
Overall, I'm interested in the applications of mathematics to medicine and physiology, and to biology in general. In particular, the mathematical methods I tend to use are dynamical systems, differential equations, and numerical methods. Of greatest interest to me are spatial and temporal pattern formation, oscillations, nonlinear waves, and excitable systems.
I'm always looking for good PhD or MSc students to join the projects. I'm also happy to supervise students for summer research projects.
Airway smooth muscle and asthma
I'm working with Mike Sanderson, Jason Bates, AnneMarie Lauzon and Merryn Tawhai to try and understand what controls the contraction of airway smooth muscle. When this goes wrong and contracts too much you get asthma, so it's a problem of major concern. We're constructing mathematical models of the calcium dynamics of an airway smooth muscle cell, and trying to understand how this interacts with the crossbridges to cause contraction.
Currently I have two postdocs (Antonio Politi and Amanda Elvin) and a PhD student (Inga Wang) working on this project.
Saliva secretion
...is regulated by the calcium dynamics of parotid acinar cells. Ted Begenisich, Jim Melvin, David Yule, Trevor Shuttleworth, Edmund Crampin and I are trying to understand how this works. This involves models of fluid secretion and fluid transport and how this is linked to calcium dynamics and ion channels.
Elan Gin is a PhD student working on this project.
GnRH neurons
The secretion of gonadotropinreleasing hormone (GnRH) is crucial for the control of development, fertility, maturation, etc. I'm working with Allan Herbison to construct models of electrical spiking and calcium oscillations in GnRH neurons, to try and understand better how GnRH secretion is controlled.
Wen Duan is a PhD student working on this project.
Calcium dynamics
Calcium is important in practically every cell type, and controls a variety of cellular processes. For example, I'm working with Peter Hunter and Mark Cannell on how to model calcium in cardiac cells, and with Martin Falcke on how to construct stochastic models of calcium dynamics. The mathematics of calcium models is being studied by Vivien Kirk, Martin Wechselberger and myself in a project that involves a lot of nonlinear bifurcations and dynamical systems. I wish I understood it. Vivien has a couple of students working on these projects.
My PhD student on this project is Shawn Means.
