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Transcranial magnetic stimulation (TMS) is a kind of brain stimulation method of producing magnetic field at the designated area of brain employing electromagnetic coils. The principle of TMS is to apply an electric field which is generated through the electromagnetic induction to neuron, thereby influencing the excitability of neuron. Though it has been used for decades, its underlying mechanism, i.e., how TMS induction electric field changes neuronal excitability, is still unknown. To address this problem, we establish a minimum neuron model under action of TMS induced electric field, analyze the mechanism from the viewpoint of action potential initial dynamical mechanism which has been proved to be the decision factor of neural coding in previous studies. Through phase plane and bifurcation analysis, we reveal the dynamical mechanism of different firing patterns of neuron. Finally, we find that the physiological basis of different excitabilities under action of TMS induced electric field, which is the different outcomes of competition between ion currents of neuron with different kinetic behaviors in sub-threshold potential.
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Keywords:
- transcranial magnetic stimulation /
- action potential initial dynamic mechanism /
- minimum neuron model /
- sub-threshold current competition
[1] Arias C O 2008 International Archives of Medicine 1 2
[2] Sewerin S, Taubert M, Vollmann H, Villringer A, Ragert P 2011 BMC Neurosci. 12 45
[3] Casali A G, Casarotto S, Rosanova M, Mariptti M, Massimini M 2010 NeuroImage 49 1459
[4] Pashut T, Wolfus S, Friedman A, Lavidor M, Bar G I, Yosef Y, Korngreen A 2011 PLoS Comput. Biol. 7 e1002022
[5] Wagner T, Valero C A, Pascual L A 2007 Annu. Rev. Biomed. Eng. 9 1
[6] Maki H 2011 Ph. D. Dissertation (Espoo: Aalto University)
[7] Miniussi C, Ruzzoli M, Walsh V 2010 Cortex 46 128
[8] Huang Y Z, Rothwell J C, Chen R S, Lu C S, Chuang W L 2011 Clin. Neurophysiol. 122 1011
[9] Rossini P M, Rossini L, Ferreri F 2010 IEEE Eng. Med. Biol. 29 84
[10] Kobayashi M, Leone A P 2003 Lancet Neurol. 2 145
[11] Censor N, Cohen G L 2011 J. Physiol. 589 21
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[14] Toporikova N, Tabak J, Freeman M E, Bertram R 2008 Neural Comput. 20 436
[15] Meng X Y, Lu Q S, Rinzel J 2011 J. Comput. Neurosci. 31 117
[16] RIchardson M J E, Brunel N, Hakim V 2003 J. Neurophysiol. 89 2538
[17] Trocme N F, Hansel D, Vreeswijk C V, Brunel N 2003 J. Neurosci. 23 11628
[18] Zeberg H, Blomberg C, Arhem P 2010 PLoS Comput. Biol. 6 e1000753
[19] Prescott S A, Koninck Y D, Sejnowski T J 2008 PLoS Comput. Biol. 4 e1000198
[20] Hodgkin A, Huxley A 1952 J. Physiol. 117 500
[21] Izhikevich E M 2005 Dynamical Systems in Neuroscience: the Geometry of Excitability and Bursting (Cambridge: The MIT Press) p1
[22] Coggan J S, Prescott S A, Bartol T M, Sejnowski T J 2010 PNAS 107 20602
[23] Xie Y, Aihara K, Kang Y M 2008 Phys. Rev. E 77 021917
[24] Liu Y, Xie Y 2010 Acta Phys. Sin. 59 2147 (in Chinese) [刘勇, 谢勇 2010 物理学报 59 2147]
[25] Wang B Y, Xu W, Xing Z C 2009 Acta Phys. Sin. 58 6590 (in Chinese) [王宝燕, 徐伟, 邢真慈 2009 物理学报 58 6590]
[26] Golomb D, Donner K, Shacham L, Shlosberg D, Amitai Y, Hansel D 2009 PLoS Comput. Biol. 3 e156
[27] Wang J, Chen L Q, Fei X Y 2007 Chaos Soliton. Fract. 31 247
[28] Gai Y, Doiron B, Kotak V, Rinzel J 2009 J. Neurophysiol. 102 3447
[29] Wang H T, Wang L F, Yu L C, Chen Y 2011 Phys. Rev. E 83 021915
[30] Gai Y, Doiron B, Rinzel J 2010 PLoS Comput. Biol. 6 e1000825
[31] Hilaire M, St Longtin A 2004 J. Comput. Neurosci. 16299
[32] Izhikevich E M 2004 IEEE Trans. Neural Networ. 15 1063
[33] Olypher A V, Prinz A A 2010 J. Comput. Neurosci. 8 20
[34] Huber M T, Braun H A 2006 Phys. Rev. E 73 1
[35] Tateno T, Robinson H P C 2005 J. Neurophysiol. 95 2650
[36] Yang Z Q 2010 Acta Phys. Sin. 59 5319 (in Chinese) [杨卓琴 2010 物理学报 59 5319]
[37] Borisyuk A, Rinzel J 2005 Models and Methods in Neurophysics (Amsterdam: Elsevier) p29
[38] Shi X, Lu Q S 2005 Chin. Phys. 14 77
[39] Zhao D J, Zeng S Y, Zhang Z Z 2010 Chin. Phys. B 19 108701
[40] Duan Y B, Hu S J, Xie Y, Xu J X, Kang Y M 2004 Chin. Phys. 13 1396
[41] Yang Z Q, Lu Q S 2006 Chin. Phys. 15 518
[42] Colwell L J, Brenner M P 2009 PLoS Comput. Biol. 5 e1000265
[43] FitzHugh R 1961 Biophysical. J. 1 445
[44] Nagumo J, Arimoto S, Yoshizawa S 1962 Proc. IRE. 50 2061
[45] Han C X, Wang J, Che Y Q, Deng B, Guo Y, Guo Y M, Liu Y Y 2010 Acta Phys. Sin. 59 5880 (in Chinese) [韩春晓, 王江, 车艳秋, 邓斌, 郭义, 郭永明, 刘阳阳 2010 物理学报 59 5880]
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[1] Arias C O 2008 International Archives of Medicine 1 2
[2] Sewerin S, Taubert M, Vollmann H, Villringer A, Ragert P 2011 BMC Neurosci. 12 45
[3] Casali A G, Casarotto S, Rosanova M, Mariptti M, Massimini M 2010 NeuroImage 49 1459
[4] Pashut T, Wolfus S, Friedman A, Lavidor M, Bar G I, Yosef Y, Korngreen A 2011 PLoS Comput. Biol. 7 e1002022
[5] Wagner T, Valero C A, Pascual L A 2007 Annu. Rev. Biomed. Eng. 9 1
[6] Maki H 2011 Ph. D. Dissertation (Espoo: Aalto University)
[7] Miniussi C, Ruzzoli M, Walsh V 2010 Cortex 46 128
[8] Huang Y Z, Rothwell J C, Chen R S, Lu C S, Chuang W L 2011 Clin. Neurophysiol. 122 1011
[9] Rossini P M, Rossini L, Ferreri F 2010 IEEE Eng. Med. Biol. 29 84
[10] Kobayashi M, Leone A P 2003 Lancet Neurol. 2 145
[11] Censor N, Cohen G L 2011 J. Physiol. 589 21
[12] Prescott S A, Ratté S, Koninck Y D, Sejnowski T J 2006 J. Neurosci. 26 9084
[13] Prescott S A, Ratté S, Koninck Y D, Sejnowski T J 2008 J. Neurophysiol. 100 3030
[14] Toporikova N, Tabak J, Freeman M E, Bertram R 2008 Neural Comput. 20 436
[15] Meng X Y, Lu Q S, Rinzel J 2011 J. Comput. Neurosci. 31 117
[16] RIchardson M J E, Brunel N, Hakim V 2003 J. Neurophysiol. 89 2538
[17] Trocme N F, Hansel D, Vreeswijk C V, Brunel N 2003 J. Neurosci. 23 11628
[18] Zeberg H, Blomberg C, Arhem P 2010 PLoS Comput. Biol. 6 e1000753
[19] Prescott S A, Koninck Y D, Sejnowski T J 2008 PLoS Comput. Biol. 4 e1000198
[20] Hodgkin A, Huxley A 1952 J. Physiol. 117 500
[21] Izhikevich E M 2005 Dynamical Systems in Neuroscience: the Geometry of Excitability and Bursting (Cambridge: The MIT Press) p1
[22] Coggan J S, Prescott S A, Bartol T M, Sejnowski T J 2010 PNAS 107 20602
[23] Xie Y, Aihara K, Kang Y M 2008 Phys. Rev. E 77 021917
[24] Liu Y, Xie Y 2010 Acta Phys. Sin. 59 2147 (in Chinese) [刘勇, 谢勇 2010 物理学报 59 2147]
[25] Wang B Y, Xu W, Xing Z C 2009 Acta Phys. Sin. 58 6590 (in Chinese) [王宝燕, 徐伟, 邢真慈 2009 物理学报 58 6590]
[26] Golomb D, Donner K, Shacham L, Shlosberg D, Amitai Y, Hansel D 2009 PLoS Comput. Biol. 3 e156
[27] Wang J, Chen L Q, Fei X Y 2007 Chaos Soliton. Fract. 31 247
[28] Gai Y, Doiron B, Kotak V, Rinzel J 2009 J. Neurophysiol. 102 3447
[29] Wang H T, Wang L F, Yu L C, Chen Y 2011 Phys. Rev. E 83 021915
[30] Gai Y, Doiron B, Rinzel J 2010 PLoS Comput. Biol. 6 e1000825
[31] Hilaire M, St Longtin A 2004 J. Comput. Neurosci. 16299
[32] Izhikevich E M 2004 IEEE Trans. Neural Networ. 15 1063
[33] Olypher A V, Prinz A A 2010 J. Comput. Neurosci. 8 20
[34] Huber M T, Braun H A 2006 Phys. Rev. E 73 1
[35] Tateno T, Robinson H P C 2005 J. Neurophysiol. 95 2650
[36] Yang Z Q 2010 Acta Phys. Sin. 59 5319 (in Chinese) [杨卓琴 2010 物理学报 59 5319]
[37] Borisyuk A, Rinzel J 2005 Models and Methods in Neurophysics (Amsterdam: Elsevier) p29
[38] Shi X, Lu Q S 2005 Chin. Phys. 14 77
[39] Zhao D J, Zeng S Y, Zhang Z Z 2010 Chin. Phys. B 19 108701
[40] Duan Y B, Hu S J, Xie Y, Xu J X, Kang Y M 2004 Chin. Phys. 13 1396
[41] Yang Z Q, Lu Q S 2006 Chin. Phys. 15 518
[42] Colwell L J, Brenner M P 2009 PLoS Comput. Biol. 5 e1000265
[43] FitzHugh R 1961 Biophysical. J. 1 445
[44] Nagumo J, Arimoto S, Yoshizawa S 1962 Proc. IRE. 50 2061
[45] Han C X, Wang J, Che Y Q, Deng B, Guo Y, Guo Y M, Liu Y Y 2010 Acta Phys. Sin. 59 5880 (in Chinese) [韩春晓, 王江, 车艳秋, 邓斌, 郭义, 郭永明, 刘阳阳 2010 物理学报 59 5880]
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