两个偶极子源EEG正问题数值模拟以及MEG反问题研究

发布时间：2018-11-15 20:30

【摘要】：近三十年来,伴随医学影像技术的发展,脑科学研究和临床诊断进入了崭新的时代,脑电图(EEG)和脑磁图(MEG)作为两种互补的医学影像技术以其极高的时间分辨率,无损伤等特性,符合未来医学诊断技术的发展趋势,成为国内外多学科领域的研究人员的重要研究方向。本文研究的是EEG/MEG影像技术中的数学问题,即正问题和反问题。EEG/MEG反问题的研究,需要大量的正问题的数值计算,所以EEG/MEG正问题的数值模拟对反问题的研究具有重要的指导意义.本文首先基于准稳态的Maxwell方程组导出了EEG/MEG正问题的积分形式场方程,针对单个电偶极子源模型建立了EEG求解脑皮电位势的数值方法；针对两个电流源偶极子源模型建立了求解脑皮电位势的近似解析表达式；针对球模型中单个电偶极子源模型和两个电偶极子源模型分别进行了数值模拟。对单个电偶极子源模型我们得到的电位势随电极位置参数变化图表明：对应不同偶极子位置电位势图形态相似,但电位势峰值不同.对于两个偶极子源模型我们针对下面三种情况进行了数值模拟：1)对每个固定的源参数,分别考察了在同一纬线上电位势随旋转角的变化,以及在同一经线上电位势随仰角的变化。结果表明：对应不同经纬线上的电位势随偶极子源参数的变化形态相近,只是电位势的大小存在差异；但电极所处的仰角对电位势的形态有一定的影响,这意味着脑皮上半部电位势与下半部电位势有差异。2)分别对固定的电极位置参数旋转角和仰角,针对每个源参数计算了电位势随另一电极位置参数的变化,结果显示对应同一固定的源参数电位势形态相近,电位势大小呈规律性变化。3)比较了每种在同一固定参数下,脑皮电位势和无穷远处电位势图。结果显示对应每种固定的参数所做的模拟,两种电位势遵循相似的规律。最后针对椭球模型和偶极子源模型,建立了脑外磁场的近似解析表达式,该表达式通过将磁场表达式中耦合的偶极子电量,偶极子的位置及传感器位置参数进行解耦,简化了MEG反问题的求解。
[Abstract]:In the past 30 years, with the development of medical imaging technology, brain science research and clinical diagnosis have entered a new era. (EEG) and (MEG) are two complementary medical imaging techniques with high time resolution. The characteristics of non-damage, which accord with the development trend of medical diagnostic technology in the future, have become an important research direction for researchers in multi-disciplinary fields at home and abroad. In this paper, we study the mathematical problems in EEG/MEG image technology, that is, forward problems and inverse problems. The study of EEG/MEG inverse problems requires a large number of numerical calculations of positive problems. So the numerical simulation of EEG/MEG forward problem is of great significance to the research of inverse problem. In this paper, the integral form field equation of the EEG/MEG forward problem is derived based on the quasi steady state Maxwell equations, and the EEG numerical method for solving the brain skin potential is established for the single electric dipole source model. An approximate analytical expression for solving the brain skin potential is established for the two current source dipole source models, and numerical simulations for the single electric dipole source model and the two electric dipole source models in the spherical model are carried out respectively. For a single electric dipole source model, we obtained the change of potential with the electrode location parameters. It is shown that the shape of the potential map corresponding to different dipole positions is similar, but the potential peak value is different. For two dipole source models, the following three cases are numerically simulated: 1) for each fixed source parameter, the variation of potential with rotation angle on the same latitude is investigated respectively. And the change of potential with elevation on the same meridional line. The results show that the variation of potential with dipole source parameters is similar to that of the potential corresponding to different meridional latitude lines, except that there are differences in the magnitude of potential. However, the elevation angle of the electrode has a certain effect on the shape of the potential, which means that the potential in the upper half of the brain is different from the potential in the lower half. 2) the rotation angle and elevation angle of the fixed electrode position parameters are obtained respectively. According to each source parameter, the change of potential with the other electrode location parameter is calculated. The results show that the potential shape of the same fixed source parameter is similar, and the potential changes regularly. 3) under the same fixed parameter, each kind of potential is compared. Brain skin potential and infinity potential map. The results show that the two potentials follow a similar law for the simulation of each fixed parameter. Finally, an approximate analytical expression of the external magnetic field is established for the ellipsoidal model and the dipole source model. The expression decouples the coupling dipole electric quantity, the position of the dipole and the sensor position parameters in the magnetic field expression. The solution of MEG inverse problem is simplified.
【学位授予单位】：上海师范大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O241.82

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