Geodesic
Karhunen--Loeve orthogonal decomposition method for problems of EEG assessment of patients with migraine
Izvestiya VUZ. Applied Nonlinear Dynamics, Tome 33 (2025) no. 1, pp. 123-139

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The purpose of this work is to identify patterns in the recordings of electroencephalograms of patients with migraine using the Karhunen–Loeve orthogonal decomposition method. The work examines the main features of electroencephalographic dynamics, and the impact on these features of сhronic migraine severity. Methods. To collect experimental data, the method of recording electroencephalograms during the modified multiple sleep latency test was used. During the experiment, studies were conducted of the subjects'reaction to the presented visual stimulus. The obtained data were processed using the Karhunen–Loeve transformation, which allows one to interpret the complex dynamics of the system from the point of view of the coexistence and interaction of coherent orthogonal space-time structures. Results. Studies have shown that the energy distribution of modes in active and sleep states can differ significantly. The character of this distribution depends on the brain zone of signal recordings, on the duration of the experiment, and on at what time point in the experiment certain stages of the subject’s reaction were recorded. It has been shown that the greatest response in the form of evoked potentials in people with migraine is most often localized in the occipital lobe of the brain, and there is a correlation of this effect with the frequency of migraine attacks. For some groups of patients, there is a connection between the severity of evoked potentials in the brain and the energy of the first, most energetic, Karhunen–Loeve mode. Conclusion. It has been shown that there is a relationship between the number of significant modes and the power of the alpha rhythm in electroencephalography signals, and the spatial localization of this effect in the occipital region of the brain can be traced. For the frontal lobe of the brain, significant differences in the distribution of the first mode were demonstrated, assessed for groups of patients with rare and frequent migraine attacks.
Keywords: multiple sleep latency test, evoked potentials, electroencephalogram, orthogonal decomposition method, Karhunen– Loeve method, space-time structures, migraine 
@article{IVP_2025_33_1_a8,
     author = {E. N. Egorov and M. O. Zhuravlev and A. E. Runnova and M. A. Evstropov and A. S. Redzhepova},
     title = {Karhunen--Loeve orthogonal decomposition method for problems of {EEG} assessment of patients with migraine},
     journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
     pages = {123--139},
     publisher = {mathdoc},
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     year = {2025},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVP_2025_33_1_a8/}
}
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E. N. Egorov; M. O. Zhuravlev; A. E. Runnova; M. A. Evstropov; A. S. Redzhepova. Karhunen--Loeve orthogonal decomposition method for problems of EEG assessment of patients with migraine. Izvestiya VUZ. Applied Nonlinear Dynamics, Tome 33 (2025) no. 1, pp. 123-139. http://geodesic.mathdoc.fr/item/IVP_2025_33_1_a8/