Auckland Bioengineering Institute


Graham Donovan

donovan-graham

Alumnus profile

After completing a PhD in Applied Mathematics at Northwestern University in 2008, Graham Donovan joined the Auckland Bioengineering Institute to work on multiscale lung modelling with Dr Merryn Tawhai.

Graham's modelling efforts were part of a large project in collaboration with Professor James Sneyd in the Department of Mathematics at Auckland and groups at the University of Massachusetts, the University of Vermont, and McGill University in Montreal. During his time at the institute Graham was working to build a multiscale model incorporating spatial scales ranging from molecule to organ which will further understanding of asthmatic airway hyper-responsiveness.

Graham's other active areas of research included stochastic modelling of optical communication systems, using variance reduction techniques for finding rare events via Monte Carlo simulations, and exploring opportunities in stochastic modelling in immunology.

In 2010 Graham joined the Department of Mathematics here at the University of Auckland as a lecturer in applied mathematics.

Read more information about Dr Donovan's research at his personal website and his University of Auckland staff profile.

Research interests

Lungs, respiration and asthma

It is estimated that 300 million people worldwide suffer from asthma. We have been working on mathematical models of physiological processes associated with asthma, especially airway hyper-responsiveness (AHR). In particular, we have developed a multiscale, spatially-distributed model incorporating four spatial scales (organ, tissue, molecule and cell) in an effort to further understanding of asthmatic AHR. We have also developed models of other physiological phenomena associated with asthma, including bronchial mucosal folding and lung-tissue viscoplasticity.

Rare-event simulation

In many systems perturbed by noise it is rare events that are the behaviors of interest, e.g., the formation of a 35 meter rogue ocean wave or a Category Five hurricane. This is also true of many engineered systems; since they are designed with typical behaviors in mind, system failures are often associated with deviations that are far from the mean. Because of this, such events can be difficult to predict. We have developed mathematical techniques to computationally simulate these rare events, particularly in optical communication systems.

Immunology and lymphocyte movement

In the lymphatic system, in order to facilitate immunological responses, specific rare T-cells must encounter specific antigen presenting cells. It has long been thought that these lymphocytes may simply move randomly about the lymph nodes in order to facilitate these rare interactions. It has recently been proposed that instead, they move about on a structural, reticular network, which may further facilitate such events. We are developing a model of lymphocyte movement on the reticular network to examine the merits of this hypothesis.

Binocular vision and amblyopia

Amblyopia, commonly known as lazy eye, is a relatively common condition occurring in as much as 3% of the population. It is associated with visual deficits, most notably compromised depth perception, and is characterised by anomalous behaviour of the systems that underlie binocular function. Moreover, normal binocular vision itself is poorly understood despite being a fundamental sensory process; improved understanding of the degenerate case of amblyopic vision will also contribute to greater understanding of binocular vision. To that end, we are working to develop a detailed mathematical model of amblyopic vision, using a competition-based model for ocular preference within the primary visual cortex, and a contrast gain-control model of binocular combination.

Selected publications