What role can mathematics play in better understanding mental health? We spoke to Professor Terry Lyons, a mathematician whose area of expertise has application in understanding complex data real-world data from multiple sources. He is the principal investigator at DataSig, and part of their work uses mathematics to better understand mental health.

This is a transcript of the podcast below, which you can access via the Mental Elf Soundcloud, iTunes or Spotify.


Mathematics and mental health. What is the connection? Except for causing me undue levels of stress in year 10, I’m not sure I’ve ever connected the two. So what can the world of mathematics contribute towards mental health research?

Mental health research has traditionally been the domain of psychologists and psychiatrists; brain people for brain problems. But there is now wide acceptance that mental health is far more holistic than that.

Looking at recent research, we can see that massively diverse aspects of life impact people’s mental health. From the level of access to parks, to the bacteria in their gut.

So I’m setting out on a journey to explore the role of researchers and professionals from different disciplines who have found themselves working in mental health research. Some of whom never even saw it coming.

My name is JJ Buckle, and I am part of the Mental Health Research Matters team. In this episode have my eyes and ears firmly fixed on the world of mathematics.

Our guest today is Professor Terry Lyons from the University of Oxford and the Alan Turing Institute who spoke to me about both his work and the role of the engineering and physical sciences community in mental health research. Let’s meet our guest.


Hi, my name is Terry Lyons. I’m a mathematician. I have been working for many years in an area of mathematics called Stochastic analysis, which is about understanding complex evolving systems.

Perhaps to my surprise, as I’m a pure mathematician interested in foundational work, over the last 10 years, it’s become apparent that the technologies I’ve been developing have some potential for application in understanding complex, messy, evolving, real-world data. And what are the areas where it’s turned out to have some value has been in the area of better understanding what’s going on in the context of a mental health issue.


Okay. And so how long have you been working as a mathematician?


I first really got interested when I was about 11 or 12, I guess I’d been working as a mathematician since I went to university. And that was in 1972.


Now I know what you’re thinking. What does mathematics have to do with mental health? The answer seemingly lies in data.

Over his career, Terry has made significant contributions to the field of mathematics and is most widely known for his development of something called rough path theory in the 1990s.

His theory takes complex, messy evolving data from what is referred to as non-linear sources, ie different sources with different complexities. And tries to make sense of that data for use in real-world applications.

Terry told me about one such application where his abilities and skills in utilising data were invaluable and a mental health project involving participants with different diagnoses.


Our special skill is that we can consume quite complex evolving data and see patterns in it through systematic mathematics that weren’t really that accessible before. And where you would have needed much, much more data to see the patterns than you do with the mathematics we’re involved with.

To give you a very concrete example. I was involved with analysing data from a trial. And in that trial, the participants, about 115 of them or something like that, collected a great deal of data about themselves over a year. And one of the things they collected was a self-monitored mood diary, where they score themselves on a mood zoom and gave themselves scores for depression and anger and things like that.

At least in theory, on a daily basis. In practice, it varied a lot. Some people did it occasionally some people did very frequently. Some people did frequently sometimes occasionally sometimes… and not everybody did it for the whole year. And that’s what I mean by messy evolving data. But we were able to work with that data.

And in an interdisciplinary little group, we were able to show quite clearly that in this particular experiment- and we were able just by looking at the complex mood data – to be able to make relatively good discrimination between the different diagnoses. So we were able to extract just from people’s self-reported mood over time, a relatively good picture of the phenotype that they represented in this experiment.

That really used the maths. With the maths we were trying to recognise about 50 features to extract our information without our maths, it would have probably taken about 800 or 900 and there wouldn’t have been enough data. So we were able to extract information out using our maths that was actually of clinical interest and relevance.


These days, Terry is working on a program called DataSig, which is part-funded by the EPSRC.

Improving detection sensitivity and making new observations in astronomical radio wave data is one goal of this program. Another stems from gesture recognition on mobile phones from people drawing Chinese characters with the tips of their fingers.

But a third goal aims to assist clinicians and mental health workers with the diagnoses paradigm. Through developing tools and modules, which aim to assist clinicians when understanding longer-term fluctuations in a patient’s mental health. The commonality between all of these is that they all require an understanding of vastly complicated data from different sources and in different formats. And that is precisely where the maths comes into it.


I think we have some really innovative perspectives on how you deal with and extract value from complex, multimodal, evolving data. The underlying technology is actually very mathematical and the basic principle of this program is to develop the underlying technologies in the context of serious applications.

Now, one of the things we’re able to do is we’re able to handle much messier, more complex data with relative ease than people are normally comfortable with.

One area where I think this arises big time is in the case of understanding real-world-human-being situations.

We have a program at the moment where. Well, actually, we won a competition against 104 other competitors worldwide for detecting sepsis on the basis of hospital records.

In some sense, it’s the same sort of challenge. You have this complex, non-stationary lots of missing data stream of information, representing somebody and how they feel. But we’re not very expert at the moment at translating that into meaningful outputs.

The combination of our data science and general data science can, if we have real data, allow one to get much better at doing that. I see it as a real, as a significant program where we can do real work, and learn how to extract. It’s very much a research project though.

It’s really still about learning how to go from the raw data to meaningful policies, about one’s health.


Could you give me some specific examples about the kind of data that might be coming in and the kind of outputs or decisions you may be able to make of that?


One area where we’ve made significant progress, I think. Is we have demonstrated as a proof of concept that people’s emotions, which are relatively short-term and fluctuate are over the long term, quite informative about how people doing. And one of the things we’re trying to do at the moment is to establish a more robust way, and a less invasive way, than maintaining a diary for actually building up sets of data that are adequate to give useful information.

And so, for example, I hope that we will be able to collaborate with one of the charities in this space, to get access to a relatively large number of participants in these trials. But one of the things we’re trying to do is learn to use facial emotion, with people’s consent of course, which could be collected pretty passively by people whenever they unlock their mobile phone. And which over months might well give quite powerful information about how people are, how they’re feeling. And whether or not they have depression or bipolar disorder or something like that. So that is an instance of the kind of data that we’re very interested in collecting, pure emotion data.

Now, funnily enough, you might think of it’s very personal, but in a way it’s the exact opposite. Whereas the video is quite personal. The stream of emotion has almost no personal information: anger, happiness, and happiness, and you can put it all to a different face and you could still have the emotions portrayed. But you wouldn’t have anything to identify it as you.

And that’s another theme in our research is to try to use our ability to handle these sorts of types of information, to make useful statements with data that isn’t personal.

One way, I tried to explain what we do with high-frequency emotions, turning into a longer-term signal, is I like to make an analogy. If you have diabetes, then actually there’s a blood test. You do every three months or so, or maybe more. And that blood test actually measures not what happens over a day. But measures what happens over a long period. right? Actually, that’s so much more useful than the blood sugar levels.

The blood sugar levels change dramatically during the day. They change after a meal, they’re up and down, up and down, up and down.

In some sense, they are diabetes, but it’s far more useful and informative to have this longer-term measure of what’s going on, which then allows you to adjust your life, change your diet, to realise that your diet is working or not working because the frequency is right.

Whereas the frequency of measuring your blood sugar is all wrong. You don’t try and control things on a half-hour basis. You need to do it over months. And I think it’s very similar to what I’m trying to achieve with emotion. I’m trying to move to a situation where you can build up long-term measures of well-being or diagnosis based upon this complicated high-frequency: ‘Did you get angry before you got depressed?’ this high-frequency vector values emotion can be quite informative about how things are. My game is to try and turn it into something which is informative.


So it seems that Terry is working in a space where he’s trying to develop systems, which allow both the patient and the clinician to better monitor symptoms, emotions, and feelings over longer periods of time in an unobtrusive way. Using data, which is depersonalised and as a truer representation of how someone is feeling longer term. Not just how they happen to be feeling on the day when they have a doctor’s appointment.

Now I wanted to get an understanding of who is involved in DataSig and what the origins of the program are.

Terry told me about the funding, which he receives from the EPSRC for this project and how collaboration with those from outside of the engineering and physical sciences community has been so important in the program’s work.


So I think it relied a lot on human, personal contact. Actually, and trust that we established at the personal level to make everything happen.

As time moves on, we’ve got a very active collaboration now between the psychiatry department to my group, where the core funding on all my sides now comes from EPSRC. And on the other side, I’m part of a BRC project. BRC is the funding mechanism through the NHS and the psychiatry department that’s very important too. And that’s given us support in ethics, support in managing a program in a way that’s compatible with all the expectations that are necessary to get right if you’re going to engage with people, which we have very limited experience of.

So that’s really important, but then it’s really important to talk with the clinicians it’s really important to do that. I mean, I, I don’t believe we could do a sensible project on our own. At least not with a group of one or two or three. You know what I mean? You need to build up that expertise. On the other hand, what we do I don’t think anybody else would do. Because we’re bringing new technology in the maths. For how you actually analyse these things.


So it’s almost various disciplines, which you work with will have their part to play in their expertise and we’re bringing them all together. You become able to do the kind of research that you all want to do.


Absolutely. Yeah.


By his own admission, Terry did not expect to end up working within mental health research. When he began his career as a mathematician in the seventies. It’s fair to say that not many of his peers are working in mental health care. But this is part of a wider trend throughout mental health research. The acknowledgement that everybody has a part to play in tackling the mental health crisis, whether they are a mathematician, a hydrologist, an architect, or a psychologist.

I wanted to get Terry’s take on the step change and what is driving it from an engineering and physical sciences perspective.


It probably comes from both sides. I’m probably the intersection to a significant extent is data. One of the real challenges, I think, in offering high-quality support to people with mental health issues is that the amount of information available to make decisions is really very limited when you consider the significance of many of the decisions and that actually take place and that people have to make about themselves. And it makes sense to try and see if you cannot gain more useful information – I don’t want to underestimate the challenges in doing so – but to get more useful information so that people are better informed about how they’re doing, whether they’ve been successful in supporting themselves. And also for the clinician to get better information about how somebody is doing.

That is a very real interest, I think, in analysing data to try and find better information that can be used. And of course, in the last period, since about 2014, the world of data has exploded and there are indeed I think some very real opportunities to do something about it.


Yeah. So is it fair to say that as the world changes and the internet of things and the amount of data available to everyone about everything kind of expands rapidly, people with backgrounds such as yourself are best placed to make sense of that data and to figure out how we can use that data to help people who are experiencing mental health problems?


Maybe, but I think that’s a very passive perspective. I think what has changed is not really well for me, maybe that was not globally true, but for me, what has changed is the ability to make sense. My technology is my research. The area I work in have basically transformed a certain set of challenges.

So we are able to consume complicated, if you like, social data or emotional data, multimodal evolving in time, and actually deduce from it quantitative information. That can then be associated with clinical outcomes or how people are feeling. And so we have ways of actually going and measuring things. It’s not really about the things being more available. It’s actually in our case more about the technology has changed so that we’re better skilled at interpreting the data.


We spoke about how, over the last five, six years, there’s been more interest in, mental health research from mathematicians, engineers, physicists, et cetera, people from this community.

Where does it go from here? Does it continue to grow as more data’s available and new tools are developed to analyse it?


Well, in my case it’s specific skill sets that allows one to answer questions when couldn’t do before. I don’t think it would have been anticipated. People don’t know about it probably don’t anticipate it even now. I think it’s for sure that research in mental health is a very good idea. I think it’s for sure that the physical sciences should encourage researchers to engage in it and to engage in research of a fundamental kind that might contribute to it.

Where it is going to go? Hopefully, better patient care. Better outcomes. It’s not all about drugs. It’s not all about anything. It’s a quite complicated canvas. But evidence is important as well. You see? I mean, maybe that’s another thing. I mean, at the end of the day, you have individuals themselves. Can you help them? You have interventions, which can be successful or less successful. You have to make decisions on basis of information. So you can innovate in any one of those areas, or you can quantify the damage to create public policy for getting more money. This is also a perfectly valid area of research to understand the consequences of doing nothing or making an incidence.


With these innovation opportunities and the increased attention on mental health research from the EPS community, I went to target to offer some advice, hints, or tips to anyone looking to follow in his footsteps and become involved in mental health research.


I think they need to find a home. They need to find supporters on the other side. In order to do these things more effectively. Then I think there’s a lot you can do. There is an enormous amount you can do. Whether it’s understanding health records…

So in Britain, we have something called CRIS, which is actually the mental health hospital records of a good proportion of the UK’s population who have at some time come into contact with the hospital services of mental health. That data is all there under lock and key in various ways, but it’s all there.

This is an interesting resource to mine, but it’s not going to work. I don’t think unless you’re collaborating with people who are on the coalface are really service users or clinicians I think you have to build up the support team on the other side.

We’re very, very lucky now that we’re integrated into the system there. I mean, I would’ve found it impossible, I think to write the ethics applications and so on. It would have taken me ages, and ages to really understand all the things you have to do, but they’ve done it before and they do it again.

And it really, really makes a big difference but it’s not just that. That’s just a sort of tip of the iceberg. They’re very busy, the patients are very busy, like everybody else. So it’s complicated. Quite complicated to really make it happen.


Can you imagine the number of researchers from the EPS community being involved in mental health research increasing? Would it become more of a core focus for the discipline?


I think it’s very contingent on the level of funding overall for mental health. because I think the good projects interact with other research. And so if, if there is research and information about mental health, then I think there will always be a lot of scope for interaction and it will expand. And I think at the moment it is expanding.

Mental health is an area where it is currently receiving after a long time being very poorly funded the research and it’s interesting a bit more, but I’m not an expert in that if you want to look at the figures and check what I’ve said. But I think the extent to which others can engage with it. Sure, it’s to an extent, the leverage by that, because I do, as I said before, think that the best outcomes come from a vibrant interaction


Before I said goodbye to Terry. I wanted to put a simple question to him, which I’m asking everyone I speak to. As a mathematician who finds himself working within a mental health context, I wanted to ask why? Why, to Terry, does mental health research matter?


Because people matter. It’s as simple as that really.


That’s it for this episode of the Mental Health Research Matters podcast. Thank you for listening and thank you to Terry for speaking to me. Make sure that you keep an eye on the Mental Health Research Matters website for further updates from the team and from across the UKRI mental health networks, we hope to see you soon.