- BSc Applied Mathematics, Warwick, 1994 (1st class)
- PhD Interdisciplinary Applied Mathematics, Warwick, 1997 (supervisor, Jonathan Sherratt)
- PDRA, University of Utah, 1997-1999
- Lecturer, Loughborough University, 1999-2003; Senior Lecturer, 2003-2004
- Reader, University of Nottingham, 2004-2013
- Professor of Mathematical Biology, 2013-date
I am particularly interested in how to deliver mathematical modelling concepts to life scientists.
I am the Head of the Mathematical Medicine and Biology Research Group.
I lead a Leverhulme Doctoral Scholarships programme in Mathematics for A Sustainable Society and the BBSRC-funded Multiscale Biology Network.
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Current PhD students: Lee Curtin, Linda Irons, Jakub Köry, Tim Whiteley
Previous PhD students: Lindsey Macdougall (2015), Michelle Baker (2015), Georgina Fenton (2014), Sunny Modhara (2014), Sotiris Prokopiou (2013), Wodu Majin (2011), Ioannis Taxidis (2011), Duncan Barrack (2010), Johanna Stamper (2009), Sabine Schamberg (2009), James Smith (2006).
Previous PDRAs: Lloyd Bridge, Alistair Middleton, Stephen Pring, Johanna Stamper, Steve Webb and Hao Zhu
My principal research interests are in the application of nonlinear mathematical models to problems in cell biology, in particular to cancer, angiogenesis (the growth of new blood vessels), developmental biology (both in animals and plants) and neuroscience. I also have an interest in ecology and immunology. I use a variety of mathematical approaches, including models for single cells, populations and tissues, and a range of tools for mathematical analysis and computer simulation. Much of this work is underpinned by multidisciplinary collaborations with life scientists, engineers, computer scientists and other mathematicians (e.g. projects on regenerative medicine and plant root growth, and the Interdisciplinary Angiogenesis Network, ANGIONET).
MODELLING THE MACROPHAGE INVASION OF TUMOURS
Even in the early stages of their development, tumours are not simply a homogeneous grouping of mutant cells; rather, they develop in tandem with normal tissue cells, and also recruit other cell types. Many solid tumours contain a high proportion of macrophages, a type of white blood cell which can have a variety of effects upon the tumour, leading to a delicate balance between growth promotion and inhibition.
ODE model for macrophage-tumour interactions: Initial research concentrated on an ODE model for the anti-tumour effects of macrophages, a type of white blood cell, and results show that while macrophages can strongly affect the cellular composition of a tumour, they cannot eliminate it altogether. Inclusion in this model of a source term of chemical regulator, corresponding to some immuno-therapeutic strategies targeting macrophages, was shown to lead to the possibility of tumour regression. A detailed bifurcation analysis demonstrated the possibility of multiple stable steady states and hysteresis.
Immunotherapy simulation (jpeg).
PDE model -- pattern formation: Tumour growth is very much a spatial phenomenon, and so the natural next step was to include spatial variation. In the consequent PDE model, random cell movement and diffusion of a chemical regulator lead to a pattern forming bifurcation behind a travelling wave front of invading tumour cells. This is explained by the rapid diffusion of chemical regulator leading to a typical long range activation---short range inhibition type mechanism. These results suggest that tumour heterogeneity may arise in part as a consequence of macrophage infiltration.
2d simulation showing evolution of a pattern behind a travelling wave of tumour invasion.
An intuitive explanation for this spatial instability is that given a local perturbation increasing the density of mutant cells, chemical regulator production will also increase locally. Then if the chemical diffuses fast enough, it will act non-locally to activate macrophages to the tumouricidal state and to stimulate an additional influx of macrophages. This will suppress non-local mutant cell growth, whilst enhancing local mutant cell growth, due to the relative suppression of local macrophage activation, so that the original perturbation will grow in time.
PDE model -- spatiotemporal irregularity: Using data from the literature I determined ranges for the parameters governing macrophage motility using a mathematical model of the experimental procedure. Including macrophage chemotaxis with these parameters led to the development of irregular wakes behind the wave front of invading tumour cells. This phenomenon was investigated using domain length as a bifurcation parameter. Stable oscillating solutions with a regular period were found to coexist with stable steady patterns for certain windows in domain length which were deduced to appear at regular intervals. Intuitively the wave front can be treated as a moving boundary, leading to the proposal that as the wave spreads out, the effective domain length passes through a series of bifurcations, so that the solution seen is always transient and irregular.
Snapshots from a two-dimensional simulation illustrating that chemotaxis leads to solutions which are irregular in space and time. For a movie of a similar simulation, click here: Chemotaxis induces spatiotemporal irregularities (mpeg) and another example (mpeg).
Future research will continue to focus on many of the above topics. For PhD opportunities, see: