Fire Patterns of HH Neuron under External Sinusoidal ELF Stimulus

Neuron as the main information carrier in neural systems is able to generate diverse fire trains in response to different stimuli. In this paper, the stimulus frequency is taken as the bifurcation parameter, and the ISI is considered to be one of the state variables. Via numerical simulation, we mainly concentrate on investigating the kinds of fire patterns that the HH neuron model displays such as period-n, bursting, and modulation fire patterns, etc. under the effect of external sinusoidal ELF electric field, and the relation between the ISI sequences and the external stimulus just like synchronization. In addition, an explanation is put forwards from the electrophysiology point of view to try to interpret why neurons generate so many different kinds of ISI sequences.

[1]  Wang Jiang,et al.  Hopf bifurcation in the Hodgkin-Huxley model exposed to ELF electrical field , 2004 .

[2]  Eugene M. Izhikevich,et al.  Neural excitability, Spiking and bursting , 2000, Int. J. Bifurc. Chaos.

[3]  Li Wang,et al.  Mode and site of acupuncture modulation in the human brain: 3D (124-ch) EEG power spectrum mapping and source imaging , 2006, NeuroImage.

[4]  P. Shorten,et al.  A Hodgkin-Huxley model exhibiting bursting oscillations , 2000, Bulletin of mathematical biology.

[5]  K. Ramasubramanian,et al.  A comparative study of computation of Lyapunov spectra with different algorithms , 1999, chao-dyn/9909029.

[6]  A. Hodgkin,et al.  A quantitative description of membrane current and its application to conduction and excitation in nerve , 1990 .

[7]  S. Finkbeiner.  Mathematical Aspects of Hodgkin-Huxley Neural Theory , 1988, The Yale Journal of Biology and Medicine.

[8]  Shinji Doi,et al.  Complex nonlinear dynamics of the Hodgkin–Huxley equations induced by time scale changes , 2001, Biological Cybernetics.

[9]  Teresa Ree Chay,et al.  BURSTING, SPIKING, CHAOS, FRACTALS, AND UNIVERSALITY IN BIOLOGICAL RHYTHMS , 1995 .

[10]  R. M. Siegel,et al.  The origins of aperiodicities in sensory neuron entrainment , 1996, Neuroscience.

[11]  J. Rinzel.  Discussion: Electrical excitability of cells, theory and experiment: Review of the Hodgkin-Huxley foundation and an update , 1990 .

[12]  Teresa Ree Chay,et al.  Electrical bursting and intracellular Ca2+ oscillations in excitable cell models , 1990, Biological Cybernetics.

[13]  Li Li,et al.  Noise Induced Multi-Mode Neural Firings in a Period Adding Bifurcation Scenario , 2003 .

[14]  Andrew C. N. Chen,et al.  Relations between brain network activation and analgesic effect induced by low vs. high frequency electrical acupoint stimulation in different subjects: a functional magnetic resonance imaging study , 2003, Brain Research.

[15]  Teresa Ree Chay,et al.  Chaos in a three-variable model of an excitable cell , 1985 .

[16]  Hideyuki Suzuki,et al.  Analysis of neural spike trains with interspike interval reconstruction , 2000, Biological Cybernetics.

[17]  Ling Hong,et al.  Crisis of interspike intervals in Hodgkin–Huxley model , 2006 .

[18]  Jiang Wang,et al.  Two-parameters Hopf bifurcation in the Hodgkin–Huxley model , 2005 .

[19]  San-Jue Hu,et al.  PERIOD-ADDING BIFURCATION WITH CHAOS IN THE INTERSPIKE INTERVALS GENERATED BY AN EXPERIMENTAL NEURAL PACEMAKER , 1997 .

[20]  Hiroyuki Kitajima,et al.  Bifurcations in Morris-Lecar neuron model , 2006, Neurocomputing.

[21]  Teresa Ree Chay,et al.  Electrical bursting and luminal calcium oscillation in excitable cell models , 1996, Biological Cybernetics.

[22]  Xu Jian-Xue,et al.  An alternating periodic－chaotic ISI sequence of HH neuron under external sinusoidal stimulus , 2004 .

[23]  Eugene M. Izhikevich,et al.  Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting , 2006 .

[24]  Zhuoqin Yang,et al.  The genesis of period-adding bursting without bursting-chaos in the Chay model , 2006 .

[25]  K. M. Tsang,et al.  Hopf bifurcation in the Hodgkin-Huxley model exposed to ELF electrical field , 2003, Proceedings of the 25th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (IEEE Cat. No.03CH37439).