Integrating Mathematics and Biology in Exercise Sciences


"I may not have gone where I intended to go, but I think I have ended up where I intended to be," author Douglas Adams once said. This is perhaps an apt description for the progression of my scientific career. I have immensely enjoyed this journey, and I feel very privileged to now be able to work as an exercise physiologist.

Exercise science is often seen as a "soft option"--a view almost unanimously voiced by my teachers, parents, and friends when I decided upon my undergraduate course at the University of Birmingham, UK, in 1992. Like many exercise science undergraduates, I suspect, my interest stemmed from my own sporting endeavours at school but also from a desire to understand the integration of our neural, respiratory, cardiovascular, muscular, and skeletal systems required for effective performance. Far from a soft option, then, exercise science is a truly interdisciplinary subject.

An Indispensable Element

Mathematics is one of the many fundamental scientific disciplines that are incorporated in the exercise sciences. Leonardo da Vinci once suggested, "No human enquiry can be a science unless it pursues its path through mathematical exposition and demonstration." This is, perhaps, a particularly appropriate premise for physiology, a quantitative science. So even though I am not a mathematician, mathematics has been an indispensable element in my career.

A MSc in human and applied physiology at Kings College London introduced me to the benefits of applying mathematics to biological problems. It was later on, however, during my PhD at St. George's Hospital Medical School London with Brian Whipp, that these skills were honed and I was able to utilise both experimental and mathematical techniques at my own particular "coal-face": the processes that provide cellular energy. We hope that with a better understanding of what constitutes "normal" function for human exercise, we will (eventually) be able to help patients with chronic diseases such as peripheral or central myopathies, metabolic disorders, and lung diseases that compromise exercise tolerance.

Changes in energy demand, for instance on the initiation of exercise, require the body to adapt quickly. Following many exercise scientists and "... sooty empirics ... having their eyes darkened, and their braines troubled with the smoak of their own furnaces ..." (Robert Boyle, 1627-1691),1 we developed a technique to "functionally track" the dynamics of these adaptations to determine how oxygen is extracted from the air and used to fuel muscular work. The integration of pulmonary gas-exchange measurement and magnetic resonance (MR) spectroscopy thus enabled us to monitor oxygen uptake and "look inside" skeletal muscles to visualise the molecular units of energy exchange during exercise. This required a multidisciplinary approach, so we forged a group encompassing physiologists, biochemists, physicists, and engineers to address the putative controllers of energy provision by oxidative phosphorylation.

MR is a relatively young discipline, owing much to Paul Lauterbur and Peter Mansfield, who jointly received the 2003 Nobel Prize in physiology and medicine for its development. It is also a particularly apt technique to exercise the abilities of a biological mathematician. Indeed, MR draws upon complex mathematical concepts, requiring its users to be familiar not only with computer programming but also with radio-wave detection and amplification, electrical filtering, Fourier transformation, and complex time-domain modelling and integration.

If experiment-based and mathematical deductions are disparate scientific approaches, they coalesce particularly well in human physiology. The dynamics of the numerous and integrated systems that combine to supply, or limit, energy provision lend themselves particularly well to mathematical modelling. Thus, mathematical modelling enabled us to assemble working hypotheses for the signalling processes that increase the rate of oxidative phosphorylation during changes in energy demand, to tease out conclusions in bioenergetic terms, and to use our data predicatively to generate new hypotheses. Mathematical techniques such as superposition and control systems analysis (allowing an internal structure to be assigned to a "black box" control system) also provided us with powerful tools to approach the problems posed by complex biological systems by "rigidly defin[ing] ... areas of doubt and uncertainty" (Douglas Adams).

Mathematical Modelling Without Mathematicians

While there were no dedicated mathematicians in our group, each of us lent our own expertise to implement various modelling strategies (both to maximise the MR technique and to model the biological responses) and interpret parameters and their dynamics in their physiological context. The success of our project owed much to the wonderful friendships that developed within our group. Such relationships need not be based on a mutual understanding of disciplines, but on a mutual affinity for solving the problem at hand. The ability of an interdisciplinary group to observe from many different angles and share thoughts provides a hugely powerful approach to conducting biological experiments. This experience has influenced, and will continue to influence, my future professional choices.

Once my PhD was completed in 1999, I decided to remain in this lab for a first postdoc, continuing our line of investigation. But when considering my next stage in 2001, I was keen to add to the tools I had developed during my 5 years at St. George's. Looking around the world, I became very interested in the superlative exercise physiology laboratory at the University of California, San Diego, which has recently been applying molecular and genetic techniques to investigate exercise intolerance in health and disease.

Peter Wagner supported me in my successful bid for a Wellcome Trust International Research Fellowship and welcomed me to the laboratory. I am, therefore, looking to the future with the positive feeling that I am well trained to apply cellular-to-systemic techniques to investigate the problems posed by the complex integrated biology of exercise. And I shall continue to "pursue [this] through mathematical exposition and demonstration"

With "darkened eyes" and "troubled braines," it is very easy to overlook the key elements of a successful working environment: For me, a friendly and sharing one will top the list. I remain a "sooty" physiologist, not a mathematician, but my experience has been greatly enhanced by the "clean" application of mathematics to physiological problems.

1 I would like to thank Professor Brian Whipp for bringing this to my attention.


Douglas Adams, The Hitchhiker's Guide to the Galaxy. Harmony Books, NY. 1980.

Robert Boyle, The Sceptical Chymist. First printed by J. Cadwell for J. Crooke, London. 1661.

Leonardo da Vinci, Quoted in D. MacHale, Comic Sections, Boole Press, Dublin. 1993.

Follow Science Careers

Search Jobs

Enter keywords, locations or job types to start searching for your new science career.

Top articles in Careers