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Isolated wave segments in a neural tissue model with volume transmission: discreteness matters

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Abstract

Isolated wave segments are a type of spatiotemporal activity that has been repeatedly reported in experimental studies of spreading depolarization on the cerebral cortex and retina of laboratory animals. However, it has been theoretically shown that such a pattern cannot be stable in a continuous excitable medium. In our work, we address this problem using the model of a discrete–continuous medium. We present the targeted numerical study of isolated wave segments, including scenarios of their emergence and an estimation of their stability to various deformations. We show that an isolated wave segment can exhibit the properties of a space-time attractor by cyclically changing its shape and approaching it from different initial conditions. Such a wave segment is not necessarily small, although small segments may occur more easily and are, therefore, more likely. Finally, we show that the behavior we found persists also under conditions of a heterogeneous propagation medium, which indicates the applicability of our findings to the analysis of spatiotemporal patterns in real nervous tissue.

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Acknowledgements

This research was supported by the Russian Science Foundation, project #22-15-00143 (sections 1, 2.1, 3.3, 3.4, 3.5, 4), and by the government of the Russian Federation, project #075-15-2022-1094 (sections 2.3, 3.1, 3.2,4).

Author information

Authors and Affiliations

  1. Department of Theoretical Physics, Kursk State University, Radishcheva st., 33, 305000, Kursk, Russia

    Andrey Yu. Verisokin & Darya V. Verveyko

  2. Department of Optics and Biophotonics, Saratov State University, Astrakhanskaya st., 83, 410012, Saratov, Russia

    Dmitry E. Postnov

Authors
  1. Andrey Yu. Verisokin
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  2. Darya V. Verveyko
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  3. Dmitry E. Postnov
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Corresponding author

Correspondence to Dmitry E. Postnov.

Additional information

Brain Physiology Meets Complex Systems. Guest editors: Thomas Penzel, Teemu Myllylä, Oxana V. Semyachkina-Glushkovskaya, Alexey Pavlov, Anatoly Karavaev.

Supplementary Information

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11734_2023_810_MOESM1_ESM.pdf

The following supporting information can be downloaded at https://doi.org/10.5281/zenodo.7576597: program code for the implementation of the model, video examples of the solutions of the proposed model that demonstrate the scenarios of SWS emergence and the Matlab code for the implementation of the cellular automaton. (PDF 156 KB)

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Supplementary file2 (PDF 30 KB)

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Verisokin, A.Y., Verveyko, D.V. & Postnov, D.E. Isolated wave segments in a neural tissue model with volume transmission: discreteness matters. Eur. Phys. J. Spec. Top. 232, 499–508 (2023). https://doi.org/10.1140/epjs/s11734-023-00810-y

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