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Tackling tumours using mathematics

Radiotherapy is often used to treat cancer cells, but all kinds of things can go wrong. An incorrect dosage can damage surrounding tissue, and what do you do if there is an organ in the way? Mathematical models have an important role to play in ensuring that radiotherapy can be conducted with a high level of precision. Marleen Keijzer ( lecturer at the Delft Institute of Applied Mathematics) and her former EEMCS student Sebastiaan Breedveld (assistant professor at Erasmus MC) discuss the role of mathematics in an ever-changing field: radiotherapy. Marleen, what first sparked your interest in mathematics within radiotherapy? In the mid-1980s, I attended a conference in America on how laser light is used for medical applications. For example, in the case of atherosclerosis, how do you deal with a constricted blood vessel? And how could lasers be used to treat a particular type of cancer? At the time, this was all relatively uncharted research territory. Soon after, I moved from Delft to the United States in order to apply a Monte Carlo method – in other words mathematics – to simulate light scattering. I wrote articles and worked with various hospitals, but decided to return in 1989. Back in the Netherlands, I completed my PhD thesis on calculating light propagation in tissue. If you put a flashlight against your cheek, most of your face will turn red. That is scattered light. But how does the light actually get there? After my PhD, I worked on several more research projects, but soon realised that I much preferred teaching and supervising students with their graduation research. For the latter, the focus was actually always on the useful application of mathematics, for example within radiotherapy. Final-year students and radiotherapy. What challenges lay ahead of them? In the field of radiotherapy, it was still possible to make major strides. Graduating students were given all the space needed to design and program their own optimisation methods. An optimised plan of this kind gives you the maximum opportunity to control the tumour and minimise the risk of damage to healthy tissue. So you search for the desired dose distribution and use optimisation to determine how the beams should relate to each other. What happens if you administer one beam here? And what consequences will that have for the dose applied there? Not so long ago, this still had to be done manually: a laboratory technician set the beams, an advanced computer program calculated the dose distribution and the laboratory technician then adjusted the beams to achieve the optimum dose distribution. The problem with radiotherapy is that it doesn’t just involve one single criterion, but numerous conflicting criteria. Optimising a radiotherapy plan could therefore easily take up a whole day. Sebastiaan Breedveld was one of your graduating students. What exactly did he do? I supervised Sebastiaan for a while, but he eventually did his PhD research at Erasmus MC – Daniel den Hoed. He was awarded his PhD cum laude on the subject of optimisation. Because laboratory technicians were having to devote a whole day to a radiotherapy plan, Sebastiaan developed a method in which optimisation was fully managed by a computer. An important component of this is the so-called wish list. For some organs, it’s perfectly clear how high the radiation dose can still be. You’re dealing with strict limits. It’s important to take account of these limits, because if the radiation dose is too high, for example in the case of spinal treatment, it may leave the patient paralysed. But the reverse is also true: if you radiate a tumour using less than the minimum dose, it may start to grow back. As well as adhering to strict limits, you need to keep the dose administered to each organ as low as possible. The wish list allows you to do this in a prioritised way (one by one). In order to guarantee quality of life, one organ is sometimes more important than the other. This is something you will also take account of when developing a treatment plan. Radiotherapy doesn't essentially solve any problems, it simply creates new opportunities. So this radiation issue is really about optimisation… Yes, that’s actually what it comes down to. After all, numerous optimisation methods are being used in radiotherapy. Nowadays, the maths are done by computers. But it still takes time. The graduation students I am now supervising are working to make this process faster and more practical while also tailoring it more effectively to the individual patient. Ideally, you want to fine-tune the plan when the patient is actually lying inside the radiotherapy device. Real time. The human body is always moving, while a radiotherapy plan is made weeks before the start of the first treatment. If the bladder is slightly fuller, it may have pushed an organ or tumour into a slightly different position, for example. With that issue in mind, we had another doctoral candidate develop a statistical model of the movements of the prostate. He analysed numerous CT scans from different patients, identified the most important movements from these and summarised it all in a model. This is a very useful application for mathematics, because as soon as you realise where the uncertainties are, you can start taking them into account. It is a very practical EEMCS issue. What challenges are there for the future? Radiotherapy techniques could be customised more. In the 1960s, they would put a piece of lead on a patient, with an opening cut out for the radiation beam at the level of the tumour. This meant that the radiation beam was limited to the tumour alone. Today, everything is done using three-dimensional CT scans, fast computer calculations and highly targeted radiation beams. There has been significant progress, but treatment could still be tailored more effectively to the individual patient. Also, planning methods are still not anything but standard. It would be great if planning methods were generally accepted and made easily accessible, so their use would not be limited to the university hospitals of wealthy countries. Marleen Keijzer is a lecturer at the Delft Institute of Applied Mathematics, also known as DIAM, at TU Delft. As part of her job, Keijzer is responsible for the first-year course in Mathematical Modelling, and teaching and coaching students is what she enjoys most. In the last decades, Marleen has supervised numerous students during their graduation projects or PhD programmes. Most of her projects were based at the Daniel den Hoed Clinic – now Erasmus MC – and concerned radiotherapy treatment planning. Together with her colleague Theresia van Essen, Marleen is currently setting up an online course In Hands-on Optimisation. Keijzer also recently became vice-chair of the TU Delft Works Council. Radiation therapy is one of the most important treatments against cancer. One of the ways to do this is through external beam radiotherapy (EBRT). A Linac (a linear particle accelerator) is often used for this treatment. The position of the angles is one of the problems you have to deal with during the preparation of the treatment. In other words: from which directions the patient is going to be irradiated. As you can see in the video, there are different degrees of freedom that can be used and combined. The device in the video is used in the majority of the hospitals. For both traditional and more contemporary treatments, think of proton therapy. Sebastiaan, what first sparked your interest in mathematics within radiotherapy? I was always eager to do something in the world of medicine. Eventually I opted for a study in Applied Mathematics at TU Delft. But I kept being attracted by the medical field. With that attraction in mind, I decided to do my graduation research on a mathematical issue with a medical application. Because Marleen lectures on the subject, I thought: ‘I would like her to supervise my graduation research!’ Via Marleen, I ended up at Erasmus MC – Daniel den Hoed in Rotterdam. How did you manage to combine mathematics and radiotherapy there? Maybe I should tell you something about radiotherapy first. Radiotherapy is used in approximately half of all diagnosed cases of cancer. Radiotherapy is all about irradiating tumours – you’re actually destroying cells. To do that effectively, you need a radiotherapy plan. This plan actually describes the settings for the radiotherapy device that will result in the desired dose distribution. What makes it problematic is that you’re dealing with ionising beams that go straight through a patient. Such a beam actually destroys everything in its path. On the one hand, you of course want to apply enough radiation to be able to eliminate the tumour. But then again, you don’t want to do this at the expense of the surrounding organs: your aim is to minimise the risk of complications as much as possible. Take a tumour in the head and neck area. If you expose the small salivary glands to an incorrect dose during irradiation, this may result in permanent damage. It may lead to a situation where the patient has to drink a little water every 30 minutes, even at night. What dose do you opt for? And how do you then distribute that dose? These are important questions that involve mathematical calculations. How did you include these questions in your own research? It’s worth knowing that my research involved two stages. The first stage was to investigate how the available equipment could be used as effectively as possible. In the Netherlands, we've seen a rapid development of most equipment, while the range of possible applications has lagged behind. Smart use of mathematical models enabled us to catch up and put the available equipment to maximum use. The second step was to answer the question: how do you distribute the dose? In order to find out, I asked a number of colleagues: what is it you would like to see in a therapy plan? Based on that input, I compiled a wish list: a list that I could use to guide the optimisation. Running through this wish list, you can work towards a radiation dose that is highly precise based on sophisticated calculations. At that time, the process was relatively new. For some organs, it’s perfectly clear how high the radiation dose can still be. You’re dealing with strict limits. How did you apply the wish list in practice? This wish list ultimately generated automated working methods. Now, there were two plans: one plan that had been developed clinically and one plan generated automatically. In order to find out which method worked best, both a clinical and an automatically generated plan were developed for 50 patients. By doing this, we hoped to achieve some kind of statistical relevance. Both variants were submitted to a doctor who was then asked: which plan would you use to treat this patient? The doctor had not been told which variant had been calculated manually or automatically. After repeating this 33 times, we ended the experiment. We found that in 32 out of 33 cases, the preference was for – what turned out to be – the automatically generated plan. The difference in quality was so convincing that from an ethical perspective we felt compelled to make an effort to treat all patients within this group in the new way. In other words, the wish list worked. The problem with radiotherapy is that it doesn’t just involve one single criterion, but numerous conflicting criteria. In the years ahead, what will be the greatest challenge in the field of radiotherapy? The HollandPTC outpatient centre – based on the TU Delft campus – recently started treating patients using proton therapy. This form of radiotherapy for cancer is new to the Netherlands. Protons are small, positively charged atomic particles that enable high-precision irradiation. This means that less radiation reaches healthy tissues, with a smaller risk of side-effects. TU Delft is working on the technical side of this study. Rotterdam and Leiden manage the medical side. But there’s another question: how can you make a radiotherapy plan even faster and more effective? Imagine you need to make last-minute changes to a plan. How then do you ensure you can go through all those gigabytes of active data as quickly as possible? Sebastiaan Breedveld studied Applied Mathematics at TU Delft. Both his Master's and PhD research focused on the automation of treatment plans within radiotherapy. Breedveld is now an associate professor at Erasmus MC, where he is continuing his research aimed at improving radiotherapy treatment methods. Would you ever change the world of radiotherapy for another one? When I started here, I thought: when I’ve done my bit, I’ll slip away and move into hydraulic engineering. I’ve now passed that point. What makes radiotherapy interesting is that new techniques are continually emerging. For example, proton therapy has been around for a decade, but at Holland PTC, the very first patient was only treated last December. Radiotherapy doesn't essentially solve any problems, it simply creates new opportunities. Text: Dave Boomkens | Photo: Mark Prins

Towards a sensible digital society

Mathematics, electrical engineering and computer science are the foundation of modern technology: they form the basis for solutions to this century's major challenges. This creates not only opportunities but also responsibilities. "As engineers, we must be aware of the fact that the digital society does not exclusively bring benefits", warns Professor John Schmitz, Dean of the Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS). Mathematics, (micro)electronics and computer science: all technical systems and hardware – from medical equipment to aircraft – require a combination of these three elements. "Take your smartphone", Professor Schmitz explains. "It contains electronic switches – integrated circuits. Designing them requires mathematics. Consider Kirchhoff's laws, which state that the sum of the voltages at a node in such a circuit equals zero; the same applies to the resistance in a loop. Solving such equations for simple circuits is manageable, but one modern integrated circuit (or microchip) contains millions of these loops. To do that, you really need to know your mathematics". Smartphones now have 100,000 times the computing power of the computers that were used for the moon landing. This was made possible by the development of micro-electronics, which in turn influenced the development of mathematics and computer science. "In the past, mathematics required a great deal of analytical solving. Current computing power and numerical methods mean we can simply calculate it all. This offers unprecedented possibilities," notes Schmitz. "In addition, all sorts of things that used to require experimental demonstration can now be partly calculated; so we don't have to conduct as many expensive experiments". Mathematics, computer science and electronics reinforce each other in this way, and are the joint foundation of modern technology – a role that Schmitz wants to put in the spotlight. Healthcare One topic that does not immediately bring EEMCS to mind is healthcare. The use of stem cells to grow tissue on electronic chips (‘Organ on Chip’) now makes it possible to conduct highly specific studies of how medicines work, in order to develop personalised individual medication. In the Bio-Informatics and Pattern Recognition research group, researchers are applying advanced data analysis in order to be able to interpret and use the ever-expanding volume of biological data (e.g. from DNA sequencing). Great things are happening in the field of medical imaging as well. "Take MRI scanners, which cost millions because of the linear magnets they require. Although these magnets have been fully optimised over time, the best possible technology is not being used to process the signals into images", explains Schmitz. "A combination of simple magnets and sophisticated image processing can produce very good image quality. This makes the devices affordable for developing countries as well". Great things are happening in the field of medical imaging as well. "Take MRI scanners, which cost millions because of the linear magnets they require. Although these magnets have been fully optimised over time, the best possible technology is not being used to process the signals into images", explains Schmitz. "A combination of simple magnets and sophisticated image processing can produce very good image quality. This makes the devices affordable for developing countries as well". However, even more information can be extracted from the more expensive scanners. "That kind of system generates a mountain of data, only a small portion of which is used in constructing two-dimensional images. By using symbols – glyphs – to represent this sea of data, computer-graphics techniques can be used to generate visual insight into all kinds of processes taking place in the tissue. The current systems can't do that. Of course, serious mathematics lies behind all this", says Schmitz. "It’s about how we visualise information in a way that humans can understand. Computer graphics could also be helpful in the cockpit, where pilots see so much data flash by that they can hardly make anything of it". Energy transition The energy transition has been called the greatest challenge of this century. According to Schmitz, this is no empty claim: "Worldwide, the majority of our energy still comes from fossil fuels. That has soon to change to 100% green energy, and electric energy will play an important role in the process". The generation of sustainable energy, the storage and conversion of energy, smart energy networks: the researchers at EEMCS are working on all the areas that will make this possible. The transition from centralised to decentralised generation and distribution will play a major role here: "Energy is increasingly becoming a two-way street. For example, locally generated energy can be delivered to the net or perhaps stored temporarily in car batteries. The network will also have to be able to cope with fluctuating supplies of solar and wind energy. We will soon be able to test exactly how that works in our new system-integration lab". Schmitz is referring to the Electrical Sustainable Power Lab (ESP Lab), a unique facility for research on the integration of all these new technologies into a single sustainable energy system. Blockchain While traditional customers are increasingly becoming ‘prosumers’ of energy, so the number of transactions is also increasing. Soon there will be questions to be answered, such as how do you charge for energy you have supplied to a neighbour. Blockchain technology – a new form of safe, distributed data storage – could be useful in this context. "Blockchain aims to generate digital confidence. That is quite an achievement in an age when our confidence in institutions is so often being undermined", argues Schmitz. How does it work? "Blockchain encrypts documents or data, and then it generates a unique code: a hash. This is done in such a way that the hash changes if something in the document changes. This means that any fraud is immediately revealed". Confidence in blockchain also has to do with the fact that the storage of each document is spread across the internet, thereby making fraud or theft virtually impossible. "Blockchain can be used for a large number of applications that currently require intermediaries, for example registering wills or taking out mortgages. It can also provide access to the financial world in areas where there are no banks", Schmitz points out. "It will soon be possible to use blockchain to arrange anything that now requires proof of identity". EEMCS is at the forefront of the development of blockchain technology. TU Delft is a founding member of the Dutch Blockchain Coalition, which is based on the campus. "All partners from society and industry are represented there: banks, government bodies, industry, notaries, insurance companies, knowledge institutions. It’s easier to interact with the field when it's so near". Education This community underpins the faculty’s aims in regard to its teaching duties. "We want to solve societal problems. This requires research, as well as engineers who are able to put that into practice. We train them, because engineers are needed in order to solve the world’s problems’, declares Schmitz. In his assessment, the teaching at TU Delft is in good shape. In a recent benchmark study by the Massachusetts Institute of Technology (MIT), TU Delft is ranked high amongst the world’s best universities of technology. "I would venture to say that the educational innovation at EEMCS is one reason that we are one of the top five in the world. The MIT report makes explicit mention of our Solar Energy MOOC and the 'blended-learning' approach in the teaching of maths." The latter project is PRIME: Project Innovation Mathematics Education. "We teach mathematics across the entire university, so we have to be able to explain it well to non-mathematics students". A combination of videos, interactive quizzes and online homework is intended to provide students with comprehensible preparation for the lectures and to improve their mathematical foundations. "We will also soon be starting a 'digital-skills' project, in which all students will learn the basic elements of programming", notes Schmitz. In addition to imparting mathematics and digital skills, the project will also make sure students – and scientists – consider the potential risks of the digital society. Risks "Digitisation has a major influence on society. When you go to a restaurant, everyone is sitting there looking at their screens. Although we could debate about whether that is good or bad, it does have a major impact on daily life", argues Schmitz. "On the other hand, some people today still do not have any connection to the internet. Do they no longer count? The government already makes it nearly impossible to do a tax return on paper". Social exclusion is only one of the risks. Schmitz explains, "We can have computers train themselves to recognise images. For example, the neural network recognises whiskers and decides that it’s seeing a cat. In time, it trains itself by adjusting a variety of weighting factors in the neural network. Although there have been no problems so far, these systems are sometimes so complicated that we no longer understand what they are doing". This could lead to potentially major dangers if, for example, we use the same systems to drive our cars, manage the stock market or arrive at medical diagnoses. We need to find ways to make deep learning and similar technologies more comprehensible. Otherwise, we could be heading for ‘Weapons of Math Destruction’, as the mathematician Cathy O’Neil describes in her book of the same name. In general, this is nothing new. "There are two sides to whatever we invent, good or bad", argues Schmitz. "As an engineer, it's important to make this visible, and therefore transparent". Digital society Until recently, this was uncharted territory. "These problems are on their way because the digital society is unstoppable. In fact, they are already here, although they are a relatively new issue. We need to be aware that these kinds of factors will be playing a role. This starts with the training of good engineers, and this means in education", observes Schmitz. Fortunately, we are not alone in this endeavour. For example, the ‘Digital Society’ programme of the Association of Universities in the Netherlands (VSNU) addresses both the opportunities and the risks. "The universities are united in saying, 'We are facing a common task'. Where is the human factor in the digital society? To what extent can we trust digital contacts and transactions? Even if we do not yet have the answers, I have high expectations that we will be able to find them if we all work together. This is how we can progress together towards a responsible digital society". More information You can view the inaugural speech of Prof. John Schmitz on demand via ths link . You can find the slides of the inaugural speech here . Text: Agaath Diemel l June 2018