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Assessment of Cortical Travelling Waves Parameters Using Radially Symmetric Solutions to Neural Field Equations with Microstructure

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Advances in Neural Computation, Machine Learning, and Cognitive Research IV (NEUROINFORMATICS 2020)

Part of the book series: Studies in Computational Intelligence ((SCI,volume 925))

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Abstract

We model cortical travelling waves by radially symmetric solutions to planar neural field equations with periodic spatial heterogeneity, which capture e.g. the microstructure observed in the primary visual cortex. We investigate the so-called bump-solutions that correspond to generation of local excitation in the brain tissue and an early stage of radially symmetric spread of cortical waves. We study how the neural medium heterogeneity and other biophysical parameters such as neuron activation threshold, the lengths and the strengths of neuronal connections affect cortical waves mathematically represented in terms of radially symmetric solutions to neural field equations with microstructure.

The reported study was funded by RFBR and FRLC, project number 20-511-23001, by RFBR, project number 20-015-00475, and in part supported by OFIm, project number 17-29-02518. The results in Sect. 2 were obtained with the support of the Russian Science Foundation (grant no. 20-11-20131) in V.A. Trapeznikov Institute of Control Sciences of RAS.

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References

  1. Muller, L., Chavane, F., Reynolds, J., Sejnowski, T.: Cortical travelling waves: mechanisms and computational principles. Nat. Rev. Neurosci. 5, 255–268 (2018)

    Article  Google Scholar 

  2. Martinet, L.E., Fiddyment, G., Madsen, J.R., Eskandar, E.N., Truccolo, W., Eden, U.T., Cash, S.S., Kramer, M.A.: Human seizures couple across spatial scales through travelling wave dynamics. Nat. Commun. 8, 14896 (2017)

    Article  Google Scholar 

  3. Ha, K., Jeon, J.: Motor imagery EEG classification using capsule networks. Sensors 19(13), 2854 (2019)

    Article  Google Scholar 

  4. Naoumenko, D., Gong, P.: Complex dynamics of propagating waves in a two-dimensional neural field. Front. Comput. Neurosci. 13(50), 1–50 (2019)

    Google Scholar 

  5. Verkhlyutov, V., Sharaev, M., Balaev, V., Osadtchi, A., Ushakov, V., Skiteva, L., Velichkovsky, B.: Towards localization of radial traveling waves in the evoked and spontaneous MEG: a solution based on the intra-cortical propagation hypothesis. Proc. Comput. Sci. 145, 617–622 (2018)

    Article  Google Scholar 

  6. Burlakov, E., Wyller, J., Ponosov, A.: Two-dimensional Amari neural field model with periodic microstructure: rotationally symmetric bump solutions. Commun. Nonl. Sci. Num. Simul. 32, 81–88 (2016)

    Article  MathSciNet  Google Scholar 

  7. Svanstedt, N., Woukeng, J.L.: Homogenization of a Wilson-Cowan model for neural fields. Nonlin. Anal. Real World Appl. 14(3), 1705–1715 (2013)

    Article  MathSciNet  Google Scholar 

  8. Burlakov, E.: On inclusions arising in neural field modeling. Differ. Equ. Dyn. Syst. (2018). https://doi.org/10.1007/s12591-018-0443-5

  9. Burlakov, E., Zhukovskiy, E., Verkhlyutov, V.: Neural field equations with neuron-dependent Heaviside-type activation function and spatial-dependent delay. Math. Meth. Appl. Sci. (2020). https://doi.org/10.1002/mma.6661

  10. Xu, W., Huang, X., Takagaki, K., Wu, J.Y.: Compression and reflection of visually evoked cortical waves. Neuron 55(1), 119–29 (2007)

    Article  Google Scholar 

  11. Burlakov, E., Nasonkina, M.: On connection between continuous and discontinuous neural field models with microstructure I. general theory. Tambov Univ. Rep. Ser. Nat. Tech. Sci. 23(121), 17–30 (2018)

    Google Scholar 

  12. Burlakov, E., Ponosov, A., Wyller, J.: Stationary solutions of continuous and discontinuous neural field equations. J. Math. Anal. Appl. 444, 47–68 (2016)

    Article  MathSciNet  Google Scholar 

  13. Radially symmetric solutions to continuous and discontinuous neural field equations. https://sites.google.com/view/vhbtw/main/rsscdnfe

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Author information

Authors and Affiliations

  1. University of Tyumen, 6 Volodarskogo St., 625003, Tyumen, Russian Federation

    Evgenii Burlakov & Ivan Malkov

  2. V.A. Trapeznikov Institute of Control Sciences of RAS, 65 Profsoyuznaya St., 117997, Moscow, Russian Federation

    Evgenii Burlakov

  3. Institute of Higher Nervous Activity and Neurophysiology of RAS, 5A Butlerova St., 117485, Moscow, Russian Federation

    Vitaly Verkhlyutov

  4. National Research Center Kurchatov Institute, 1 Akademika Kurchatova pl., 123182, Moscow, Russian Federation

    Vadim Ushakov

  5. National Research Nuclear University MEPhI, 31 Kashirskoe hwy, 115409, Moscow, Russian Federation

    Vadim Ushakov

  6. Institute for Advanced Brain Studies, Lomonosov Moscow State University, GSP-1, Leninskie Gory, 119991, Moscow, Russian Federation

    Vadim Ushakov

Authors
  1. Evgenii Burlakov
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  2. Vitaly Verkhlyutov
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  3. Ivan Malkov
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  4. Vadim Ushakov
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Corresponding author

Correspondence to Evgenii Burlakov .

Editor information

Editors and Affiliations

  1. Scientific Research Institute for System Analysis, Russian Academy of Sciences, Moscow, Russia

    Boris Kryzhanovsky

  2. Scientific Research Institute for System Analysis, Russian Academy of Sciences, Moscow, Russia

    Witali Dunin-Barkowski

  3. Scientific Research Institute for System Analysis, Russian Academy of Sciences, Moscow, Russia

    Vladimir Redko

  4. Moscow Aviation Institute (National Research University), Moscow, Russia

    Yury Tiumentsev

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Burlakov, E., Verkhlyutov, V., Malkov, I., Ushakov, V. (2021). Assessment of Cortical Travelling Waves Parameters Using Radially Symmetric Solutions to Neural Field Equations with Microstructure. In: Kryzhanovsky, B., Dunin-Barkowski, W., Redko, V., Tiumentsev, Y. (eds) Advances in Neural Computation, Machine Learning, and Cognitive Research IV. NEUROINFORMATICS 2020. Studies in Computational Intelligence, vol 925. Springer, Cham. https://doi.org/10.1007/978-3-030-60577-3_5

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