The Formation Mechanism of Defects, Spiral Wave in the Network of Neurons

PLoS ONE

Volumn 8, Issue 1, 2013, Pages

  Wu, Xinyi ^a   Ma, Jun ^a  

^a LANZHOU UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

CALCIUM CHANNEL; POTASSIUM CHANNEL;

ADDITIVE GAUSSIAN WHITE NOISE; ARTICLE; BLOCKING FACTOR; BRAIN CORTEX; CALCIUM CONDUCTANCE; CELL FRACTIONATION; CHANNEL NOISE; CONTROLLED STUDY; EVOLUTION; MEMBRANE POTENTIAL; MORRIS LECAR NEURON; NERVE CELL; NERVE CELL NETWORK; NERVE EXCITABILITY; NOISE; POTASSIUM CONDUCTANCE; SPIRAL WAVE; WAVEFORM;

ANIMALS; COMPUTER SIMULATION; ION CHANNELS; MEMBRANE POTENTIALS; MODELS, NEUROLOGICAL; NERVE NET; NEURONS; THORACICA;

EID: 84873142292     PISSN: None     EISSN: 19326203     Source Type: Journal    
DOI: 10.1371/journal.pone.0055403     Document Type: Article

References (63)

1. Hagan P S (1982) Spiral waves in reaction-Diffusion Equations. SIAM J Appl Math 42 762-786.
2. Cross M C, Hohenberg P C, (1993) Pattern formation outside of equilibrium. Rev Mod Phys 65: 851-1112.
3. Hildebrand M, Bär M, Eiswirth M, (1995) Statistics of topological defects and spatiotemporal chaos in a reaction-diffusion system. Phys Rev Lett 75: 1503-1506.
4. Schulze T P, Kohn R V, (1995) A geometric model for coarsening during spiral-mode growth of thin films. Physica D 132: 520-542.
5. Kapral R, (1995) Pattern formation in chemical system. Physica D 86: 149-157.
6. Kistler W M, Seitz R, van Hemmen J L, (1998) Modeling collective excitations in cortical tissue. Physcia D 114: 273-295.
7. Yagisita H, Mimura M, Yamada M, (1998) Spiral wave behaviors in an excitable reaction- diffusion system on a sphere. Physica D 124: 126-136.
8. Gollub J P, Langer J S, (1999) Pattern formation in nonequilibrium physics. Rev Mod Phys 71: 396-403.
9. Ouyang Q, Swinney H L, Li G (2000) Transition from Spirals to Defect-Mediated Turbulence Driven by a Doppler Instability. Phys Rev Lett 84 1047-1051.
10. Christoph J, Eiswirth M, (2002) Theory of electrochemical pattern formation. Chaos 12: 215-230.
11. Roth B J, (2001) Meandering of spiral waves in anisotropic cardiac tissue. Physica D 150: 127-136.
12. Bordyugov G, Engel H, (2007) Continuation of spiral waves. Physica D 228: 49-58.
13. Nie H C, Gao J H, Zhan M, (2011) Pattern formation of coupled spiral waves in bilayer systems: Rich dynamics and high-frequency dominance. Phys Rev E 84: 056204.
14. Pivik L, (1995) Autowaves and spatial-temporal chaos in CNNs-Part I: a tutorial. IEEE Trans Circuits Syst I 42 (12): 638-649.
15. Hu G, Xiao J H, Chua L O, Pivka L, (1998) Controlling spiral waves in a model of two-dimensional arrays of Chua's circuits. Phys Rev Lett 80: 1884.
16. He D H, Hu G, Zhan M, (2002) Pattern formation of spiral waves in an inhomogeneous medium with small-world connections. Phys Rev E 65: 055204.
17. Roxin A, Riecke H, Solla S A, (2004) Self-sustained activity in a small-world network of excitable neurons. Phys Rev Lett 92: 98101.
18. Sinha S, Saramaki J, Kaski K, (2007) Emergence of self-sustained patterns in small-world excitable media. Phys Rev E 76: 015101.
19. Wang Q Y, Perc M, Duan Z S, Chen G R, (2008) Delay-enhanced coherence of spiral waves in noisy Hodgkin-Huxley neuronal networks. Phys Lett A 372: 5681-5687.
20. Erichsen R, Brunnet LG, (2008) Multistability in networks of Hindmarsh-Rose neurons. Phys Rev E 78: 061917.
21. Jiang L L, Zhou T, Perc M, Huang X, Wang B H, (2009) Emergence of target waves in paced populations of cyclically competing species. New J Phys 11: 103001.
22. Ma J, Yang L J, Wu Y, Zhang C R, (2010) Spiral wave in the small-world networks of Hodgkin-Huxley neurons. Commun Theor Phys 54: 583-588.
23. X H Liao, Q Z Xia, Y Qian, Zhang L S, Hu G, et al. (2011) Pattern formation in oscillatory complex networks consisting of excitable nodes. Phys Rev E 83: 056204.
24. Tang Z, Li Y Y, Xi L, Jia B, Gu H G, (2012) Spiral waves and multiple spatial coherence resonances induced by the colored noise in neuronal network. Commun Theor Phys 57: 61-67.
25. Gu H G, Jia B, Li Y Y,Chen G R (2013) White noise-induced spiral waves and multiple spatial coherence resonances in a neuronal network with type I excitability. Physica A doi:10.1016/j.physa.2012.11.049.
26. Samie F H, Mandapati R, Gray R A, Watanabe Y, Zuur C, et al. (2000) A Mechanism of Transition From Ventricular Fibrillation to Tachycardia. Circ Res 86: 684-691.
27. Samie F H, Jalife J, (2001) Mechanisms underlying ventricular tachycardia and its transition to ventricular fibrillation in the structurally normal heart. Cardiovasc Res 50: 242-250.
28. Sinha S, Pande A, Pandit R, (2001) Defibrillation via the elimination of spiral turbulence in a model for ventricular fibrillation. Phys Rev Lett 86: 3678-3681.
29. Kremmydas G P, Holden A V, (2002) Spiral-wave meandering in reaction-diffusion models of ventricular muscle. Chaos, Solitons and Fractals 13: 1659-1669.
30. Christini D J, Glass M, (2002) Introduction: Mapping and control of complex cardiac arrhythmias. Chaos 12: 732-739.
31. Nash M P, Panfilov A V, (2004) Electromechanical model of excitable tissue to study reentrant cardiac arrhythmias. Prog Biophys Mol Biol 85: 501-522.
32. Puwal S, Roth B J, (2009) Optimization of feedback pacing for defibrillation. IEEE Trans Biomed Eng 56: 532-534.
33. Cao Z J, Li P F, Zhang H, Xie F G, Hu G, (2007) Turbulence control with local pacing and its implication in cardiac defibrillation. Chaos 17: 105107.
34. Zhang H, Cao Z J, Wu N J, Ying H P, Hu G, (2005) Suppress winfree turbulence by local forcing excitable systems. Phys Rev Lett 94: 188301.
35. Yuan G Y, Wang G R, Chen S G, (2005) Control of spiral waves and spatiotemporal chaos by periodic perturbation near the boundary. Europhys Lett 72: 908.
36. Lou Q, Chen J X, Y H Zhao, Shen F R, Fu Y, et al. (2012) Control of turbulence in heterogeneous excitable media. Phys Rev E 85: 026213.
37. Fenton F H, Cherry E M, Hastings H M, Evans S J, (2002) Multiple mechanisms of spiral wave breakup. Chaos 12: 852-892.
38. Jensen F G, Sporring J, Sørensen P G, (2002) Tracking target and spiral waves. Chaos 12: 16-26.
39. Stich M, Mikhailov A S, (2006) Target patterns in two-dimensional heterogeneous oscillatory reaction-diffusion systems. Physica D 215: 38-45.
40. Perc M, (2007) Effects of small-world connectivity on noise-induced temporal and spatial order in neural media. Chaos, Solitons & Fractals 31: 280-290.
41. Ma J, Wang C N, Jin W Y, Wu Y, (2010) Transition from spiral wave to target wave and other coherent structures in the networks of Hodgkin-Huxley Neurons. Appl Math Comput 217: 3844-3852.
42. Zhang H, Hu B B, Hu G, (2003) Suppression of spiral waves and spatiotemporal chaos by generating target waves in excitable media. Phys Rev E 68: 026134.
43. Liu F C, Wang X F, Li X C, Dong L F, (2007) Controlling spiral wave with target wave in oscillatory systems. Chin Phys 16: 2640-2643.
44. Ma J, Wu N J, Ying H P, Yuan L H, (2006) Suppression of Spiral Waves and Spatiotemporal Chaos Under the Local Self-adaptive Coupling Interactions. Commun Theor Phys 45: 121-126.
45. Ma J, Jin W Y, Li Y L, (2007) Suppression of Spiral Waves by Generating a Self-exciting Target Wave. Chin J Chem Phys 20: 53-58.
46. Qian Y, Wang C J, Shi H S, Mi Y Y, Huang X D, (2011) Self-sustained target waves in excitable media with only a long-range link. Chin Phys B 20: 108201.
47. Gao J H, Zhan M, (2007) Target waves in oscillatory media by variable block method. Phys Lett A 371: 96-100.
48. Aranson I, Kessler D, Mitkov I, (1995) Drift of spiral wave in excitable media. Physica D 85: 142-155.
49. Zykov V S, (2009) Kinematics of rigidly rotating spiral waves. Physica D 238: 931-940.
50. Hou Z H, Xin H W, (2002) Noise-sustained spiral waves: effect of spatial and temporal memory. Phys Rev Lett 89: 280601.
51. Huang X Y, Troy W C, Yang Q, Ma H T, Laing C R, et al. (2004) Spiral waves in disinhibited mammalian cortex. J Neurosci 24: 9897-9902.
52. Schiff S J, Huang X Y, Wu J Y, (2007) Dynamical evolution of spatiotemporal patterns in mammalian middle cortex. Phys Rev Lett 98: 178102.
53. Huang X Y, Xu W F, Liang J M, Takagaki K, Gao X, et al. (2010) Spiral Wave Dynamics in Neocortex. Neuron 60: 978-990.
54. Huang L, Ma J, Tang J, Li F, (2012) Transition of Ordered Waves in Neuronal Network Induced by Diffusive Poisoning of Ion Channels. J Biol Syst 20: 1250015.
55. Ma J, Wu Y, Wu N J, Guo H Y (2013) Detection of ordered wave in the networks of neurons with changeable connection, Sci China Phys, Mecha Astro (in press).
56. Cai M C, Pan J T, Zhang H, (2012) Electric-field-sustained spiral waves in subexcitable media. Phys Rev E 86: 016208.
57. Gonze D, Bernard S, Waltermann C, Kramer A, Herzel H, (2005) Spontaneous synchronization of coupled circadian oscillators. Biophys J 89: 120-129.
58. Morris C, Leacar H, (1981) Voltage oscillations in the barnacle giant muscle fiber. Biophy J 35: 193-213.
59. Keynes R D, Rojas E, Taylor R E, Vergara J, (1973) Calcium and potassium systems a giant barnacle muscle fibre under membrane potential control. J Physiol (London) 229: 409-455.
60. Rinzel J, Ermentrout G B (1989) Analysis of neuronal excitability and oscillations, C Koch and I. Segev (Eds.), Methods in neuronal Modeling:from synapses to Networks. MIT press, London.
61. Smith G, (2002) Modeling the Stochastic Gating of Ion Channels. Computational Cell Biology 20: 285-319.
62. Crotti P (2011) Analysis of coherence resonance near bifurcation points in the stochastic Class II Morris-Lecar model. Master thesis, University of Fribourg Switzerland.
63. Schmid G, Goychuk I, Hänggi P, (2004) Effect of channel block on the spiking activity of excitable membranes in a stochastic Hodgkin-Huxley model. Phys Biol 1: 61-66.