Emergence of spiral wave induced by defects block

Abstract The development of spiral wave in the regular network of Hindmarsh–Rose neurons with nearest-neighbor connection is investigated under no-flux and/or periodical boundary condition, respectively. At first, specific initial values are selected to detect the formation of spiral wave, it is found that the developed state is controlled by the bifurcation s , which controls the electric activity of neuron from spiking to burst behavior, and different developed states are observed. Furthermore, the formation of ordered wave induced by the defect block in the network of neurons is also investigated. In the numerical studies, the first step is to generate target-like wave by imposing a discrepant forcing current (not periodical signal) on a local region, the second step is to produce an artificial defect by setting the variables in a local area to zero. The supposed defect is used to block the propagation of target wave in the network, and the condition for spiral wave emergence is investigated in a numerical way. It indicates that the existence of defect in the media accounts for the emergence of spiral wave though most of the previous works used to simulate the development of spiral wave by using specific initial values. A statistical factor of synchronization in the two-dimensional space is defined to detect the appearance and robustness of spiral wave in the network of neurons. It is confirmed that the contour profile of the developed pattern is dependent on the intensity of coupling and defects block.

[1]  Markus Bär,et al.  Bifurcation and stability analysis of rotating chemical spirals in circular domains: boundary-induced meandering and stabilization. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  A. Charles,et al.  Spiral intercellular calcium waves in hippocampal slice cultures. , 1998, Journal of neurophysiology.

[3]  M. Bär,et al.  Nucleation of spiral wave patterns at surface defects. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  Jun Tang,et al.  Propagation and Synchronization of Ca2+ Spiral Waves in Excitable Media , 2011, Int. J. Bifurc. Chaos.

[5]  The influence of diversity on spiral wave in the cardiac tissue , 2012 .

[6]  J. Hindmarsh,et al.  A model of neuronal bursting using three coupled first order differential equations , 1984, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[7]  Ladislav Pivka.  Autowaves and spatio-temporal chaos in CNNs. II. A tutorial , 1995 .

[8]  Matjaž Perc,et al.  Effects of small-world connectivity on noise-induced temporal and spatial order in neural media , 2007 .

[9]  A. Zhabotinsky,et al.  Concentration Wave Propagation in Two-dimensional Liquid-phase Self-oscillating System , 1970, Nature.

[10]  Eugene M. Izhikevich,et al.  Which model to use for cortical spiking neurons? , 2004, IEEE Transactions on Neural Networks.

[11]  Ma Jun,et al.  Evolution of Spiral Waves under Modulated Electric Fields , 2005 .

[12]  M. Ozer,et al.  Stochastic resonance on Newman–Watts networks of Hodgkin–Huxley neurons with local periodic driving , 2009 .

[13]  Q Ouyang,et al.  Experimental and numerical studies of noise-induced coherent patterns in a subexcitable system. , 2002, Physical review letters.

[14]  Aiguo Xu,et al.  Spiral waves in excitable media due to noise and periodic forcing , 2011 .

[15]  Yu Qian,et al.  Control of Spiral Wave breakup by Spatiotemporal Modulation , 2011, Int. J. Bifurc. Chaos.

[16]  S C Müller,et al.  Elimination of spiral waves in cardiac tissue by multiple electrical shocks. , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[17]  Steven J. Schiff,et al.  Dynamical evolution of spatiotemporal patterns in mammalian middle cortex. , 2007 .

[18]  Recai Kiliç,et al.  Experimental realizations of the HR neuron model with programmable hardware and synchronization applications , 2012 .

[19]  M. Cross,et al.  Pattern formation outside of equilibrium , 1993 .

[20]  Ya Jia,et al.  Numerical study of IP3-dependent Ca2+ spiral waves in Xenopus oocytes , 2008 .

[21]  马军,et al.  Suppression of spiral waves using intermittent local electric shock , 2007 .

[22]  L. J. Leon,et al.  Spatiotemporal evolution of ventricular fibrillation , 1998, Nature.

[23]  L. Pivka.  Autowave and spatio-temporal chaos in CNNs-Part I and II : A tutorial , 1995 .

[24]  Alessandro Torcini,et al.  Doppler effect of nonlinear waves and superspirals in oscillatory media. , 2003, Physical review letters.

[25]  The investigation of the minimum size of the domain supporting a spiral wave in oscillatory media , 2006 .

[26]  Meng Zhan,et al.  Pattern formation of spiral waves in an inhomogeneous medium with small-world connections. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  Hu Gang,et al.  Doppler instability of antispiral waves in discrete oscillatory reaction?diffusion media , 2010 .

[28]  Kenneth Showalter,et al.  Control of waves, patterns and turbulence in chemical systems , 2006 .

[29]  D. Clapham,et al.  Spiral calcium wave propagation and annihilation in Xenopus laevis oocytes. , 1991, Science.

[30]  Wuyin Jin,et al.  Spiral wave death, breakup induced by ion channel poisoning on regular Hodgkin–Huxley neuronal networks , 2012 .

[31]  Hong Zhang,et al.  Resonant drift of two-armed spirals by a periodic advective field and periodic modulation of excitability. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[32]  Gang Hu,et al.  Turbulence control with local pacing and its implication in cardiac defibrillation. , 2007, Chaos.

[33]  Engel,et al.  Spatiotemporal concentration patterns in a surface reaction: Propagating and standing waves, rotating spirals, and turbulence. , 1990, Physical review letters.

[34]  R Erichsen,et al.  Multistability in networks of Hindmarsh-Rose neurons. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[35]  Jian-Young Wu,et al.  Propagating Waves of Activity in the Neocortex: What They Are, What They Do , 2008, The Neuroscientist : a review journal bringing neurobiology, neurology and psychiatry.

[36]  Bambi Hu,et al.  Suppression of spirals and turbulence in inhomogeneous excitable media. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[37]  Huaguang Gu,et al.  Spiral Waves and Multiple Spatial Coherence Resonances Induced by Colored Noise in Neuronal Network , 2012 .

[38]  Giorgio Metta,et al.  A Role for Cortical Spiral Waves in Visual Attention? , 2011, FET.

[39]  Jian-Young Wu,et al.  Spiral Waves in Disinhibited Mammalian Neocortex , 2004, The Journal of Neuroscience.

[40]  Bär,et al.  Statistics of Topological Defects and Spatiotemporal Chaos in a Reaction-Diffusion System. , 1995, Physical review letters.

[41]  A. Hodgkin,et al.  A quantitative description of membrane current and its application to conduction and excitation in nerve , 1952, The Journal of physiology.

[42]  Viktor Varga,et al.  Complex Propagation Patterns Characterize Human Cortical Activity during Slow-Wave Sleep , 2011, The Journal of Neuroscience.

[43]  Jun Ma,et al.  Detecting the breakup of spiral waves in small-world networks of neurons due to channel block , 2012 .

[44]  G. Hu,et al.  Active and passive control of spiral turbulence in excitable media. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[45]  Jun Ma,et al.  COLLECTIVE BEHAVIORS OF SPIRAL WAVES IN THE NETWORKS OF HODGKIN-HUXLEY NEURONS IN PRESENCE OF CHANNEL NOISE , 2010 .

[46]  Matjaz Perc,et al.  Controlling the spontaneous spiking regularity via channel blocking on Newman-Watts networks of Hodgkin-Huxley neurons , 2009, 0905.3084.

[47]  M. Zhan,et al.  Pattern formation of coupled spiral waves in bilayer systems: rich dynamics and high-frequency dominance. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[48]  J. Hindmarsh,et al.  A model of the nerve impulse using two first-order differential equations , 1982, Nature.

[49]  Z. Duan,et al.  Delay-enhanced coherence of spiral waves in noisy Hodgkin–Huxley neuronal networks , 2008 .

[50]  M. Zhan,et al.  Phase synchronization of a pair of spiral waves. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[51]  M. Or-Guil,et al.  Mechanism for spiral wave breakup in excitable and oscillatory media. , 2004, Physical review letters.

[52]  R. Gray,et al.  Spatial and temporal organization during cardiac fibrillation , 1998, Nature.

[53]  Yan Liu,et al.  Control of turbulence in heterogeneous excitable media. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[54]  Markus Bär,et al.  Spiral waves in a surface reaction: Model calculations , 1994 .

[55]  Jian-Young Wu,et al.  Spiral Wave Dynamics in Neocortex , 2010, Neuron.

[56]  Matjaž Perc,et al.  Pacemaker-guided noise-induced spatial periodicity in excitable media , 2009 .

[57]  Jysoo Lee,et al.  Spiral waves in a coupled network of sine-circle maps. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[58]  Huaguang Gu,et al.  Multiple spatial coherence resonance induced by the stochastic signal in neuronal networks near a saddle-node bifurcation , 2010 .

[59]  H. Ying,et al.  Inwardly rotating spirals in nonuniform excitable media. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[60]  M. Nash,et al.  Electromechanical model of excitable tissue to study reentrant cardiac arrhythmias. , 2004, Progress in biophysics and molecular biology.

[61]  Ya Jia,et al.  Robustness and breakup of the spiral wave in a two-dimensional lattice network of neurons , 2010 .

[62]  Jun Ma,et al.  Chaos control, spiral wave formation, and the emergence of spatiotemporal chaos in networked Chua circuits , 2012 .