Almost all our research is devoted to the understanding of complex phenomena associated with nonlinear oscillators.
Oscillations are a universal phenomenon in living systems. They manifest on all
lengthscales ranging from the molecular, through cellular and organ, up to the
whole-body scale, and even to entire populations. Correspondingly, they are
characterised by a huge range of timescales. Familiar examples include the
heartbeat and respiration, the circadian (day-night) cycle, and ovulation
Often, these oscillatory processes interact with each other in very complex ways that can only be understood through the application of ideas and methods from nonlinear dynamics. To understand what is happening, we model the processes with nonlinear oscillators and study their behaviour in the presence of noise (the random fluctuations from the rest of the system). We propose numerical and theoretical methods to deal with coupled ensembles or individual oscillatory processes in a deterministic and/or stochastic way.
We are especially interested in the influence of the oscillators on each other - their mutual interactions. The resultant modulation and synchronisation phenomena occur in physiology in just the same way that they do for coupled oscillators in physics. Comparison of the model phenomena with physiological data measured for healthy subjects in our laboratory and for patients in our collaborating hospitals is illuminating and characterising diverse conditions and diseases.
Applications: So far, we have completed or engaged on studies of the oscillatory changes that take place in healthy ageing, anæsthesia, exercise at altitude, congestive heart failure, hypertension, diabetes mellitus, post-acute myocardial infarction, paraplegia, tetraplegia, and cancer. We have used Bayesian inferential dynamics to model population cycling in ecology and have embarked on a study of the ion channels in cellular membranes, treating the permeating ion as a Brownian particle. Importantly our research is being developed in close collaboration with clinicians, so that potentially useful applications can quickly be spotted and evaluated.
BRACCIA Project: Investigated interactions between the brain and cardiovascular oscillations and how they change in anæsthesia.
Publications include "EUProfile 2009, The Truth About Anaesthesia ".