A Simulation Study Of The Abnormal EEG Morphology By The Numerical Method In A 3-D Space

The research of electroencephalogram (EEG) is of great significance and clinical importance in the study of the neural activity in a brain. Based on the realistic head model, the finite element method (FEM) can be used efficiently to solve the simulation of the EEG in such complex situation, such as the complex geometry, boundary conditions, multi homogeneous media and inhomogeneous media. There are two key problems in the field of EEG forward problem and EEG inverse problem. EEG forward problem is the basis for the EEG inverse problem, which is one of the key factor to the EEG inverse problem It's usually called the calculation of potentials on the cortex as the forward problem in the nerve system. Nowadays, the concept of the equivalent source is usually accepted, that regards the electrical activity of an excitable neuron as being the activity of the equivalent source. In this paper, a novel method is presented to simulate the abnormal EEG morphology such as the spikes with two phases in the 3-D solution space. The abnormal spikes often occur in the epileptic seizure and the interval of the seizure. Here, based on the homogeneous sphere as the head model, also as well the solution space, the abnormal spike is regarded as being original from the dynamic activity of equivalent currents source. The finite element method (FEM) is utilized with the help of the ANSYS7.0 software. The morphology of the spike with two phases is obtained and it is also shown that the abnormal spikes are original from the abnormally discharge process in the brain and the interval of the spikes (IS) can be lengthened with the increasing in the concentration of the intracellular Ca²⁺ ([Ca²⁺]_i). It can be helpful to understand the mechanism of the abnormal EEG morphology from the microcosmic viewpoints. This thesis is further focused on the 3-D anisotropic EEG forward problem and satisfactory simulation results are obtained. The thesis is organized as follows:1. In chapter 1, research on FEM used in the EEG forward problem is introduced briefly, not only including its development, key problems and application prospects but also including the recent progress, existing problems and the trends in the future. The structure of the thesis and the main results of the research are presented.2. In chapter 2 and chapter 3, the forward problem of EEG and some nerve models were introduced. Then the best appropriate model was chosen.3. In chapter 3, the 20d tetrahedral element was used in FEM to enhance the numerical accuracy and computational efficiency. A new computationally efficient approach to calculate the stiffness matrix of the second-order tetrahedral elements has been developed for second-order tetrahedral finite element models to avoid calculating the complex 3-D integral. The 3-D anisotropic EEG forward problem was also solved by the proposed FEMwith 20d tetrahedral element.4. In chapter 5 and chapter 6, the simulation results were obtained by FEM in a 3-D space. It is concluded that the spikes with two phases are original from the abnormally discharge process in the brain and the interval of the spikes (IS) can be lengthened with the increasing in the concentration of the intracellular Ca2+ ([Ca2+]i)...