有限元法和电位多极展开理论计算各向异性介质球头模型电位分布的研究

发布时间：2018-06-21 11:14

本文选题：脑电正问题 + 有限元法　；参考：《贵州大学》2008年硕士论文

【摘要】： 脑功能的研究是生命科学研究中的前沿领域之一,其中脑电源的探索在临床、康复、认知研究中占有重要地位,因此对脑电信号的研究就成为脑研究的热点之一。在脑电正问题研究中,脑神经元所产生的电活动可用电流偶极子来模拟。1.本文提出把大脑看作各向异性介质球,即同时考虑电容效应、电导效应对脑内电流偶极子产生的电位的影响,并用有限元法推导出偶极子在各向异性介质球模型中的电位分布计算公式。结果表明介质的电容效应对电位分布是有影响的,反映了大脑活组织电特性,对外来不同频率的信号刺激有不同的响应。同时有限元法对大脑内某一区域内电位分布求解表明,测量较深层组织的电特性变化敏感的特点,可获得更多的测量信息。2.建立在三层介质球模型基础上,运用电位多极展开理论对处于球内电流偶极子产生电位的解析解,并运用非线性动力学分析。
[Abstract]:The study of brain function is one of the frontier fields in life science, in which the exploration of brain power plays an important role in clinical, rehabilitation and cognitive research. Therefore, the study of EEG has become one of the hotspots of brain research. In the study of the positive problem of EEG, the electrical activity produced by the brain neurons can be simulated by the current dipole. In this paper, the brain is regarded as an anisotropic medium sphere, that is, the effect of capacitance and conductance on the potential produced by the current dipole in the brain is considered simultaneously. The formula of potential distribution of dipole in anisotropic medium sphere model is derived by finite element method. The results show that the capacitance effect of the medium has an effect on the potential distribution, which reflects the electrical properties of the brain living tissue, and has different responses to the external signal stimuli at different frequencies. At the same time, the finite element method is used to solve the potential distribution in a certain region of the brain. It shows that measuring the electrical characteristics of deeper tissues is sensitive and can obtain more information. Based on the three-layer dielectric sphere model, the potential multipole expansion theory is applied to the analytical solution of the potential generated by the current dipole in the sphere, and the nonlinear dynamic analysis is used.
【学位授予单位】：贵州大学
【学位级别】：硕士
【学位授予年份】：2008
【分类号】：R35

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