Mechanism of Spontaneous Formation of Spiral Wave in Neuronal Network with Unidirectional Coupling

doi:10.19596/j.cnki.1001-246x.8134

Abstract

Abstract: A two-dimensional neuronal network with unidirectional coupling is constructed, and information transmission entropy is introduced to describe the directed information transmission. Hindmarsh-Rose neuron model is used to study mechanism of spontaneous generation of ordered waves such as spiral waves in the network. Numerical simulation shows that the network can appear spontaneously spiral wave, traveling wave, target wave and plane wave with appropriately selected strength of coupling and distance of unidirectional coupling. It is found that generation of various ordered waves is related to intermittently directed information transmission in the network. Entropy resonance occurs as single or multiple spiral waves appear in the network. Intermittently directed information transmission is also observed in the network with noise, inhibitory coupling and repulsive coupling when spiral wave and multiple spiral waves are spontaneously appeared. Self-sustaining long plane waves are observed for the first time. It is due to persistent strong directed information transmission in the network.

Key words: Hindmarsh-Rose neuron, unidirectional coupling, spiral wave, information transmission entropy

CLC Number:

O415.6

HUANG Zhijing, BAI Jing, TANG Guoning. Mechanism of Spontaneous Formation of Spiral Wave in Neuronal Network with Unidirectional Coupling[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2020, 37(5): 612-622.

References

[1] WINFREE A T. Spiral waves of chemical activity[J]. Science, 1972, 175(4022):634-636.
[2] DAVIDENKO J M, PERTSOV A V, SALOMONSZ R, et al. Stationary and drifting spiral waves of excitation inisolated cardiac muscle[J]. Nature, 1992, 355(6358):349-351.
[3] SKANES A C, MANDAPATI R, BERENFELD O, et al. Spatiotemporal periodicity during atrial fibrillation in the isolated sheep heart[J]. Circulation, 1998, 98(12):1236-1248.
[4] HUANG X Y, TROY W C, YANG Q, et al. Spiral waves in disinhibited mammalian neocortex[J]. Journal of Neurosci, 2004, 24(44):9897-9902.
[5] HUANG X Y, XU W F, LIANG J M, et al. Spiral wave dynamics in neocortex[J]. Neuron, 2010, 68(5):978-990.
[6] JATFE L F. Calcium waves[J]. Philosophical Transactions of the Royal Society B, 2008, 363(1495):1311-1317.
[7] ROSTAMI Z, JAFARI S. Defects formation and spiral waves in a network of neurons in presence of electromagnetic induction[J]. Cognitive Neurodynamics, 2018, 12(2):235-254.
[8] NICLLA E M, BRUSCH L, BÄR M. Antispiral waves as sources in oscillatory reaction-diffusion media[J]. The Journal of Physical Chemistry B, 2004, 108(38):14733-14740.
[9] VIVENTI J, KIM D H, VIGELAND L, et al. Flexible, foldable, actively multiplexed, high-density electrode array for mapping brain activity in vivo[J]. Nature Neuroscience, 2011, 14(12):1599-1605.
[10] YAO Y G, DENG H Y, MA C Z, et al. Impact of bounded noise and rewiring on the formation and instability of spiral waves in a small-world network of Hodgkin-Huxley neurons[J]. PLOSONE, 2017, 12(1):e0171273.
[11] NANTHAKUMAR K, WALCOTT G P, MELNICK S, et al. Epicardial organization of human ventricular fibrillation[J]. Heart Rhythm, 2004, 1(1):14-23.
[12] EISEN A, RUFF C T, BRAUNWALD E, et al. Sudden cardiac death in patients with atrial fibrillation:Insights from the ENGAGE AF-TIMI 48 trial[J]. Journal of the American Heart Association, 2016, 5(7):e003735.
[13] YU Y, SANTOS L M, MATTIACE L A, et al. Reentrant spiral waves of spreading depression cause macular degeneration in hypoglycemic chicken retina[J]. Proceedings of the National Academy of Sciences, 2012, 109(7):2585-2589.
[14] ZHANG J, TANG J, MA J, et al. The dynamics of spiral tip adjacent to inhomogeneity in cardiac tissue[J]. Physica A, 2018, 491:340-346.
[15] LI T C, LI B W, ZHENG B, et al. A quantitative theory for phase-locking of meandering spiral waves in a rotating external field[J]. New Journal of Physics, 2019, 21(4):043012.
[16] LV L, GE L, GAO L, et al. Synchronization transmission of spiral wave and turbulence in uncertain time-delay neuronal networks[J]. Physica A:Statistical Mechanics and Its Applications, 2019, 525:64-71.
[17] WANG Y, SONG D, GAO X, et al. Effect of network structural perturbations on spiral wave patterns[J]. Nonlinear Dynamics, 2018, 93(3):1671-1680.
[18] YUAN G, WANG X, WANG G, et al. Spiral dynamics under feedback derived from a square-shaped domain in the complex Ginzburg-Landau equation[J]. International Journal of Modern Physics B, 2019, 33(5):1950015.
[19] YAO Y, CAO W, PEI Q, et al. Breakup of spiral wave and order-disorder spatial pattern transition induced by spatially uniform cross-correlated Sine-Wiener noises in a regular network of Hodgkin-Huxley neurons[J]. Complexity, 2018, 2018:1-10.
[20] ZHANG X L, TAN H L, TANG G N, et al. Mechanical deformation of myocardial tissue with cellular automaton[J]. Chinese Journal of Computational Physics, 2018, 35(3):294-302.
[21] YANG C Y, LIU H Y, TANG G N. Simulation on control of spiral wave by two-stage pulse force[J]. Chinese Journal of Computational Physics, 2014, 31(5):625-630.
[22] CHEN S Y, YUAN G Y, WU G, et al. Effect of Lévy noise and periodic force on dynamics of spiral waves[J]. Chinese Journal of Computational Physics, 2012, 29(4):620-626.
[23] ZHONG M, TANG G N. Suppression of spiral waves and spatiotemporal chaos in cardiac tissues with controll of calcium and potassium ionic currents[J]. Chinese Journal of Computational Physics, 2011, 28(1):119-124.
[24] ZIMIK S, PANDIT R. Reentry via high-frequency pacing in a mathematical model for human-ventricular cardiac tissue with a localized fibrotic region[J]. Scientific Reports, 2017, 7(1):15350.
[25] JUNG P, CORNELL-BELLA, MADDENKS, et al. Noise-induced spiral waves in astrocyte syncytia show evidence of self-organized criticality[J]. Journal of Neurophysiology, 1998, 79(2):1098-1101.
[26] YAO Y, DENG H, YI M, et al. Impact of bounded noise on the formation and instability of spiral wave in a 2D lattice of neurons[J]. Scientific Reports, 2017, 7(1):43151.
[27] QIN H, MA J, REN G, et al. Field coupling-induced wave propagation and pattern stability in a two-layer neuronal network under noise[J]. International Journal of Modern Physics B, 2018, 32:1850298.
[28] LI Y, JIA B, ZHANG X, et al. Spatial patterns in a network composed of neurons with different excitabilities induced by autapse[J]. The European Physical Journal Special Topics, 2018, 227(7-9):821-835.
[29] QIN H X, MA J, WANG C N, et al. Autapse-induced target wave, spiral wave in regular network of neurons[J]. Science China:Physics, Mechanics & Astronomy, 2014, 57(10):1918-1926.
[30] 汪芃, 李倩昀, 黄志精, 等. 在兴奋-抑制混沌神经元网络中有序波的自发形成[J]. 物理学报, 2018, 67(27):170501.
[31] 黄志精, 李倩昀, 白婧, 等. 在具有排斥耦合的神经元网络中有序斑图的熵测量[J]. 物理学报, 2019, 68(11):110503.
[32] ROBINSON S R, HAMPSON E C G M, MUNRO M N, et al. Unidirectional coupling of gap junctions between neuroglia[J]. Science, 1993, 262(5136):1072-1074.
[33] USHA K, SUBHA P A, NAYAK C R. The route to synchrony via drum head mode and mixed oscillatory state in star coupled Hindmarsh-Rose neural network[J]. Chaos, Solitons and Fractals, 2018, 108:25-31.
[34] HINDMARSH J L, ROSE R M. A model of neuronal bursting using three coupled first order differential equations[J]. Proceedings of the Royal Society B:Biological Sciences, 1984, 221(1222):87-102.
[35] ADHIKARI B M, PRASAD A, DHAMALA M. Time-delay-induced phase-transition to synchrony in coupled bursting neurons[J]. Chaos:An Interdisciplinary Journal of Nonlinear Science, 2011, 21(2):023116.