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Computer simulation of reverberating spreading depression in a network of cell automata. (English) Zbl 0301.92007

Summary: A homogeneous network of cellular automata, representing a two-dimensional model of neural tissue, was used for simulation of periodic processes generated by spreading cortical depression. The transitional function μ and the function of the output \(\gamma\) of each cellular automationA at the timet is explicitly determined by its state and the input signals from 4 adjacent cells at timet-1. Computer experiments (IBM 370-135) in networks consisting of 1000 or 7200 cells illustrated the development of periodic generators due to 1) reverberation around obstacles with the perimeter exceeding the wavelength of the process: 2) reverberation in intact tissue (with zero perimeter of the obstacle); 3) formation of a stable focus of periodic activity (deterministic-stochastic oscillator). Results of computer experiments are compared with electrophysiological observations.

MSC:

92B05 General biology and biomathematics
68U20 Simulation (MSC2010)
68W99 Algorithms in computer science
68Q45 Formal languages and automata
94C10 Switching theory, application of Boolean algebra; Boolean functions (MSC2010)
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[1] Bureš, J., Burešová, O., Křivánek, J.: The mechanism and applications of Leão’s spreading depression of electroencephalographic activity. New York-London: Academic Press 1974
[2] Codd, E.F.: Cellular automata. New York-London: Academic Press 1968 · Zbl 0213.18301
[3] Farley, B.G.: Computers in biomedical research. New York-London: Academic Press 1965
[4] Kuypers, K., Smith, I.: Kybernetik12, 216 (1973) · Zbl 0256.92006 · doi:10.1007/BF00270574
[5] Leão, A.A.P.: J. Neurophysiol.7, 359 (1944)
[6] Letychevsky, A.A., Reshodko, L.V.: Kibernetika (Kiyev)5, 137 (1972)
[7] Matsuura, T., Bureš, J.: Exp. Brain Res.12, 238 (1971) · doi:10.1007/BF00237916
[8] Minsky, M.L.: Computation: finite and infinite machines. Englewood Cliffs, N.Y.: Prentice-Hall 1967 · Zbl 0195.02402
[9] Moe, G.K., Rheinboldt, W.C., Abildskov, I.A.: Amer. Heart J.67, 200 (1964) · doi:10.1016/0002-8703(64)90371-0
[10] Reshodko, L.V.: Zh. Obshch. Biol.35, 80 (1974a)
[11] Reshodko, L.V.: Kybernetika (Prague)10, 409 (1974b)
[12] Selfridge, O.: Arch. Inst. Cardiol. Mex.18, 177 (1948)
[13] Shibata, M., Bureš, J., J. Neurophysiol.35, 381 (1972)
[14] Shibata, M., Bureš, J.: Activitas nerv. sup. (Praha)16, 2 (1973)
[15] Shibata, M., Bureš, J.: J. Neurobiol.5, 107 (1974) · doi:10.1002/neu.480050203
[16] Smith III., A.R.: Information and Control18, 466 (1971) · Zbl 0222.94057 · doi:10.1016/S0019-9958(71)90501-8
[17] Vollmar, R.: Angewandte Informatie6, 249 (1973)
[18] von der Malsburg, C.: Kybernetik14, 85 (1973) · doi:10.1007/BF00288907
[19] Wiener, N., Rosenblueth, A.: Arch. Inst. Cardiol. Mex.16, 205 (1946)
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