基于有限元对脑内神经元电活动研究

发布时间：2018-07-06 14:33

本文选题：脑电 + 正问题　；参考：《郑州大学》2012年硕士论文

【摘要】：借助于脑电图(Electroencephalogram, EEG)对大脑皮层电位分布进行分析被视为是确定脑内电活动源的一种行之有效的方法,一般在正常情况下,脑电图描述的皮层电位都呈现出一定的规律性；然而,当脑组织发生病变或者功能改变时,相应的规律性就会遭到破坏(比如说波形的改变),本文的研究目的就是利用有限元仿真模型对神经兴奋组织的电活动进行模拟,得到脑组织发生病变时在模型表面产生的电位分布,研究利用头皮表面电位分布逆溯脑内电活动偶极子源的优化算法,从而协助癫痫等脑部疾病的诊断与临床治疗,同时也有助于更深入地探讨大脑的神经机理活动等。脑电研究领域主要涉及两个方面：脑电正问题和脑电逆问题,对脑电正问题的研究是求解逆问题的关键基础,正问题能否正确地得到计算直接影响到脑内电活动源定位的准确性。本文基于均匀球和三层同心球模型利用有限元分析了大脑头皮表面电位的分布情况,根据生物电磁场理论推导了求解脑电场的有限元方程,在给定偶极子作用下求解模型表面的电位分布,从而验证了仿真模型的有效性,但是对比三层球头模型与均匀球头模型的仿真结果,前者表现出了较好的近似性。此外,进一步分析了不同头模型下偶极子参数(位置、方向和大小)对皮层表面电位分布产生的影响,并在相同路径下对这些差异进行比较分析,为以后各种头模型下脑电正问题的求解提供借鉴信息。最后借助于测得的头皮电位数据逆推了产生脑内电活动的兴奋源,根据头皮电位计算值与观测值的最佳拟合来设计目标函数,为了得到更稳定、误差最小且唯一的偶极源解,对目标函数进行正则化处理,并结合粒子群算法实现对目标函数的优化,通过对施加约束条件矩阵前后的反演数据与测量数据进行比较,仿真结果表明施加约束条件后偶极子源的定位精确度要比正则化处理前有很大提高。
[Abstract]:The analysis of the cortical potential distribution by Electroencephalogram (EEG) is regarded as an effective method for determining the source of electrical activity in the brain. Generally, the cortical potential described by the electroencephalogram presents certain regularity under normal conditions; however, when the brain tissue changes or changes in function, it is appropriate. The regularity will be destroyed (such as the change of the waveform). The purpose of this study is to simulate the electrical activity of the nerve excited tissue by the finite element simulation model, obtain the potential distribution on the model surface when the brain tissue is diseased, and study the advantage of the potential distribution of the scalp surface potential distribution back to the dipole source of the electrical activity in the brain. The algorithm can assist in the diagnosis and clinical treatment of epilepsy and other brain diseases. It also helps to further explore the neural mechanism of the brain.
The field of electroencephalography is mainly involved in two aspects: the positive problem of EEG and the inverse problem of EEG. The research on the positive problem of EEG is the key basis for solving the inverse problem. The correctness of the problem can directly affect the accuracy of the location of the electrical activity source in the brain. The finite element analysis is used in this paper based on the uniform sphere and the three layer concentric ball model. The distribution of the surface potential of the cerebral scalp is derived, and the finite element equation for the solution of the electric field is derived according to the theory of the biological electromagnetic field. The potential distribution of the model surface is solved under the given dipole effect, and the validity of the simulation model is verified. However, compared with the simulation results of the three layer ball head model and the homogeneous spherical head model, the former shows the comparison. In addition, the influence of the dipole parameters (position, direction and size) on the cortical surface potential distribution under the different head models is further analyzed, and the differences are compared and analyzed in the same path, which can provide reference information for solving the problem of EEG positive in the subsequent head models.
Finally, by using the measured scalp potential data, the excitatory source that produces the electrical activity in the brain is pushed back, and the target function is designed according to the optimal fitting of the calculated value of the scalp potential and the observed value. In order to get more stable, minimum and only dipole source solution, the objective function is regularized and the target function is realized with the particle swarm optimization algorithm. The optimization of the number is compared with the measured data before and after the application of the constraint condition matrix. The simulation results show that the positioning accuracy of the dipole source is greatly improved after the application of the constraint conditions.
【学位授予单位】：郑州大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：R338

【引证文献】