Let's take math to heart. Entropy in cardiac research | Faculty of Applied Physics and Mathematics at the Gdańsk University of Technology

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Let's take math to heart. Entropy in cardiac research

More than 11 million new cases of cardiovascular disease are reported annually in Europe. Also in Poland, these diseases constitute a large social problem and are the greatest threat to the health of the inhabitants of our country. One of the basic diagnostic tools in cardiology is an ECG - a non-invasive test that shows the bioelectric activity of the heart. It is the ECG records that provide valuable data for scientists from Gdańsk University of Technology who want to use sophisticated mathematics to assist cardiologists in even more effective diagnostics.

The ECG records of a healthy person and a sick person look different. It is, of course, the doctor's job to spot these, sometimes quite subtle, differences. However, the electrocardiogram provides a great deal of data. Some of them are not analyzed as part of standard medical procedures because more advanced methods are needed for their characterization. This is where mathematics comes in handy, and more precisely - the theory of chaos and the theory of dynamical systems.

"A Healthy Heart Dances"

– It is commonly believed that a healthy heart beats in one rhythm, it is even said that it runs steadily, like a "Swiss watch". Nothing could be more wrong – explains prof. Grzegorz Graff, head of the Department of Differential Equations and Applications of Mathematics at the Faculty of Applied Physics and Mathematics. – It is the complexity of the rhythm, its changeability and unpredictability that are the symptoms of health, because they mean that the heart is easily adaptable to changing external conditions, new challenges that the body faces. "A healthy heart dances, and a seriously ill one marches steadily" – prof. Ary Goldberger used to say. An almost completely "rigid", steady heart rhythm is observed especially in heart transplant patients.

To measure the heart rate complexity, mathematicians use entropy. It is a measure of the degree of disorder of the tested system. To put it simply, entropy can be used to measure the complexity and unpredictability of a given process.

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

Calculating the entropy for an ECG recording is a quick and simple method. It can be a great help in situations where every second matters - for example during military operations or terrorist attacks. At such times, there is very little time to assess the victim's condition and pre-select those who require immediate intervention.

– It turned out that thanks to the determination of the entropy value, based on the express, one-minute ECG recording, it is possible to deduce who should be saved in the first place. Inspired by this research, our team took a closer look at another cardiac problem: syncope. Most often, they are sudden and unexpected, significantly impeding the normal daily functioning of patients. To diagnose the syncope we often use the so-called tilt test, provoking syncope in laboratory conditions. Thanks to this test it is possible to assess the work of the circulatory system when changing the position from lying to standing. The analysis of the entropy of the heart rhythm sometimes allows to determine whether a person has a tendency for fainting or not, even before performing the upright standing, based on the analysis of the patient's ECG in the supine position.

The idea of the Fahrenheit Union of Universities in practice

Research on the application of entropy values and other non-linear measures in cardiology is of an interdisciplinary nature. The group working on this subject includes doctors from the Medical University of Gdańsk under the supervision of prof. Krzysztof Narkiewicz, mathematicians from Gdańsk University of Technology in the team of prof. Grzegorz Graff and physicists from the University of Gdańsk in the group led by prof. Danuta Makowiec.

–Due to the complexity of the issue, only the cooperation of so many specialists in various fields can guarantee the success of the research – emphasizes prof. Graff – and it also shows how the idea of the Fahrenheit Union of 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, because his wife is also a scientist and also a cardiologist. Discussions on the fields covered and the exchange of experiences were one of the reasons for starting joint research work.

– As a researcher, I have the comfort that at any time I can consult my doubts regarding the medical side of the research issues with a specialist doctor who can devote time to me. Although mathematics provides powerful tools, in medical applications they cannot be considered in isolation from the physiological context: the results must broaden our understanding of the functioning of the organism or possible pathologies.

Recommendations and research plans

Scientists strive to develop some recommendations that are useful "at the bedside". The ideal situation would be that of treating diabetes. Knowing the norm limits, we know which blood glucose level is appropriate for the body and which is harmful. Simply speaking, if the reference values for entropy for a healthy heart could be established, the task of cardiologists would be much easier.

– However, it should be remembered that there are many variants of entropy and many heart diseases of various etiologies. Work on mathematical tools is currently underway, and we are investigating which of them are the most effective. There is still a long way to go to formulate generally applicable statements and recommendations that doctors can use. In particular, it is necessary to analyze data from a very large number of patients – emphasizes the scientist – but some of our results are already met with considerable interest by doctors from the Polish Cardiac Society, who already use some non-linear methods in clinical practice.

Scientists are also working on using machine learning algorithms in conjunction with certain geometric indices in the diagnosis of strokes. These methods, based on the analysis of ECG data, may prove to be promising especially in detecting the effects of cerebral ischemia, sometimes imperceptible even by the patients themselves, and having a significant impact on the health condition. Interestingly, the methods used so far have proved to be ineffective in diagnosing patients who have experienced such transient ischemic episodes, so the significantly new approach may be clinically very useful.

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