FEM In 3D Anisotropic EEG Forward Problem And CIT

The research of Electroencephalogram (EEG) is of great significance and clinical importance in the study of the cognitive function and neural activity of a brain. The reslistic head model can be built by Finite Element Method (FEM) for its strong ability of disposal for complex geometry, boundary conditions, multi homogeneous media and inhomogeneous media. There are two key problems in the field of EEG, EEG forward problem and EEG inverse problem. EEG forward problem is the basis of the EEG inverse problem. Generally, EEG inverse problem depends on the accuracy and efficiency of the computational method of EEG forward problem. This thesis concentrates on FEM with both 1st Tetrahedral element and 2^nd Tetrahedral element for 3D anisotropic EEG Forward problem and Cortical Imaging Technique (CIT), and satisfactory simulation results are obtained. The thesis is organized as follows:In chapter 1, the meaning of the research on FEM for EEG Forward problem and CIT was introduced briefly, and its development, key problems, and application prospects were stated in detail. The research progress, existing problems, and the development trend on EEG Forward Problem and CIT are summarized. And the structure of the thesis and the main results of the research are presented.In chapter 2, the 3D anisotropic EEG Foreard Problem with 1^st tetrahedral FEM was introduced. The FEM is used to solve the 3D anisotropic EEG Foreard Problem and a new method to enhance the accuracy of FEM has been presented to overcome the disadvantage of FEM in dealing with current dipole sources.In chapter 3, the 2^nd tetrahedral element was used in FEM to enhance numerical accuracy and computational efficiency. A new computationally efficient approach to calculate the stiffness matrix of second-order tetrahedral elements has been developed for second-order tetrahedral finite element models to avoid the calculation of complex 3D integral. The 3D anisotropic EEG forward problem was soleved by the proposed FEM with 2^nd tetrahedral element.In chapter 4, a realistic head model was built by a convenient approach which integrates the functions of several softwares and avoids the complex calculation needed to build the realistic head model in current approachs.In chapter 5, a new algorithm for solving the 3D anisotropic CIT Forward Problem by EFM was presented, which avoids calculating the inverse matrix directly and therefore makes it possible to study CIT with complex realistic head model or the model with many elements.