One of the interesting and important aspects of this work is visualising the dynamics of mathematical equations that model processes which vary with time. It can be awe-inspiring to watch a computed surface that was hidden in the equations appear on the computer screen as a beautiful, artistic object. Indeed, many people know me because of images I have created – particularly one which I then went on to crochet as a beautiful three-dimensional structure. This attracted worldwide interest and I now regularly receive emails from other scientists who have learnt about my work and want to use my methods for their applications.
How can a neuron be the same as a power plant?
Currently, one of my favourite research projects is a collaborative study with Arthur Sherman at the National Institutes of Health in Bethesda, USA. The project looks at the behaviour of neuron cells in the brain. The membrane that encloses the cell contains tiny channels through which ions like potassium or calcium can enter and exit the cell. The chemical processes that regulate these channels produce electrical currents that generate a varying voltage potential across the cell membrane. This oscillatory electrical activity is the basis for all cell signaling in the brain, which is needed to initiate muscle contraction, tissue growth, insulin secretion, and so on. Our goal is to understand how this process can be influenced so that we may be able to control or even cure diseases like Parkinson’s and diabetes.
My contribution to the project is to determine the boundaries of particular behaviour. For example, in laboratory experiments extra electrical current is applied to a neuron cell in order to measure its response. The oscillatory electrical activity of the cell membrane is disturbed, which influences the calcium uptake of the cell. With my computational methods, I can find the precise boundary between a net increase in calcium uptake (low voltage) and a net decrease (high voltage), based on the theoretical equations of the process. From the results I can tell the experimentalist how long to apply the added current of a certain strength, in order to get the required effect.
From the point of view of engineering mathematics, the cell activity is like an electronic circuit and it is no surprise that the model equations are, in fact, rather similar. This can often cause great confusion for the non-specialist: surely, a neuron cell cannot be the same as an electrical power plant? Indeed it is not, but it is quite a mathematical challenge to explain why they are different. The mechanisms for creating a current and how this influences the voltage potential are rather similar, albeit on completely different scales. Hence, the equations that describe these processes are very similar, and the techniques that one uses to study their dynamics work for both.
I like this property of mathematical equations
I very much like this property of mathematical equations. As soon as the equations are there, one can forget about their physical meaning and study them in their own right. Only at the end must the mathematical results be translated back to what it means for the neuron cell – or the power plant for that matter. The mathematical analysis naturally extracts common features of applications that lead to similar equations, so in a mathematical sense we know precisely what the effects of the similarities are. Engineering mathematics, therefore, is in a unique position to point out where techniques that are commonly used in, say, power electronics may also be beneficial in a seemingly completely different area, such as neuron science. This breadth of mathematics is precisely what is needed for making substantial progress in modern technologies.
Given that it is such an interesting and exciting area in which to work, I do find it surprising that there are so few women working in this field. Most people would agree that it is not easy to have a successful academic career of any kind – you have to work hard and be very good at what you do. So everybody, men and women alike, has moments of doubt – are you good enough, can you do it, why not just quit and give it all up? Why is it then that women tend to lose their confidence so much quicker?
From talking to other academics, I have formed the opinion that there is a big difference in the way others influence this personal battle. Men rarely need to defend their career choices against critical comments from close friends or family, a supervisor, or head of department. Women, on the other hand, often get well-meant, but negative advice from those who should have been giving encouragement and support. I know from personal experience that it is, therefore, extremely important to be inspired by successful role models.
At the moment there is not a single female professor in the Engineering Faculty and only 11 per cent of the Faculty’s full-time academic staff are female. This compares with 34 per cent of full-time female academic staff across the University as a whole. For undergraduate students, the number of females in the Engineering Faculty is 14 per cent, compared with 52 per cent of females across the whole University. Hence, it is clear that engineering has a long way to go. More female role models in engineering would be key to changing our (incorrect) opinions that engineering is just for men.