Numerical Simulation Of EEG And MEG Positive Problems In Non - Spherical Brain Model

EEG (electroencephalography) and MEG (magnetoencephalography) are two kinds of medical imaging technologies to study the cognition function and the diagnosis of diseases. Compared with other medical imaging, EEG and MEG have the advantage of no damage, non-intrusive and high temporal resolution, which is suitable for studying the process of the dynamic changes for the neuronal activity of the brain. The EEG forward problem is to solve the scalp electric potential by the neural current sources. The EEG inverse problem is to locate the neural current sources through the measurement of scalp electric potential. The MEG forward problem is to solve magnetic field outside the brain by the neural cur-rent source. The MEG inverse problem is to determine the current sources in the brain by measuring magnetic field outside the brain. The study of the inverse problem of EEG and MEG is close related to the forward EEG and MEG problems, which needs a large number of EEG/MEG forward problem calculation. Therefore, the results of EEG/MEG forward problems has guiding significance.In the study of EEG/MEG problems choosing proper head model has prime impor-tance. Most previous work used sphere geometry to approximate the human head. But the error using sphere head model has been reported in some studies. And the effect of the model geometry on EEG/MEG problems are also studied. Recently, The study of EEG/MEG using non-spherical head model has been the major trend.In this paper we use analytic geometry, the ovoid head model to approximate the human head, which includes the sphere head model, aiming to study the effects of head model on the scalp potential (EEG) and the magnetic field (MEG.). We apply weighted residual method based on compact trial function to numerically implement simulations for different head models and current dipole parameters. Potential maps are compared in different head models. We also show the map of potential produced by primary current. We investigate the variation rules of the scalp potentials versus the dipole location and direction. We also present the map of the components of magnetic fields versus dipole location and direction. We use weighted residual method based on different basis functions to perform simulations, which, on the one hand, shows the reliability of the results. On the other hand we test the computational efficiency of the different basis functions.The whole paper is divided into four parts:In chapter 1 we introduce the history of the EEG/MEG. electrophysiological basis, detection device and its mathematical problem-s. The second chapter includes the quasi-static Maxwell Equations and the head model. We present the field equations of the EEG/MEG. In chapter 3, we apply weighted residual method based on the compact trial function to solve the forward problems of EEG/MEG. In the fourth chapter, we perform the numerical simulations for scalp potentials and mag-netic fields in different head models and current dipole parameters, analyze the simulation results and present the conclusions.