大脑神经元电活动数值解法的研究
摘要
大脑是意识的主体,脑科学的研究一直吸引着众多研究者。大脑结构复杂,脑细胞之间除了宏观的电、磁等方面的联系外,还有分子的交换以及基本粒子的交换活动。对控制着人类思维、意识、学习和记忆等高级功能的大脑进行模拟仿真分析是目前研究大脑有效且无创的方法之一。脑电仿真是按一定的仿真算法模拟脑电产生、传播过程,然后根据某一时刻兴奋的神经组织所产生的动作电位和兴奋源的位置、大小和方向,用有限元法等数值算法求出兴奋的神经元在体表产生的电位。有了脑电仿真模型,通过设置模型参数可以仿真多种神经疾病。借助神经病理时体表电位的分布情况和脑电仿真模型,有助于研究神经异常形成的机理。
本文从细胞静息电位和动作电位角度阐述生物组织的电特性,介绍神经元动作电位的产生、脑电产生的机理、脑电图的检测等;并从电磁学角度对大脑自身产生的电磁场进行数学描述,给出大脑电磁场问题的相关计算和脑电场有限元分析法的求解过程。用具有一定偶极矩的电流偶极子等效模型可以模拟大脑神经元电活动,本文采用不同偶极矩的单偶极子、偶极矩随时间变化的单偶极子、双偶极子作用于等效的四层同心球大脑模型产生的脑电场问题进行仿真,并对单偶极子作用于大脑等效模型产生的磁场进行仿真。分析仿真结果发现,用电流偶极子模型能较好地模拟神经元电活动产生的脑电场和脑磁场,仿真结果和脑电场的解析解吻合较好。由仿真结果可知,大脑表面距离神经元电活动源较近的区域产生的电位高,随着大脑兴奋源和观测点距离的增大,观测点的电位降低;不同强度的神经元电活动产生的脑电磁场强度是不同的。最后介绍根据头皮电位逆推大脑兴奋源位置和大小等信息的脑电逆问题求解方法。对脑电进行病理和认知等方面的分析可获得大脑神经活动源的信息,为临床上大脑病变的预防、诊断提供可靠地依据和参考。
Brain is the sources of consciousness. Many scientific researchers are always attracted by the study of cerebrum. The configuration of brain is complex; cerebral cell connects with each other not only by macroscopically electricity and magnetism, but also by the change of molecular and elementary particle. Simulation is one of available and no-hurt ways to study brain which controls thought, consciousness, study, memory and so on. An aggregation of morphologically similar cells and associated intercellular matter acting together performs electrical activity. It is a way to simulate the production of electric potential between parts of brain in common use. Firstly, it needs simulate the processing of cause and spread of electric potential between parts of brain; then it needs to work out electric potential on the surface of head from the model which was used for further imitating its characteristics based on the electric activity originated by the excited nerve cell and the magnitude, orientation of nerve cell. Once we succeed in gaining the model of brain, we can imitate the process of much abnormal disease of the nervous system by setting the parameters of model. We can study the mechanism thoroughly, through which abnormity of brain comes into being on the basis of electric potential on the surface of scalp and model we previously design to study brain.
This article tells of the electrical characteristic of biologic tissue from the angles of resting potential and action potential relating to cell. It also introduces the process of producing action potential, the mechanism and measurement of brain wave and also. It describes and calculates the electric field caused by brain on the principle of electromagnetism too. It gives the process of calculating brain’s electric field using finite-element analysis subsequently. Electric dipole with electric dipole moment can simulate the electric activity of neuron. Aimed at four spheres with one centre of a circle representing head, this article simulates the problem of brain’s electric field using the model of one current dipole with difference electric dipole moment and moment changes along with time based on finite-element analysis. The model of two current dipoles is also used in the article to compare with those results of one. Afterward, it simulates the magnetic field characterized by the existence of electric field of brain on the heap of single electric dipole. The article compares and analyzes the similarities and differences of those electrocardiograms gained through stimulation. Through the comparison of results, we found using the model of electric dipole can simulate electric field and magnetic produced by neuron. The results of simulation are accordance with the truth. The conclusion of simulation shows that potential of the area which closes up the dipole is high, while the potential of scalp is lower with the increase of the distance between the point of observation and the dipole. The electric activity of neuron with different intensity and orientation may come into being electromagnetic which is different from each other. At last, the article describes ways and means available to deduce the coordinate and intensity of neuron by the process of reverse-calculation according to the potential of scalp. We can obtain the information of neuron’s activity through the analysis on EEG to study of diseases of brain and its causes, processes, development, and consequences ,which provides the evidence and reference of brain’illness to help diagnoses and prevention.
本文从细胞静息电位和动作电位角度阐述生物组织的电特性,介绍神经元动作电位的产生、脑电产生的机理、脑电图的检测等;并从电磁学角度对大脑自身产生的电磁场进行数学描述,给出大脑电磁场问题的相关计算和脑电场有限元分析法的求解过程。用具有一定偶极矩的电流偶极子等效模型可以模拟大脑神经元电活动,本文采用不同偶极矩的单偶极子、偶极矩随时间变化的单偶极子、双偶极子作用于等效的四层同心球大脑模型产生的脑电场问题进行仿真,并对单偶极子作用于大脑等效模型产生的磁场进行仿真。分析仿真结果发现,用电流偶极子模型能较好地模拟神经元电活动产生的脑电场和脑磁场,仿真结果和脑电场的解析解吻合较好。由仿真结果可知,大脑表面距离神经元电活动源较近的区域产生的电位高,随着大脑兴奋源和观测点距离的增大,观测点的电位降低;不同强度的神经元电活动产生的脑电磁场强度是不同的。最后介绍根据头皮电位逆推大脑兴奋源位置和大小等信息的脑电逆问题求解方法。对脑电进行病理和认知等方面的分析可获得大脑神经活动源的信息,为临床上大脑病变的预防、诊断提供可靠地依据和参考。
Brain is the sources of consciousness. Many scientific researchers are always attracted by the study of cerebrum. The configuration of brain is complex; cerebral cell connects with each other not only by macroscopically electricity and magnetism, but also by the change of molecular and elementary particle. Simulation is one of available and no-hurt ways to study brain which controls thought, consciousness, study, memory and so on. An aggregation of morphologically similar cells and associated intercellular matter acting together performs electrical activity. It is a way to simulate the production of electric potential between parts of brain in common use. Firstly, it needs simulate the processing of cause and spread of electric potential between parts of brain; then it needs to work out electric potential on the surface of head from the model which was used for further imitating its characteristics based on the electric activity originated by the excited nerve cell and the magnitude, orientation of nerve cell. Once we succeed in gaining the model of brain, we can imitate the process of much abnormal disease of the nervous system by setting the parameters of model. We can study the mechanism thoroughly, through which abnormity of brain comes into being on the basis of electric potential on the surface of scalp and model we previously design to study brain.
This article tells of the electrical characteristic of biologic tissue from the angles of resting potential and action potential relating to cell. It also introduces the process of producing action potential, the mechanism and measurement of brain wave and also. It describes and calculates the electric field caused by brain on the principle of electromagnetism too. It gives the process of calculating brain’s electric field using finite-element analysis subsequently. Electric dipole with electric dipole moment can simulate the electric activity of neuron. Aimed at four spheres with one centre of a circle representing head, this article simulates the problem of brain’s electric field using the model of one current dipole with difference electric dipole moment and moment changes along with time based on finite-element analysis. The model of two current dipoles is also used in the article to compare with those results of one. Afterward, it simulates the magnetic field characterized by the existence of electric field of brain on the heap of single electric dipole. The article compares and analyzes the similarities and differences of those electrocardiograms gained through stimulation. Through the comparison of results, we found using the model of electric dipole can simulate electric field and magnetic produced by neuron. The results of simulation are accordance with the truth. The conclusion of simulation shows that potential of the area which closes up the dipole is high, while the potential of scalp is lower with the increase of the distance between the point of observation and the dipole. The electric activity of neuron with different intensity and orientation may come into being electromagnetic which is different from each other. At last, the article describes ways and means available to deduce the coordinate and intensity of neuron by the process of reverse-calculation according to the potential of scalp. We can obtain the information of neuron’s activity through the analysis on EEG to study of diseases of brain and its causes, processes, development, and consequences ,which provides the evidence and reference of brain’illness to help diagnoses and prevention.
引文
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[2]李国栋,生物磁学-应用、技术、原理,北京:国防工业出版社, 1993:88-93
[3] Awada KA,Jackson DE,Williams JT, et al, computational aspects of finite element modeling in EEG source localization, IEEE Trans BME, 1997.44(8):736
[4] Bradlley CP, Harris GM,Pullan AJ, the computational performance of a high-order coupled PEM/BEM procedure in electropotential problems, IEEE Trans BME, 2001.48(11):1238
[5] M. Roth and J.C.Shaw, Potential a theoretical consideration of its significance in terms of electrical field theory, Electroencephalogr.Clin.Neurophysiol, 1955.7285:292-934
[6] J.C.de Munck, the potential distribution in a layered anisotropic spherical volume conductor, Apply Phys, 1988.64:464-470
[7] C.D.Geisler and G..L.Gerstein, the surface EEG in relation to its sources,Electroencephalogr Clin Neurophysiol, 1961.13:927-934
[8] R.C.Barr.T.C.Pilkington, J.P.Boinneau, and M.S.Spach, determing surface potentials from current dipoles with appliance to electrocardiography, IEEE Trans Biomed Eng, 1966.13:88-92
[9] Manfred Fuchs, Michael Wagner, Jom Kastner, boundary element method Volume conductor models for EEG source reconstruction , Clinical Neurophysiology, 2001.112:1400-1407
[10] David Weinstein, Leonid Zhukov, et al, Lead-field bases for EEG source imaging, Annals of Biomedical Engineering, 2000.28(9):1059-1064
[11] R.N.Kavanagh, T. M. Darcey, D.Lehmann, and D. H. Fender, evaluation of methods for three-dimensional localization of electrical sources in the human brain, IEEE Trans Biomed Eng., 1978.24:421-429
[12] D.H. Fender, models of the human brain and the surrounding media: their influence on the reliability of source localization, J.Clin.Neurophysiol, 1991.4:381-390
[13]王云华,脑电逆问题数值方法的研究:[博士学位论文],北京:清华大学,1992
[14]郑旭媛,难治性癫痫脑电偶极子源定位的研究:[博士学位论文],天津:天津大学,2003
[15] Shtmeberg AS,Uzbekov MG,Shikhov SN,et,al, species specificity age factorsand various neurochemical correlates of the animal spontaneous behavior after exposure to electromagnetic field of the ultra low intensity, Vyssh Nerv Deiat Im I P Pavlo-va, 2000.50:703-715
[16] Forss N . magnetoencephalography(MEG) in epilepsy surgery . Acta Neurochur(supp1),1997.58:81-84
[17]国家自然科学基金委员会.自然科学学科发展战略调研报告:生物物理学.北京:科学出版社,1995
[18]陈宜张,神经系统点生理学,北京:人民卫生出版社,1983
[19]徐文龙,陶贵生,夏灵,MRI梯度磁场下人体心脏感应涡流仿真研究,中国计量学院学报,2005.16(3):195-198
[20] A.L.Hodgkin, A.F. Huxley, a quantitative description of membrane current and its application to conduction and excitation in nerve, Journal of Physiology, 1952, 11(7):500-544
[21]欧阳楷,陈心怡,刘卫芳等.基于H-H方程的神经元模型.北京:生物医学工程,1997.16(2):102-106
[22]商立军,李豫蓉,杨贵忠,用于心脏电生理研究的动物模型,动物医学进展,2002.23(2):85-86
[23] L.LIano,J.Dressen, M.Kano,A.Konnerth, intradendritic release of calcium induced by glutamate in cerebellar, Purkinje Cells. Neuron, 1991, 7:577-583
[24] H .Ozek,R.J.Stevens,et al, simultaneous measurement of membrane potential cytosolic Ca2+ and tension in intact smooth muscle, A m.J.Physiol., 1991.260(C):917-925
[25] Gordon M .Shepherd著,蔡南山译,Neurobiology,上海:复旦大学出版社,1990:41-48
[26] Creutfeldt,O.D, neuronal mechanisms underlying the EEG in "Basic Mechanisms of The Epilepsies”, Little Brown, Boston, 1969:397-410
[27]黄远桂,吴声伶,临床脑电图学,北京:人民卫生出版社,1998:1-9
[28] Maestu F, Ortiz T , Fernandez A ,e t al, Spanish language mapping using MEG: a validation study, Neuroimage, 2002.17 (3):1579-1586
[29]阮迪云,寿天德.神经生理学,北京:中国科学技术出版社,1996:81
[30] He B,Musha T, effects of cavity on EEG dipole Localization and their relations with the surface electrode locations. international journal of biomedical computing, 1989.24:269
[31] D.B.Gaselowitz, multipole representation for an equivalent cardiac generator, Proc IRE, 1966.48:75-79
[32] R.M.Arthuiand D.B.Geselowitz, effect of inhomogeneties on the apparent location and magnitude of a cardiac current dipole source, IEEE Trans Biome Eng, 1970.17:717-723
[33] P.BERG and M. Scherg, a fast method for forward computation of multiple-shell spherical head models, Electroencephalogr Clin Neurophysiology, 1994.90:58-64
[34]张磊,蒋式勤,王磊等,基于单电流偶极子的心脏磁场反演计算,北京:现代科学仪器, 2005.4:30-34
[35]刘浩,彭松.电流偶极子在均匀导电球模型中电位解析解的数值验证,北京:生物医学工程杂志,2004.21(3):367-370
[36]雷威,张晓兵等,电磁场理论以及应用,南京:南京大学出版社,2005:12-30
[37] Schnerder MR, a multistage process for computing virtual dipolar sources of EEG discharges form surface information, IEEE Trans Biomedical Engineering, 1972.1:1-12
[38] Barnard ACL, Duck IM, and Lynn MS, the application of Electromagnetic theory to Electrocardiology, Biophys.J, 1967.7:443-461
[39] S.Rush and D. A. Driscoll, current distribution in the brain from surface electrodes, Anesth Analg, 1968.47:717-723
[40] Jaakko, Malmivuo, et al., Bioelectromagnetism, New York: Oxford University Press, 1995.133-147
[41] Yehuda Salu,et al, an improved method for localizing electric brain dipoles, IEEE Trans on BME, 1990.37(7):699-705
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