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The physical parameters, e.g. power and phase, are usually employed in the neural analysis of brain rhythms, which are important in brain function and disease diagnosis. Though there has been extensive work, how both parameters are related to the electrical properties of brain tissue and the sources of brain rhythms has not been fully understood. To address the issue, a simulation is done based on the theory of dipole current. When referring to the solution to the forward problem in electroencephalograph, the brain is regarded as a homogenous sphere model, the electrical features of brain tissue are described by an isotropic electrical conductivity. The source of brain rhythms is simulated by the quasi-static dipole current whose activity is described as a sine oscillation at low frequency. The electrical field generated by the dipole current is considered to be quasi-static. By changing the amplitude and the phase time course of oscillatory dipole current, the distribution of potentials produced by the dipole current at a time-point could be calculated by applying the finite element method to the sphere model. Over a time period of sine oscillation, the oscillatory potentials regarded as the brain rhythms could be produced. Instantaneous power and phase of simulated rhythms are estimated by Hilbert transform, and then a method of phase stability in narrow-band is developed for a single oscillator. To highlight this method, three manners are employed to describe it, i.e., mean relative phase value termed phase preserved index, histogram on rose plane, and phase sorting with the help of EEGLAB. Finally the relationship between two physical parameters and the electrical features of brain tissue/the source activity of brain rhythms is investigated under the conditions of (an) isotropy of conductivity, linear or nonlinear phase dynamics and amplitude, eccentricity of dipole current, etc. The statistical methods of t-test and bootstrapping technology are performed respectively to show the significance of power and phase stability. It is obtained that the power of simulated rhythms decreases with the increase of electrical conductivity, and it is not only proportional to the square of the amplitude of dipole current, but also correlated with the anisotropy of conductivity and the locations of dipole current as well as meshes on the sphere model, however no relevance to other factors. On the contrary, the phase stability of simulated rhythms is correlated only with the non-linear time course of their own phase dynamics. The results imply that the power of brain rhythms is related to many factors such as brain tissue and amplitude of rhythm generator as well as placements of recording electrodes, but the phase stability is related only to the non-linear phase dynamics of brain rhythms. Thus, the electrical significance of the power is more complicated than that of the phase stability. This work might be helpful for understanding in depth the significance of both physical parameters from the perspective of electricity. The narrow-band phase stability of simulated rhythms could highlight the non-linear phase dynamics. It is hypothesized that the phase stability could not only map the synchrony in the neural activity as a custom means of phase coherence, but also reflect directly the non-linearity in phase dynamics, and the more divergent the phase dynamics, the lower the phase stability is, and vice verse. Therefore it is suggested that the phase stability of brain rhythms could be related closely to the non-linear factors to affect the phase dynamics of brain rhythms, e.g., the non-linear phase dynamics of rhythm generators. It is also suggested that both parameters of power and phase stability would offer more neural information.
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Keywords:
- electroencephalograph forward problem /
- narrow band phase stability /
- dipole current /
- anisotropy
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[2] Mormann F, Fell J, Axmacher N, Weber B, Lehnertz K, Elger C E, Fernandez G 2005 Hippocampus 15 890
[3] Lachaux J P, Rodriguez E, Martinerie J, Varela F J 1999 Human Brain Mapping 8 194
[4] Chauviere L, Rafrafi N, Thinus-Blanc C, Bartolomei F, Esclapez M, Bernard C 2009 J. Neurosci. 29 5402
[5] Uhlhaas P J, Singer W 2006 Neuron 52 155
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[7] Kraskov A, Quiroga R Q, Reddy L, Fried I, Koch C 2007 J. Cogn. Neurosci. 19 479
[8] Ali M O J 2006 Proc. Natl. Acad. Sci. USA 13 2948
[9] Mormann F, Lehnertz K, David P, Elger C E 2000 Phys. D 144 358
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[11] Delorme A, Makeig S 2004 J. Neurosci. Methods 134 9
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[19] Ge M L, Guo B Q, Chen X, Sun Y, Chen S H, Zheng Y, Zhang H J, Sun W 2014 Acta Physiol. Sin. 66 118 (in Chinese) [葛曼玲, 郭宝强, 陈雪, 孙英, 陈盛华, 郑颖, 张惠娟, 孙伟 2014 生理学报 66 118]
[20] De Munck J C, van Dijk B W, Spekreijse H 1988 IEEE Trans. Biomed. Eng. 35 960
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[29] Chen C, Li D G, Jiang Z G, Liu H B 2012 Acta Phys. Sin. 61 244101 (in Chinese) [陈聪, 李定国, 蒋治国, 刘华波 2012 物理学报 61 244101]
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[31] Zhang Y C, Ding L, Drongelen W V, Hecox K, Frim D M, He B 2006 Neuroimage 31 1513
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[33] Wolters C H, Anwander A, Tricoche X, Weinstein D, Koch M A, MacLeod R S 2006 Neuroimage 30 813
[34] Li J, Yan D D 2009 J. China Jiliang Univ. 20 180 (in Chinese) [李璟, 闫丹丹 2009 中国计量学院学报 20 180 ]
[35] Tuch D S, Wedeen V J, Dale A M, George J S, Belliveau J W 2001 Proc. Natl. Acad. Sci. USA 98 11697
[36] Yan Y, Nunez P L, Hart R T 1991 Med. Biol. Eng. Comput. 29 475
[37] McAdams E T, Jossinet J 1995 Physiol. Meas. 16 A1
[38] Ma X S, Zhang J S, Wang P 1995 Fundamentals of Electromagnetic Fields (Beijing: Tsinghua University Press) pp1-352 (in Chinese) [马信山, 张济世, 王平 1995 电磁场基础 (北京: 清华大学出版社) 第1-352页]
[39] Brody D A, Terry F H, Ideker R E 1973 IEEE Trans. Biomed. Eng. 20 141
[40] Yao D Z 2003 Electricity Theory and Methods of Bran Function Detection (Beijing: Science Press) pp1-336 (in Chinese) [尧德中 2003 脑功能探测的电学理论与方法 (北京: 科学出版社) 第1-336页]
[41] Rosenblum M G, Pikovsky A S, Kurths J 1996 Phys. Rev. Lett. 76 1804
[42] Mormanna F, Kreuz T, Andrzejak R G, David P, Lehnertz K, Elger C E 2003 Epilepsy Res. 53 173
[43] Krusienski D J 2012 Brain Res. Bull. 87 130
[44] Sih G C, Tang K K 2012 Theor. Appl. Fract. Mech. 62 1
[45] Schnitzler A, Gross J 2005 Nat. Rev. Neurosci. 6 285
[46] Wang X J 2010 Physiol. Rev. 90 1195
[47] Fujisaka H, Yamada T 1983 Prog. Theor. Phys. 69 32
[48] Abascal J F, Arridge S R, Atkinson D, Horesh R, Fabrizi L, de Lucia M, Horesh L, Bayford R H, Holder D S 2008 Neuroimage 43 258
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[1] Buzsaki G 2006 Rhythm of the Brain (New York: Oxford University Press) pp1-464
[2] Mormann F, Fell J, Axmacher N, Weber B, Lehnertz K, Elger C E, Fernandez G 2005 Hippocampus 15 890
[3] Lachaux J P, Rodriguez E, Martinerie J, Varela F J 1999 Human Brain Mapping 8 194
[4] Chauviere L, Rafrafi N, Thinus-Blanc C, Bartolomei F, Esclapez M, Bernard C 2009 J. Neurosci. 29 5402
[5] Uhlhaas P J, Singer W 2006 Neuron 52 155
[6] Winson J 1978 Science 201 160
[7] Kraskov A, Quiroga R Q, Reddy L, Fried I, Koch C 2007 J. Cogn. Neurosci. 19 479
[8] Ali M O J 2006 Proc. Natl. Acad. Sci. USA 13 2948
[9] Mormann F, Lehnertz K, David P, Elger C E 2000 Phys. D 144 358
[10] Zhang D D, Luo Y J 2011 Adv. Psychol. Sci. 19 487 (in Chinese) [张丹丹, 罗跃嘉 2011 心理科学进展 19 487]
[11] Delorme A, Makeig S 2004 J. Neurosci. Methods 134 9
[12] Gramfort A, Luessi M, Larson E, Engemann D A, Strohmeier D, Brodbeck C, Parkkonen L, Hamalainen M S 2013 Neuroimage 86 446
[13] Litvak V, Mattout J, Kiebel S, Phillips C, Henson R, Kilner J, Barnes G, Oostenveld R, Daunizeau J, Flandin G, Penny W, Friston K 2011 Comput. Intell. Neurosci. 2011 852961
[14] Wiener N 1956 J. Phys. Soc. Jpn. 18 499
[15] Wiener N 1957 Proc. Rudolf Virchow Med. Soc. City NY 16 109
[16] Qiu J H, Li Y T, Xu K H, Yang Z, Zhang T 2008 Acta Biophys. Sin. 24 221 (in Chinese) [裘嘉恒, 李雅堂, 许坤涵, 杨卓, 张涛 2008 生物物理学报 24 221]
[17] Zheng C G, Quan M N, Yang Z, Zhang T 2011 Neurosci. Lett. 490 52
[18] Ge M L, Wang D H, Dong G Y, Guo B Q, Gao R G, Sun W, Zhang J J, Liu H S 2013 Experimen. Neurol. 250 136
[19] Ge M L, Guo B Q, Chen X, Sun Y, Chen S H, Zheng Y, Zhang H J, Sun W 2014 Acta Physiol. Sin. 66 118 (in Chinese) [葛曼玲, 郭宝强, 陈雪, 孙英, 陈盛华, 郑颖, 张惠娟, 孙伟 2014 生理学报 66 118]
[20] De Munck J C, van Dijk B W, Spekreijse H 1988 IEEE Trans. Biomed. Eng. 35 960
[21] da Silva F L, van Rotterdam A 1982 Biophysical Aspects of EEG, MEG Generation, 15 In: Niedermeyer E, da Silva F L eds. Electroencephalography: Basic Principles, Clinical Applications and Related Fields (Baltimore MD: Lippincott Williams & Wilkins) pp1-1156
[22] Yao D Z 1998 Chin. J. Biomed. Engineer. 17 97 (in Chinese) [尧德中 1998 中国生物医学工程学报 17 97]
[23] Zhu H Y, Li J, Luo B 2002 Acta Phys. Sin. 51 2393 (in Chinese) [朱红毅, 李军, 罗斌 2002 物理学报 51 2393]
[24] Wu C Q, Zhao S 2007 Acta Phys. Sin. 56 5180 (in Chinese) [吴重庆, 赵爽 2007 物理学报 56 5180]
[25] Wan B K, Xue Z J, Cheng L L, Zhu X 2006 Prog. Nat. Sci. 16 881 (in Chinese) [万柏坤, 薛召军, 程龙龙, 朱欣 2006 自然科学进展 16 881]
[26] Li J, Wang K, Liu J, Zhu S A, He B 2007 Chin. J. Sens. Actuat. 20 1736 (in Chinese) [李璟, 王琨, 刘君, 朱善安, He Bin 2007 传感技术学报 20 1736]
[27] Kim S, Kim T S, Zhou Y, Singh M 2003 IEEE Trans. Nucl. Sci. 50 133
[28] Gulrajani R M 1998 Bioelectricity and Biomagnetism (New York: John Wiley and Sons Inc) pp1-744
[29] Chen C, Li D G, Jiang Z G, Liu H B 2012 Acta Phys. Sin. 61 244101 (in Chinese) [陈聪, 李定国, 蒋治国, 刘华波 2012 物理学报 61 244101]
[30] Haueisen J, Tuch D S, Ramon C, Schimpf P H, Wedeen V J, George J S, Belliveau J W 2002 Neuroimage 15 159
[31] Zhang Y C, Ding L, Drongelen W V, Hecox K, Frim D M, He B 2006 Neuroimage 31 1513
[32] Nunez P L, Srinivasan R, Westdorp A F, Wijesinghe R S, Tucker D M, Silberstein R B, Cadusch P J 1997 Electroencephalogr. Clin. Neurophysiol. 103 499
[33] Wolters C H, Anwander A, Tricoche X, Weinstein D, Koch M A, MacLeod R S 2006 Neuroimage 30 813
[34] Li J, Yan D D 2009 J. China Jiliang Univ. 20 180 (in Chinese) [李璟, 闫丹丹 2009 中国计量学院学报 20 180 ]
[35] Tuch D S, Wedeen V J, Dale A M, George J S, Belliveau J W 2001 Proc. Natl. Acad. Sci. USA 98 11697
[36] Yan Y, Nunez P L, Hart R T 1991 Med. Biol. Eng. Comput. 29 475
[37] McAdams E T, Jossinet J 1995 Physiol. Meas. 16 A1
[38] Ma X S, Zhang J S, Wang P 1995 Fundamentals of Electromagnetic Fields (Beijing: Tsinghua University Press) pp1-352 (in Chinese) [马信山, 张济世, 王平 1995 电磁场基础 (北京: 清华大学出版社) 第1-352页]
[39] Brody D A, Terry F H, Ideker R E 1973 IEEE Trans. Biomed. Eng. 20 141
[40] Yao D Z 2003 Electricity Theory and Methods of Bran Function Detection (Beijing: Science Press) pp1-336 (in Chinese) [尧德中 2003 脑功能探测的电学理论与方法 (北京: 科学出版社) 第1-336页]
[41] Rosenblum M G, Pikovsky A S, Kurths J 1996 Phys. Rev. Lett. 76 1804
[42] Mormanna F, Kreuz T, Andrzejak R G, David P, Lehnertz K, Elger C E 2003 Epilepsy Res. 53 173
[43] Krusienski D J 2012 Brain Res. Bull. 87 130
[44] Sih G C, Tang K K 2012 Theor. Appl. Fract. Mech. 62 1
[45] Schnitzler A, Gross J 2005 Nat. Rev. Neurosci. 6 285
[46] Wang X J 2010 Physiol. Rev. 90 1195
[47] Fujisaka H, Yamada T 1983 Prog. Theor. Phys. 69 32
[48] Abascal J F, Arridge S R, Atkinson D, Horesh R, Fabrizi L, de Lucia M, Horesh L, Bayford R H, Holder D S 2008 Neuroimage 43 258
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