Karhunen--Loeve orthogonal decomposition method for problems of EEG assessment of patients with migraine

E. N. Egorov ; M. O. Zhuravlev ; A. E. Runnova ; M. A. Evstropov ; A. S. Redzhepova

Izvestiya VUZ. Applied Nonlinear Dynamics, Tome 33 (2025) no. 1, pp. 123-139.

Résumé

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.

Détail

Keywords: multiple sleep latency test, evoked potentials, electroencephalogram, orthogonal decomposition method, Karhunen– Loeve method, space-time structures, migraine

Bibliographie

[1] Feyissa A. M., Tatum W. O., “Adult EEG”, Handbook of clinical neurology, 160 (2019), 103–124 | DOI

[2] Lin Z., Zhang Ch., Wu W., Gao X., “Frequency recognition based on canonical correlation analysis for SSVEP-based BCIs”, IEEE transactions on biomedical engineering, 53:12 (2006), 2610–2614 | DOI

[3] Adeli H., Zhou Z., Dadmehr N., “Analysis of EEG records in an epileptic patient using wavelet transform”, Journal of neuroscience methods, 123:1 (2003), 69–87 | DOI

[4] Hansen S. T., Hemakom A., Safeldt M. G., Krohne L. K., Madsen K. H., Siebner H. R., Mandic D. P., Hansen L. K., “Unmixing oscillatory brain activity by eeg source localization and empirical mode decomposition”, Computational intelligence and neuroscience, 2019:4 (2019), 1-15 | DOI

[5] Karhunen K., Über lineare Methoden in der Wahrscheinlichkeitsrechnung, Universitat Helsinki, Helsinki, 1947, 79 pp.

[6] Loeve M., Functions Aleatories de Seconde Ordre, Hermann, Paris, 1948

[7] Tu Dzh., Gonsales R., Printsipy raspoznavaniya obrazov, Mir, M., 1978, 414 pp.

[8] Gonsales R., Vuds R., Tsifrovaya obrabotka izobrazhenii, Tekhnosfera, Moskva, 2012, 1104 pp.

[9] Hotelling H., “Analysis of a Complex of Statistical Variables into Principal Components”, J. Educ. Psychol., 24 (1933), 498–520

[10] Kramer H. P., Mathews M. V., “A Linear coding for transmitting a set of correlated signals”, IRE Trans. Info. Theory, 2:3 (1956), 41–46 | DOI

[11] Prett U., Tsifrovaya obrabotka izobrazhenii, Mir, M., 1982

[12] Duda R. O., Hart P. E., “Use of the Hough Transformation to Detect Lines and Curves in Pictures”, Comm. ACM, 15:1 (1972), 11–15

[13] Duda R. O, Hart P. E., Stork D. G., Pattern Classification, John Wiley and Sons, New York, 2001, 654 pp. | DOI

[14] Jonak K., Syta A., Karakula-Juchnowicz H., Krukow P., “The clinical application of EEG-signals recurrence analysis as a measure of functional connectivity: Comparative case study of patients with various neuropsychiatric disorders”, Brain sciences, 10:6 (2020), 380 | DOI

[15] Onton J., Westerfield M., Makeig S., Townsend J., “Imaging human EEG dynamics using independent component analysis”, Neuroscience and biobehavioral reviews, 30:6 (2006), 808–822 | DOI

[16] Ramakrishnan A. G., Satyanarayana J. V., “Reconstruction of EEG from limited channel acquisition using estimated signal correlation”, Biomedical Signal Processing and Control, 27 (2016), 164–173 | DOI

[17] Wongsawat Y., Oraintara S., Rao K. R., “Integer sub-optimal Karhunen-Loeve transform for multi-channel lossless EEG compression”, 14th European Signal Processing Conference (Florence, Italy), 2006, 1–5

[18] Wongsawat Y. Oraintara S., Tanaka T., Rao K. R., “Lossless multi-channel EEG compression”, IEEE International Symposium on Circuits and Systems, IEEE, 2006 | DOI

[19] Babadi B., McKinney S. M., Tarokh V., Ellenbogen J. M., “DiBa: A Data-Driven Bayesian Algorithm for Sleep Spindle Detection”, IEEE Transactions on Biomedical Engineering, 59:2, P (2012), 483–493 | DOI

[20] Kuriakose S., Titus G., “Karhunen-loeve transform for sleep spindle detection”, 3rd International Conference on Devices, Circuits and Systems (ICDCS) (Coimbatore, India), 2016, 249–253. | DOI

[21] Vural C., Murat Y., “Determination of sleep stage separation ability of features extracted from EEG signals using principle component analysis”, Journal of medical systems, 34:1 (2010), 83 | DOI

[22] Klonowski W., Jernajczyk W., Niedzielska K., Ritz A., “Quantitative measure of complexity of EEG signal dynamics”, Acta neurobiologiae experimentalis, 59:4 (1999), 315–321 | DOI

[23] Fuchs A., Kelso S., Haken H., “Phase transitions in the human brain: Spatial mode dynamics”, International Journal of Bifurcation and Chaos - IJBC, 2:4 (1992), 917–939 | DOI

[24] Jirsa V. K., Friedrich R., Haken H., “Reconstruction of the spatio-temporal dynamics of a human magnetoencephalogram”, Physica D: Nonlinear Phenomena, 89 (1995), 100–122 | DOI

[25] Anderson C. W., Devulapalli S. V., Stolz E., “Determining Mental State from EEG Signals Using Parallel Implementations of Neural Networks”, Sci. Program, 4:3 (1995), 171–183 | DOI

[26] Lamothe R. Stroink G., “Orthogonal expansions: Their applicability to signal extraction in electrophysiological mapping data”, Medical and biological engineering and computing, 29 (1991), 522–528 | DOI

[27] Broomhead D. S., King G. P., “Extracting qualitative dynamics from experimental data”, Physica D Nonlinear Phenomena, 20:2–3 (1986), 217–236 | DOI

[28] Rahman M. A., Haque M. M., Anjum A., Mollah M. N., Ahmad M., “Classification of motor imagery events from prefrontal hemodynamics for BCI application”, Proceedings of International Joint Conference on Computational Intelligence. Algorithms for Intelligent Systems, eds. Uddin M. S., Bansal J. C., Springer, Singapore, 2020, 11–23 | DOI

[29] Littner M. R., Kushida C., Wise M., Davila D. G., Morgenthaler T., Lee-Chiong T., Hirshkowitz M., Loube D. L., Bailey D., Berry R. B., Kapen S., Kramer M., “Practice parameters for clinical use of the multiple sleep latency test and the maintenance of wakefulness test”, Sleep, 28:1 (2005), 113–121 | DOI

[30] Schubring D., Kraus M., Stolz C., Weiler N., Keim D. A., Schupp H., “Virtual reality potentiates emotion and task effects of Alpha/Beta brain oscillations”, Brain Sciences, 10:8 (2020), 537 | DOI

[31] Iscan Z., Nikulin V. V., “Steady state visual evoked potential (SSVEP) based brain-computer interface (BCI) performance under different perturbations”, PloS one, 13:1 (2018) | DOI

[32] Parsamyan R. R., Posnenkova O. M., Zhuravlev M. O., Selskii A. O., Kiselev A. R., Fisun A. V., Runnova A. E., “Khronizatsiya golovnoi boli: analiz vyzvannykh potentsialov na stimul”, Rossiiskii zhurnal boli, 22:1 (2024), 18–26 | DOI

[33] Vatanabe S., “Razlozhenie Karunena–Loeva i faktornyi analiz. Teoriya i prilozheniya”, Avtomaticheskii analiz slozhnykh izobrazhenii, ed. Braverman E. M., Mir, M., 309 pp.

[34] Trubetskov D. I., Hramov A. E., Egorov E. N., Filatov R. A., Kalinin Y. A., Koronovskii A. A., “Experimental and Theoretical Study of Chaotic Microwave Oscillations and Pattern Formation in Non-relativistic Electron Beam with Virtual Cathode”, IEEE International Vacuum Electronics Conference held Jointly with 2006 IEEE International Vacuum Electron Sources, IEEE, Monterey, 2006, 527–528 | DOI

[35] Egorov E. N., Makarov V. V., Hramov A. E., “Analyzing the formation of coherent structures in a helical electron flow with a virtual cathode”, Bull. Russ. Acad. Sci. Phys., 78 (2014), 1246–1249 | DOI

[36] Egorov E. N., Hramov A. E., “Formation of coherent structures in helical electron beam with a virtual cathode”, 24th International Crimean Conference Microwave and Telecommunication Technology (Sevastopol, Russia), 2014, 845–846

[37] Runnova A., Zhuravlev M., Shamionov R., Parsamyan R., Egorov E., Kiselev A., Selskii A., Akimova O., Karavaev A., Kurths J., “Spatial patterns in EEG activity during monotonous sound perception test”, Eur. Phys. J. Plus, 136 (2021), 735 | DOI

[38] Bazanova O. M., Vernon D., “Interpreting EEG alpha activity”, Neuroscience and Biobehavioral Reviews, 44 (2014), 94–110 | DOI

[39] Simonyan M. S., Novikov M. Yu., “Izmenenie prostranstvennoi struktury aktivnosti golovnogo mozga pri dlitelnoi monotonnoi zritelnoi nagruzke”, Trudy VII Vserossiiskoi konferentsii «Nelineinaya dinamika v kognitivnykh issledovaniyakh - 2021», 144–146

[40] Zhuravlev M., Novikov M., Parsamyan R., Selskii A., Runnova A., “The Objective Assessment of Event-Related Potentials: An Influence of Chronic Pain on ERP Parameters”, Neuroscience bulletin, 39:7 (2023), 1105–1116 | DOI