Mathematical and computational modelling of temporal and spatiotemporal phenomena on a number of areas in the life sciences, including developmental biology, physiology and cancer biology.
I am an applied mathematician. My research is interdisciplinary and involves constructing mathematical models of spatiotemporal processes in biology. The aim is to represent within a mathematical framework the key features in poorly understood biological and medical systems with the view to enhance our scientific understanding through analysis of the models. My main research is in biological and medical systems which involve spatiotemporal dynamics. The models and their study suggest experimental avenues which help to increase our biological understanding and highlight the practical importance of mathematical models.
I have worked in a number of diverse areas but have focussed primarily on: self-organisation during embryonic development; normal and abnormal wound healing; cancer growth. The unifying underlying theme in these seemingly quite different areas is that of the spatiotemporal dynamics of cell movement and differentiation being determined by cell signalling and response to interacting chemical and mechanical cues. These processes act across several different length and time scales and most of my research has concentrated on modelling at one particular scale, and using mathematical techniques and numerical simulation to thoroughly investigate the derived models in order to gain insight into the biology. This is a necessary precursor to my more recent interests, which are to couple models across many different scales.