Entropy in cardiovascular research. The idea of the Fahrenheit Universities in practice

Over 11 million new cases of cardiovascular disease are recorded every year in Europe. Also in Poland, these diseases constitute a major social problem and the greatest threat to the health of our country's inhabitants. One of the basic diagnostic tools in cardiology remains the ECG recording - a non-invasive test that shows the bioelectrical activity of the heart. It is ECG recordings that provide valuable data for scientists from the Gdańsk University of Technology, who use sophisticated mathematics to help cardiologists in an even more effective diagnosis.

ECG records of a healthy person and a sick person look different. Finding these, sometimes quite subtle, differences is obviously a doctor's job. However, the electrocardiographic record provides a great deal of data. Some of them are not analysed as part of standard medical procedures because more advanced methods are needed to characterise them. This is where mathematics comes to the rescue, or more precisely, chaos theory and the theory of dynamic systems.

'A healthy heart dances'.

- 'It is commonly thought that a healthy heart beats with a single rhythm, it is even said that it runs steadily like a "Swiss watch". Nothing could be further from the truth,' explains prof. Grzegorz Graff, Head of the Department of Differential Equations and Applications of Mathematics at the Faculty of Technical Physics and Applied Mathematics. - 'It is the complexity of the rhythm, its variability and unpredictability that are a sign of health because they mean that the heart can adapt to changing external conditions, new challenges that constantly appear before the organism. "A healthy heart dances, while a severely diseased one marches steadily along"- prof. Ary Goldberger used to say. Especially in heart transplant patients, an almost completely "rigid" heart rhythm is observed.'.

To measure the complexity of the heart rhythm, mathematicians use entropy. It is a measure of the degree of disorder in the system under study. In simplest terms, entropy measures the complexity and unpredictability of a process.

- 'If the heart rhythm is very regular, for example in transplant patients, entropy will be close to zero, because we know with a high degree of certainty what the recording of subsequent heartbeats will look like. The more unpredictable the rhythm, the higher the entropy value, but it cannot be too high, because then we can also deal with pathological states,' explains the scientist.

The calculation of entropy in the case of ECG recording is a quick and simple method. It can be of great help in situations where every second counts - for example, during warfare or terrorist attacks. In such moments, there is very little time to assess the condition of the victim and make a preliminary selection of those requiring immediate intervention.

- 'We found that by determining the entropy value from an express, one-minute ECG recording, we can deduce who needs to be rescued first. Inspired by this research, our team looked at another cardiac problem: collapses. They are most often sudden and unexpected and make it significantly more difficult for patients to function normally in everyday life. For the diagnosis of a faint, the so-called tilt test is used, which provokes a faint in the laboratory, and thanks to which it is possible to assess the work of the cardiovascular system during the change of position from lying to standing. Analysis of the entropy of the heart rhythm sometimes makes it possible to determine whether someone has a preference for fainting or not, even before upright standing is performed, based on an analysis of the patient's ECG in the lying position.'

The idea of Fahrenheit Universities in practice

Research on the application of entropy values and other non-linear measures in cardiology is interdisciplinary. The group working on this topic includes physicians from the Medical University of Gdańsk under the direction of prof. Krzysztof Narkiewicz, mathematicians from the Technical University of Gdańsk in the team of prof. Grzegorz Graff, and physicists from the University of Gdańsk in the group headed by prof. Danuta Makowiec.

- 'Due to the complexity of the issue, only the cooperation of so many specialists from different fields can guarantee the success of the research,' - emphasizes prof. Graff - and at the same time it shows how the idea of the Fahrenheit Universities is naturally implemented in scientific life.

The scientist combines mathematics and cardiology not only in his professional life, but also in his personal life, as his wife is also a scientist and, in addition, a cardiologist. Discussions about their respective fields and the exchange of experiences were one of the reasons for starting the joint research work.

- 'As a researcher, I have the comfort of being able to consult a specialist at any time on the medical side of the issues I am investigating, and she can give me his time. Although mathematics provides powerful tools, in medical applications they cannot be considered in isolation from the physiological context: the results must broaden our knowledge about the functioning of the organism or possible pathologies.'.

More information: read on the website of Gdańsk University of Technology


Maciej Dzwonnik/PG