What I’d like to know is why is a mathematician here?

By John Terry

It’s a question I’ve been asked more than once, and one that will be asked more often, as mathematical and computational tools become increasingly used in the diagnosis, prognosis and treatment of disease.

So why is a mathematician here, and what does a mathematical model offer? A mathematical model – formed from a set of differential equations – describes how something evolves over time. This is potentially significant for medicine since for many chronic health conditions symptoms can wax and wane over time, they can be non-specific and the condition can progress in ways that can be difficult to predict.

A good example is epilepsy: a serious neurological condition which is characterised by the tendency to have recurrent, spontaneous seizures, at apparently random intervals.

At present epilepsy is often difficult to diagnose quickly. To meet the definition of having “recurrent, spontaneous, seizures” you must have at least two or more. Currently, a GP or neurologist can take a case history from which it may be possible to diagnose, but usually one or more diagnostic tests are needed, using a device called an electroencephalogram (EEG).

The EEG is a set of electrodes that are placed on the scalp and measure the electrical activity that emerges from the activity of thousands of neurons in the cortex (the upper layer of the brain) beneath the electrode.

A routine EEG might last for up to an hour, or longer; sometimes an overnight EEG, or a portable kit can be used to take recordings over several days. Neurologists use this test to look for “signatures” of seizures; typically highly rhythmic high-amplitude patterns that appear across several regions of the brain simultaneously. But – by definition – seizures occur at apparently random intervals, so what happens if a seizure doesn’t happen during the EEG test?

Here in the Centre for Biomedical Modelling and Analysis in Exeter, we have been developing a new approach for diagnosing epilepsy based on research that we have published since 2012. Our research has shown that the electrical activity within brain regions, and the way in which these regions communicate with each other, is altered in people with epilepsy and this provides the environment within which seizures can emerge.

The approach we propose, which has been published in the leading journal Epilepsia, uses information contained in the EEG to create a computer model representation of the brain. The computer model can then be used to see how the brain activity of the individual changes over time, and in particular do we see seizures occurring? If we do, then it suggests that the individual is likely to have epilepsy. One of the many advantages of our approach is that we do not need to wait for seizures to occur in real-life. We can recreate a year’s worth of brain activity in a matter of minutes.

Our preliminary findings – where we studied 38 people who were suspected of having epilepsy – suggest that we can now use just 20 seconds of EEG data and deliver a similar level of performance to what is currently achieved clinically through the monitoring methods I described early.

We are very excited by what this new diagnosis could offer, and we’re working with clinical partners to expand the number of people in our study, and to design a computer tool that can assist neurologists in the diagnostic process.


A computational biomarker of idiopathic generalized epilepsy from resting state EEG by Helmuth Schmidt, Wessel Woldman, Marc Goodfellow, FA Chowdhury, M Koutroumanidis, S Jewell, MP Richardson and John R Terry is published online by Epilepsia.

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