title: The formation mechanism of defects, spiral wave in the network of neurons.
abstract: A regular network of neurons is constructed by using the Morris-Lecar (ML) neuron with the ion channels being considered, and the potential mechnism of the formation of a spiral wave is investigated in detail. Several spiral waves are initiated by blocking the target wave with artificial defects and/or partial blocking (poisoning) in ion channels. Furthermore, possible conditions for spiral wave formation and the effect of partial channel blocking are discussed completely. Our results are summarized as follows. 1) The emergence of a target wave depends on the transmembrane currents with diversity, which mapped from the external forcing current and this kind of diversity is associated with spatial heterogeneity in the media. 2) Distinct spiral wave could be induced to occupy the network when the target wave is broken by partially blocking the ion channels of a fraction of neurons (local poisoned area), and these generated spiral waves are similar with the spiral waves induced by artificial defects. It is confirmed that partial channel blocking of some neurons in the network could play a similar role in breaking a target wave as do artificial defects; 3) Channel noise and additive Gaussian white noise are also considered, and it is confirmed that spiral waves are also induced in the network in the presence of noise. According to the results mentioned above, we conclude that appropriate poisoning in ion channels of neurons in the network acts as 'defects' on the evolution of the spatiotemporal pattern, and accounts for the emergence of a spiral wave in the network of neurons. These results could be helpful to understand the potential cause of the formation and development of spiral waves in the cortex of a neuronal system.
authors: Department of Physics, Lanzhou University of Technology, Lanzhou, China.
authors: Xinyi
authors: X
authors: Wu
authors: Jun
authors: J
authors: Ma
mesh_terms: D000818:Animals; D003198:Computer Simulation; D007473:Ion Channels / Q000378:metabolism*; D008564:Membrane Potentials / Q000502:physiology*; D008959:Models, Neurological; D009415:Nerve Net; D009474:Neurons / Q000166:cytology / Q000502:physiology*; D001468:Thoracica
chemical_list: D007473:Ion Channels
references: Phys Rev Lett. 2005 May 13;94(18):188301
references: 15904413
references: Phys Rev Lett. 2001 Apr 16;86(16):3678-81
references: 11328052
references: Prog Biophys Mol Biol. 2004 Jun-Jul;85(2-3):501-22
references: 15142759
references: Phys Biol. 2004 Jun;1(1-2):61-6
references: 16204823
references: Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Aug;68(2 Pt 2):026134
references: 14525076
references: Neuron. 2010 Dec 9;68(5):978-990
references: 21145009
references: IEEE Trans Biomed Eng. 2009 Feb;56(2):532-4
references: 19342333
references: Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Feb;85(2 Pt 2):026213
references: 22463305
references: Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Nov;84(5 Pt 2):056204
references: 22181481
references: J Neurosci. 2004 Nov 3;24(44):9897-902
references: 15525774
references: Cardiovasc Res. 2001 May;50(2):242-50
references: 11334828
references: Phys Rev Lett. 2004 May 14;92(19):198101
references: 15169447
references: Phys Rev Lett. 1995 Aug 21;75(8):1503-1506
references: 10060314
references: Circ Res. 2000 Mar 31;86(6):684-91
references: 10747005
references: J Physiol. 1973 Mar;229(2):409-55
references: 4724831
references: Chaos. 2002 Mar;12(1):215-230
references: 12779549
references: Phys Rev Lett. 2007 Apr 27;98(17):178102
references: 17501537
references: Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Jul;76(1 Pt 2):015101
references: 17677522
references: Chaos. 2007 Mar;17(1):015107
references: 17411264
references: Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Dec;78(6 Pt 1):061917
references: 19256878
references: Chaos. 2002 Mar;12(1):16-26
references: 12779528
references: Biophys J. 2005 Jul;89(1):120-9
references: 15849258
references: Phys Rev Lett. 2000 Jan 31;84(5):1047-50
references: 11017437
references: Chaos. 2002 Sep;12(3):852-892
references: 12779613
references: Chaos. 2002 Sep;12(3):732-739
references: 12779601
references: Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Jul;86(1 Pt 2):016208
references: 23005508
references: Phys Rev E Stat Nonlin Soft Matter Phys. 2002 May;65(5 Pt 2):055204
references: 12059631
references: Phys Rev Lett. 2002 Dec 31;89(28 Pt 1):280601
references: 12513128
references: Phys Rev E Stat Nonlin Soft Matter Phys. 2011 May;83(5 Pt 2):056204
references: 21728627
references: Biophys J. 1981 Jul;35(1):193-213
references: 7260316