Multifractal brain and early stages of multiple sclerosis

Cedit: Adobe Stock
Cedit: Adobe Stock

Electrical brain signals in patients with multiple sclerosis, a disease mainly associated with the slowing-down of information processing and a lack of motor coordination, show traces of multifractality, scientists from four Polish research institutions have found.

Multifractal analyses of electrical signals flowing from the brain can help in early determination of the severity of the disease, demonstrated by scientists working in the 'Biologically inspired neural networks' project of the Foundation for Polish Science. The study involved experts from the Jagiellonian University (UJ), Cracow University of Technology, SWPS University (USWPS) in Katowice and the Institute of Nuclear Physics of the Polish Academy of Sciences (IFJ PAN) in Kraków, where multifractal analyses were carried out.

At the fractal analysis stage, the experts from the Institute of Nuclear Physics of the Polish Academy of Sciences noticed that the electrical signals emanating from the brains of healthy people showed the presence of certain long-range trends, making the graphs of their electrical activity visually smoother than in patients with multiple sclerosis, whose brains sent out more 'jagged' signals. But when multifractals are involved, the situation changes: the electrical signals emitted by the brains of healthy people have less structural complexity than in MS patients.

'In people with early-stage multiple sclerosis, the communication between neurons is more complex. However, the neurons are not fully independent of each other, as they are still jointly responsible for the formation of the EEG signal, and therefore we observe a tangle of fractals, i.e. multifractals. In contrast, in the control, healthy group the individual fractal components are more regular, fit together better and the multifractal structure becomes more difficult to see,’ says Dr. Paweł Oświęcimka from the Department of Complex Systems Theory at the Institute of Nuclear Physics of the Polish Academy of Sciences.


Professor Tadeusz Marek from the Department of Psychology at SWPS University said: ’The existence of complex signal organisation in multiple sclerosis sufferers may indicate compensatory processes in the brain's neural networks. The brain attempts to compensate for the deficit created by the disease and seeks ways around damaged areas, leading to a reorganisation of the network. The functions of these areas try to be taken over by other, still efficiently working groups of neurons, which manifests itself in an increase in the complexity of electrical activity.’

Differences in the complexity of the EEG signal (yellow and red colours) in a specific brain area between the group with advanced multiple sclerosis and the control group, and multifractal spectra calculated for the group of patients (red line) and for the control group (blue line). (Source: Institute of Nuclear Physics of the Polish Academy of Sciences)

Summarising the results of the analysis of multifractal EEG recordings, Professor Marek says that they are proving to be a highly sensitive tool for detecting compensatory processes occurring in the neural networks of the brain in the early phase of multiple sclerosis development.

Multiple sclerosis is an incurable disease that leads to the degeneration of the central nervous system, manifesting as motor and sensory disorders. Its course can only be mitigated, the more effectively the earlier the disease is detected.

The study participants were selected by researchers and doctors from the Department of Neurology at the Jagiellonian University Medical College and the Department of Neurology at the JU Hospital. The group with diagnosed early-stage multiple sclerosis was eventually reduced to 38 subjects, and the control group to 27. Electroencephalographic (EEG) data were collected several times over a two-year period, each time involving the subjects in different tasks. 

The electrical activity of the brain was measured using 256 electrodes, each sampled 1,000 times per second. Before the actual analysis, the signals were cleaned, removing, for example, artefacts caused by eye blinks, They were combined into groups corresponding to 20 brain areas.


'The total amount of collected data is so large that it will take our team years to complete a full set of multifractal analyses. Therefore, the paper we have just published in Biomedical Signal Processing and Control discusses only the readings collected during the earliest phase of the measurements, concerning the situation when the subjects taking one of the two prescribed pharmaceuticals did not perform any activity during the measurements,’ says Dr. Oświęcimka.

He adds that the search for multifractal relationships is computationally demanding. It has only started to become more widespread in the last decade or so, together with the increase in computing power of computers and the development of software. As a result, in many areas of scientific activity, multifractals are only at the stage of 'taking their first steps'. 

'One such area is the analysis of the complexity of electrical signals emitted by the human brain, especially in the context of degenerative changes taking place in it,’ Dr. Oświęcimka continues.

He says that the basic feature of 'ordinary' fractals is their self-similarity: by enlarging them, sooner or later we see a structure that is very similar, or even identical to the initial one. When we combine several fractals, the result is generally noise. However, there are mathematical operations that weave fractals into complex structures that retain the capacity for self-similarity. In ordinary fractals, self-similarity appears when we scale any fragment by a factor that is always constant for that fractal, whereas different fragments of multifractals must be scaled in different ways. This feature means that, while analyses using ordinary fractals allow linear correlations, such as trends, to be picked up, multifractals can reveal the existence of less obvious, non-linear correlations.


A questionnaire survey, which is inherently highly subjective, is currently used for assessing the progression of multiple sclerosis in patients. More objective examinations require the use of magnetic resonance imaging and are therefore not only invasive but also highly cost-intensive.

According to the researchers, discovering the relationship between a patient's condition and the multifractal complexity of their brain's electrical activity would allow for an objective assessment, using a non-invasive and easy-to-use measurement technique.

The results reported in the paper are the first phase of analyses of the EEG signals collected during this scientific project. The remaining electroencephalographic data are currently being processed. The scope of the research was broader and also included brain imaging using structural and functional magnetic resonance techniques. These resulted in a series of images showing cross-sections from which the structure of the brain and changes in the blood supply and oxygenation of its various areas can be reconstructed. The search for multifractal harbingers of multiple sclerosis will therefore continue - in not one, but four dimensions.

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