dundee. Philip is a mathematician with a wide interest especially in biomedical topics, from Tumour Modelling, Somitogenesis and Hair follicle growth patterning, to DNA repair mechanisms, Intestinal crypt modelling, and Discrete to continuum models of cell populations. The latter will be the subject of his talk.

Abstract

The scale on which a given biological problem is mathematically 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 from the solutions. 

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.  

The discussions will continue over biscuits and tea/coffee after the seminar. 

Hope to see many of you!