ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

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Egorov N. M., Sysoeva M. V., Ponomarenko V. I., Kornilov M. V., Sysoev I. V. Ring generator of neuron-like activity with tunable frequency. Izvestiya VUZ. Applied Nonlinear Dynamics, 2023, vol. 31, iss. 1, pp. 103-120. DOI: 10.18500/0869-6632-003025, EDN: AXLDTJ

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Ring generator of neuron-like activity with tunable frequency

Egorov Nikita Mikhailovich, Yuri Gagarin State Technical University of Saratov
Sysoeva Marina Vyacheslavovna, Yuri Gagarin State Technical University of Saratov
Ponomarenko Vladimir Ivanovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Kornilov Maksim Vyacheslavovich, Saratov State University
Sysoev Ilya Vyacheslavovich, Saratov State University

The aim of the work is to build a radiophysical generator of neuron-like activity with a frequency tunable in various ways, corresponding to modern ideas about the structure of the hippocampus and the generation of pathological epileptic rhythms in it. Methods. The elements of the generator are radio engineering implementations of the complete FitzHugh– Nagumo neuron and the electronic implementation of a chemical synapse in the form of a sigmoid function with a delayed argument. The simulation was carried out in the SPICE simulator. Results. Various ways of introducing delay into the coupling are considered: an ideal delay line, a phase filter with a rheostat, one tunable Bessel filter, and a sequence of non-tunable Bessel filters. For circuit implementation, the approach using a Bessel filter with a rheostat is recognized as optimal as a compromise between simplicity and minimization of signal distortion. The dependences of the oscillation frequency on the number of elements in the ring and the delay time are constructed. The bistability of generation regimes is studied for certain values of the parameters. The effect of inclusion of inhibitory elements (interneurons) in the circuit is considered. Conclusion. The constructed ring generator models the experimentally observed properties of the dynamics of epileptic discharge fundamental frequency in limbic epilepsy. It is able to reproduce the occurrence of oscillations as a result of external short-term driving, smooth and sharp frequency tuning, the coexistence of different modes with the same parameters.

This study was supported by Russian Science Foundation, grant No. 19-72-10030-P,
  1. Lodi M, Shilnikov AL, Storace M. Design principles for central pattern generators with preset rhythms. IEEE Transactions on Neural Networks and Learning Systems. 2020;31(9):3658–3669. DOI: 10.1109/TNNLS.2019.2945637.
  2. Kurkin SA, Kulminskiy DD, Ponomarenko VI, Prokhorov MD, Astakhov SV, Hramov AE. Central pattern generator based on self-sustained oscillator coupled to a chain of oscillatory circuits. Chaos. 2022;32(3):033117. DOI: 10.1063/5.0077789.
  3. Mahowald M, Douglas R. A silicon neuron. Nature. 1991;354(6354):515–518. DOI: 10.1038/ 354515a0.
  4. Rasche C, Douglas R. An improved silicon neuron. Analog Integrated Circuits and Signal Processing. 2000;23(3):227–236. DOI: 10.1023/A:1008357931826. 
  5. van Schaik A. Building blocks for electronic spiking neural networks. Neural Networks. 2001; 14(6–7):617–628. DOI: 10.1016/S0893-6080(01)00067-3.
  6. Dmitrichev AS, Kasatkin DV, Klinshov VV, Kirillov SY, Maslennikov OV, Shchapin DS, Nekorkin VI. Nonlinear dynamical models of neurons: Review. Izvestiya VUZ. Applied Nonlinear Dynamics. 2018;26(4):5–58. DOI: 10.18500/0869-6632-2018-26-4-5-58.
  7. FitzHugh R. Impulses and physiological states in theoretical models of nerve membrane. Biophysical Journal. 1961;1(6):445–466. DOI: 10.1016/S0006-3495(61)86902-6.
  8. Nagumo J, Arimoto S, Yoshizawa S. An active pulse transmission line simulating nerve axon. Proceedings of the IRE. 1962;50(10):2061–2070. DOI: 10.1109/JRPROC.1962.288235.
  9. Hodgkin AL, Huxley AF. A quantitative description of membrane current and its application to conduction and excitation in nerve. The Journal of Physiology. 1952;117(4):500–544. DOI: 10.1113/jphysiol.1952.sp004764.
  10. Binczak S, Jacquir S, Bilbault JM, Kazantsev VB, Nekorkin VI. Experimental study of electrical FitzHugh–Nagumo neurons with modified excitability. Neural Networks. 2006;19(5):684–693. DOI: 10.1016/j.neunet.2005.07.011.
  11. Kulminskiy DD, Ponomarenko VI, Prokhorov MD, Hramov AE. Synchronization in ensembles of delay-coupled nonidentical neuronlike oscillators. Nonlinear Dynamics. 2019;98(1):735–748. DOI: 10.1007/s11071-019-05224-x.
  12. Egorov NM, Ponomarenko VI, Sysoev IV, Sysoeva MV. Simulation of epileptiform activity using network of neuron-like radio technical oscillators. Technical Physics. 2021;66(3):505–514. DOI: 10.1134/S1063784221030063.
  13. Egorov NM, Ponomarenko VI, Melnikova SN, Sysoev IV, Sysoeva MV. Common mechanisms of attractorless oscillatory regimes in radioengineering models of brain thalamocortical network. Izvestiya VUZ. Applied Nonlinear Dynamics. 2021;29(6):927–942 (in Russian). DOI: 10.18500/0869-6632-2021-29-6-927-942.
  14. Egorov NM, Kulminskiy DD, Sysoev IV, Ponomarenko VI, Sysoeva MV. Transient dynamics in electronic neuron-like circuits in application to modeling epileptic seizures. Nonlinear Dynamics. 2022;108(4):4231–4242. DOI: 10.1007/s11071-022-07379-6.
  15. Kapustnikov AA, Sysoeva MV, Sysoev IV. The modeling of spike-wave discharges in brain with small oscillatory neural networks. Mathematical Biology and Bioinformatics. 2020;15(2):138–147 (in Russian). DOI: 10.17537/2020.15.138.
  16. Kapustnikov AA, Sysoeva MV, Sysoev IV. Transient dynamics in a class of mathematical models of epileptic seizures. Communications in Nonlinear Science and Numerical Simulation. 2022;109:106284. DOI: 10.1016/j.cnsns.2022.106284.
  17. Egorov NM, Sysoev IV, Ponomarenko VI, Sysoeva MV. Epileptiform activity generation by an ensemble of complete electronic FitzHugh-Nagumo oscillators connected by a sigmoid couplings. In: Proceedings of SPIE. Vol. 12194. Computational Biophysics and Nanobiophotonics. Bellingham: SPIE; 2022. P. 1219403. DOI: 10.1117/12.2623993.
  18. Egorov NM, Sysoev IV, Ponomarenko VI, Sysoeva MV. Complex regimes in electronic neuron-like oscillators with sigmoid coupling. Chaos, Solitons & Fractals. 2022;160:112171. DOI: 10.1016/j.chaos.2022.112171.
  19. Rabinovich MI, Zaks MA, Varona P. Sequential dynamics of complex networks in mind: Consciousness and creativity. Physics Reports. 2020;883:1–32. DOI: 10.1016/j.physrep.2020.08.003.
  20. Wang Q, Perc M, Duan Z, Chen G. Impact of delays and rewiring on the dynamics of small world neuronal networks with two types of coupling. Physica A: Statistical Mechanics and its Applications. 2010;389(16):3299–3306. DOI: 10.1016/j.physa.2010.03.031.
  21. Winder S. Analog and Digital Filter Design. 2nd edition. USA: Elsevier; 2002. 458 p. DOI: 10.1016/B978-0-7506-7547-5.X5000-3.
  22. Banerjee T, Biswas D, Sarkar BC. Anticipatory, complete and lag synchronization of chaos and hyperchaos in a nonlinear delay-coupled time-delayed system. Nonlinear Dynamics. 2013; 72(1–2):321–332. DOI: 10.1007/s11071-012-0716-4.
  23. Srinivasan K, Raja Mohamed I, Murali K, Lakshmanan M, Sinha S. Design of time delayed chaotic circuit with threshold controller. International Journal of Bifurcation and Chaos. 2011;21(3): 725–735. DOI: 10.1142/S0218127411028751.
  24. Karki J. Active Low-Pass Filter Design. Texas: Texas Instruments; 2000. 24 p.
  25. Cao P, Fan H, Wang D, Shu H, Yang B, Han Y, Dong J. Compensation circuit design for tuned half-wavelength transmission lines based on Bessel filter. International Journal of Electrical Power & Energy Systems. 2022;134:107335. DOI: 10.1016/j.ijepes.2021.107335.
  26. Buscarino A, Fortuna L, Frasca M, Sciuto G. Design of time-delay chaotic electronic circuits. IEEE Transactions on Circuits and Systems I: Regular Papers. 2011;58(8):1888–1896. DOI: 10.1109/TCSI.2011.2107190.
  27. Rudy B, Fishell G, Lee S, Hjerling-Leffler J. Three groups of interneurons account for nearly 100% of neocortical GABAergic neurons. Developmental Neurobiology. 2011;71(1):45–61. DOI: 10.1002/dneu.20853.
  28. Vinogradova OS. Hippocampus as comparator: Role of the two input and two output systems of the hippocampus in selection and registration of information. Hippocampus. 2001;11(5):578–598. DOI: 10.1002/hipo.1073.
  29. Sysoev IV, Kornilov MV, Makarova NA, Sysoeva MV, Vinogradova LV. Modeling limbic seizure initiation with an ensemble of delay coupled neuroscillator. In: Lacarbonara W, Balachandran B, Leamy MJ, Ma J, Tenreiro Machado JA, Stepan G, editors. Advances in Nonlinear Dynamics. NODYCON Conference Proceedings Series. Cham: Springer; 2022. P. 73–81. DOI: 10.1007/978- 3-030-81170-9_7.
  30. Nelson TS, Suhr CL, Freestone DR, Lai A, Halliday AJ, McLean KJ, Burkitt AN, Cook MJ. Closed-loop seizure control with very high frequency electrical stimulation at seizure onset in the GAERS model of absence epilepsy. International Journal of Neural Systems. 2011;21(2):163–173. DOI: 10.1142/S0129065711002717.
  31. van Heukelum S, Kelderhuis J, Janssen P, van Luijtelaar G, Luttjohann A. Timing of high-frequency cortical stimulation in a genetic absence model. Neuroscience. 2016;324:191–201. DOI: 10.1016/j.neuroscience.2016.02.070.
  32. Lopes da Silva F. Neural mechanisms underlying brain waves: from neural membranes to networks. Electroencephalography and Clinical Neurophysiology. 1991;79(2):81–93. DOI: 10.1016/0013- 4694(91)90044-5.
  33. Schnitzler A, Gross J. Normal and pathological oscillatory communication in the brain. Nature Reviews Neuroscience. 2005;6(4):285–296. DOI: 10.1038/nrn1650.
  34. Benca R, Duncan MJ, Frank E, McClung C, Nelson RJ, Vicentic A. Biological rhythms, higher brain function, and behavior: Gaps, opportunities, and challenges. Brain Research Reviews. 2009;62(1):57–70. DOI: 10.1016/j.brainresrev.2009.09.005.
  35. Buzsaki G. Rhythms of the Brain. Oxford: Oxford University Press; 2006. 448 p. DOI: 10.1093/acprof:oso/9780195301069.001.0001.
  36. Rudrauf D, Douiri A, Kovach C, Lachaux JP, Cosmelli D, Chavez M, Adam C, Renault B, Martinerie J, Le Van Quyen M. Frequency flows and the time-frequency dynamics of multivariate phase synchronization in brain signals. NeuroImage. 2006;31(1):209–227. DOI: 10.1016/ j.neuroimage.2005.11.021.
  37. Good LB, Sabesan S, Marsh ST, Tsakalis K, Treiman D, Iasemidis L. Control of synchronization of brain dynamics leads to control of epileptic seizures in rodents. International Journal of Neural Systems. 2009;19(3):173–196. DOI: 10.1142/S0129065709001951.
  38. Paz JT, Huguenard JR. Microcircuits and their interactions in epilepsy: is the focus out of focus? Nature Neuroscience. 2015;18(3):351–359. DOI: 10.1038/nn.3950.
  39. Sysoeva MV, Vinogradova LV, Perescis M, van Rijn CM, Sysoev IV. Revealing changes in directed interstructural couplingsat limbic seizures, induced by injection of cb1 receptor antagonist using nonlinear granger causality method. I.P. Pavlov Journal of Higher Nervous Activity. 2019;69(6):752–767 (in Russian). DOI: 10.1134/S0044467719060121.
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