Informacionnye TehnologiiInformacionnye TehnologiiИнформационные технологии1684-6400New Technologies Publishing House70733410.17587/it.32.273-280Information technologies in biomedical systemsИнформационные технологии в биомедицинских системахResearch ArticleAn approach to determining the epicenter of a traveling wave with an inhomogeneous distribution of braking effectsЛокализация эпицентра бегущей волны с неоднородным распределением тормозящих эффектовMalkovI. N.МальковИ. Н.
Russian Federation

Postgraduate Student

аспирант

i.n.malkov@yandex.ruUniversity of TyumenТюменский государственный университет090520263252732800905202609052026Copyright ©; 2026, Informacionnye TehnologiiCopyright ©; 2026, Информационные технологии2026Informacionnye TehnologiiИнформационные технологииhttps://journals.eco-vector.com/1684-6400/article/view/707334

The purpose of this study is to develop a method for determining the epicenter of a traveling wave of electrical activity in the human cortex, taking into account the heterogeneous distribution of inhibitory effects. For this purpose, a mathematical model of an Amari-type neural field is used, which allows taking into account the directional variability of the travelling wave velocity. Within the framework of the hypothesis of radially asymmetric wave propagation, an algorithm has been developed that includes numerical simulation of the wave process, approximation of experimental data, and minimization of the error functional. The main result of the work is to clarify the position of the epicenter of the wave based on a comparison of calculated and experimental MEG data.

Целью настоящего исследования является разработка метода определения эпицентра бегущей волны электрической активности на коре головного мозга человека с учетом неоднородного распределения тормозящих эффектов. Для этого используется математическая модель нейронного поля типа Амари, позволяющая учитывать направленную изменчивость скорости распространения волны. В рамках гипотезы о радиально-асимметричном распространении волны разработан алгоритм, включающий численное моделирование волнового процесса, аппроксимацию экспериментальных данных и минимизацию функционала ошибки. Основным результатом работы является уточнение положения эпицентра волны на основе сопоставления расчетных и экспериментальных данных магнитоэнцефалографии.

neural field modelcortical traveling wavesevoked neural activityasymmetric traveling wavesrestoration of traveling wave parametersмодель нейронного полякортикальные бегущие волнывызванная нейронная активностьасимметричные бегущие волнывосстановление параметров бегущей волныРоссийский научный фондRussian Science Foundation23-11-20020The present research is supported by the Russian Science Foundation (project № 23-11-20020, https://rscf.ru/project/23-11-20020).Работа выполнена при финансовой поддержке РНФ (проект № 23-11-20020, https://rscf.ru/project/23-11-20020).Goodfellow Ya., Bendjio I., Courville А. Deep Learning, 2nd ed., Moscow, DMK Press, 2018, 652 p. (in Russian).Гудфеллоу Я., Бенджио И., Курвилль А. Глубокое обучение / Пер. с анг. А. А. Слинкина. М.: ДМК Пресс, 2018. 652 с.Kureichik V. M., Lebedev B. K., Lebedev O. K. Search Adaptation: Theory and Practice, Moscow, Fizmatlit, 2006, 272 p. (in Russian).Курейчик В. М., Лебедев Б. К., Лебедев О. К. Поисковая адаптация: теория и практика. М.: Физматлит, 2006. 272 с.Arbabyazd L., Shen K., Wang Z., Hofmann-Apitius M., Ritter P., McIntosh AR., Battaglia D., Jirsa V. Virtual connectomic datasets in Alzheimer’s disease and aging using whole brain network dynamics modelling, eNeuro, 2021, vol. 8, no. 4, pp. 1—33.Arbabyazd L., Shen K., Wang Z., Hofmann-Apitius M., Ritter P., McIntosh A. R., Battaglia D., Jirsa V. Virtual connectomic datasets in Alzheimer’s disease and aging using whole brain network dynamics modelling // eNeuro. 2021.Atmania R., Burlakov E. O., Malkov I. N. On existence and stability of ring solutions to Amari neural field equation with periodic microstructure and Heaviside activation function, Russian Universities Reports. Mathematics, 2022, vol. 27, no. 140, pp. 318—327.Atmania R., Burlakov E. O., Malkov I. N. On existence and stability of ring solutions to Amari neural field equation with periodic microstructure and Heaviside activation function // Russian Universities Reports. Mathematics. 2022. N. 27 (140). P. 318—327.Bressloff P. C., Carroll S. R. Laminar Neural Field Model of Laterally Propagating Waves of Orientation Selectivity, PLOS Computational Biology, 2015, vol. 11, no. 10.Bressloff P. C., Carroll S. R. Laminar Neural Field Model of Laterally Propagating Waves of Orientation Selectivity // PLOS Computational Biology. 2015. N. 11 (10). e1004545.Burlakov E. On Inclusions Arising in Neural Field Modeling, Differential Equations and Dynamical Systems, 2021, vol. 29, pp. 765—787.Burlakov E. On Inclusions Arising in Neural Field Modeling // Differential Equations and Dynamical Systems. 2021. Vol. 29. P. 765—787.Burlakov E., Oleynik A., Ponosov А. Travelling Waves in Neural Fields with Continuous and Discontinuous Neuronal Activation, Mathematics, 2025, vol. 13, no. 5.Burlakov E., Oleynik A., Ponosov А. Travelling Waves in Neural Fields with Continuous and Discontinuous Neuronal Activation // Mathematics. 2025. Vol. 13, N. 5. P. 701.Burlakov E., Verkhlyutov V., Malkov I. On well-posedness of a mathematical model of evoked activity in the primary visual cortex, Russian Universities Reports. Mathematics, 2024, vol. 29, no. 145, pp. 43—50.Burlakov E., Verkhlyutov V., Malkov I. On well-posedness of a mathematical model of evoked activity in the primary visual cortex // Russian Universities Reports. Mathematics. 2024. P. 43—50.Burlakov E., Verkhlyutov V., Ushakov V. А Simple Human Brain Model Reproducing Evoked MEG Based on Neural Field Theory, Advances in Neural Computation, Machine Learning, and Cognitive Research V. NEUROINFORMATICS 2021. Studies in Computational Intelligence, 2022, vol. 1008, pp. 109—116.Burlakov E., Verkhlyutov V., Ushakov V. А Simple Human Brain Model Reproducing Evoked MEG Based on Neural Field Theory // Advances in Neural Computation, Machine Learning, and Cognitive Research V. NEUROINFORMATICS 2021. Studies in Computational Intelligence. 2022. No-. 1008. P. 109—116.Burlakov E., Zhukovskiy E., Verkhlyutov V. Neural field equations with neuron-dependent Heaviside-type activation function and spatial-dependent delay, Mathematical Methods in the Applied Sciences, 2020, vol. 44, no. 15, pp. 11895—11903.Burlakov E., Zhukovskiy E., Verkhlyutov V. Neural field equations with neuron-dependent Heaviside-type activation function and spatial-dependent delay // Mathematical Methods in the Applied Sciences. 2020. N. 1—9.Coombes S., Schmidt H., Laing C. R., Svanstedt N., Wyller J. A. Waves in random neural media, Discrete and Continuous Dynamical Systems, 2012, vol. 32, no. 8, pp. 2951—2970.Coombes S., Schmidt H., Laing C. R., Svanstedt N., Wyller J. A. Waves in random neural media // Discrete and Continuous Dynamical Systems. 2012. N. 32 (8). P. 2951—2970.Kuznetsova A. A., Ossadtchi А. E. Analysis of the Local Dynamics of Interictal Discharge Propagation Using a Traveling Wave Model, Neuroscience and Behavioral Physiology, 2022, vol. 52, pp. 1436—1447.Kuznetsova A. A., Ossadtchi А. E. Analysis of the Local Dynamics of Interictal Discharge Propagation Using a Traveling Wave Model // Neuroscience and Behavioral Physiology. 2022. N. 52. P. 1436—1447.Malkov I., Burlakov E., Verkhlyutov V. M., Ushakov V. А Model of Travelling Waves in the Neural Medium with Directional Variability of Inhibitory Effects, Advances in Neural Computation, Machine Learning, and Cognitive Research VIII, Springer, 2024, pp. 244—253.Malkov I., Burlakov E., Verkhlyutov V. M., Ushakov V. А Model of Travelling Waves in the Neural Medium with Directional Variability of Inhibitory Effects // Advances in Neural Computation, Machine Learning, and Cognitive Research VIII. Springer. 2024. P. 3—13.Mapelli J., Gandolfi D., Giuliani E., Casali S., Congi L., Barbieri A., D’Angelo E., Bigiani А. The effects of the general anesthetic sevoflurane on neurotransmission: an experimental and computational study, Scientific Reports, 2021, vol. 11, no. 1.Mapelli J., Gandolfi D., Giuliani E., Casali S., Congi L., Barbieri A., D’Angelo E., Bigiani А. The effects of the general anesthetic sevoflurane on neurotransmission: an experimental and computational study // Scientific Reports. 2021. N. 11 (1). P. 4335.Nielsen B. F., Wyller J. A. Ill-posed point neuron models, The Journal of Mathematical Neuroscience, 2016, vol. 6, no. 1.Nielsen B. F., Wyller J. A. Ill-posed point neuron models // The Journal of Mathematical Neuroscience. 2016. Vol. 6, N. 1. P. 7.Pinto D., Ermentrout G. Spatially structured activity in synaptically coupled neuronal networks: 1. Traveling fronts and pulses, SIAM Journal on Applied Mathematics, 2001, vol. 62, no. 1, pp. 206—225.Pinto D., Ermentrout G. Spatially structured activity in synaptically coupled neuronal networks: 1. Traveling fronts and pulses // SIAM Journal on Applied Mathematics. 2001. N. 62. P. 206—225.Pinto D. J., Jackson R. K., Wayne C. E. Existence and stability of traveling pulses in a continuous neuronal network, SIAM Journal on Applied Mathematics, 2005, vol. 4, no. 4, pp. 954—984.Pinto D. J., Jackson R. K., Wayne C. E. Existence and stability of traveling pulses in a continuous neuronal network // SIAM Journal on Applied Mathematics. 2005. N. 4 (4). P. 954—984.Potthast R., Graben P. B. Existence and properties of solutions for neural field equations, Mathematical Methods in the Applied Sciences, 2010, vol. 33, no. 8, pp. 935—949.Potthast R., Graben P. B. Existence and properties of solutions for neural field equations // Mathematical Methods in the Applied Sciences. 2010. N. 8. P. 935—949.Tadel F., Baillet S., Mosher J. C., Pantazis D., Leahy R. M. Brainstorm: a user friendly application for MEG/EEG analysis, Computational Intelligence and Neuroscience, 2011, vol. 2011, no. 1.Tadel F., Baillet S., Mosher J. C., Pantazis D., Leahy R. M. Brainstorm: a user friendly application for MEG/EEG analysis // Computational Intelligence and Neuroscience. 2011. N. 879716. P. 1—13.Tieck J. C. V., Secker K., Kaiser J., Roennau A., Dillmann R. Soft-grasping with an anthropomorphic robotic hand using spiking neurons, IEEE Robotics and Automation Letters, 2021, vol. 6, no. 2, pp. 2894—2901.Tieck J. C. V., Secker K., Kaiser J., Roennau A., Dillmann R. Soft-grasping with an anthropomorphic robotic hand using spiking neurons // IEEE Robotics and Automation Letters. 2021. N. 6 (2). P. 2894—2901.Verkhlyutov V. M., Sharaev M., Balaev V., Osadtchi A., Ushakov V., Skiteva L., Velichkovsky В. Towards localization of radial traveling waves in the evoked and spontaneous MEG: А solution based on the intra-cortical propagation hypothesis, Procedia Computer Science, 2018, vol. 145, no. 3, pp. 617—622.Verkhlyutov V. M., Sharaev M., Balaev V., Osadtchi A., Ushakov V., Skiteva L., Velichkovsky В. Towards localization of radial traveling waves in the evoked and spontaneous MEG: А solution based on the intra-cortical propagation hypothesis // Procedia Computer Science. 2018. N. 145. P. 617—622.